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Design of Molecules and Materials for Applications in Clean Energy, Catalysis and Molecular Machines Through Quantum Mechanics, Molecular Dynamics and Monte Carlo Simulations
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Mendoza-Cortes, Jose Luis
(2012)
Design of Molecules and Materials for Applications in Clean Energy, Catalysis and Molecular Machines Through Quantum Mechanics, Molecular Dynamics and Monte Carlo Simulations.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/PQ74-HK88.
Abstract
We use a multiparadigm, multiscale strategy based on quantum mechanics (QM), first-principles QM-based molecular mechanics (MD) and grand canonical Monte Carlo (GCMC) to rationally design new molecules and materials for clean energy (H
and CH
storage), catalysis (O
evolution, metal organic complexes) and molecular architectures (rotaxanes, hydrogels). This thesis is organized in seven chapters and shows that it is crucial to understand the scale of the system to be studied, the insight obtained can be used to rationally design new molecules and materials for desirable applications; as well as to guide and complement experimental studies. Chapter 1 discusses the specific details of the proposed methodology, including the theoretical underpinning of each modeling paradigm, potential limitations, and how we use these for in silico characterization and design optimization. Chapter 2 covers the structure prediction and characterization of metal-organic complex arrays (MOCA) through QM and force-field-based molecular mechanics. The methodology is inspired by the approach used for enzymatic systems, considering that experimentally determining their three-dimensional structure remains an open challenge. Chapter 3 describes the use of transition state theory for the calculation of reaction rates in polymer hydrogel network formation. This enables the determination of optimum concentrations for polymerization reactions and preparation of coarse-grained force elds. Chapter 4 describes the work performed on Stoddard's rotaxane dumbbells, where we explained origin for the template-directed synthesis through QM-derived free energies. We also give a consistent explanation for the role of the counter anion. Chapter 5 presents the simulation results for a tetranuclear cluster model for O
evolution, based on CaMn
and Mn
clusters. We demonstrate how to calculate their oxidation potentials and propose new molecular designs that resemble the oxygen evolution complex (OEC) both structurally and electronically. Chapter 6 presents our findings for CH
storage. Using a second-order Moller-Plesset perturbation theory force field and GCMC we propose a framework for optimal delivery. Chapter 7 presents our designed materials for hydrogen storage and the validation of our methodology against experimental results. We based our predictions in QM and GCMC calculations through the development of our own first-principles vdW force eld. Our results demonstrate novel frameworks capable of achieving the DOE energy density target for 2015. Finally, we show the generalization of adsorption phenomena for any porous material based on topological constraints.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Clean energy; hydrogen storage; methane storage; oxygen evolution; molecular machines; quantum
mechanics; molecular dynamics; Monte Carlo
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Goddard, William A., III
Thesis Committee:
Goddard, William A., III (chair)
Fultz, Brent T.
Agapie, Theodor
Greer, Julia R.
Johnson, William Lewis
Defense Date:
17 May 2012
Record Number:
CaltechTHESIS:05292012-220632933
Persistent URL:
DOI:
10.7907/PQ74-HK88
ORCID:
Author
ORCID
Mendoza-Cortes, Jose Luis
0000-0001-5184-1406
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
7091
Collection:
CaltechTHESIS
Deposited By:
Jose Mendoza Cortes
Deposited On:
31 May 2012 16:08
Last Modified:
28 Oct 2025 19:35
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Design of molecules and materials for applications in clean
energy, catalysis and molecular machines through quantum
mechanics, molecular dynamics and Monte Carlo simulations

Thesis by

Jose L. Mendoza-Cortes

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

2012
(Defended May 17 2012)

c 2012
Jose L. Mendoza-Cortes

iii

Dedicated to:
Azucena A. Cortes-Gaspar

Acknowledgments
I am in debt to my advisor Prof. William A. Goddard for his patience and discussions during my
doctoral studies. I am deeply thankful to him for allowing me to pursue an independent way of
doing research and showing me how to be a better scientist.
I would like to thank also many collaborators during these years: Prof. Omar M. Yaghi, Dr.
Hiroyasu Furukawa, Dr. Ravinder Abrol, Dr. Andres Jaramillo-Botero, Dr. Robert Nielsen, Dr.
Tod A. Pascal and Prof. Theodor Agapie. I learnt many things about science through discussions
with them.
My special thanks to Prof. Yaghi, who has been an exemplary scientist and helped me to improve
as a scientist. I also would like to thank Dr. Furukawa who was patient and tough enough with his
vast experience.
I would like to acknowledge some of my colleagues for fruitful discussions about different scientific
topics; Dr. Jamil Tahir-Kheli, Wei-Guang Liu, Ted Yu, Fan Liu, Ross Fu, Jacob Kanady, Emily Y.
Tsui, Vaclav Cvicek and Hai Xiao. It is amazing how much you can learn by discussing with your
colleagues.
Also I would like to thank the support of my friends over the years; there are many of them
spread over the world but specially Jorge Cholula, currently in Germany and Naoki Aratani from
Japan. I would like to thank Ernie Mercado for allowing me to have some Mexican food on campus.
My gratitude to the California Institute of Technology which provided me with fellowship during
my first year and also to the Roberto Rocca Program for providing support for two years.
Finally I would like to acknowledge my mother Azucena A. Cortes-Gaspar and Yuan Liu for
being a great support in my life.

Abstract
We use a multiparadigm, multiscale strategy based on quantum mechanics (QM), first-principles
QM-based molecular mechanics (MD) and grand canonical Monte Carlo (GCMC) to rationally design new molecules and materials for clean energy (H2 and CH4 storage), catalysis (O2 evolution,
metal-organic complexes) and molecular architectures (rotaxanes, hydrogels). This thesis is organized in seven chapters and shows that it is crucial to understand the scale of the system to be
studied, the insight obtained can be used to rationally design new molecules and materials for desirable applications; as well as to guide and complement experimental studies. Chapter 1 discusses
the specific details of the proposed methodology, including the theoretical underpinning of each
modeling paradigm, potential limitations, and how we use these for in silico characterization and
design optimization. Chapter 2 covers the structure prediction and characterization of metal-organic
complex arrays (MOCA) through QM and force-field-based molecular mechanics. The methodology
is inspired by the approach used for enzymatic systems, considering that experimentally determining their three-dimensional structure remains an open challenge. Chapter 3 describes the use of
transition state theory for the calculation of reaction rates in polymer hydrogel network formation.
This enables the determination of optimum concentrations for polymerization reactions and preparation of coarse-grained force fields. Chapter 4 describes the work performed on Stoddard’s rotaxane
dumbbells, where we explained origin for the template-directed synthesis through QM-derived free
energies. We also give a consistent explanation for the role of the counter anion. Chapter 5 presents
the simulation results for a tetranuclear cluster model for O2 evolution, based on CaMn3 04 and
Mn4 O4 clusters. We demonstrate how to calculate their oxidation potentials and propose new
molecular designs that resemble the oxygen evolution complex (OEC) both structurally and electronically. Chapter 6 presents our findings for CH4 storage. Using a second-order Møller-Plesset
perturbation theory force field and GCMC we propose a framework for optimal delivery. Chapter 7 presents our designed materials for hydrogen storage and the validation of our methodology
against experimental results. We based our predictions in QM and GCMC calculations through the
development of our own first-principles vdW force field. Our results demonstrate novel frameworks
capable of achieving the DOE energy density target for 2015. Finally, we show the generalization of
adsorption phenomena for any porous material based on topological constraints.

Contents
Acknowledgments

Abstract

List of Tables

xiii

List of Figures

xxi

1 Introduction

2 Prediction of Structures of Metal-Organic Complex Arrays (MOCA)

2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Method I: QM/MM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2

Quantum Mechanical Calculations . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.1

The case of Platinum (Pt) . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.2

The case of Rhodium (Rh) . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.3

The case of Ruthenium (Ru) . . . . . . . . . . . . . . . . . . . . . .

2.2.2.4

Dimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.3

Structures Obtained from QM/MM . . . . . . . . . . . . . . . . . . . . . . .

2.2.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Method II: Structure Prediction Inspired in Enzymes . . . . . . . . . . . . . . . . . .

2.3.1

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.2

Generation of Conformers for All Compounds . . . . . . . . . . . . . . . . . .

2.3.3

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

3 Coarse-Grained Potential for Hydrogels from Quantum Mechanics

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1

Molecular Mechanics and Quantum Mechanics . . . . . . . . . . . . . . . . .

vii
3.2.2
3.3

The Finite Extensible No Linear Elastic (FENE) Potential . . . . . . . . . .

FENE Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.1

3.3.2

3.3.1.1

Quantum Mechanics for the Dihedral Angles in the [aam-aam] Dimer 29

3.3.1.2

Quantum Mechanics for the Dihedral Angles in the [xlinker] Monomer 31

Bond Strength and the FENE Potential . . . . . . . . . . . . . . . . . . . . .

3.3.2.1

Quantum Mechanics of [aam-aam] . . . . . . . . . . . . . . . . . . .

3.3.2.2

Quantum Mechanics of [amps-aam] . . . . . . . . . . . . . . . . . .

3.3.2.3

Quantum Mechanics of [amps-amps] . . . . . . . . . . . . . . . . . .

3.3.2.4

Quantum Mechanics of [xlinker] . . . . . . . . . . . . . . . . . . . .

3.3.2.5

Quantum Mechanics of [xlinker-xlinker] . . . . . . . . . . . . . . . .

3.3.2.6

Quantum Mechanics of [xlinker-aam]

. . . . . . . . . . . . . . . . .

3.3.2.7

Quantum Mechanics of [xlinker-amps] . . . . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Reaction Rates from Transition State Theory . . . . . . . . . . . . . . . . . . . . . .

3.4.1

Reaction Rates in Gas Phase and Water . . . . . . . . . . . . . . . . . . . . .

3.4.2

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.3
3.4

Dihedral Conformation and the FENE Potential . . . . . . . . . . . . . . . .

4 Origin of the Positive Cooperativity in the Template-Directed Formation of
Molecular Machines

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1

Experimental Coordinates vs MM vs QM . . . . . . . . . . . . . . . . . . . .

4.3.2

Origin of the Positive Cooperativity . . . . . . . . . . . . . . . . . . . . . . .

4.3.3

Role of the Counter Anion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4

5 Design of New Models for the Oxygen Evolving Complex

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3.1

Validation of the Computational Methodology: Geometry . . . . . . . . . . .

5.3.2

Validation of the Computational Methodology: Redox Potentials . . . . . . .

5.3.3

Prediction of New Models that Resemble the OEC Both Structurally and

5.4

Electronically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

viii
6 Methane Storage in Metal-Organic Frameworks and Covalent-Organic Frameworks
6.1

Adsorption Mechanism and Uptake of Methane (CH4 ) in Covalent-Organic Frameworks: Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.2.1

Force Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.2.2

QM Determination of the vdW Force Field Parameters . . . . . . .

6.1.2.3

GCMC Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.2.4

Structural Characteristics of COFs . . . . . . . . . . . . . . . . . . .

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.3

6.1.3.1

sorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.3.2

Gravimetric Methane Uptake in Other COFs . . . . . . . . . . . . .

6.1.3.3

Adsorption Mechanism of Methane in COFs . . . . . . . . . . . . .

6.1.3.4

Isosteric Heat of Adsorption . . . . . . . . . . . . . . . . . . . . . .

6.1.3.5

Delivery Amount in COFs . . . . . . . . . . . . . . . . . . . . . . .

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Design of Covalent Organic Frameworks for Methane Storage . . . . . . . . . . . . .

6.2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2.1

Force Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2.2

Electrostatic Interactions . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2.3

Grand Canonical Monte Carlo . . . . . . . . . . . . . . . . . . . . .

6.2.2.4

Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.2.5

Topological Consideration in the Design of COFs

. . . . . . . . . .

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.3.1

Delivery Volumetric Uptake in Designed COFs . . . . . . . . . . . .

6.2.3.2

Isosteric Heat of Adsorption . . . . . . . . . . . . . . . . . . . . . .

6.2.3.3

Stability of COFs . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.3.4

Comparisons to Previous Computational Studies . . . . . . . . . . .

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1.4
6.2

Comparison Between Theoretical and Experimental Methane Ad-

6.2.3

6.2.4

7 Clean Energy (H2 ) Storage in Metal-Organic Frameworks and Covalent-Organic
Frameworks

ix
7.1

High H2 Uptake in Li-, Na-, K- Metalated Covalent-Organic Frameworks and MetalOrganic Frameworks at 298 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.1.2

Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1.2.1

Quantum Mechanics Calculations and Development of the Parameters for Nonbond Interactions . . . . . . . . . . . . . . . . . . . . . . 101

7.1.3

7.1.4
7.2

7.1.2.2

Valence Bond Force Field . . . . . . . . . . . . . . . . . . . . . . . . 102

7.1.2.3

Grand Canonical Monte Carlo Loading Curves . . . . . . . . . . . . 102

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.3.1

Nature of the Chemical Bond for the Li-Benzene (Li-Bz) Systems . 103

7.1.3.2

Gravimetric Uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.1.3.3

Volumetric Uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.1.3.4

Isosteric Heat of Adsorption . . . . . . . . . . . . . . . . . . . . . . 113

7.1.3.5

Adsorption Mechanism of Molecular Hydrogen . . . . . . . . . . . . 113

7.1.3.6

Comparisons to Previous Computational Studies . . . . . . . . . . . 115

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Dependence of the H2 Binding Energies Strength on the Transition Metal and Organic
Linker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.1.1

Types of Interactions for H2 . . . . . . . . . . . . . . . . . . . . . . 117

7.2.1.2

Langmuir Theory and the Optimal Enthalpy . . . . . . . . . . . . . 119

7.2.2

Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.2.3

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.2.4

7.2.3.1

Current Linkers Used in Porous Frameworks . . . . . . . . . . . . . 122

7.2.3.2

Proposed Linkers Based on Experimental Crystal Structures . . . . 132

7.2.3.3

Alternative Strategy to Metalate COFs and MOFs . . . . . . . . . . 135

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Appendix

139

A Quantum Mechanical Calculations and Geometries on the Formation of Molecular Machines

140

A.1 All QM Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.2 Geometries for the R Family (2R-D-2PF6 , 1R-D-2PF6 , 2R-D-2PF6 ) and for the R’
Family (2R-Dp-2PF6 , 1R-Dp-2PF6 , 2R-Dp-2PF6 ) . . . . . . . . . . . . . . . . . . . . 144
A.2.1 2R-D-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
A.2.2 1R-D-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

A.2.3 0R-D-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
A.2.4 2R-Dp-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
A.2.5 1R-Dp-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A.2.6 0R-Dp-2PF6 -M06L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
B Generalization of the Sorption Process with Multilayers for Non-Self-Interacting
Atoms and Molecules

171

B.1 Given a Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.2 Determine the Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
B.3 Gibbs Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
B.3.1 Monolayer Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
B.3.2 Restricted Multilayer Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
B.4 Hydrogen Molecule Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
B.4.1 Monolayer Theory in H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
B.4.2 Multilayer Theory in H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
B.5 Supplementary Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
B.5.1 NIST Data for H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Bibliography

181

List of Tables
1.1

Ensembles for statistical mechanics. E stands for energy of the state; T , temperature;
V , volume; N , number of particles; µ, chemical potential. β is given by 1/(kT ), where
k is the Boltzmann constant. The denominators Ω, Q, Ξ and ∆ are the partition
functions for each ensemble. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

DFT energies for the Rh cis and trans . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Binding energies (Ebind ) for the different dimers obtained from DFT/MO6-2X and
basis set LACVP**/6-31G** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

Energies for the top 10 conformers. R stands for rank. All the energies are in kcal/mol. 22

3.1

Energies for dihedral in the aam-aam . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

FENE parameters obtained for different dihedral for the [aam-aam] dimer . . . . . . .

3.3

[xlinker] FENE parameters for the FENE potential from QM . . . . . . . . . . . . . .

3.4

[aam-amps] FENE parameters for the FENE potential from QM . . . . . . . . . . . .

3.5

[amps-amps] parameters for the FENE potential from QM

. . . . . . . . . . . . . . .

3.6

FENE parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.7

[xlinker-xlinker] parameters for the FENE potential from QM . . . . . . . . . . . . . .

3.8

[xlinker-aam] parameters for the FENE potential from QM . . . . . . . . . . . . . . .

3.9

[xlinker-amps] parameters for the FENE potential from QM . . . . . . . . . . . . . . .

3.10

All the parameters for the FENE potential from QM. I and II stand for different
explored C-C bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.11

Parameters for water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.12

Free energy (G) of all the reactions in gas phase. Energies are in kcal/mol. . . . . . .

3.13

Free energy obtained from QM and the derived reaction constant (k) from TST . . .

4.1

Reaction kinetics on the formation of the R family, which is the combination of nR + D 49

4.2

Reaction kinetics on the formation of the R’ family, which is the combination of nR +
Dp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xii
4.3

Root mean square distance (RMSD) for the comparison between experimental structure
for 2R·2PF6 and the QM and MM methods. Column 2 and 3 shows the estimation
of the R(π−π ) interaction for benzene (Bz) in the stopper of the dumbbell (D), first
rotaxane (R1) and second rotaxane (R2)

4.4

. . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of binding energies for the Formation of 1R-2PF6 and 2R-2PF6 . All the
units are in kcal/mol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

gas

∆G

solv

and ∆G

gas

∆G

and ∆G

solv

Bond distances for the fourth Mn shown and its first coordination shell as it is shown
in Figure 5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1

Oxidation/reduction potentials for the Mn4 O4 compounds with respect to ferrocene/
ferrocenium. Solvent: dimethylacetamide (DMA). . . . . . . . . . . . . . . . . . . . .

5.3

Oxidation/reduction potentials for the Mn3 CaO4 compound with respect to ferrocene/
ferrocenium. Solvents: dimethylacetamide (DMA) and dimethylformamide (DMF). . .

5.2

Dipole moments (µ, /Debye) obtained from Electrostatic potential (ESP) charges and
Mulliken charges. The ESP and Mulliken charges have been normalized. . . . . . . . .

5.1

with respect to isolated rotaxanes rings and dumbbell. All the units

are in kcal/mol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7

with respect to isolated rotaxanes rings and dumbbell. The solvent

used is CH3 CN. All the units are in kcal/mol. . . . . . . . . . . . . . . . . . . . . . . .
4.6

Pore size (P Size ), surface area (SA ), pore volume (VP ), and density of the Framework
without guest molecules (ρ) for the studied COF series . . . . . . . . . . . . . . . . .

6.2

Nonbonded FF parameters developed to fit the RI-MP2 calculations . . . . . . . . . .

6.3

Most-stable interaction geometries for clusters considered in this work . . . . . . . . .

6.4

Isosteric heat of adsorption (Qst ), surface area (S A ), pore volume (V P ), and uptake of
the framework series at 298 K (Where Tot = total, Exc = excess, and Del = delivery)

6.5

MD statistics for the frameworks obtained at 298 K . . . . . . . . . . . . . . . . . . .

7.1

Properties of the frameworks used in this work: surface area (S A ), pore volume (V P ),
and density (ρ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.2

Nonbonded FF parameters used for this study based on MP2 for Li and CCSD(T) for
Na and K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.3

Electronic energy for the optimized systems using different basis sets (6-31G**++ and
6-311G**++) and different functionals (M06 and B3LYP) is presented . . . . . . . . . 104

7.4

Zero-point energy (ZPE), vibrational enthalpy (Hvib ), total enthalpy (Htot ), vibrational
entropy (Svib ), total entropy (Stot ), and solvation energy (Esolv ) obtained for the different compounds for 298.15 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xiii
7.5

Different interactions H2 can have with other entities that can be used to tune the
∆H ◦ ads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.6

DOE targets for H2 storage system for light-duty vehicle and the estimation of the
optimal ∆H ◦ ads under these conditions using the Langmuir model . . . . . . . . . . . 120

7.7

Delivery amount obtained using ideals ∆H ◦ ads and different temperatures . . . . . . . 121

7.8

Binding energies (∆H ◦ bind ) obtained for the ground state of linker BBH and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln + H2 .
The H-H bond of isolated H2 is 0.741 Å . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.9

Binding energies (∆H ◦ bind ) obtained for the ground state of linkers PIP and PIPE and
different number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln
+ H2 . The H-H bond of isolated H2 is 0.741 Å . . . . . . . . . . . . . . . . . . . . . . 127

7.10

Binding energies (∆H ◦ bind ) obtained for the ground state of linker PIA and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln + H2 .
The H-H bond of isolated H2 is 0.741 Å . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.11

Binding energies (∆H ◦ bind ) obtained for the ground state of linker BPY and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(II)Cl2 + H2 .
The H-H bond of isolated H2 is 0.741 Å . . . . . . . . . . . . . . . . . . . . . . . . . . 132

7.12

Binding energies (∆H ◦ bind ) obtained for the ground state of linker BPYM and different number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(II)Cl2 +
H2 . The H-H bond of isolated H2 is 0.741 Å

7.13

. . . . . . . . . . . . . . . . . . . . . . . 134

Binding energies (∆H ◦ bind ) obtained for the ground state of all linkers (BBH, PIP,
PIPE, PIA, BPY, and BPYM) + Pd shown in Figure 7.19 reacting with different
number of H2 . For each case the spin is 0. The H-H bond of isolated H2 is 0.741 Å . . 137

A.1

Free energies in gas and solvated phase including quantum corrections. The solvent
used is CH3 CN. Units:kcal/mol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

A.2

Electronic Energy (E,scf), Zero Point Energy (ZPE), Solvation energy for CH3 CN
(Esolv). Units:kcal/mol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

A.3

Free energies in gas and solvated phase including quantum corrections. The solvent
used is CH3 CN. Units:kcal/mol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

A.4

Electronic Energy (E , scf), Zero Point Energy (ZPE), Solvation energy for CH3 CN
(Esolv). Units:kcal/mol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

xiv

List of Figures
1.1

Theoretical multiparadigms. (a) was adapted from [1], (b) is courtesy of Julius Su, and
Part (c) is courtesy of Andres Jaramillo-Botero. . . . . . . . . . . . . . . . . . . . . .

1.2

Uptake for CH4 for COFs and MOFs and observation of the sorption mechanism for
the uptake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3

The design of two new COFs that overcome the DOE target at room temperature.
They perform better than MOF-177, currently on the market. . . . . . . . . . . . . .

1.4

MOF200-Li and COF102-Li reach the 2015 DOE target. . . . . . . . . . . . . . . . . .

2.1

Metal-organic complex arrays (MOCA). QM was used for the black part, including the
metal. MM was used for the pink part. Fmoc stands for fluorenylmethyloxycarbonyl.

2.2

Structures used for the QM calculations. For the calculations in gas phase we did not
use the counter anion but the absolute charge that is shown. . . . . . . . . . . . . . .

2.3

Coordinate scan for the dihedrals CCCC and CCCO of the Pt case. The pink lines
indicate the dihedral angle used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4

Different dihedral angles tested for the Rh complex. The pink lines indicate the dihedral
angle used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5

Ru complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.6

3D-representation of the optimized structure obtained for each of the dimers considered
in this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.7

Final configuration obtained using the QM/MM method for all the arrays denominated
MOCA A, B, C, D, E and F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.8

Population of all conformers generated for MOCA A to F . . . . . . . . . . . . . . . .

2.9

Population of conformers generated for Compound A, B, C, D, E and F . . . . . . . .

2.10

Top 1st conformer for all compounds obtained by using method II . . . . . . . . . . .

3.1

Example of the FENE potential. The repulsive part acts from 0 to 21/6 σ (bottom).
The attractive potential acts from 0 to R0 = 1.5 σ (middle). The combination of both
terms make the FENE potential (top). In this case, = 1.0, σ = 1.0, thus K = 30, R0
= 1.5, and 21/6 σ = 1.12.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv
3.2

All monomers used are presented: (a) acrylamide (71.08) (b) 2-acrylamido-2-methyl
propane sulfonate−1 (206.24 g/mol) (c) sodium 2-acrylamido-2-methyl propane sulfonate (229.23 g/mol) and (d) N,N’-methylenediacryl amide(154.17 g/mol). . . . . . .

3.3

The dihedral used for the aam-aam dimer is shown in (a) and (b) with magenta and
green colors, respectively. The 360◦ point should be equivalent to the O◦ for a constrained dihedral scan, however we executed a relaxed scan. . . . . . . . . . . . . . . .

3.4

Bond energies for aam-aam with dihedrals 173.9 and 179.4

. . . . . . . . . . . . . .

3.5

xlinker dihedral used. (a) The structure used is shown in red and the dihedral angle

29
30

explored is magenta. (b) 3D representation of the xlinker with the dihedral used shown
in green. The blue dots in (c) are reoptimized structures with the dihedrals shown in
green. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6

Bond scan for most stable xlinker dihedrals . . . . . . . . . . . . . . . . . . . . . . . .

3.7

Bond strength for a used conformation of aam-aam

3.8

[aam-aam] FENE potential for structures in Figure 3.7

. . . . . . . . . . . . . . . . .

3.9

amps-aam used. The scan used is shown with a magenta arrow. . . . . . . . . . . . .

3.10

[amps-aam] FENE potential for structures in Figure 3.9 . . . . . . . . . . . . . . . . .

3.11

amps-amps neutral and anion used. The scan used is shown with a magenta arrow. .

3.12

[amps-amps] FENE potential for structures in Figure 3.11 . . . . . . . . . . . . . . . .

3.13

xlinker used. The scan used is shown with a magenta arrow. . . . . . . . . . . . . . .

3.14

[amps-amps] FENE potential for structures in Figure 3.13 . . . . . . . . . . . . . . . .

3.15

xlinker-xlinker used. The C-C bond scan used is shown with a magenta arrow. . . . .

3.16

[amps-amps] FENE potential for structures in Figure 3.15 . . . . . . . . . . . . . . . .

3.17

xlinker-aam used. The scan used is shown with a magenta arrow. . . . . . . . . . . . .

3.18

[xlinker-aam] FENE potential for structures in Figure 3.17 . . . . . . . . . . . . . . .

3.19

xlinker-amps used. The scan used is shown with a magenta arrow. (b) and (e) are

. . . . . . . . . . . . . . . . . . .

equivalent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.20

[xlinker-aam] FENE potential for structures in Figure 3.19 . . . . . . . . . . . . . . .

3.21

All QM results around the equilibration point . . . . . . . . . . . . . . . . . . . . . . .

3.22

For all studied reactions, the free radical polymerization mechanism is assumed . . . .

3.23

This plot shows the product (left) and reactant (right) . . . . . . . . . . . . . . . . . .

4.1

Reaction for the template directed formation of rotaxanes for the (a) R Family and for

4.2

the (b) R’ family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XRD structure vs different theoretical methods. . . . . . . . . . . . . . . . . . . . . .

xvi
4.3

Compounds for the R family (a,b and c; xR-D-2PF6 ) and for the R’ family (d,e and f;
xR-Dp-2PF6 ). Colors are C: grey, O:red, N:blue, F: green, P:purple and H:not shown.
rotaxanes are colored in full red in order to distinguish them from the atoms in the
dumbbell.

4.4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Distances for the optimized structure for the (a) 2R-D-2PF6 (R family) and for (b)
2R-Dp-2PF6 (R’ family). In the R family we observe rotaxane-rotaxane interaction
while in the R’ family, the distance between rotaxane rings is too large for them to
interact. Distance between stopper and rotoxane ring is marked in black. Distance
between first and second rotoxane is marked in red. Distance between first and second
-NH2 - site is marked in blue. The optimal rotaxane-rotaxane interaction distance is
3.6 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

xR-D-2anion compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6

xR-Dp-2anion compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7

Free energies in the gas phase for (a) gas phase and (b) solvated phase for the R
Family: 2R-D-2PF6 and 2R-D-2F (top) and for the R’ Family: 2R-Dp-2PF6 and 2R−
Dp-2F (bottom). The positive cooperativity is only observed with the PF−
6 (or I , not

shown) counter anion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8

Dipole moments (µ) from ESP charges obtained for the (a) R Family (2R-D-2PF6 and
2R-D-2F) and for the (b) R’ family (2R-Dp-2PF6 and 2R-Dp-2F) . . . . . . . . . . .

5.1

(a) Fundamental chemical reactions that take place in the production of O2 that start
with the conversion of solar energy (hν) to an electron and a hole in the chlorophyll
center called P680 . (b) The catalytic cycle of the Oxygen-evolving complex (OEC) is
shown where every oxidation is defined as a S-state (Sn ). (Inset) The full description
of the OEC is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

Complexes synthesized in the Agapie group containing (left) a Mn3 Ca and (right) a
Mn4 cubane. Notice how the Ca in Mn3 at the top have been substituted by one Mn
to give Mn4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3

Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light
blue, O; red, C; grey, H; white) and theory (black) using the full ligand. We show
the root mean square (RMS) to compare all the atoms in the structure (top) and the
cubane (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xvii
5.4

Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light
blue, O; red, C; grey, H; white) and theory (black) using the simplified ligand. We
show the root mean square (RMS) to compare all the atoms in the structure (top) and
the cubane (bottom). The structures with this simplified ligand are almost identical
to the ones obtained with the full ligand (Figure 5.3). . . . . . . . . . . . . . . . . . .

5.5

Oxidation/reduction for the Mn3 CaO4 compound. Color code: Ca; magenta, Mn; light
blue, O; red, C and H; black. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6

Oxidations/reductions for the Mn4 O4 compound. Color code: Ca; magenta, Mn; light
blue, O; red, N; dark blue, C and H; black

5.7

. . . . . . . . . . . . . . . . . . . . . . . .

New models for the OEC that includes the fourth Mn giving a CaMn4 O4 type cluster;
(a) CaMn4 -NH2 , similar to S1 (b) CaMn4 -bipy, similar to S1 and (c) CaMn4 -acac,
similar to S2 . Color code: Ca; magenta, Mn; light blue, O; red, N; dark blue, C; black
and H; grey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1

Molecular structures of building units used for COF synthesis (outside black box) and
their COF formation reactions (green box, boroxine; blue box, ester) . . . . . . . . . .

6.2

Atomic connectivity and structure of crystalline products for (a) 2D-COFs and (b) 3DCOFs. Unit cells are shown in blue lines. Atom colors: C, black; O, red; B, pink; Si,
yellow; H, blue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3

Comparison of the optimized FF energies with QM (MP2-RI) for four configurations:
(a) CH4 -CH4 ; (b) C6 H6 -CH4 ; (c) B3 O3 H3 -CH4 ; (d) Si(CH4 )4-CH4 . FF results are
shown as dashed lines while the QM results are shown by empty symbols. Each configuration has four plausible geometrical structures shown to the right, where C atoms
are brown, B pink, O red, Si yellow, and H white. Configurations interacting through
the edges are not shown. The insets show the accuracy in fitting to the equilibrium
distance. Data plotted here as the BSSE corrections are included in the Supporting
Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4

Predicted (open triangles) and experimental (closed circles) methane isotherms at 298 K
in excess uptake gravimetric units (wt %): (a) COF-5; (b) COF-8. The total predicted
uptake is shown by open squares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5

Predicted gravimetric methane isotherms at 298 K: (a) total and (b) excess uptake
isotherms. We have also validated our calculations for MOF-177 with experiments and
these are included for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xviii
6.6

Ensemble average from the GCMC steps for methane adsorption in 2D-COFs at various
pressures. Atom colors are the same as in Figure 6.2; the average of the methane gas
molecules is shown in blue. The accessible surface is shown in purple and was calculated
using the vdw radii of every atom of the framework and the methane kinetic radii: (a)
COF-10, pore diameter = 35 Å; (b) COF-5, pore diameter = 27 Å; (c) COF-8, pore
diameter = 16 Å; (d) COF-6, pore diameter = 11 Å. . . . . . . . . . . . . . . . . . . .

6.7

Ensemble average of methane molecules at different pressures: (a) COF-103; (b) COF105; (b) COF-108. Atom colors: C, gray; O, red; Si, yellow; B, pink. The average
of the methane gas molecules is in blue. The accessible surface was calculated as in
Figure 6.6. COF-102 has the same sorption profile as COF-103 and it is not shown. .

6.8

(a)Predicted Qst values for COFs as a function of pressure. We have added the calculated values for MOF-177 for comparison. (b) VP versus Qst for COFs. There are two
groups, based on the structural analysis: 2D-COFs (-1, -5, -6, -8, -10), which laid in a
line with the same slope. Also the 3D-COFs (-102, -103, -105, -108) have a common
line. Both lines coincide at VP ∼ 1.53 cm3 /g and Qst ∼ 10.6 kJ/mol. . . . . . . . . .

6.9

Predicted volumetric methane isotherms at 298 K for COFs: (a) total uptake isotherm
and (b) delivery uptake isotherm (the difference between the total amount at pressure
p and that at 5 bar). Here the black dashed line indicates the uptake for free CH4 gas.
MOF-177 uptake is added for comparison. . . . . . . . . . . . . . . . . . . . . . . . . .

6.10

Building blocks used in this study for designing new COFs. The inset shows the types
of condensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.11

CH4 uptake for the best COF performers. The delivery amount using a base pressure
of 1 bar is reported. The best performers at 35 bar are shown along with some that
perform best at 300 bar. Solid lines indicate published compounds. . . . . . . . . . . .

6.12

Heat of adsorption calculated for the compounds in Figure 6.11. The results for the
remaining compounds are in the Supporting Information. . . . . . . . . . . . . . . . .

6.13

Lattice parameter variations obtained from MD for several COFs. The lattice parameters are in Angstroms (Å) and time in nanoseconds (ns). COF-103 and COF-105-Ethtrans are not shown; the statistics are summarized in Table 6.5.

7.1

. . . . . . . . . . . .

Structures of the Li-doped COFs and MOFs studied in this work. Hydrogen atoms
have been omitted for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.2

Calculations of the thermodynamics for the Li species were obtained using M06 and
B3LYP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xix
7.3

(a) Molecular orbital (MO) diagram for Li-Bz system. Units for the vertical axis are
Hartrees. (b) Highest occupied molecular orbital (HOMO) for the Li-Bz for the gas
phase, for the implicit THF and for explicit THF obtained from M06 and B3LYP.
Atoms colors are C, green; H, white; and Li, pink. The colors of the orbitals yellow
and dark blue represent an arbitrary positive and negative sign. (c) Mulliken and
electrostatic charges for Li-Bz (g), Li-Bz (implicit THF), and Li-Bz (explicit THF) . . 107

7.4

Delivery gravimetric uptake obtained for the studied COFs and MOFs, also the metalated analogs with Li, Na, and K are shown. MOF180 and MOF205 as well as the
metalated cases are reported in the SI. In (a), we show the delivery amount using 1 bar
as the basis, while in (b) we show the delivery amount using 5 bar as the basis. The
error bars at each calculated point are shown, while on some cases they are too small
to fit inside the symbols.

7.5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

We show the correlation of pore volume (V P ) vs wt% delivery for different COFs:
pristine (dotted line), COF-Li (double dotted line), COF-Na (continuous line), and
COF-K (dashed line). In (a) 1 bar is used as the basis, while in (b) it is 5 bar.
Different colors represent different pressures. . . . . . . . . . . . . . . . . . . . . . . . 111

7.6

Delivery volumetric uptake obtained for the pristine, Li-, Na-, and K-metalated COFs
and MOFs are shown. In (a) we used 1 bar as the basis, while in (b) we used 5 bar as
the basis. The error bars at each calculated point are shown, and in some cases, they
are too small to fit inside the symbols. Bulk H2 is shown for comparison. . . . . . . . 112

7.7

Heat of adsorption obtained for the pristine COFs and MOFs, as well as the analogs
metalated with Li, Na, and K. MOF180 and MOF205 as well as for the metalated cases
are reported in the SI. Top plots show the error bars at each calculated point, and in
the bottom plots, the error bars are too small to fit inside the symbols. . . . . . . . . 114

7.8

Sorption mechanism for pure and Li-metalated COF102 . . . . . . . . . . . . . . . . . 114

7.9

We show the ensemble average of molecular hydrogen for MOF177 (bottom) and
MOF177-Li (top) at 298 K. Atoms colors are Zn, purple; C, gray; O, red; and the
average of molecular hydrogen is shown in green. MOF200, MOF180, and MOF210
have a similar mechanism to MOF177 and they are not shown; the same applies to
their metalated analogs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.10

We show the ensemble average of molecular hydrogen for MOF205 (bottom) and
MOF205-Li (top) at 298 K. Atom colors are the same as in Figure 7.9.

7.11

. . . . . . . . 115

Interactions H2 can have; noncovalent interactions and orbital interactions. The molecular orbital diagram and the H-H bond distances (from crystallography and NMR) are
adapted from reference [2]. (*) A strong external field is needed to create a dipole in H2 .118

xx
7.12

We show the normalized uptake (n/nm = uptake/sorption capacity) for three different
temperature conditions (left: 233K, center: 298K, right: 358K) using the Langmuir
model and ∆S◦ = -8R. We can see that the magnitude ∆H ads have a strong effect on
the amount that can be delivered between 3 and 100 bar, i.e., a small value (3 kJ/mol)
gives poor uptake and poor delivery, a large value (25 kJ/mol) gives high uptake but
poor delivery. The ideal ∆H ads gives both a high uptake and high delivery. . . . . . . 120

7.13

Connectivity developed in linkers used for COFs and MOFs where sites for metalation
are present. The pink circle indicates the sites where transition metals can be placed.

7.14

122

Different binding energies ∆H bind at 298K obtained for BBH ligand interacting with
four physisorbed H2 . We have focused on isoelectronic TM. PdCl2 is shown for comparison. The error bars estimate the different configurations. Mn(II), Cr(III) and Ni(II)
show strong interactions with the first H2 but there is no evidence of formation of
hydride (Table 7.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.15

Different binding energies ∆H ◦ bind at 298K obtained for the PIPE ligand interacting
with four physisorbed H2 . PdCl2 is shown for comparison. The error bars estimates
the different configurations. Mn(II), Cr(III) and Cu(II) show strong interactions with
the first H2 but there is no evidence of formation of hydride (Table 7.9). . . . . . . . . 128

7.16

Different binding energies ∆H ◦ bind at 298K obtained for the PIA ligand interacting
with four physisorbed H2 . We have focused on isoelectronic TM. PdCl2 are shown for
comparison. The error bars estimate the different configurations. Mn(II), Cr(III) and
Sc(II) show strong interactions with the first H2 but there is no evidence of formation
of hydride (Table 7.10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.17

Different binding energies ∆H ◦ bind at 298K obtained for the BPY ligand interacting with four physisorbed H2 . We have focused on isoelectronic TM. The error bars
estimate the different configurations.

7.18

. . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Different binding energies ∆H bind at 298K obtained for the BPYM ligand interacting with four physisorbed H2 . We have focused on isoelectronic TM. The error bars
estimate the different configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

7.19

Alternative option for metalating the linkers using metallic Pd(0). Our calculations
show that all these reactions are favorable, and therefore it should be a viable mode
for putting metals inside extended structure. Note that in the reaction from PIP to
PIPE, we did not consider a counter cation for PIPE; this makes the reaction with
H+ extremely favorable. The inset shows the calculated pKa for PIP/PIPE. . . . . . 136

xxi
7.20

(left) Our calculations showed that Pd(0) binds to the different linkers studied here.
(Right) The plot shows the energetics when the H2 interacts with the compounds
formed with Pd(0) shown in Figure 7.19. The first H2 forms a hydride converting
the Pd(0) into Pd(II). The subsequent H2 interacts strongly by physisorption with the
formed Pd(II)H2 . BPYM shows two H2 bound chemically because it has two Pd per
linker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

B.1

Topological constrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

B.2

Determination of number of adsorption sites . . . . . . . . . . . . . . . . . . . . . . . 172

B.3

Assumption from Langmuir theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

B.4

Isotherms of H2 uptake using our generalization . . . . . . . . . . . . . . . . . . . . . 177

B.5

Isotherms of H2 uptake using our generalization . . . . . . . . . . . . . . . . . . . . . 177

B.6

Isotherm of H2 uptake using the theory by Bhatia and Myers . . . . . . . . . . . . . . 177

B.7

Assumption for the multilayer theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

B.8

Assumption for the multilayer theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

B.9

Models studied with DFT/MO6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

B.10

Experimental data for ∆H of H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

B.11

Experimental data for S◦1 bar of H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Chapter 1

Introduction
The intention of this chapter is to give the reader a short introduction to the theory involved in
the simulations described in every chapter. For a broader description of the theory the reader is
encourage to consult the books by Jensen and the one by Cramer.[1, 3]
Our understanding of particles moving started with Newton’s three laws and more specifically
his second law:
F = ma.
From this point of view we learned that since p = mv then,
F=

dp
dv
=m
= ma
dt
dt

and we assumed at the time that m = constant. We also thought that we could predict the
trajectory/interaction of every particle of the universe back and forward if we could determine the
position and momentum at a given time in space of each one. However there were two revolutions
that changed this view, the relativistic theory by Einstein and quantum mechanics.
The relativistic theory by Einstein found that at high velocities mass is no longer a constant, and
that the maximum velocity any particle can reach is the velocity of light (c). This can be abstracted
in the following equation:
m= p

m0
1 − v 2 /c2

where m0 is the mass at rest, v the velocity of the particle and m is now the relativistic mass.
Quantum mechanics was the second revolution, and this theory was developed when the so-called
classical mechanics theory of Newton/Einstein could not explain the phenomenon of small particles,
such as the spectra of the hydrogen atom. The foundation of the old theory was that the energy was
a continuum. It turned out that when the particles are small (as with electrons), other forces prevail

in the interaction and another theory is needed. The explanation was then quantum mechanics,
which at low velocities is represented in the Schrödinger equation:
HΨ = i
where
H=

p2
2m

dΨ
dt

+V.

This theory was further developed to include the relativistic postulate of Einstein. This was done
by Dirac and the equation resembles the one at low velocities:
HΨ = i

dΨ
dt

but with a difference in the expression for the Hamiltonian operator:
H = (cα · p+βmc2 )+V.
In here, the α and β are 4×4 matrices and thus the relativistic wave function has three components.
In the limit of c → ∞, the Dirac equation reduced to the Schrödinger equation and the large
components of the wave function reduce to the α and β spin-orbitals.[1]
From these equations, in principle, we could calculate all the kinetics of any one particle. However,
there is the three-body problem, which means that we can solve analytically the expression for the
interaction of two particles, but that if we have three particles, the equations are no longer solvable
by exact methods, only by approximate methods. This is a big drawback to the initial belief that
we can calculate all the interactions of all particles. All this view is syntesized in Figure 1.1a. It
is commonly understood that relativistic effects started to be observed at 1/3 c and that quantum
effects started to be observed at 1 atomic mass unit (amu).
Many techniques have been created to get to a certain degree of accuracy to a solution to the
many-body problem. These techniques are created by using the formulas for classical and quantum
mechanics and the power of computers to numerically calculate many interactions. Techniques in
the domain of classical mechanics are included within the so-called molecular dynamics (MD) or
molecular mechanics (MM), which basically uses Newtons equations, and treats every part with a
model of balls and strings with a potential assigned to every interaction. Techniques in the domain
of quantum mechanics include: the Hartree-Fock method (HF), density functional theory (DFT),
Møller-Plesset perturbation theory (MP2,MP3,..), coupled cluster (CC), configuration interaction
(CI), and so on. They use basis sets or plane waves to represent electrons and protons.[1, 3]
These are methods to calculate interaction between particles and the equation of motion. Now
we will use these expressions to calculate the energy at different temperatures, and thus the entropy.

(a) Mass versus Velocity

(b) Length versus Time

Figure 1.1: Theoretical multiparadigms. (a) was adapted from [1], (b) is courtesy of Julius Su, and
Part (c) is courtesy of Andres Jaramillo-Botero.
Entrophy(S) is defined as the logarithm of the number of states accesible(g) to the system (S =
kB log g). Thus the more states are available the higer the entropy. At absolute zero temperature,
the ground state multiplicity (g(0)) has a well-defined multiplicitly. From the quantum point of
view, at absolute zero the system is in its lowest sets of quantum states. And, the relation between
temperature and entropy is given by 1/T = (∂S/∂U )N,V .[4] Therefore, at room temperature we can
reduce the macroscopic problem two variables; length and time where the corresponding number
of particles increase as shown in Figure 1.1b. If a higher temperature is used and the number of
particles is increased, where the time is still in the nanosecond range, then the paradigms changes
as it is shown in Figure 1.1c.
Now we review briefly some concepts of statistical mechanics to obtain temperature dependence.
An statistical ensemble represents a probability distribution of microscopic states of the system.
For a system taking only discrete values of energy, the probability distribution is characterized
by the probability πi of finding the system in a particular microscopic state i with energy level

Ei . Finding the probability distribution will give us the answer about the mean of any quantity
(ensemble average) we want to know from the system. Since the ensemble average is dependent on
the ensemble chosen, the expression is different and we show such properties on Table 1.1.
However, the mean obtained for a given physical quantity doesn’t depend on the ensemble chosen
at the thermodynamic limit. In this expression the denominator is known as the partition function
and to obtain is the main goal of methods such as molecular dynamics trajectories or Monte Carlo
methods. The denominators on Table 1.1; Ω, Q, Ξ and ∆ are the partition function for each ensemble.
This function allows us to calculate all the thermodynamically properties under the conditions of
the ensemble. The derivation and expression of the partition function for each ensamble is beyond
the scope of this chapter but there are many resources where this can be found.[5, 4]
Table 1.1: Ensembles for statistical mechanics. E stands for energy of the state; T , temperature;
V , volume; N , number of particles; µ, chemical potential. β is given by 1/(kT ), where k is the
Boltzmann constant. The denominators Ω, Q, Ξ and ∆ are the partition functions for each ensemble.
Ensemble

Independent variables

Probability distribution

Microcanonical
Canonical

(E,V,N)
(T,V,N)

πi = Ω1
1 −βEi
π(Ei ) = Q

Grand Canonical
Isothermal isobaric

(T,V,µ)
(T,P,N)

π(Ei , Ni ) = Ξ1 e−β(Ei +µNi )
1 −β(Ei +P Vi )
π(Ei , Vi ) = ∆

In Chapter 2, we use Molecular Mechanics (MM) combined with Quantum Mechanics (QM) to
calculate different energies of structures. In Chapter 3, we use QM to calculate transition states
and develop a coarse grained force field for molecular dynamics (MD). Chapters 4 and 5 uses QM
based methods to predict the energetics of different molecules such as redox potential and electronic
configurations. Finally, in Chapter 6 and Chapter 7, we use QM to calculate the interaction potential
for many molecular components and then we use the Grand Canonical ensemble to obtain the number
of interacting particles for a given chemical potential.
The highlight of Chapter 2 is that we can predict structures for this future catalyst and we
enumerate the characteristics of the building parts in order to have a two- or three-centered reaction
center. The most important results that we found in Chapter 3 is that we can predict the reactions
rates for cross linking polymers and this can be compared to the brute-force coarse grained force
field.
In Chapter 4 present the origin of the positive cooperativity with the results obtained from
free energy. The origin is the optimal distance between the rotaxanes rings which allows them to
interact to get positive cooperativity in the template-directed formation of these rotaxane/dumbbell
complexes. We also found that the role of the counter anion is to tune the charge population on
the -NH+
2 - recognition site so that the larger (softer) the counter anion the more charge on the

recognition site and the more interaction with the rotaxane ring is obtained. The interaction with
the recognition site serves as the first directed template mechanism (clipping) for the formation of
the rotaxane rings. This has many implications for the future synthesis of rotaxanes because we
predict that we can control the positive cooperativity by changing the charge population on the
recognition site by tuning the softness of the counter anion.
In Chapter 5, presents new models that have oxidation states that are similar to the S0 , S1 and
S2 states of the biological oxygen evolution complex (OEC). We have accomplished these different
electronic states by modifying the original host ligand or by adding common linkers such as bipyridine
or acetylacetonate. Thus we show that we can obtain compounds that resemble the OEC both
structurally and electronically.
In chapter 6, I validated our methodology by comparing with experiments (Figure 1.2). I also
report for the first time the methane uptake for benchmark MOF-177. Along the way I investigated
for the first time the sorption mechanism by studying the ensemble for the methane uptake in
Covalent-Organic Frameworks (COFs).

Figure 1.2: Uptake for CH4 for COFs and MOFs and observation of the sorption mechanism for the
uptake
In the second part of this chapter (Figure 1.3) I present predictions for new COFs that have an
optimal structure for methane uptake that reach the DOE target. I calculate the uptake up to 300
bar and found that two new structures COF-102-Ant and COF-103-Eth-trans have an optimal pore
diameter for an optimal delivery amount of methane.
In Chapter 7, I present for the first time the H2 uptake for the new generation of Metal-Organic
Frameworks and we compare them to the most representative COFs (Figure 1.4). I then propose a
method to increase the H2 uptake at room temperature by metaling the organic linkers with alkaline
metals. I found that MOF-200-Li and COF-102-Li reach the 2015 DOE target. In the second part of
this chapter we present another metalation strategy using transition metals (TM). I found that for
delivery amount (real amount usable) metalation is another option to obtain higher binding energy

OH
Si

OH
OH

15.00 Angstroms

20.00 Angstroms

COF102-Ant

COF103-Eth-trans

Figure 1.3: The design of two new COFs that overcome the DOE target at room temperature. They
perform better than MOF-177, currently on the market.
with H2 . I use Quantum Mechanical calculations to obtain the binding energy and to predict a new
strategy to metalate ligand sites.

HOMO orbitals

HOMO-gas

HOMO-THF Implicit

HOMO-THF Explicit

Figure 1.4: MOF200-Li and COF102-Li reach the 2015 DOE target.

Chapter 2

Prediction of Structures of
Metal-Organic Complex Arrays
(MOCA)
Jose L. Mendoza-Cortes, Vaclav Cvicek, Ravinder Abrol, William A. Goddard III

2.1

Introduction

We implement two methods with the objective of finding the most stable conformational state of
the structures denominated as metal-organic complex arrays (MOCA). The main objective is to
understand such possible structures in order to predict possible enzymatic activity.
MOCA are terpyridine appended and L-tyrosine protected with Fluorenylmethyloxycarbonyl
(Fmoc) molecules that are metalated selectively with Pt(II), Rh(III) or Ru(II) ions. These building
block then are assembled into a sequence using protocols of solid state peptide synthesis.[6]
The structures that are available experimentally are mono-, di-, tri-, tetra-, penta- and hexamers
containing one of the three previously selected transition metals.[6] The structures used in this
study are shown in Figure 2.1. However the 3D coordinates of such structures are not available
experimentally. Such knowledge is important because we can predict the possible catalytic activity
due to the folding of structure and possible accessible sites for a specific molecule. The structure can
be studied by NMR but the 3D-dimensional coordinates can be very challenging due to the difficulty
in crystalizing such molecules.
This chapter is divided in two parts; each part offers a different approach to the problem. The
first part uses a quantum mechanics – molecular mechanics (QM/MM) approach, while the second
part uses a method inspired from enzyme structure prediction.

2.2

Method I: QM/MM

Method I uses a hybrid method combining quantum mechanics (QM) and molecular mechanics
(MM). It is important to mention that we are not interested in the boundary between the QM and
MM Hamiltonian; we are only interested in the bonding and position of the monomers. Therefore,
this method is a simple generation of the coordinates around the metal with QM, while the rest is
handled by MM (Figure 2.1).

2.2.1

Methodology

Quantum Mechanics (QM). We used density functional theory (DFT) with a functional that has
been corrected for dispersion interaction: M06-2X[7]. In some cases we used B3LYP[8] hybrid DFT
functional as comparison. All the calculations we performed in the Jaguar code.[9] Here we used
the 6-31G** basis set. We used mainly M06-2X because it gives the best estimation for π − π
interaction energies and in this problem we will have many such interactions. For the TM we
used the Los Alamos LACVP**++, which includes relativistic effective core potentials.[10] The
unrestricted open-shell procedure for the self-consistent field calculations was used. All geometries
were optimized using the analytic Hessian to determine that the local minimum has no negative
curvatures (imaginary frequencies).
Molecular Mechanics (MM). During minimization the organics were optimized with universal
force field (UFF) [11] but the QM structures were kept constant. We use a cutoff of 12 Å, for the
noncovalent interactions. The charges used for the QM part are the Mulliken charges; while the MM
part is from the QeQ calculations.[12]

2.2.2

Quantum Mechanical Calculations

We first optimize the geometries from QM for the metal centers. We realized that there are only
three metallic centers needed to construct all the present MOCA. These units are shown in Figure
2.2. It is important to note that these structures have charges due to the metallic center, and the
counter anion is present in the liquid solution. However, in our calculations in the gas phase of these
complexes we use a total charge of +1 for Pt, 0 for Rh and +2 for Ru. This way our optimization
reaches equilibrium faster and we do not have to deal with the different configuration interactions
that the counter anion could have with the metallic complex. The charge is dispersed over the entire
structure and this is close to have a soft anion such as CO2 CF3 − . Thus we do not expect to have a
major difference in the structure versus using explicit counter anion.

2CO2CF3-

CO2CF3-

CO2CF3
Cl
F3CO2C
Rh

Pt+

Ru2+

2CO2CF3-

Ru2+

H2N

CO2CF3-

Pt+

Fmoc

H2N

Fmoc

H2N

Fmoc

H2N

Pt+

Fmoc

CO2CF3Cl

(a) Compound A (b) Compound B

Pt+
CO2CF3Cl

Rh
CO2CF3
CO2CF3

(d) Compound D

2CO2CF3-

F3CO2C

CO2CF3
Cl
Rh

CO2CF3
CO2CF3
Rh

Ru2+

2CO2CF3-

CO2CF3
Cl

F3CO2C

Ru2+

Fmoc
H2N

Pt+

Pt+
CO2CF3-

CO2CF3Cl

Fmoc

CO2CF3-

(e) Compound E

CO2CF3Cl

H2N

CO2CF3
CO2CF3
Rh

Pt+
CO2CF3Cl

(f) Compound F

Figure 2.1: Metal-organic complex arrays (MOCA). QM was used for the black part, including the
metal. MM was used for the pink part. Fmoc stands for fluorenylmethyloxycarbonyl.
2.2.2.1

The case of Platinum (Pt)

The first compound we studied was the Pt complex. We started by optimizing the structure with
our QM method and we checked that there were not imaginary frequencies. Once we reached the

Cl
Cl

Pt+

CO2CF3
CO2CF3
Rh

(a) Pt

Ru2+

(b) Rh

Figure 2.2: Structures used for the QM calculations. For the calculations in gas phase we did not
use the counter anion but the absolute charge that is shown.
optimized structure we realized that we might have obtained a local minimum. This compound
has two main degrees of freedom: the dihedral angles between the benzenes (CCCC) and the one
including a benzene and the OH (CCCO). Such dihedrals are illustrated in Figure 2.3.
In order to find the global minimum we assume that the dihedral conformer would be the major
differentiator. Thus we carried a coordinate scan for these dihedral angles, each step of 30◦ .
The first dihedral angle studied is the CCCC angle. The results are shown in Figure 2.3a and b.
The plot suggests that the most stable configurations are at 30, 150, 210 and 330◦ . We can see that
the barriers are different between 30 and 150◦ versus 150 and 210◦ . For the first one we have a high
barrier of 3.5 kcal/mol while for the second one we have a barrier of 2.1 kcal/mol. The same values
are repeated for the 210 and 330◦ and for 330 and 30◦ . We would expect to see only one type of
barrier but this suggests that the OH might be playing a role. This is a low-resolution scan to give
us an idea of the kind of energy surface for this degree of freedom. Next we optimize the structure
starting with the dihedral angle mentioned before. For a specific example, we arbitrarily start with
the 330◦ and find that optimized structure has a value of 324◦ . For our purposes the plot suggests
that the profile for the 4 states is equivalent and we do not need to optimize this dihedral angle to a
higher resolution. This information can be stored in our structure generator code to give the same
probability to each of these angles.
Secondly, we studied the CCCO dihedral as shown in Figure 2.3c and the results are shown in
Figure 2.3d. We used the same procedure as for CCCC and we found a more standard dihedral
profile: one type of barrier with three equivalent angles. We can see from the plot that under
consideration of the resolution of the conformer scan, there are two equivalent angles at 0 and 180◦
(where the angle at 0◦ is the same as at 360◦ .) Each of these has a difference of 0.1 kcal/mol.

11
The barrier for the dihedral rotation is 2.6 kcal/mol. This is intermediate to the one obtained
for the CCCC dihedral. This can be understood as the OH wanting to be in the same place as
the benzene since the free electrons of the oxygen atom can interact with the π electrons from the
benzene ring. To make sure that we found the correct angles we performed an optimization of the
structure, arbitrarily choosing the 0◦ . The optimized structure had a value of 1.1◦ suggesting that
our resolution is good enough to use these three angles as equivalent in our generator of structures.
DFT/MO6-2X
-1666.71

DFT/MO6-2X

dihedral-CCCC

-1666.71

Pt+

-1666.71

E (/au)

-1666.72

-1666.72
E (/au)

dihedral-CCCO

-1666.71

Pt+

-1666.72

-1666.72
-1666.72
-1666.72
-1666.72

-1666.72

-1666.72
-1666.72

(a) Dihedral

100
150
200
250
Dihedral angle (degrees)

(b) Dihedral CCCC

300

350

-1666.72

100
150
200
250
Dihedral angle (degrees)

300

350

(d) Dihedral CCCO

Figure 2.3: Coordinate scan for the dihedrals CCCC and CCCO of the Pt case. The pink lines
indicate the dihedral angle used.

2.2.2.2

The case of Rhodium (Rh)

The next case we study is the Rh complex. This particular complex can have two isomers due to
one Cl− and two CO2 CF3 − . QM calculations with MO6-2X and B3LYP were performed to discern
which isomer is the most stable. The results are shown in Table 2.1. We found that the most stable
isomer is the cis conformation by more than 10 kcal/mol. When we observed the optimized structure
of the cis configuration we found there is an interaction between the C-H from one of the pyridines
and the O from the ester of the equatorial CO2 CF3 − groups at a distance of 2.17 Å. The Mulliken
charge on the H is of +0.22 and the O is -0.45. The atomic electrostatic potential charge (ESP) for
the H is +0.20 and for the O is -0.52. This interaction can be characterize it as a hydrogen bond
with a C-H· · ·O nature.[13, 14] Thus we used the cis isomer for all the following calculations.
Table 2.1: DFT energies for the Rh cis and trans
Functional

Ecis (kcal/mol)

Etrans (kcal/mol)

MO6-2X
B3LYP

0.0
0.0

12.1
10.3

We then proceeded to find the most stable configuration for the two dihedral angles present in
the linker. The linker is the same as the one used for Pt+1 , however this time the metal center, Rh,

12
has a formal charge of zero.
The first dihedral we calculated is the CCCC of the adjacent benzene ring, as it is shown in
Figure 2.4a. The result for the scan is shown in Figure 2.4b and it was as we expected: similar to
the Pt+1 case, with four major local minima. However, for this case we found that all the barriers
are basically equivalent (2.7 kcal/mol) and the local minima are similar (different by 0.5 kcal/mol).
The barrier for the Rh case is smaller compared to the highest barrier (3.5 kcal/mol) and larger
than the lowest barrier (2.1 kcal/mol) of the Pt+1 case. We should remember that the resolution
to explore this dihedral was of a 30◦ step. Therefore we use 30, 150, 210 and 330◦ dihedrals as
equivalent in our structure generator code.
Our next explored dihedral CCCO is shown in Figure 2.4c. We expected this profile for Rh(0) to
be similar to the one obtained for Pt+1 . We observed such a case; however this time we calculated
a higher-resolution energy profile. We measured the energy every 10◦ . The results are shown in
Figure 2.4d. As we can see, the dihedral has two equivalent barriers but this depends on the initial
state. That is, from 0 to 90◦ the barrier is 1.9 kcal/mol, but if we start from 180◦ then the barrier to
either 0 or 360◦ is 2.1 kcal/mol. These barriers are smaller than the Pt+1 case of 2.6 kcal/mol. This
is still within the intrinsic error of our QM calculations because the state at 0 and 180◦ differ by
only 0.2 kcal/mol. It is important to mention that with our current approach we get an equivalent
energy between 170, 180 and 190◦ . All these angles, 0, 170, 180 and 190 have the same probability
of being generated when used in our random structure generator.
DFT/MO6-2X
-2709.32

-2709.32
E (/au)

-2709.32

dihedral-CCCO

-2709.32

CO2CF3
CO2CF3
Cl
Rh

-2709.32
-2709.33
E (/au)

CO2CF3
CO2CF3
Cl
Rh

DFT/MO6-2X
-2709.32

dihedral-CCCC

-2709.33
-2709.33

-2709.33
-2709.33
-2709.33
-2709.33
-2709.33

-2709.33

(a) Dihedral

100
150
200
250
Dihedral angle (degrees)

300

(b) Dihedral CCCC

350

100
150
200
250
Dihedral angle (degrees)

300

350

(d) Dihedral CCCO

Figure 2.4: Different dihedral angles tested for the Rh complex. The pink lines indicate the dihedral
angle used.

2.2.2.3

The case of Ruthenium (Ru)

The last unit we studied was the Ru+2 case. We followed the same procedure as the one used for
Pt+1 and Rh(0). For this compound we have two linkers that differ only on the tails, CH2 OH versus
CH3 . Therefore we have three different dihedral angles.
The first dihedral angle we studied was the CCCC formed by the pyridine and benzene group as

13
shown in Figure 2.5a. Our QM results for this scan are shown in Figure 2.5b. As we can see, the
profile is very similar to the one we encountered in the Pt+1 case with two kinds of barriers. We
found four minima which are at 30, 150, 210 and 330◦ and we found two barriers. The first barrier of
3.6 kcal/mol is between 30 and 150◦ (repeated between 210 and 330◦ ) and the second barrier of 2.5
kcal/mol is between 150 and 210◦ (repeated between 330 and 30◦ ). These are similar in magnitude
to the barriers calculated for the Pt+1 compound: 3.5 and 2.1, respectively.
We also explored the energetics of the other CCCC dihedral bond as it is shown in Figure 2.5c.
The results are almost identical to the former CCCC dihedral of the same compound, as we should
expect, and this is shown in Figure 2.5d. There are four minima at 30, 150, 210 and 330◦ . There
are also two kinds of barrier, a high barrier of 3.6 kcal/mol (between 30–150◦ , as well as in between
210–330◦ ) and a low one of 2.3 kcal/mol (between 150–210◦ and in between 330 and 30◦ ). As we
expect, it is basically the same as the dihedral CCCC shown in Figure 2.5a and b. Therefore all
these angles are used as equivalent when generating random structures.
Finally, we also explored the CCCO dihedral in the tail of linker containing the OH group (Figure
2.5e). The results are plotted in Figure 2.5d. We can see that the profile of the energetics are very
similar to the Pt+1 and Rh(0) cases. The barrier is 1.4 kcal/mol, and this is the lowest among the
CCCO studied cases.
DFT/MO6-2X
-2193.55

DFT/MO6-2X
-2193.55

dihedral-CCCC

-2193.55

Ru2+

E (/au)

Ru2+

E (/au)

-2193.55

100
150
200
250
Dihedral angle (degrees)

300

350

(b)

dihedral-CCCO

-2193.85

Ru2+

-2193.85

-2193.86

(e)

100
150
200
250
Dihedral angle (degrees)

(d)

DFT/MO6-2X

E (/au)

(a)

dihedral-CCCC

-2193.55

100
150
200
250
Dihedral angle (degrees)

(f) Scan 3 CCCO

Figure 2.5: Ru complex

300

350

300

350

14
2.2.2.4

Dimers

The last parameters we obtained from QM calculations are the energy interactions between dimers.
We calculated such interaction because when observing Figure 2.2 we can observe that such interaction will play an important role in the folding or general structure of the MOCA.
Thus, we optimize the geometry for all possible dimer interactions. There are only 6 possible
dimer interactions; Pt+1 -Pt+1 , Pt+1 -Rh(0), Pt+1 -Ru+2 , Rh(0)-Rh(0), Rh(0)-Ru+2 and Ru+2 -Ru+2 .
Our DFT/MO6-2X results are shown in Table 2.2.
Since we did not use counter anion for the positively charged complexes, we obtain a repulsive
energy for the interaction containing two positively charged molecules. Such is the case of Pt+1 Pt+1 , Pt+1 -Ru+2 and Ru+2 -Ru+2 . The magnitude of the repulsion is positively correlated with the
magnitude of the charge present in the dimers. The least repulsion interaction is for the Pt+1 -Pt+1
dimer (12.6 kcal/mol), followed by the Pt+1 -Ru+2 (33.2 kcal/mol) and Ru+2 -Ru+2 (119.3 kcal/mol).
On the other hand, when only one of the complexes is a charged species then the energy is
attractive. This is the case for the Pt+1 -Rh(0), Rh(0)-Rh(0) and Rh(0)-Ru+2 interactions. All the
magnitude of the attractive interactions are very similar; around 35 kcal/mol.
Table 2.2: Binding energies (Ebind ) for the different dimers obtained from DFT/MO6-2X and basis
set LACVP**/6-31G**
Dimer
+1

Pt -Pt
Pt+1 -Rh(0)
Pt+1 -Ru+2
Rh(0)-Rh(0)
Rh(0)-Ru+2
Ru+2 -Ru+2

Functional

Ebind (kcal/mol)

MO6-2X
MO6-2X
MO6-2X
MO6-2X
MO6-2X
MO6-2X

12.6
-36.9
33.2
-33.6
-35.7
119.3

The geometry obtained for the Pt+1 -Pt+1 dimer is shown in Figure 2.6a. The energetics for the
dimers is repulsive, however the intramolecular distance of the optimized structure is around 3.3
Å. This might sound contradictory; however it can be explained in the following manner. During
minimization we started from an initial state and we found a minimum, this bottom of the well can
be above zero or below zero in magnitude. Therefore we obtained a minimum but the magnitude
of the well is above zero. If molecular dynamics (MD) were to be performed this dimer would fall
apart because the bottom of the well can be escaped and the repulsion forces would prevail. We did
not calculate the effect of having counter anions around the dimer to see if the forces would become
attractive. This is because in our generator of structures we keep a positive charge, therefore these
calculations are in accordance with our intentions of not using counter anions when building the full
MOCA.

15
The optimized dimer structure for Pt+1 -Rh(0) dimer is shown in Figure 2.6b. The nature of this
interaction is attractive and this binding energy is 36.9 kcal/mol. For this structure we found three
sources of attractive interactions. First there are π − π interactions between two pyridine molecules
separated by almost 3.5 Å. The magnitude of this interaction is not considerable when compared
to H bond. For example, the benzene dimer has binding energy of 2–3 kcal/mol.[15] The second
source is a hydrogen bond interaction between the F of the CO2 CF3 − ligand linked to Rh(0) and
the H from the pyridine ring bounded to Pt+1 . This hydrogen bond can be represented as a typical
C-H· · ·F. The distance between these atoms is around 3.0 Å. This is a typical distance for a moderate
hydrogen bond with mostly electrostatic interactions.[13, 14]. The Mulliken population charge for
the C-H from pyridine is +0.19 and for the F from equatorial CF3 is -0.29. The atomic electrostatic
potential charge (ESP) for H from pyridine is +0.13 and -0.17 for F in the same hydrogen bond.
Finally, the third source of interaction is another hydrogen bond that occurs between the OH at
the tails of both linkers. This H bond can be thought of as a typical O-H· · ·O interaction. In this
interaction the hydrogen bond donor, OH, is from the linker from the Pt+1 , and the acceptor, O,
from the Rh(0) linker. The distance between H and the acceptor O is 2.0 Å, this is typical distance
for this interaction.[14] The Mulliken charge for H is +0.36 (ESP=+0.40) and for O is -0.57 (ESP=0.60). This is more evidence of such hydrogen bond. These three attractive interactions can count
for the binding of 36.9 kcal/mol for this dimer.
The next dimer interaction we studied was the Pt+1 -Ru+2 and the optimized structure is shown
in Figure 2.6c. The energy for this interaction is very repulsive (33.2 kcal/mol). The value is
three times more repulsive than the Pt+1 -Pt+1 case; this is because there are more positive charges
involved. The layers formed by the ligands from both metals is separated by 3.3 Å. This distance
is between the only two pyridines that interact. The optimized dimer structure is again a local
minima that depends on our initial guess, and it has a positive value. The optimized value finds
the bottom of the well even if the bottom of the well is above zero. To put it another way, we went
from very repulsive interaction to the least repulsive configuration. Classical MD or ab initio MD
would then escape this local minima and the dimer would fall apart. For our purposes, we need the
charges and the nature of the interaction for our structure generator. In the optimized local minimal
obtained we found two interactions that can be considered as a hydrogen bond. This occurs between
the O in the tail of the ligand of Ru and the C-H from the ligand bound to Pt. The distance of
the H to the O for this C-H· · ·O interaction is 3.2 Å. The Mulliken charge for H is +0.18 (ESP
charge=+0.19) and for O is -0.48 (ESP charge=-0.56). The second interaction is between the H
from the C-H belonging to a benzene ring of the Ru+2 and the Cl bound to the Pt. The separation
of this C-H· · ·Cl interaction is 2.9 Å. The Mulliken charge for H is +0.16 (ESP charge=+0.04) and
for Cl is -0.33 (ESP charge=-0.46). The ESP charges for H give a qualitatively different result than
Mulliken charges for the hydrogen in this case.

16
Next, we studied the interaction of the Rh(0)-Rh(0) dimer. The optimized structure is shown in
Figure 2.6d. This interaction is attractive, with a magnitude of 33.6 kcal/mol. For this case, we no
longer have the O-H· · ·O interaction as in the Pt+1 -Rh(0) case. However, in this dimer there are
still three types of interactions: dispersion forces and two types of hydrogen bonds. The dispersion
forces are responsible for the close distances between the benzene and the pyridine rings of both
linkers. This distance varies from 3.1 Åfor the benzene-benzene interaction, and 3.4 Åfor pyridinepyridine. The contribution to the binding should not be significant since the value for the benzene
dimer is 2–3 kcal/mol [15], however for the H bond, this interaction can go from less than 4 to 40
kcal/mol.[16] Also the first type of hydrogen bond that we observed is a three-centered hydrogen
bond that has the form C-H1· · ·Cl· · ·H2-C, with the C-H belonging to the same pyridine ring. The
distance for this interaction is around 2.7 Å. To corroborate that there is a hydrogen bond we also
calculated the Mulliken and ESP charges. We found that H1 and H2 have Mulliken charges of +0.15
and +0.16, respectively. On the other hand, Cl has a Mulliken charge of -0.38. The ESP charges
for H1, H2 and Cl are +0.15, +0.16 and -0.46, respectively, which are very similar to the Mulliken
charges. Finally, the second type of hydrogen bond occurring in this dimer is rather interesting. It is
a four-centered hydrogen bond which involves three different H atoms (H1, H2 and H3) interacting
with a single Cl atom. Each of these H atoms belongs to a different pyridine ring. The C-H. . .Cl
distances are around 2.5 Å. In order to fully characterize such an H bond, we calculate its Mulliken
and ESP charges. The Mulliken charges for H1, H2, H3 and Cl are +0.12, +0.14, +0.13 and -0.41,
respectively, while the ESP charges are +0.13, +0.13, +0.15 and -0.41 for the same atoms. Both
methods give the same result: the electronegative atom Cl is forming a hydrogen bond with the
H of the C-H present in three different pyridines. This can be characterized as a strong hydrogen
bond.[13, 14]
The fifth dimer we studied was the interaction of the Rh(0)-Ru+2 . The optimized structure
is shown in Figure 2.6e. This interaction is attractive, as we can see from the binding energy: 35.7 kcal/mol. There are three main types of interaction that are responsible for this, dispersion
interaction and two types of hydrogen bonds, just as in the case of the other dimers with attractive
interactions. First, the dispersion interactions can be observed because of the π − π stacking formed
by the pyridines rings from both metal complexes. The distance for their separation is 3.2 Å. This
interaction is not typically very strong in magnitude; for example, for the benzene-benzene dimer
the binding energy is 2–3 kcal/mol in gas phase.[15] Therefore most of the contribution should come
from the hydrogen bonding. The first strong interaction we have in this dimer is a three-centered
hydrogen bond C1-H1· · ·O· · ·H2-C2 formed by the two C-H from a pyridine of Rh(0) and the O
from the OH tail present in the Ru ligand. The separation for the H1· · ·O bond is 2.6 Å, and the
separation for the H2· · ·O is 2.5 Å. The Mulliken charges for the H1, H2 and O are +0.15, +0.17
and -0.57, respectively, while the ESP charges are +0.15, +0.13 and -0.61 for the same atoms. The

17
second strong interaction is a three-centered hydrogen bond that includes H10, H11 and H12 from
different pyridine in the same linker bound to Ru+2 , interacting with a Cl bound to Rh(0). The
distances for H10· · ·Cl, H11· · ·Cl and H12· · ·Cl are 2.8, 2.4 and 2.4 Å. The Mulliken charges for
H10, H11, H12 and Cl are +0.12, +0.18, +0.19 and -0.46 (ESP charges are +0.11, +0.16, +0.14
and -0.50), respectively. The H10· · ·Cl can be considered weaker than the other two hydrogen bonds
because of their longer distance and lower charge difference, either Mulliken or ESP charges.
Finally, we studied the dimer which is formed by complexes with the Ru+2 -Ru+2 metal centers.
We started with a guess of this interaction and we minimized the structure, then we found the
geometry that is shown in 2.6f. As we discussed above, even we get a repulsive energy of 119.4
kcal/mol we obtain this dimer separated by only 3.4 Å, this is because we found a local minima
which is above zero in magnitude. If the true global minima needs to be found then an MD method
is necessary, with this we will observe the dimer going apart from each other. This dimer is a case
where the small dispersion interaction is competing against a strong Coulomb repulsion of a charge
+2 interacting with another charge +2.

(a) Pt+1 -Pt+1 dimer

(b) Pt+1 -Rh(0) dimer

(d) Rh(0)-Rh(0) dimer

(e) Rh(0)-Ru+2 dimer

(f) Ru+2 -Ru+2 dimer

Figure 2.6: 3D-representation of the optimized structure obtained for each of the dimers considered
in this study.

2.2.3

Structures Obtained from QM/MM

Using all this knowledge we have obtained from QM calculation we then proceeded to generate
structures for the MOCA. As it was discussed before, the QM structures were used with the MM
part calculated for the peptides. The partition for the interactions are shown in Figure 2.1. The
big problem with the QM/MM method is how to define the interface between the two methods. In

18
order to avoid such problem, we use the geometries generated by QM as described above and we
only allow relaxing the atoms from the peptide. This way we keep the information from QM and we
do not have to define the Hessian in the interface. Therefore, this method is more like a constrained
MM. Next we defined a cutoff for the van der Waals of 12 Å, these interactions are assigned even for
the structure obtained from the QM. The purpose is to capture any noncovalent interaction within
this MM scheme. We minimized the structures using the UFF force field and a conjugated gradient
minimization scheme with at least 5,000,000 steps. From this we obtained the structures shown
in Figure 2.7. In these structures we used the Mulliken charges into the MM code, while we use
Qeq[12] charges for the peptides. Before the minimization we equilibrate the charges in order to
keep a proper global consistency.
The perspective used for these structures does not show all the details about the interactions
having place. For example for the compound A (Figure 2.7a) the aromatic ring of Fluorenylmethyloxycarbonyl (Fmoc) is interacting with the benzene ring of the L-tyrosine, the closest distance for
the benzene-benzene of these two entities is 3.5 Å. There is also a small interaction between the C-H
from Fmoc and the O of L-tyrosine. The C-H· · ·O interaction distance is 3.6 Å, and the charges for
the H and O atoms after minimization are +0.11 and -0.32, respectively.
Compound B has an array than can be described as Fmoc-(L-tyrosine-Pt)-(L-tyrosine-Pt). We
also found other interactions that are not easy to see for the optimized compound B (Figure 2.7b).
The first interaction is between the aromatic ring of Fmoc and the benzene of the linker of the
farthest Pt+1 . The closest distances for these rings are 3.5 and 3.7 Å. The second interaction is a
weak hydrogen bond between the H in the CH2 of the Fmoc group and the O in the tail of the
farthest L-tyrosine. The separation for the C-H· · ·O is 3.2 Å, and the charges for these atoms are
+0.11 for the H and -0.33 for the O. The Pt+1 are far apart with a distance of 28.6 Å, which suggest

that it might have low catalytic activity.
Compound C can be described as an Fmoc-(L-tyrosine-Ru)-(L-tyrosine-Pt)-(L-tyrosine-Rh) array. The optimized structure for this compound is shown in Figure 2.7c. The Fmoc in compound
D interacts slightly with the benzene of the Pt+1 ligand, their separation at the closest range is of
3.9 Å. There is also a hydrogen bond between the H of the CH2 from the tail of the Ru+2 ligand
and the O of the carbonyl from the L-tyrosine-Pt. The distance for this C-H· · ·O is of 2.8 Å. The
charges for the H and O involved in the H bond are +0.14 and -0.51, respectively. The distance
between the metal centers are as follows: the Ru-Pt distance is 32.3 Å, the Pt-Rh distance is 32.1
Å, and the Rh-Ru distance is 18.5 Å.
Compound D is formed by four metal centers and the array is described as Fmoc-(L-tyrosinePt1)-(L-tyrosine-Pt2)-(L-tyrosine-Rh)-(L-tyrosine-Ru). The optimized structure is shown in Figure
2.7d. For these compounds we do not observe an obvious intramolecular interaction except for the
aromatic ring of Fmoc interacting with the benzene ring present in linker of Pt1. The arrangement

19
formed by the four metallic centers of this molecule resembles a distorted rectangle with each metallic
center in one of the corners. The distorted square then has the following distances between metallic
centers: Pt1-Pt2; 28.2, Pt2-Ru; 17.2, Ru-Rh; 30.1 and Rh-Pt1; 20.7 Å. Thus, this array looks less
promising for a catalytic multicenter. We can see that the Rh for this case does not interact with
the Ru because it is too close for the dihedral to align in this interaction.
Compound E is formed by five metal centers and the array is described as Fmoc-(L-tyrosine-Rh1)(L-tyrosine-Pt1)-(L-tyrosine-Ru)-(L-tyrosine-Pt2)-(L-tyrosine-Rh2). The aromatic ring of Fmoc in
this molecule is interacting with the benzene ring of the linker bound to Pt1. We also found two
interesting H bond between a cabonyl and the H of an amine. The first C=O· · ·H-N interaction is at
the distance of 2.4 Å, with the O having a charge of -0.42 and the H a charge of +0.21. The carbonyl
belongs to the Fmoc group and the -NH belong to the peptide of L-tyrosine-Pt1. The second of this
type of interaction is between the C=O from the 3rd peptide; (L-tyrosine-Ru) and the NH from the
5th peptide (L-tyrosine-Rh2). The distance for the C=O· · ·H-N interaction is 2.6 Å, and the charges
for the O and for the H are -0.51 and +0.21, respectively. The distances between the closest metallic
centers are as follow: Rh1-Ru; 12.3, Ru-Rh2; 12.1, Pt1-Pt2; 16.3 with all units in Å. All the other
distances between metal centers is beyond 26 Å. The Rh is more likely to interact with the second
nearest neighbors, as we can observe for this case and Rh1 interacting with Ru or Ru interacting
with Rh1 which are separated for one monomer with Pt.
Compund F is the final array we studied, the sequence is described as Fmoc-(L-tyrosine-Pt1)-(Ltyrosine-Rh1)-(L-tyrosine-Pt2)- (L-tyrosine-Ru)-(L-tyrosine-Pt3)-(L-tyrosine-Rh2). The aromatic
ring of Fmoc is interacting this time with the benzene ring of the linker bound to Pt1. We also
found a hydrogen bond C=O· · ·H-N that is apart by a distance of 2.4 Å, with the O having a charge
of -0.51 and the H a charge of +0.21. The carbonyl belongs to the 1st peptide (L-tyrosine-Pt1) and
the -NH belong to the 3rd peptide (L-tyrosine-Pt2). However, the most relevant interaction found
for this structure is the H bond of nature F· · ·H-C, with the F from the CO2 CF3 − ligand bound to
Rh2 and H from one of the pyridines bound to the Ru. The H bond between the F and H is of 2.7
Å. The charges for H and F are +0.19 and -0.32, respectively. This interaction makes the Ru-Rh2
distance only 10.9 Å apart! The other other relevant distances are: Pt1-Pt2; 14.4, Pt2-Pt3; 12.7,
and Rh1-Ru; 21.9 Å. All the other intermetallic distances are over 25 Å.

2.2.4

Conclusions

Our procedure suggest that the more Rh(0) we put in our array, more closer interactions will occur,
thus more chances of generating catalytic activity. The monomer containing Rh(0) will interact with
the second nearest neighbor because it is at the perfect distance so that the dihedrals can align for
optimal interaction. We observed this for compound E and F, where the Rh are separated from Ru
by 1 monomer. We found that when Rh(0) is used, the F of the CO2 CF3 − ligand can form moderate,

(a) A

(b) B

(d) D

(e) E

(f) F

Figure 2.7: Final configuration obtained using the QM/MM method for all the arrays denominated
MOCA A, B, C, D, E and F
mostly electrostatic H bonds between the linkers of the metallic centers and this can help to create a
multicenter multi catalytic region. We also found that the hydrogen bond network happens mostly
in the polypeptide chain when CO2 CF3 − of the Rh(0) is not involved. The metallic centers do not
interact with peptidic part due to the rigidity of their ligands.

2.3

Method II: Structure Prediction Inspired in Enzymes

This method uses a random generator in order to sample completely random structures. This is in
order to capture the folding and most likely interaction in the MOCA compounds.

2.3.1

Methodology

The QM structures obtained from QM were used here. This means that all the most stable dihedral
angles, as well as the bond lengths were conserved. These optimized structures were attached to
the backbone peptide (organic part) and the conformers were generated with a random generator
approach. This code generates 2,000–20,000 conformers of the compounds A, B, C, D, E and F. We
then run 1,000 steps minimization of the whole structure with the Universal Force Field[11] while
the structures obtained from QM were left constant. We then analyze the different conformers and
classify them according to their energies with the lowest being the most favorable.

2.3.2

Generation of Conformers for All Compounds

We randomly generated a large number of possible conformations of the considered structures by
sampling all the possible orientations of the rotatable torsions. First, we generated the peptide
backbone with torsions from the Ramachandran distribution, then we added the tyrosine side chain.
Dihedral N-CA -CB -CG was chosen randomly from the three local minima. Finally, we added the

21
functional groups with metal, again randomly sampling the rotatable torsions, which were described
in the previous section.
Because the number of conformers is proportional to the number of degrees of freedom we generated 2,000 to 20,000 configurations for the compounds A to F, where A has less degree of freedom
than B, and so on. Then we executed 1,000 steps with the conjugated gradient minimization scheme.
This allows us to scan through a big database of structures.
The landscape for the ranking of all the generated structures can be observed in Figure 2.8.
We assume there are enough configurations because there is a low enough dip in the beginning of
the plot. In other words, there are a few structures with energy lower than the energy of a typical
randomly generated structure.
Energies of the configurations
1000

Energy (kcal/mol)

800

1mer
2mer
3mer
4mer
5mer
6mer

600

400

200

4000

8000

12000

16000

20000

Rank

Figure 2.8: Population of all conformers generated for MOCA A to F. Color code: 1mer(A), red;
2mer(B), green; 3mer(C), navy blue; 4mer(D), cyan; 5mer(E), light blue; and 6mer(F), yellow.
In order to determine our best configuration we take the 10 most stable configurations. We can
see that we obtain the most stable configuration when we zoom in for the first ranks. In Figure 2.9a
and b, we can see that how the configurations for A converges to the most stable ones with 2,000
structures. This is the same case for compound B which the convergence plot can be observed in
Figure 2.9c and d for 4,000 structures. For compound C, 10,000 structures were used (Figure 2.9e
and f) For compounds D, E and F; 20,000 conformers were used and the convergence curve can be
seen in Figure 2.9g-f.
The top 10 structures based on the energies are shown on Table 2.3. The energies presented
in this Table are with respect to the UFF parameters. Thus we present these numbers taking into
account that the relative values are the ones with physical meaning. That is the more positive the
number, the more unstable the structure and the relative value between two structures represent
which one is the most stable; with the lowest being the most stable. We can see that for compound
A, the conformer ranked 1st differs from rank 2nd by 0.65 kcal/mol. For compound B, this difference
is 1.27 kcal/mol. Compound C shows a gap of 1.83 kcal/mol. Compund D, E, F shows bigger gaps

22
Energies of the configurations

Energies of the configurations

600

Energies of the configurations

180

1mer

1000
2mer

7.5

2mer
900

178
500

800

5.5
4.5

400

Energy (kcal/mol)

300

200

Energy (kcal/mol)

176
6.5

174
172
170
168

600
500
400
300

100
166

3.5

200

164

100

500

1000
Rank

Rank

(a) Compound A

1500

2000

100

Energies of the configurations

190

800

255

250

2000

4000

Rank

6000

8000

10000

2000

Rank

(e) Compound C

100

5000

20000

Energies of the configurations

520
5mer

15000

(h) Compound D

Energies of the configurations

10000

10000
Rank

(g) Compound D

Energies of the configurations

5mer

60
Rank

(f) Compound C

Energies of the configurations

8000
6mer

6mer

9000

410

2500

1000

240

100

420

3000

500

3500

1500
245

200

4000

4500

260

Energy (kcal/mol)

1000

400

160

3500

4000

1200

600

165

3000

4mer

265

Energy (kcal/mol)

170

2500

5000

1400

175

2000
Rank

5500
4mer

1600

180

1500

Energies of the configurations

270
3mer

1800
185

1000

(d) Compound B

Energies of the configurations

2000
3mer

500

Rank

(b) Compound A

Energies of the configurations

Energy (kcal/mol)

700

7000

500
8000

400

6000
5000
4000
3000

Energy (kcal/mol)

370

Energy (kcal/mol)

380

6000

480

7000
390

460

440

420

360

5000
4000
3000
2000

2000
400

350

1000

340

100

380

5000

Rank

10000

15000

20000

Rank

(i) Compound E

100

5000

Rank

(j) Compound E

10000

15000

20000

Rank

(k) Compound F

(l) Compound F

Figure 2.9: Population of conformers generated for Compound A, B, C, D, E and F
of 11.0, 3.23 and 58.2 kca/mol, respectively. This demonstrates that for compound D and F, we
have a very low relative minima compared to the second choice, while for compounds E; the top
three conformers are closer in energy. Compound A, B and C have fewer degrees of freedom which
causes the energy states to be closer.
Table 2.3: Energies for the top 10 conformers. R stands for rank. All the energies are in kcal/mol.
Compound A

Compound B

Compound C

Compound D

Compound E

Compound F

Energy
3.42
4.07
4.15
4.48
4.62
4.66
4.79
4.85
4.93
4.95

Energy
164.06
165.33
166.76
167.54
168.75
169.22
169.23
169.54
169.76
170.63

Energy
163.10
164.93
169.54
171.79
173.32
173.56
173.59
174.79
175.47
175.92

Energy
241.53
252.53
252.80
253.48
253.94
254.60
255.78
256.94
257.07
257.22

Energy
342.78
346.01
349.11
373.82
374.46
384.65
385.80
389.10
389.99
390.24

Energy
398.44
456.65
463.54
465.39
469.89
471.33
471.89
472.14
473.19
474.18

23
The structures ranked as 1st for each of the compounds are shown in Figure 2.10. Compound A
obtained by this method (Figure 2.10a) resembles the one obtained by method I (Figure 2.7a). The
main difference is the structure obtained by method II does not have the Fmoc interacting with the
O of L-tyrosine. The distance for C-H· · ·O interaction is 5.0 Å (compared to 3.6 Å from method
I). The root mean square (RMS) for the comparison between these two structures is 4.2.
The structure obtained for B is shown in Figure 2.10b. In this structure we do not find any
interaction between the Fmoc and the benzene ring of the L-tyrosine or the linkers. There are not
hydrogen bonds as in the structure for B found by method I (Figure 2.7b). The Pt+1 -Pt+1 distances
are 22.6 Å which is a smaller distance to the one obtained from method I; 28.6 Å. When overlapping
the structures obtained for B from method I and II, we found that the RMS is 7.86.
Method II gives for Compound C the structure shown in 2.10c. The structure obtained with
method II does not show C-H· · ·O Hydrogen bond as the one obtained from Method I (Figure 2.7c).
However, there is a very interesting feature found for this structure. The distance between the center
Rh to Ru is of only 10.1 Å! This is similar to this type of interaction found for compound E and F
from method I. Compound C can be defines as the array : Fmoc-(L-tyrosine-Ru)-(L-tyrosine-Pt)(L-tyrosine-Rh). From our conclusions of method I, we found that the Rh-Ru interaction can be
found once the Rh and the Ru are separated by one monomer. We did not find this interaction from
method I for compound C but we found such configuration as the most stable from method II. This
shows the complementary of both methods to gives a nearly full representation of the important
interactions and most stable structures. This suggests that also compound C can have catalytic
processes where these two metals can be involved at the same time. The structures for C from the
two different methods give similar structures with a RMS of 7.28.
The optimized structure obtained for compound D obtained from method II is shown in Figure
2.10d. Compound D can be described as an Fmoc-(L-tyrosine-Pt1)-(L-tyrosine-Pt2)-(L-tyrosineRh)-(L-tyrosine-Ru) sequence. In the most stable structure generated from this method we observe
a very interesting interaction between the Rh and Pt1 at a distance 10.3 Å. This is the main difference
with the structure generated from method I, where such interaction was not found (Figure 2.7d).
This also corroborates our postulate that Rh can interact with a second nearest neighbor, and in
this case is the monomer with Pt1. The RMS for the overlap of the structures of D obtained from
Method I and II is 10.1, which indicates they are not very similar.
Compound E can be represented as follows; Fmoc-(L-tyrosine1-Rh1)-(L-tyrosine2-Pt1)-(L-tyrosine3-Ru)-(L-tyrosine4-Pt2)-(L-tyrosine5-Rh2) and the optimized structure obtained from method I
is shown in Figure 2.10e. The Fmoc interacts slightly with the benzene ring from the L-tyrosine
binded to Rh1, their separation is about 3.7 Å. There are also two hydrogen bonds of nature NH· · ·O=C between L-tyrosine1(C=O) and L-tyrosine3(N-H), as well as between L-tyrosine3(C=O)
and L-tyrosine5(N-H). The separations are 2.9 and 3.3 Å, respectively. However the most important

24
feature found in this structure is the interaction between Rh1 and Pt1. The separation for this
metallic center is 7.1 Å, which is the closest interaction we found for any structure. In this interaction
of dimers we found a hydrogen bond between the F from the CO2 CF3 ligand bounded to Rh1 and
the C-H from the pyridine bounded to Pt1. The separation for this C-H· · ·F interaction is 2.9 Å with
charges for F of -0.32 and for H of +0.17. This kind of interaction in a dimer was already suggested
by our QM calculations but it was not observed for the structure E obtained from method I (Figure
2.7e). The RMS for the overlap of the most stable structures obtained from method I and method
II is 9.3. This would suggest they are very different however they mostly differ in one dihedral that
contains Rh1 and Rh2. This explains why we do not observe the Rh-Ru close interaction but the
Rh-Pt interaction with this method.
Compound F is described by the array Fmoc-(L-tyrosine-Pt1)-(L-tyrosine-Rh1)-(L-tyrosine-Pt2)(L-tyrosine-Ru)-(L-tyrosine-Pt3)-(L-tyrosine-Rh2) and the structure obtained from method II is
shown in Figure 2.10f. The main interaction observed for this structure is the presence of the dimer
interaction between Pt1 and Rh2. It is the same type of interaction observed for compound E. The
Pt1 and Rh2 centers are separated by 7.9 Å. There is also a hydrogen bond between the C-H from
the pyridine bounded to Pt1 and the F from the CO2 CF3 ligand bounded to Rh2. The separation
for the C-H· · ·F interaction is 3.1 Å with charges for H of +0.18 and for F of -0.32. It is also
interesting to note that the adjacent F interacts with the Pt1 center since they are separated by 3.3
Å. The structure from method I and II when overlapped gives a RMS of 16.0 which suggest that
these structures are very different.

2.3.3

Conclusions

Compound C have a structure with the Rh-Ru distance of 10.1 Å, similar to the distance for this
interaction found for compound E and F obtained from Method I. We did not find this interaction
from method I for compound C but we found such configuration as the most stable from method II.
This also strongly supports our earlier conclusions that Rh(0) is necessary to obtain close distances
between metallic centers and if Rh-Ru interaction were to occur, they should be separated by one
monomer. Method II also shows for the first time that compound D can present interactions between
Rh and Pt. For this type of interaction they do not necessarily need to be second nearest neighbors
since the Rh-Pt is not as restricted as the Rh-Ru interaction. This interaction is also observed for
compound E and F between Rh and Pt, however we did not observe the Rh-Ru close interactions
given by method I for these cases. Our observations show the complementary of both methods,
method I observes the Rh-Rh interactions and method II observes the Rh-Pt interactions.
If Rh is used as a way to increase interactions in the MOCA, the next generation of arrays may
try to contain earth abundant elements for catalysis in energy production such as Cu for oxidation
of methane, [17, 18] Ni/Fe for production of molecular hydrogen, [19] or Mn/Ca for production of

OOOOLLLLDDDDEEEENNNN
MOOOLLLDDDEEENNN

OOOOLLLLDDDD
MOOOLLL

defaults used
defaults used

point 0

defaults used

OOOOLLLLDDDDEEEENNNN
MOOOLLLDDDEEENNN

(a) 1st A

(b) 1st B

OOOOLLLLDDDDEEEENNNN
MOOOLLLDDDEEENNN

(d) 1st D

OOOOLLLLDDDDEEEENNNN
MOOOLLLDDDEEENNN

defaults used

defaults used
point 0

point 0

(e) 1st E

(f) 1st F

Figure 2.10: Top 1st conformer for all compounds obtained by using method II
molecular oxygen. [20].

Chapter 3

Coarse-Grained Potential for
Hydrogels from Quantum
Mechanics
Jose L. Mendoza-Cortes, Andres Jaramillo-Botero, William A. Goddard III

3.1

Introduction

Hydrogels are aqueous polymer systems that may exhibit significant strength depending on their
composition and structure (e.g. crosslinking). The equilibrium between strength and elasticity
makes these materials a potential scaffolding material for cartilage, tendons and ligaments.[21]
There have been many attempts to understand the source of the strength in double network
polymer hydrogels at the molecular level, and through the use of atomistic molecular simulations.[22]
However, modeling and simulation of important events that occur during the synthesis process,
such as percolation, are beyond the capabilities of current atomistic Molecular Dynamics (MD)
simulations. To overcome some of these limitations, in particular those associated with the large
length and time scales, we proposed the use of a coarse-grained model parameterized from the finer
atomistic scale. [23, 24]
Thus, this chapter describes a coarse grained Force Field parameterized from quantum mechanics (QM) in order to understand the dynamics of polymer hydrogels. The specific polymers
described as an example of the parameterization procedure are poly-acrylamide (poly-[aam]) and
poly-2-acrylamido-2-2methylpropanesulfonic acid (poly-[amps]).
We also provide insights from Transition State Theory (TST) theory on the reaction rates required for cross-linking polymerization. From the reaction constants we determine to which degree
the concentration of each monomer is optimal for cross-linking and how this relates to percolation
and strength of the model hydrogels.

3.2

Methodology

This section present the methods used from Quantum Mechanics (QM) to calculate the potential
energy that can be fitted to a functional form which defines the coarse grained potential.

3.2.1

Molecular Mechanics and Quantum Mechanics

In order to have a good initial guess of the structural features of monomers, dimers, trimers, or
even tetramers, we minimized these with the Dreiding force field. [25] The initial guess obtained
from molecular mechanics were used to calculate the potential curve of bond breaking and dihedral
angles using first principles QM. For this, we used Unrestricted Density Functional Theory (UDFT)
with the M06-2X[7] functional as implemented in the Jaguar code[9] and a 6-31G** basis set. All
geometries were optimized using the analytic Hessian to confirm that the local minimum had no
negative curvature (imaginary frequencies). By studying the transition state we confirm that there
is one and only one imaginary frequency.

3.2.2

The Finite Extensible No Linear Elastic (FENE) Potential

FENE stands for Finite Extensible Nonlinear Elastic. It was initially proposed by Kremer and
Grest.[26]
E = −0.5KR02 ln

1−

2 #
+ 4

σ 12

σ 6

(3.1)

The first term extends to R0 , the maximum extent of the bond. The 2nd term is a cutoff at
21/6 σ, the minimum of the Lennard-Jones (LJ) potential. Where, and σ are obtained from QM
and the other terms are derived from these two terms, this is K = 30 /σ 2 and R0 = 1.5 σ. The
units are = energy, σ = distance, K = energy/distance2 , and R0 = distance.
A basic example of this functional form is shown in Figure 3.1. The plot of the FENE potential
contains the following parameters = 1.0 and σ = 1.0. With this parameter we can derive the rest,
K = 30 /σ 2 = 30, R0 = 1.5 σ = 1.5 and the cuttoff for the LJ is 21/6 σ = 1.12. In other words,
when a particle A is described by the FENE potential, anything that is within a distance of 1.5 is
going to have interaction with this particle A (mainly attraction). That is if a particle B gets in this
range of another particle, particle B will continue to get closer due to the attractive interaction. At
1.12, a repulsive force will start acting on particle B. If particle B gets closer, it will experiment a
stronger repulsive force, just as in the LJ potential. So far we have not defined the units, so we can
assume for now they are atomic units.

28
FENE
60
Total FENE
atractive FENE
LJ-repulsive FENE

40
30
20
10
0.8

0.85

0.9

0.95

1.05
distance

1.1

1.15

1.2

1.1

1.15

1.2

1.1

1.15

1.2

FENE
35
Attractive FENE
30

25
20
15
10
0.8

0.85

0.9

0.95

1.05
distance

FENE
45
40
35
30
25
20
15
10

LJ-repulsive FENE

0.8

0.85

0.9

0.95

1.05
distance

Figure 3.1: Example of the FENE potential. The repulsive part acts from 0 to 21/6 σ (bottom). The
attractive potential acts from 0 to R0 = 1.5 σ (middle). The combination of both terms make the
FENE potential (top). In this case, = 1.0, σ = 1.0, thus K = 30, R0 = 1.5, and 21/6 σ = 1.12.

3.3

FENE Potential

We describe our results obtained for the different models of monomers used and their bond strength.
The potential curve obtained was used to fit the terms of the FENE potential.
The monomers used on this study are acrylamide ([aam]), 2-acrylamido-2-methyl propane sulfonate ([amps]−1 ), sodium 2-acrylamido-2-methyl propane sulfonate ([amps]) and N,N ’-methylenediacrylamide ([xlinker]). Their chemical structure are shown in Figure 3.2.
We studied both the anion and neutral version of [amps] and we will show that this matters for
the parameters obtained for the FENE potential. In general we are interested in a neutral oligomer
to model the hydrogels properties, however the partially charged hydrogel could exist when the water
concentration is low, hence we report both parameters.

NH2
(a) aam

SO3-

(b) amps−1

SO3-Na+

(d) xlinker

Figure 3.2: All monomers used are presented: (a) acrylamide (71.08) (b) 2-acrylamido-2-methyl
propane sulfonate−1 (206.24 g/mol) (c) sodium 2-acrylamido-2-methyl propane sulfonate (229.23
g/mol) and (d) N,N’-methylenediacryl amide(154.17 g/mol).
As we can see from the structure, the dihedral angles are key in describing the larger-scale
conformal motions of polymers built from these units. Therefore we first study if the dihedral
angle correlation with the FENE potential form. Next, we study the parameters obtained when
dimers, trimers and tetramers are formed and how the FENE parameters correlates with the type
of interaction.

3.3.1

Dihedral Conformation and the FENE Potential

Dihedral are the principal degree of freedom necessary to develop accurate FENE parameters from
QM. The advantage of these monomers is that when the double bond is converted into a radical
for the polymerization and formation of the dimer or higher olygomers, each dimer creates only one
new dihedral bond.
To show such interaction we show in Figure 3.3a-b the dihedral angle created when the aam-aam
dimer is formed. We executed QM calculation with the procedure described to calculate the energy
surface for this dihedral. The result is shown in Figure 3.3c. The dihedral surface energy is not
symetrical.
3.3.1.1

Quantum Mechanics for the Dihedral Angles in the [aam-aam] Dimer
DFT/MO6-2X
-495.64
dihedral-aam-aam
dihedral-aam-aam

-495.642
-495.644
-495.646

E (/au)

-495.648

-495.65
-495.652

-495.654
-495.656

H2N
(a) aam-aam dihedral

-495.658

NH2

-495.66

(b) aam-aam dihedral

100
150
200
250
Dihedral angle (degrees)

300

350

Figure 3.3: The dihedral used for the aam-aam dimer is shown in (a) and (b) with magenta and
green colors, respectively. The 360◦ point should be equivalent to the O◦ for a constrained dihedral
scan, however we executed a relaxed scan.
The value for the dihedral of the starting optimized structure shown in Figure 3.3b is 6 dihedral

30
= 204.1◦ . However, the scan showed there are other conformers with lower energies: 6 dihe = 170◦ ,
6 dihe = 180◦ and 6 dihe = 187◦ . Thus, optimizations with these starting geometries were performed

and the results are depicted by the blue squares in Figure 3.3c.
After further optimization we found that: 6 dihe = 170.0◦ goes to 6 dihe = 173.9◦ , 6 dihe = 180.0◦
goes to 6 dihe = 174.0◦ , 6 dihe = 187.0◦ goes to 6 dihe = 179.4◦ . We observed that two structures
converge to almost the same dihedral angle and almost the same energy, see Table 3.1. We pick the
geometry with lowest energy, i.e. dihedral 173.9◦ .
Table 3.1: Energies for dihedral in the aam-aam
Angle (/degrees)
6 dihe = 173.9◦
6 dihe = 174.0◦

Energy (/au)
−495.657144
−495.657138

We then explored how the different most stable dihedral correlates to the FENE potential terms.
The QM curve for investigating the bond strength is shown in Figure 3.4. We can see that the
dihedrals have a different well depth, however both have the same equilibrium value. This is expected
considering it represents the same C-C bond as shown in Figure 3.7.
DFT/MO6-2X

DFT/MO6-2X

0.3

-0.174
aam-aam-dihedral=173.9
aam-aam-dihedral=179.4

0.25

aam-aam-dihedral=173.9
aam-aam-dihedral=179.4

-0.176

0.2

-0.178

0.15

-0.18
E (/au)

E (/au)

0.1
0.05

-0.182
-0.184

-0.186

-0.05

-0.188

-0.1

-0.19

-0.15
-0.2

-0.192

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

(a) aam-aam dihedrals

2.4

1.4

1.45

1.5
1.55
1.6
Coordinate distance (A)

1.65

1.7

(b) aam-aam dihedrals

Figure 3.4: Bond energies for aam-aam with dihedrals 173.9◦ and 179.4◦
Table 3.2 shows the FENE parameters obtained by fitting to the dihedral terms described. For
comparison we also include the FENE parameters obtained from another optimized structure with
less stable dihedral (204.1◦ ).
As we discussed earlier, the QM results shows that the same distance for the C-C bond should be
expected independently of the configuration used. This is captured by the FENE σ parameters, i.e.
it is the same for all configurations. On the other hand, our QM results suggested that the different
configurations would result in a different well depth, which also captured by the FENE potential
and the different values for the parameter.
From this we can conclude that the FENE potential capture the qualitative parts of QM. From
this we can conclude that the dihedral configuration used does not influe significatively the result

31
Table 3.2: FENE parameters obtained for different dihedral for the [aam-aam] dimer
Combination
[aam-aam] (204.1◦ )
[aam-aam] (173.9◦ )
[aam-aam] (179.4◦ )

Bond
(C-C)
(C-C)
(C-C)

σ (Å)
1.55
1.55
1.55

(au)
0.188
0.189
0.191

K (au/Å2 )
2.35
2.36
2.38

R0 (Å)
2.33
2.33
2.33

obtained for the FENE terms. The absolute numbers of the FENE potential does not have a physical
meaning but the relative quantities does.
3.3.1.2

Quantum Mechanics for the Dihedral Angles in the [xlinker] Monomer

We repeat the process for the different units involved in the polymerization, this section corresponds
to the xlinker. The dihedral is shown in Figure 3.5a.
DFT/MO6-2X
-456.332
dihedral-xlinker
dihedral-xlinker
-456.334

E (/au)

-456.336

-456.338

-456.34

-456.342

-456.344

(a) xlinker dihedral

-456.346

(b) xlinker dihedral

100
150
200
250
Dihedral angle (degrees)

300

350

Figure 3.5: xlinker dihedral used. (a) The structure used is shown in red and the dihedral angle
explored is magenta. (b) 3D representation of the xlinker with the dihedral used shown in green.
The blue dots in (c) are reoptimized structures with the dihedrals shown in green.
We started with the optimized geometry shown in Figure 3.5b. The value for the dihedral of
this structure is 6 dihedral = 103.4◦ . The results of a full dihedral scan are shown in Figure 3.5b.
The lowest laying conformers have a dihedral value of, 6 dihe = 103.4◦ , 6 dihe = 90.0◦ , 6 dihe =
270.0◦ . Dihedral angles of 90.0◦ and 270.0◦ should be similar in energy, however we re-optimize the
geometries. The results for this second optimization is shown in Figure 3.6c as blue dots. Some of
the dihedral angles change slightly while one remains the same. This is, the starting 6 dihe = 90.0◦
reconverged to 6 dihe = 90.0◦ , while the starting 6 dihe = 103.4◦ reconverged to 6 dihe = 100.8◦ and
the starting 6 dihe = 270.0◦ reconverged to 6 dihe = 281.3◦ .
Then we scan the bond strength for the most stable dihedral angles with our QM procedure.
The scanned bond is shown in Figure 3.13. The results for the three dihedral angles are show in
Figure 3.6. We observe that all the energies, minima and distance to the minima are the same. This
is different to the dimer [aam-aam] case where there is a small difference in the depth well.
Therefore, the corresponding xlinker dihedral does not affect the FENE potential parameters.

32
DFT/MO6-2X

DFT/MO6-2X

0.15

-0.175
dihe=90
dihe=100.8
dihe=281.3

0.1

dihe=90
dihe=100.8
dihe=281.3
-0.18

E (/au)

0.05

-0.05

-0.1

-0.185

-0.19

-0.15

-0.2

-0.195

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

(a) xlinker dihedrals

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

(b) xlinker dihedrals

Figure 3.6: Bond scan for most stable xlinker dihedrals
Table 3.3: [xlinker] FENE parameters for the FENE potential from QM
Combination
[xlinker] (90.0◦ )
[xlinker] (100.8◦ )
[xlinker] (281.3◦ )

3.3.2

bond
(N-C)
(N-C)
(N-C)

σ (Å)
1.45
1.45
1.45

(au)
0.192
0.192
0.192

R0 (Å)
2.175
2.175
2.175

K (au/Å2 )
2.74
2.74
2.74

Bond Strength and the FENE Potential

This section describes in more detail the QM results for the monomer and dimer bonds involved in
the hydrogel polymerization. We will use only one dihedral angle of one optimized geometry since
we demonstrated in the previous section that any optimized structure with a given dihedral angle
will give FENE terms that do not vary considerably from the the dihedral global minima. The
FENE potential is intended for coarse grained systems, which means that many vibrational modes
are smeared out, in order to make the calculation faster. Therefore small variation in the for a
given interaction will not have a big effect when the full simulation is considered.
3.3.2.1

Quantum Mechanics of [aam-aam]

The first interaction we considered is the bond strength in the formation of a aam-aam dimer. The
structure of such dimer is shown in Figure 3.7a. As we discussed previously the different dihedral
angle gives essentially the same FENE parameters. As an example we show the optimized structure
with dihedral 204.1◦ in Figure 3.7b. The energy surface for the C-C bond for the union of two dimers
is shown in 3.7c.
After fittting, the FENE terms obtained for this bond in this interaction we obtained K = 2.35,
R0 = 2.33, = 0.188 and σ = 1.55. The FENE potential for these parameters are shown in Figure
3.7. We discussed the other FENE terms obtained for other dihedral angles and all the results are
shown Table 3.5.

33
DFT/MO6-2X
0.3
aam---aam
0.25
0.2
0.15

E (/au)

0.1

0.05
-0.05
-0.1

H2N

NH2

-0.15
-0.2

(a) aam-aam

(b) aam-aam

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

Figure 3.7: Bond strength for a used conformation of aam-aam
Fitting DFT/MO6-2X vs FENE
25
fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

E (/au)

20
15
10
1.2

1.3

1.4

1.5

1.6

1.7

1.8

Coordinate distance (A)

E (/au)

Fitting DFT/MO6-2X vs FENE
5.5
4.5
3.5
2.5
1.5

fit: Attractive FENE

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Coordinate distance (A)
Fitting DFT/MO6-2X vs FENE
25
fit: LJ-repulsive FENE
E (/au)

20
15
10
1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

Figure 3.8: [aam-aam] FENE potential for structures in Figure 3.7
3.3.2.2

Quantum Mechanics of [amps-aam]

Next, we calculated the bond energy surface for the C-C bond in the amps-aam dimer. We must
remember that the amps monomer can be neutral o anionic. The interactions used for the study of
the C-C bond between aam and amps are shown in Figure 3.9a and d. We optimized the configuration
with our QM scheme and we obtained the structures shown in Figure 3.9b and e. The conformation
obtained for the neutral case and anionic case are slightly different. Then we calculated the energy
surface for the same C-C bond and the results are shown in 3.9c and f.
The energy surface was then fitted to the FENE potential (Figure 3.10) and we obtained the
parameters shown in Table 3.4. The parameters for both cases are basically the same. Therefore,
we conclude that the use of anion or neutral species in the aam-amps formation does not change the
final FENE parameters. Another way to look at it is that the FENE potential can not differentiate
between the charged molecule and the anion molecules when this dimer forms.

34
DFT/MO6-2X
0.3
amps---aam---neutral
0.25
0.2
0.15

E (/au)

0.1

0.05

SO3-Na+

-0.05
-0.1

H2N

-0.15

-0.2

(a) aam-amps(0)

(b) aam-amps(0)

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

E (/au)

0.1

SO3-

0.05
-0.05
-0.1
-0.15

H2N

-0.2

(d) aam-amps−1

(e) aam-amps−1

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

(f) aam-amps−1

Figure 3.9: amps-aam used. The scan used is shown with a magenta arrow.
Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

E (/au)

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

5.5
4.5
3.5
2.5
1.5

1.8

fit: Attractive FENE

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Coordinate distance ( /A)

Fitting DFT/MO6-2X vs FENE

fit: LJ-repulsive FENE

20
E (/au)

E (/au)

1.8

Fitting DFT/MO6-2X vs FENE

fit: Attractive FENE
E (/au)

E (/au)

Fitting DFT/MO6-2X vs FENE
5.5
4.5
3.5
2.5
1.5

1.7

15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Coordinate distance ( /A)

(b) aam-amps−1

(a) aam-amps(0)

Figure 3.10: [amps-aam] FENE potential for structures in Figure 3.9
Table 3.4: [aam-amps] FENE parameters for the FENE potential from QM
Combination
[aam-amps](0)
[aam-amps]−1

3.3.2.3

Bond
(C-C)
(C-C)

σ (Å)
1.55
1.55

(au)
0.194
0.193

R0 (Å)
2.33
2.33

K (au/Å2 )
2.42
2.41

Quantum Mechanics of [amps-amps]

We then proceed to calculate the strength for the amps-amps dimer. This interaction can have three
types of species: amps-amps(0), amps-amps−1 and amps−1 -amps−1 . However, for our purposes we

35
only considered the [amps-amps(0)] and [amps-amps−2 ] species as it shown in Figure 3.11a and d.
We built these models with the DREIDING force field and then we optimized them with our QM
method. The resulting structures are shown in Figure 3.11b and e. We can see that for the case of
the neutral species, the Na+ atoms used remains around the SO−
3 group as we should expect. Then
we proceed to break the C-C bond that connects both monomers. The surface energy obtained for
this bond is shown in Figure 3.11c and f.
DFT/MO6-2X
0.25
amps---amps---neutral
0.2
0.15
0.1

E (/au)

0.05
-0.05

SO3-Na+

-0.1
-0.15
-0.2

-0.25

(a) amps-amps(0)

(b) amps-amps(0)

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

E (/au)

0.1

SO3-

0.05

-0.05
-0.1
-0.15

-0.2

(d) amps-amps−2

(e) amps-amps−2

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

(f) amps-amps−2

Figure 3.11: amps-amps neutral and anion used. The scan used is shown with a magenta arrow.
Using these energy surfaces, we fitted them into the FENE potential form. The results are
shown in Table 3.5. The parameter for this interactions change drastically from the neutral to the
full anionic forms in the parameter, 0.205 for the neutral case and 0.155 for the anionic case. As in
the other interactions the σ remains 1.55 as we expected. Since K is directly correlated to the , we
also obtained different K values. The stronger bond is for the neutral form as we can see from the
larger value for . This can be understood from the interaction between Na+ and the SO−
3 group,
which makes it more harder to pull two species with larger masses apart. Thus, when used in MD,
this potential should include different relative masses for each species.
Table 3.5: [amps-amps] parameters for the FENE potential from QM
Combination
[amps-amps](0)
[amps-amps]−2

Bond
(C-C)
(C-C)

σ (Å)
1.55
1.55

(au)
0.205
0.155

R0 (Å)
2.33
2.33

K (au/Å2 )
2.56
1.94

The FENE form for these parameters is shown in Figure 3.12. This indicates that the FENE

36
parameters are able to differentiate between a full anionic form and the neutral form but is not
specific enough to differentiate the aam-amps interaction when either anion or neutral species is
used for amps.
Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE

25
fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

E (/au)

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.2

1.8

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

E (/au)

fit: Attractive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

4.5
3.5
2.5
1.5

fit: Attractive FENE

1.2

1.8

1.3

E (/au)

fit: LJ-repulsive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE
20
18
16
14
12
10

1.8

Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE
4.5
3.5
2.5
1.5

1.7

1.8

20
18
16
14
12
10

fit: LJ-repulsive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

(b) amps-amps−2

(a) amps-amps(0)

Figure 3.12: [amps-amps] FENE potential for structures in Figure 3.11

3.3.2.4

Quantum Mechanics of [xlinker]

We studied the strength of the N-C bond in the xlinker. This is in case we need to study C-N
bond breaking during the polymerization reaction. The bond explored in xlinker is shown in Figure
3.13a. while the optimized structure used for the construction of the bond surface energy is shown
in Figure 3.13b. The results for the scan from 1 to 2.5 Å is show in Figure 3.13c.
DFT/MO6-2X
0.15
xlinker
0.1

E (/au)

0.05

-0.05

-0.1

-0.15

(a) xlinker

-0.2

(b) xlinker

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

Figure 3.13: xlinker used. The scan used is shown with a magenta arrow.
Again, we used these QM results to fit the FENE potential. The parameters obtained are shown
in Table 3.6. We observe that N-C bond is shorter then the C-C bond according to the σ FENE
parameter. However, so far the C-N bond strength from this monomer is not stronger or weaker
than the C-C bonds explored. The value is between the values obtained for the C-C bonds. Since

37
the C-N bond is not participating in the polymerization, there could be a case where we need to
separate the xlinker slightly, and this term would serve for such purpose. However for our current
MD purposes we will not use these FENE term but only the C-C term. The FENE potential from
fitting these parameters are shown in Figure 3.14.
Table 3.6: FENE parameters
Combination
[xlinker]

Bond
(N-C)

σ (Å)
1.45

(au)
0.192

R0 (Å)
2.175

K (au/Å2 )
2.74

FENE
20
18
16
14
12
10

Total FENE
atractive FENE
LJ-repulsive FENE

1.1

1.2

1.3

1.4
1.5
distance

1.6

1.7

1.8

FENE
Attractive FENE

1.1

1.2

1.3

1.4
1.5
distance

1.6

1.7

1.8

FENE
18
16
14
12
10

LJ-repulsive FENE

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

distance

Figure 3.14: [amps-amps] FENE potential for structures in Figure 3.13

3.3.2.5

Quantum Mechanics of [xlinker-xlinker]

In this section we show the C-C FENE terms derived from QM. The C-C bond chosen is shown in
Figure 3.15a. As in the other cases we built this dimer using the Dreiding force field and optimized
the structure with molecular mechanics. Then we optimized the resulting structure with our QM
method. The structure obtained from this procedure is shown in Figure 3.15b. We then scan the
C-C bond to obtain the potential surface shown in Figure 3.15c.
Table 3.7: [xlinker-xlinker] parameters for the FENE potential from QM
Combination
[xlinker-xlinker]

σ (Å)
1.55

(au)
0.173

R0 (Å)
2.33

K (au/Å2 )
2.16

This is the form of FENE with the parameters: K = 2.16, R0 = 2.33, = 0.173, σ = 1.55.
Fitting the energy surface for the C-C bond shown, we obtain the FENE parameters in Table

38
DFT/MO6-2X
0.3
xlinker-xlinker
0.25
0.2
0.15

E (/au)

0.1
0.05
-0.05

-0.1
-0.15
-0.2

(a) xlinker-xlinker

(b) xlinker-xlinker

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

Figure 3.15: xlinker-xlinker used. The C-C bond scan used is shown with a magenta arrow.
Fitting DFT/MO6-2X vs FENE
25
fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

E (/au)

20
15
10
1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

E (/au)

Fitting DFT/MO6-2X vs FENE
5.5
4.5
3.5
2.5
1.5

fit: Attractive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

Fitting DFT/MO6-2X vs FENE
25
fit: LJ-repulsive FENE
E (/au)

20
15
10
1.2

1.3

1.4
1.5
1.6
Coordinate distance ( /A)

1.7

1.8

Figure 3.16: [amps-amps] FENE potential for structures in Figure 3.15
3.7. Just like all other cases the σ value is the same for the C-C bond, however we found that the
is the lowest value from all the interaction considered so far. This could be an indication that
self-polymerization of [xlinker] is not the main interaction but the cross linking of [xlinker] with
[aam] and [amps]. In this sense the FENE potential is able to capture such trend since in real
experiments, when the [xlinker] is added to the mixture of [aam] or [amps] the cross linking occurs
but the [xlinker-xlinker] formation is not seen in big quantities in the product. The parameters
obtained for this interaction in the FENE potential are shown in Figure 3.16.
3.3.2.6

Quantum Mechanics of [xlinker-aam]

Calculations for the [xlinker-aam] interactions were also executed. For this interaction we decided
to study the two types of bonds between [xlinker] and [aam] (Figure 3.17a and d). Although in the
coarse grained potential every monomer will be represented as a bead, we need to make sure that
at the atomistic level we capture the most stable configuration with the FENE description. We
optimized the geometry for the [xlinker-aam] with the procedure described before and we obtained
the configuration shown in Figure 3.17b, which is the same as Figure 3.17e. We then scan the

39
strength of the two types of C-C bonds that occur between these two monomers. The results are
shown in Figure 3.17c and f.
DFT/MO6-2X
0.25
aam-xlinker-aam-left
0.2
0.15

H2N

E (/au)

0.1

0.05
-0.05

NH2

-0.1
-0.15

NH2

H2N

-0.2

(a) xlinker-aam-I

(b) xlinker-aam-I

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

H2N

E (/au)

0.1

0.05
-0.05

NH2

-0.1
-0.15
-0.2

NH2

H2N

(d) xlinker-aam-II

(e) xlinker-aam-II

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

(f) xlinker-aam-II

Figure 3.17: xlinker-aam used. The scan used is shown with a magenta arrow.
From fitting our QM results to the FENE potential we obtained the parameters shown in Table
3.8. As we can see, the C-C distance represented by the FENE potential by σ are the same. And
the depth of the well for the two types of C-C bonds are very similar. We found that the the C-C
bond type I is stronger than the type II ( is larger; 0.196 versus 0.191). However there is not a
considerable difference. Therefore, it is a good approximation to use either C-C bond possibility, as
we did in the last cases. Since the coarse grain MD is not going to capture the type of C-C bond
between these two monomers, we will use the terms with the largest , in this case 0.196.
Table 3.8: [xlinker-aam] parameters for the FENE potential from QM
Combination
[xlinker-aam]-I
[xlinker-aam]-II

3.3.2.7

Bond
(C-C)
(C-C)

σ (Å)
1.55
1.55

(au)
0.196
0.191

R0 (Å)
2.33
2.33

K (au/Å2 )
2.45
2.38

Quantum Mechanics of [xlinker-amps]

Just as in the [aam-amps] and [amps-amps] interaction, in the [xlinker-amps] interaction we can
have two types of species, neutral or anionic. However we found that for the case of [amps-amps],
the neutral dimers results in the strongest interactions ( = 0.205 for the neutral versus 0.155 for the
anionic dimer). Therefore we use the neutral dimer to estimate the FENE parameters. We studied

40
Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

20
E (/au)

E (/au)

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

6.5
5.5
4.5
3.5
2.5
1.5

fit: Attractive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

5.5
4.5
3.5
2.5
1.5

1.8

fit: Attractive FENE

1.2

1.3

Fitting DFT/MO6-2X vs FENE

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

Fitting DFT/MO6-2X vs FENE

fit: LJ-repulsive FENE

E (/au)

1.7

Fitting DFT/MO6-2X vs FENE

E (/au)

Fitting DFT/MO6-2X vs FENE

15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

1.2

(a) Neutral

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

(b) Anion

Figure 3.18: [xlinker-aam] FENE potential for structures in Figure 3.17
the two forms in which [xlinker] can bind to [amps]. The bonds explored are shown in Figure 3.19a
and d. We optimized the structure with our MM method, and then with the QM scheme. The final
structure is shown in Figure 3.19b and e. Then we proceeded to build the bond energy curve for the
two types of C-C bonds. The results from QM are shown in Figure 3.19c and f.
We used these results to construct the FENE parameters. The terms obtained are shown in
Table 3.9 and plotted in Figure 3.20. Just like the other cases and as we should expect the σ is the
same for both cases, 1.55. However we observe that in this case we obtain different values for the
, 0.192 for bond I and 0.208 for bond II. The difference is 0.016 and this is the largest difference
observed for the same conformation. Thus, we use of 0.208 for our future calculations. This value
of is comparable to the one obtained for the amps − amps neutral interaction, which we found was
0.205. This suggest that the bond were amps is involved has a stronger interaction with xlinker and
itself than with the [aam] monomer.
Table 3.9: [xlinker-amps] parameters for the FENE potential from QM
Combination
[xlinker-amps]-I
[xlinker-amps]-II

3.3.3

Bond
(C-C)
(C-C)

σ (Å)
1.55
1.55

(au)
0.192
0.208

R0 (Å)
2.33
2.33

K (au/Å2 )
2.40
2.60

Conclusions

The obtained FENE potential parameters are shown in Table 3.10. The σ is the same for all cases
considering they are C-C bond types. However the depth of the well changes depending on the

41
DFT/MO6-2X
0.25
amps-xlinker-amps-left
0.2

SO3-Na+

0.15
0.1

E (/au)

0.05
-0.05

-0.1
-0.15
-0.2

SO3-Na+

(a) xlinker-amps-I

(b) xlinker-amps-I

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

SO3-Na+

0.2
0.15

0.1
E (/au)

0.05
-0.05

-0.1
-0.15
-0.2

SO3-Na+

(d) xlinker-amps-II

(e) xlinker-amps-II

1.2

1.4

1.6
1.8
Coordinate distance (A)

2.2

2.4

(f) xlinker-amps-II

Figure 3.19: xlinker-amps used. The scan used is shown with a magenta arrow. (b) and (e) are
equivalent.
Fitting DFT/MO6-2X vs FENE

Fitting DFT/MO6-2X vs FENE

30
fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

fit: TOTAL FENE
fit: Attractive FENE
fit: LJ-repulsive FENE

25
E (/au)

E (/au)

15
10

20
15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

5.5
4.5
3.5
2.5
1.5

fit: Attractive FENE

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

6.5
5.5
4.5
3.5
2.5
1.5

1.8

fit: Attractive FENE

1.2

1.3

Fitting DFT/MO6-2X vs FENE

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

Fitting DFT/MO6-2X vs FENE

30
fit: LJ-repulsive FENE

fit: LJ-repulsive FENE

25
E (/au)

20
E (/au)

1.7

Fitting DFT/MO6-2X vs FENE

E (/au)

Fitting DFT/MO6-2X vs FENE

15
10

20
15
10

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

(a) Neutral

1.7

1.8

1.2

1.3

1.4
1.5
1.6
Coordinate distance (A)

1.7

1.8

(b) Anion

Figure 3.20: [xlinker-aam] FENE potential for structures in Figure 3.19
interacting monomers. All these terms are obtained for either the neutral, which indicates that the
Na+ has been included for the [amps], and the anionic species (absence of Na+ ). The bigger the
depth the stronger the bond. Since K depends proportionally to and all the σ are the same, then
will also be larger for the larger depth.
A fast way to compare the quality of the FENE potential is to compare the QM trends with the
FENE trend. In Figure 3.21a we show the neutral species for the interaction between [aam] and
[amps]. We can see that the stronger interaction is for [amps-amps], followed by [amps-aam] and

42
Table 3.10: All the parameters for the FENE potential from QM. I and II stand for different explored
C-C bonds
Combination
[xlinker-amps]-I
[xlinker-amps]-II
[xlinker-aam]-I
[xlinker-aam]-II
[xlinker-xlinker]
[amps-amps](0)
[amps-amps]−2
[aam-amps](0)
[aam-amps]−1
[aam-aam]

(bond)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)
(C-C)

σ (Å)
1.55
1.55
1.55
1.55
1.55
1.55
1.55
1.55
1.55
1.55

(au)
0.192
0.208
0.196
0.191
0.173
0.205
0.155
0.194
0.193
0.191

K (au/Å2 )
2.40
2.60
2.45
2.38
2.16
2.56
1.94
2.42
2.41
2.38

R0 (Å)
2.33
2.33
2.33
2.33
2.33
2.33
2.33
2.33
2.33
2.33

the weakest among these three is the [aam-aam]. For the FENE potential terms, the strength of the
bond for each interaction is given by the value of . For the [amps-amps] we have the largest value
for (0.205) followed by [amps-aam](0.194) and then [aam-aam] (0.191). This is the same trend
obtained for the QM calculation.
DFT/MO6-2X

DFT/MO6-2X

-0.13

-0.172
aam-aam
amps-aam-neutral
amps-amps-neutral

-0.174

aam-aam
amps-aam-anion
amps-amps-anion

-0.14

-0.176

-0.15

-0.178

E (/au)

-0.18
-0.182

-0.16

-0.17

-0.184
-0.186

-0.18

-0.188

-0.19
-0.19

-0.2

-0.192
1.4

1.45

1.5

1.55

1.6

1.65

1.7

Coordinate distance (A)

(a) Neutral

1.4

1.45

1.5

1.55

1.6

1.65

1.7

Coordinate distance (A)

(b) Anion

Figure 3.21: All QM results around the equilibration point
Our main objective was to calculate the interaction between neutral species. However, the FENE
potential is able to capture the trend obtained from QM for anionic species. In Figure 3.21b we
show the energy surface for the C-C for the interaction between [aam] and [amps]−1 . We can see
that QM predicts the interaction in the [amps-aam]1 dimer to be the strongest followed by [aamaam] and finally [amps-amps]2 as the weakest. If we observe the FENE terms we found that the
[amps-aam]1 interaction has the the largest (0.193), therefore the strongest interaction, followed
by [aam-aam]1 (0.191) and [amps-amps]2 (0.155).
Conclusions for [xlinker-aam] and [xlinker-amps]
Finally the FENE terms obtained from QM determines that for the cross-linking reaction when
the xlinker is used the [xlinker-amps] will be dominant due to the largest = 0.208 followed by

43
[xlinker-aam]2 with = 0.196. The values for these two species are almost the same so there will
be no an evident preference for either one and the concentration for each species will play the
main role, just as in the experiments. The FENE parameters predict that there will not be much
self-polymerization for the xlinker as we can see from the small = 0.173, this is also observed in
experiments. When the three species [amps], [aam] and [xlinker] are mixed in the same concentration,
the FENE parameters predicts that the main reaction is between [xlinker] and [amps], as well as selfpolymerization of [amps] since they have the largest . In experiments however, smaller concentration
of [amps] is used, compared to [aam], perhaps because of this reason and since cross-polymerization
is needed.
A coarse grain bead model used in an MD scheme with the developed FENE interactions enables
an improved sampling, over a fully atomistic model, of the conformational space of the polymers.
Appropriate bead masses should be set for each monomer bead, and from our analysis we suggest a
mass of 1 for aam, 4 for amps, and 2 for the xlinker.

3.4

Reaction Rates from Transition State Theory

Here we calculate the reaction rates between the different species discussed in the previous section
from Transition State Theory (TST). Using Eyring equation of TST [27] for calculating rates of
reaction we have:
A+B *
) [AB]‡ → P
TST assumes that even when the reactants and products are not in equilibrium with each other,
the activated complexes are in quasi-equilibrium with the reactants. The equilibrium constant K ‡
for the quasi-equilibrium can be written as
K‡ =

[AB]‡
[A][B]

where [ ] = concentration mol/L, thus the concentration of the transition state is [AB]‡ =
‡ ‡
K ‡ [A][B] and the rate equation for the production of product is d[P
dt = k [AB] = k K [A][B] =

k[A][B] Here, the rate constant k is given by k = k ‡ K ‡ . k ‡ is directly proportional to the frequency of
the vibrational mode responsible for converting the activated complex to the product; the frequency
of this vibrational mode is ν. Every vibration does not necessarily lead to the formation of product,
so a proportionality constant κ, referred to as the transmission coefficient, is introduced to account
for this effect. So k ‡ can be rewritten as k ‡ = κν.
For the equilibrium constant K ‡ , statistical mechanics leads to a temperature dependent expres‡

sion given as K ‡ = [(kB T )/(hν)]e−(∆G )/(RT ) . Combining the new expressions for k ‡ and K ‡ , a new

44
rate constant expression can be written, which is given as

k = k ‡ K ‡ = κ[(kB T )/(h)]e−(∆G )/(RT )
Since ∆G = ∆H − T ∆S, the rate constant expression can be expanded, giving the Eyring

equation k = κ[(kB T )/(h)]e(−∆S )/(R) e(−∆H )/(RT ) . In order to determine the reaction rates we
calculate the transition state energy and then apply TST to obtain the reaction constant.

3.4.1

Reaction Rates in Gas Phase and Water

The polymerization reaction used in the synthesis of hydrogels is a free radical mechanism. In
real experiments, first one monomer is polymerized with excess xlinker [21]. This way cross-linking
polymers of only [aam] and [xlinker] is created first which we call P[aam,xlinker] and in a different reaction, the cross linking polymers of only [amps] and [xlinker] is created, which we call
P[amps,xlinker]. If double network polymers are needed, normally one would prepare a single network first, wash excess x-linker, and add the second component in linear form with a low xlinker
concentration.
The concentration of the monomers in any case is very low since the water content is about 90%.
Therefore our QM calculation in gas phase and implicit water solvent can capture the reaction rates
for real experiments because low concentration of reactants are required. This is because in the
implicit solvent case we assume low concentration of the reactant, since we do not consider multiple
monomer-monomer interactions. The reactions we studied are shown in Figure 3.22. We do not
consider the aam-aam and the amps-amps interaction since we assume that all the interactions
will come from the x-linker interaction with these two monomers or with itself since x-linker is the
initiator of the reaction and generally present in a higher concentration. If higher concentrations
of [aam] or [amps] compared to [xlinker] are used, then the energies for this interaction should be
calculated.
Since the free radical polymerization reaction is used in real experiments we calculate the possible
reactions when the xlinker is the initiator, 3.22a, c and e. Also we considered the case that the
polymerization continues with the free radical now in the [aam] or [amps]. As we discussed before,
in real experiment the concentration of [aam] and [amps] are relatively small compared to the
[xlinker]. Thus this new free radical will have more probability of finding [xlinker] and this case is
calculated in the second possibility illustrated in Figure 3.22b, d and f.
For our implicit solvent calculations we used the Poisson-Boltzmann solvation model (PBF)
approximation [28, 29] and the parameters for these calculation are shown in Table 3.11. We first
optimized the structure in gas phase and then the solvent correction was added. Then we found the
transition state for each geometry and the results are show in Figure 3.23. This is a plot were the

H2N

(a) aam-xlinker, Reaction 1

(d) amps-xlinker, Reaction 2

SO3-Na+

(b) aam-xlinker, Reaction 2

(e) xlinker-xlinker, Reaction 1

(f) xlinker-xlinker, Reaction 2

Figure 3.22: For all studied reactions, the free radical polymerization mechanism is assumed
doublet was calculated for the transition state and the full scan for the formation of reactants and
products is shown. The plots for the water cases are not shown but the free energies calculation
with water solvent were performed and all the results are shown in Table 3.12.
Table 3.11: Parameters for water
Dielectric constant
Probe Radius

-780.575

-1723.41

-780.59
xlinker-aam-case1-rate1

-1723.42
xlinker-amps-case1-rate1

xlinker-aam-case1-rate2

-780.58

xlinker-amps-case1-rate2

-1723.41

-780.595

-780.585

-1723.43

-1723.42

-780.6
Reactants

-1723.43
Reactants

Reactants

-1723.44

-780.595

-780.61

-1723.43

-1723.44

-780.6

-780.615

-780.605

-780.62

-780.61

-780.625

-780.615

-1723.43

-780.63

-780.62

-780.635
1.4 1.6 1.8

2.2 2.4 2.6 2.8
Coordinate reaction

3.2 3.4 3.6

1.4 1.6 1.8

(a) aam-xlinker,rxn-1

2.2 2.4 2.6 2.8
Coordinate reaction

-1723.45

-1723.44

-1723.46
-1723.46
Products

-1723.45

3.2 3.4 3.6

-1723.45

-1723.44

-1723.45

Products

E (/au)

-1723.42
E (/au)

-780.605
E (/au)

-780.59

1.4 1.6 1.8

Products

-1723.47

2.2 2.4 2.6 2.8
Coordinate reaction

3.2 3.4 3.6

(b) aam-xlinker,rxn-2

-1065.97

-1065.99
xlinker-xlinker-case1-rate1

1.4

1.6

1.8

2.2 2.4 2.6 2.8
Coordinate reaction

3.2

3.4

(d) amps-xlinker,rxn-2

xlinker-xlinker-case1-rate2

-1065.98

-1066

-1065.98

-1066

-1065.99

-1066.01

-1065.99
Reactants
-1066

E (/au)

Reactants

E (/au)

80.37
1.40 A

-1066.01
-1066.02

-1066

-1066.02

-1066.01

-1066.03

-1066.01
-1066.02

-1066.03
Products

Products
1.4 1.6 1.8

-1066.04

2.2 2.4 2.6 2.8
Coordinate reaction

3.2 3.4 3.6

(e) xlinker-xlinker,rxn-1

1.4

1.6

1.8

2.2 2.4 2.6 2.8
Coordinate reaction

3.2

3.4

(f) xlinker-xlinker,rxn-1

Figure 3.23: This plot shows the product (left) and reactant (right)
The Free energies (∆G) for the gas phase changes when solvation is used as we should expected.

46
The degree of this change should depend on the charge and size of each species, since these are the
main factors that are affected by the solvation. For example, the free energies for the [xlinker-aam]
we found that the main changes in the free energy are for the radical and neutral [xlinker].
An important factor that should be pointed out is that due to the nature of the free radical
polymerization, we can have different modes of reaction for a given asymmetrical double (C1 = C2)
that reacts with a another asymmetrical double bound (C1’ = C2’). This is because the free radical
can be in either of the carbons and reacts with any of the carbons of the other double bond. This
four modes can be represented as: C1-C2·—C1’ = C2’, C1-C2·—C2’ = C1’, C2-C1·—C1’ = C2’,
and C2-C1·—C2’ = C1’.
For our calculations we only consider one mode, assuming that the other modes will be very
similar in energy. This is because even the carbons that are acting in the double bond are not
identical, they are primarily CH=CH2 bonds. This point is shown when we consider two modes for
the xlinker-xlinker interaction (Figure 3.22e and f). The radical can be in the primary or secondary
carbon in the xlinker, then we calculate the energy when they react with the secondary carbon of
another xlinker. The activation energy for both cases are very similar, for the primary C. reacting
with the secondary C in the double bond we have ∆G‡ = +12.7 while for the secondary C. reacting
with the secondary C in the double bond we obtained ∆G‡ = +14.1. The distance between these
two cases in water gets reduced even further ∆G‡ = +20.6 for the former case and ∆G‡ = +21.7 for
the latter. This suggests that our assumption of considering only one mode of reaction is acceptable,
specially when solvation is used.

3.4.2

Conclusions

The calculation of the activation energy gives us several insights about the kinetics of this polymerization. Using the Eyring equation from TST we can estimate the reaction constant. The results
are shown in Table 3.13. The reactions are slower in water solvent. This is because the organic part
of the monomers does not interact strongly with the polar water. This can be seen clearly in Table
3.12, where all the structures gets destabilized by the water solvent. However in both scenarios,
[xlinker]· is ten times slower than the reaction that starts [aam]· or the analog that starts with
[amps]·. The implication is that since the initiation for the reaction ([xlinker]· reacting with [aam]
or [amps]) is slower than the propagation (reaction of [aam]· or [amps]· with [xlinker]). I assume
that the propagation is a reaction with [xlinker] because it is in higher concentration.
From the reaction constants, we found that in the initiation with the ([xlinker]· species in water
the reaction with [amps] is slightly faster than with [aam]. Our results also indicate that the self
polymerization reaction for the [xlinker] is not important since it is two orders of magnitude slower
than the cross linking polymerization. All these observation are relevant to experimental results
when low concentrations of [amps] or [aam] are used, with respect to xlinker concentration. Water

47
Table 3.12: Free energy (G) of all the reactions in gas phase. Energies are in kcal/mol.
xlinker-aam (Gas phase)
reaction 1
reaction 2
G‡
-30.4
G‡
-31.2
Gaam
-18.7
Gaam.
-19.5
Gxlinker. -26.4
Gxlinker
-24.5
+12.8
+14.7 ∆G‡2
∆G‡1

xlinker-aam (In water)
reaction 1
reaction 2
G‡
-24.4
G‡
-23.9
Gaam
-17.8
Gaam.
-18.8
Gxlinker. -25.9
Gxlinker
-23.0
+17.9
+19.3 ∆G‡2
∆G‡1

xlinker-amps (Gas phase)
reaction 1
reaction 2
G‡
-38.6
G‡
-39.1
Gamps
-28.1
Gamps.
-29.3
Gxlinker. -26.4
Gxlinker
-24.5
+14.7
+16.6 ∆G‡4
∆G‡3

xlinker-amps (In water)
reaction 1
reaction 2
G‡
-33.3
G‡
-32.2
Gamps
-26.4
Gamps.
-27.3
Gxlinker. -25.9
Gxlinker
-23.0
+18.1
+19.0 ∆G‡4
∆G‡3

xlinker-xlinker (Gas phase)
reaction 1
reaction 2
G‡
-38.2
G‡
-37.4
Gxlinker
-24.5
Gxlinker. -27.0
Gxlinker. -26.4
Gxlinker
-24.5
∆G‡5
+12.7 ∆G‡6
+14.1

xlinker-xlinker (In water)
reaction 1
reaction 2
G‡
-28.3
G‡
-27.7
Gxlinker
-23.0
Gxlinker. -26.4
Gxlinker. -25.9
Gxlinker
-23.0
∆G‡5
+20.6 ∆G‡6
+21.7

Table 3.13: Free energy obtained from QM and the derived reaction constant (k) from TST
Gas phase
∆G‡rxn
+14.7
+12.8
+15.9
+14.7
+12.7
+14.1

1.03E+02
2.54E+03
1.35E+01
1.03E+02
3.01E+03
2.82E+02

In Water
∆G‡rxn
+19.3
+17.9
+19.0
+18.1
+20.6
+21.7

4.33E-02
4.61E-01
7.19E-02
3.29E-01
4.82E-03
7.52E-04

Reaction rates
v1 = ka−x· [aam][xlinker·]
v2 = ka·−x [aam·][xlinker]
v3 = km−x· [amps][xlinker·]
v4 = km·−x [amps·][xlinker]
v5 = kx−x· [xlinker][xlinker·]
v6 = kx·−x [xlinker·][xlinker]

content in a hydrogel is normally high, i.e. 80-90 weight percent content.
Our results also suggest that for the propagation reaction in water, the reaction between [aam]·
and [xlinker] is slightly faster than [amps]· and [xlinker]. This is in the opposite order for the
initiation reaction with [xlinker]·. This might be a source for getting close reaction rates when
equimolar quantities of [aam] and [amps] are used with an excess of [xlinker].
Therefore, the coarse grained MD obtained with the FENE potential should find the same trends
obtained from TST and the same relative energies.

Chapter 4

Origin of the Positive
Cooperativity in the
Template-Directed Formation of
Molecular Machines
Jose L. Mendoza-Cortes, William A. Goddard III

4.1

Introduction

Molecules with mechanical bonds are of great interest for synthetic chemists. This lead to the
creation of the field termed mechanically interlocked molecules.[30] Rotaxanes are macromolecules
that interacts trough noncovalent interactions with another host molecule. This pair is usually
subject to chemical changes that make the rotaxane change the position on the host molecule without
forming new bond between the rotaxane and the host.
The most common strategies by which rotaxanes can be synthesized are capping, clipping and
slipping.[31] The discovery of highly efficient protocols through the clipping mechanism made feasible the preparation of rotaxanes of different order and complexity.[32, 33, 34] One of the most
popular clipping reactions is the reversible imine bond formation, that when combined to template
directed interactions (noncovalent interactions such as dispersion and coulombic) leads to a high
yield synthesis.[35]
We investigate the formation of rotaxanes through imine bonds formation which interacts with
Dumbbells (D and Dp) as it is shown in Figure 4.1.[36] Both hosts D and Dp have the recognition
sites -NH+
2 - and C6 H4 -(OCH3 )2 stoppers at each end, however they differ in their separation. For D:
the separation fragments is given by -[CH2 CH2 NH+
2 CH2 ]n- while for Dp is -[C6 H4 CH2 NH2 CH2 ]n-

(Figure 4.1). This separation seems to play a crucial role in the thermodynamics and kinetics (Figure
4.1 and Figure 4.2). On one side the template directed synthesis is observed while in the other case is

49
not. Although the experiments have been able to differentiate both cases, the quantitative energetics
for this phenomenon is not clear. Thus, in this chapter we present the role of the dispersion forces
(pi-pi interaction, hydrogen bonds) as well as Coulombic interactions (counteranion) in the formation
of these rotaxanes and we compare our results to the experimental observations.
a)

OMe

MeO

OMe

nPF6H2

MeO

n-1

nPF6-

NH2

Dp=
Dumbell-w/phenyl

H2N

n= 2, 3, 4, 7, 11, 15, 19

n-1

MeO

CD3CN/RT

nPF6N

H2N

nPF6N

NH2

CD3CN/RT

OMe

n= 2, 3, 7, 11

OMe

D=
Dumbell

OMe

MeO

n-1

R family = R-D

OMe

n-1

R' family = R-Dp

Figure 4.1: Reaction for the template directed formation of rotaxanes for the (a) R Family and for
the (b) R’ family
Table 4.1: Reaction kinetics on the formation of the R family, which is the combination of
nR + D
compound
no.

[n]
rotaxane

rings

time to reach
equilibrium a

isolated
yield (%)

no. of imine
bonds

yield per imine
bond (%)

2R2+
3R3+
4R4+
7R7+
11R11+
15R15+
19R19+

12
16
20

11
15
19

<5min
<5min
<5min
6h
10h
12h
14h

93
90
88
94
98
93
90

14
22
30
38

98.2
98.3
98.4
99.6
99.9
99.8
99.7

4.2

Equilibrium times were determined by monitoring the clipping reaction by 1 H NMR spectroscopy until no changes in the spectra were observed

Methodology

Quantum Mechanics (QM) We start with the experimental structures and the optimized them using
the MO6-L functional[7] and for C, H, O, N, P, F we used the 6-31G** basis set[37, 38] and electron
Core potential for I: LAV3P**[10] as implemented in Jaguar[9]. All geometries were optimized using
the analytic Hessian to determine that the local minima have no negative curvatures (imaginary

50
Table 4.2: Reaction kinetics on the formation of the R’ family, which is the combination of
nR + Dp
compound
no.

[n]
rotaxane

rings

time to reach isolated
equilibriumb a yield (%)

no. of imine
bonds

yield per imine
bond (%)

2R’2+
3R’3+
7R’7+
11R’11+

<5min
<5min
20min
30min

96.3
94.7
98.2
99.3

86
72
78
85

Equilibrium times were determined by monitoring the clipping reaction by 1 H NMR spectroscopy until no changes in the spectra were observed

frequencies). The vibrational frequencies from the analytic Hessian were used to calculate the
zero-point energy correction at 0 K. Solvent corrections were applied using the single point selfconsistent Poisson-Boltzmann continuum solvation model for acetonitrile (=37.5 and R0 =2.18 ) as
implemented in the PBF module[28] in the Jaguar code. This methodology has proved to give the
best agreement with experiments.[39]
Molecular Mechanics (MM) For higher order rotaxanes, it is necessary to use molecular mechanics
(QM) and the force field (FF) validation is the key for generating plausible structures. In this case
we analyze the Dreiding[25] as well as the OPLS[40] Force Field and we compare with the quantum
mechanical calculations. We used the conjugated gradient minimization scheme with at least 5000
steps or until convergence criteria of 0.05 kcal/mol were obtained. The charges for Dreiding were
obtained from Qeq[12] while for OPLS they are inbuilt in this FF.

4.3

Results and Discussion

4.3.1

Experimental Coordinates vs MM vs QM

In order to validate our methodology for these systems we compare the Xray diffraction coordinates
(XRD) with the minimized structures obtained from QM and MM. We show the results on Figure
4.2 and Figure 4.3. We found that MM gives a good estimate of the general geometry since it gives a
small root mean square distance (RMSD) of around 0.35. On the other hand the QM method gives
a larger error (RMSD=0.638). However as we expected the QM method gives the best estimation
of the pi-pi interaction followed by the Dreiding FF, while the worst estimation of this interaction is
given by the OPLS-FF (Figure 4.3). Because we suspect that the pi-pi interactions as well as other
dispersion interactions are the main factor to determine the formation of these structures, we prefer
to use the QM methodology.
Furthermore, the QM method is the only one which can gives physically meaningful energetics
in gas phase as it can be seen in Figure 4.4. The MM method does not give binding energies for the
Dreiding FF while the OPLS FF presents an strange behavior of an extremely high binding energy

51
(-500 kcal/mol) for the first rotaxane while a repulsive energy for the second ring (+149 kcal/mol).
However the QM method is very consistent, giving a binding energy for the first and second rotaxane
of -26.1 and -60.6 kcal/mol, respectively. Thus QM is the only method to represent correctly the
energetics of these systems.

(a) XRD vs Dreiding2.21

(b) XRD vs Dreiding3

(d) XRD vs M06-L

Figure 4.2: Comparison of XRD experimental determined structure versus different theoretical methods used. Colors are C: grey, O:red, N:blue and H: white. In the figures the unicolor represents the
structure obtained after minimization with MM or QM

4.3.2

Origin of the Positive Cooperativity

The most puzzling part of these compounds is to find the reason behind the loose of positive cooperativity when the different Dumbbells are used (D versus Dp). Thus, we also calculate the geometries
and energetics for the R’s family up to 2 rotaxanes and they are shown in Figure 4.3. The geometries
for the R’ family (Dp + rotaxanes) are not available from crystal diffraction experiments but our
QM methodology can estimate these structures with acceptable accuracy.
The main difference between the dumbbells D and Dp is the extra phenyl in the latter case.

52
Table 4.3: Root mean square distance (RMSD) for the comparison between experimental structure
for 2R·2PF6 and the QM and MM methods. Column 2 and 3 shows the estimation of the R(π−π )
interaction for benzene (Bz) in the stopper of the dumbbell (D), first rotaxane (R1) and second
rotaxane (R2)
2R·2PF6

RMSD
Bz(D)-Bz(R1)

RMSD
Bz(R1)-Bz(R2)

RMSD
All atoms

Experimental XRD
Dreiding2.21/Qeq
Dreiding3/Qeq
OPLS2005
MO6L/6-31G**

0.153
0.186
0.235
0.152

0.109
0.608
0.446
0.106

0.375
0.311
0.320
0.638

Table 4.4: Comparison of binding energies for
the Formation of 1R-2PF6 and 2R-2PF6 . All
the units are in kcal/mol.
Method

[1R]2PF6
Gas phase

[2R]2PF6
Gas phase

Dreiding2.21/Qeq
Dreiding3/Qeq
OPLS2005
MO6L/6-31G**

35.7
32.7
-500
-26.1

52.5
22.8
149
-60.6

(a) 2R-D-2PF6

(b) 1R-D-2PF6

(d) 2R-Dp-2PF6

(e) 1R-Dp-2PF6

(f) 0R-Dp-2PF6

Figure 4.3: Compounds for the R family (a,b and c; xR-D-2PF6 ) and for the R’ family (d,e and f;
xR-Dp-2PF6 ). Colors are C: grey, O:red, N:blue, F: green, P:purple and H:not shown. rotaxanes
are colored in full red in order to distinguish them from the atoms in the dumbbell.
This makes the rotaxanes rings to be more separated and most likely this determines the interaction strength between these rings. To the best of our knowledge, the quantification for the forces

53
being involved in these compounds has not been determined. In other words, we do not know
the energetics (enthalpies or free energies) for the interaction of the -(CH2 )NH+
2 (CH2 )- site or the
-(C6 H4 CH2 )NH+
2 (CH2 )- site with the rotaxane. There are several hydrogen bond being involved in
this interaction of the types N-H· · ·O and N-H· · ·N which is important to quantify.

Thus, we calculate the strength of the interactions between a rotaxane ring and the -NH+
2 - site

as well as the interaction with the stopper for the R and R’ compounds. The results are shown in
Figure 4.5. We can see that the interaction of the rotaxane ring with the stopper is almost negligible,
since the ∆Ggas is -1.7 kcal/mol while with CH3 CN is -3.2. We must remember that interaction
is the same for the the R and R’ family of compounds. Also the interaction of the rotaxane ring
with the (CH3 )NH+
2 (CH3 ) (-NH2 -) site or the -(C6 H5 CH2 )NH2 (CH3 )- (-NH2 ’-) site is very similar

∆Ggas -26.7 and -25.4 kcal/mol, respectively. The values for ∆Gsolvated are more different because
of the inherent difference in the size for the -NH+
2 - and the -NH2 ’- site so the bigger molecule gains

more energy when it is solvated in CH3 CN, this gives -22.3 and -26.4 kcal/mol, respectively.
Next we compare this partition of interaction to the full system of 2 rotaxanes, 2 stoppers and
2 recognition sites -NH2 - for the R family in order to find the source of the positive cooperativity.
Our results show that in gas phase, the first rotaxane ring in the 1R-D-2PF6 systems only interacts
with the recognition site, since the strength of this interaction is almost the same as isolate strength
gas
of the -NH+
-26.7 and -26.1 kcal, respectively. This implies that there is not interaction
2 - site; ∆G

between the rotaxane ring and the stopper when the first rotaxane ring is added. This can be
observed from the optimized structure shown in Figure 4.3b, where the benzene ring of the rotaxane
have a distance of the 4.1 Å with the benzene ring of the stopper (The optimal interaction distance
is 3.4 Å). The ∆Gsolv for the isolated -NH+
2 - site and the full system with the -NH2 - recognition

site differ for more than 10 kcal/mol, most likely because the difference in the size of the systems,
the full system 1R-D-2PF6 has more surface than the 1R-NH+
2 (CH3 )2 , thus the solvation is more
favorable for the full system than for the individual parts. However when the second rotaxane
ring is added to the sys-tem (2R-D-2PF6 system), the interaction between the rotaxane rings and
the stopper is recovered. This can be deduced because the energetics for the full system 2R-D2PF6 contains 2 interactions of rotaxane/-NH+
2 - nature, 2 interactions of rotaxane/stopper type
and one interaction of Rotaxane-Rotaxane (R-R). This correspond to a partition of ∆Ggas of -26.7
x 2 kcal/mol (2 rotax-ane/-NH+
2 -) + -1.7 x 2 kcal/mol (2 rotaxane/stopper) and -8.6 kcal/mol (1
R-R) equals to -65.4 kcal/mol [the full system gives -25.4(first rotaxane)-60.6(second rotaxane) =
-86.0 kcal/mol]. If the solvation is included this can be partitioned as ∆G solv of -22.3 x 2 kcal/mol
(2 rotax-ane/-NH+
2 -) plus -3.2 x 2 kcal/mol (2 rotaxane/stopper) and -8.8 kcal/mol (1 R-R) equals
to -59.8 kcal/mol [the QM calculations for the full system gives -51.4 (first rotaxane) - 33.1 (second
rotaxane) = -84.5 kcal/mol]. The total free energy of the full system should more than the sum of
the individual components for the positive-cooperativity to be present. Thus is an example where

54
the sum of interaction when all the components are together is more than the sum of the individual
ones.
On the other hand for the R’ family, the first rotaxane ring interacts strongly not only with the
benzene ring of the stopper but also with the benzene ring of the dumbbell Dp. This can be better
observed in Figure 4.3b. The distance of the pyridine ring from the rotaxane ring with the benzene
ring of the stopper is 3.9 Å, while the distance with the benzene ring of the Dumbbell Dp is 3.6 Å.
This is reflected in the energetics of the system. Figure 4.5 shows that for the system 1R-Dp-2PF6 we
obtain ∆Ggas equals to -60.6 kcal/mol and ∆Gsolv equals to -48.2 kcal/mol. The energetics obtained
gas
for the full system cannot be described as 1 rotaxane/-NH+
=-25.4 kcal/mol,
2 ’- interaction (∆G

∆Gsolv =-26.4 kcal/mol) and 1 rotaxane/stopper interaction (∆Ggas =-1.7, ∆Gsolv =-3.2 kcal/mol).
The difference of ∆Ggas =-33.5 and ∆Gsolv =-18.6 can be assigned to the extra interaction of the
rotaxane ring with the benzene ring next to the -NH+
2 ’- site of the Dumbbell Dp. When the second
rotaxane ring is added the main difference between the R and the R’ family becomes obvious.
For the second rotaxane ring in the 2R-Dp-2PF6 compound, we have the interaction energy of
only ∆Ggas =-20.5 kcal/mol, this is almost the same interaction strength as the rotaxane/-NH+
2 ’interaction site which is ∆Ggas =-25.4 kcal/mol. When the species are solvated, the same comparison
is valid, for the extra rotaxane ring in the full system the interaction is ∆Gsolv =-25.1 kcal/mol, this
solv
is very similar to the rotaxane/-NH+
=-26.4 kcal/mol. This shows
2 ’- interaction site with ∆G

that there is not Rotoxane-Rotoxane interaction for the R’ family due to the long distance between
these rotaxane rings. This is also observed from the thermodynamics for this rotaxane - rotaxane
interaction at 5.0 Å, that gives positive ∆Hgas , ∆Ggas and ∆Gsolv (Table 4.5).
Thus we have found the origin of the positive cooperativity in the Template-directed formation
of these rotaxane/dumbbell complexes; the distance between the rotaxanes rings should be optimal
for them to interact and this is will give the positive interaction. This can be better visualized in
Figure 4.4 where the important interaction distances are shown. The distance between the first and
second -NH2 - site of the 2R-D-2PF6 (R family) is of 4.8 Å, while the distance between the first and
the second rotaxane ring is of 4.0 Å, this is because the rotaxane ring are slightly twisted trying to
interact with each other (Figure 4.3a). This rotaxane-rotaxane distance is close to the ideal value
of 3.6 Å. On the other hand, for the 2R-Dp-2PF6 (R’ family), the distance between the first and
the second -NH2 ’- site increase to 7.1 Å, because the extra phenyl ring in between. This makes the
distance between the first and second rotaxane to be longer for this compound; 5.0 Å. This is a long
even though the rotaxane rings are twisted to a small degree to maximize interactions (Figure 4.3d).
This is a difference of 1 Å; between the distance among rotaxanes in the R versus the R’ family.
This long distance between rotaxanes in the R’ compound makes their interactions to be negligible.

55
Table 4.5: ∆Ggas and ∆Gsolv with respect to isolated rotaxanes rings and dumbbell. The solvent
used is CH3 CN. All the units are in kcal/mol.
Compound

∆Hgas

∆Ggas

∆Gsolv

1R—(Stopper site)
R family
1R—1R (4.0 Å) a
1R—(NH2 site)b
1R-D-2PF6
2R-D-2PF6
R’ family
1R—1R (5.0 Å) c
1R—(NH2 ’ site)d
1R-Dp-2PF6
2R-Dp-2PF6

-16.3

-1.7

-3.2

-26.6
-45.9
-41.2
-85.7

-8.6
-26.7
-26.1
-60.6

-8.8
-22.3
-33.1
-51.4

1.9
-43.3
-75.7
-45.7

4.7
-25.4
-60.6
-20.5

3.2
-26.4
-48.2
-25.1

This is the distance for rotaxana - rotaxane
interaction distance for the 2R-D-2PF6 .
To estimate the strength of this site, we have
used the compound (CH3 )2 NH2 +
This is the rotaxane-rotaxane interaction distance for the 2R-Dp-2PF6 system.
To estimate the strength of this site, we have
used the compound (CH3 )(C6 H5 CH2 )NH2 +
a)

R family (R+D)
4.0 Å

3.4 Å

R' family (R-Dp)
5.0 Å

3.4 Å

3.7 Å

2PF6OMe

MeO

2PF6-

3.8 Å

OMe

MeO

OMe

4.8 Å

7.1 Å

Figure 4.4: Distances for the optimized structure for the (a) 2R-D-2PF6 (R family) and for (b)
2R-Dp-2PF6 (R’ family). In the R family we observe rotaxane-rotaxane interaction while in the
R’ family, the distance between rotaxane rings is too large for them to interact. Distance between
stopper and rotoxane ring is marked in black. Distance between first and second rotoxane is marked
in red. Distance between first and second -NH2 - site is marked in blue. The optimal rotaxanerotaxane interaction distance is 3.6 Å.

4.3.3

Role of the Counter Anion

Once we have found the source of the positive cooperativity, we decide to study the role of the
counteranion in these systems. For that purpose, we calculate the geometries of the 2R-D, 1R-D
and D systems with different anions beside PF−
6 ; I , F and with overall charge of +2 (Figure 4.5).

This is also done with the 2R-Dp, 1R-Dp and Dp systems (Figure 4.7).
In general the rotaxane - rotaxane distance is affected while the position of the anion are closer
to the -NH+
2 - site of each compound. When we compared the optimized structures for the R family

(a) 2R-D-2I

(b) 1R-D-2I

(d) 2R-D-2F

(e) 1R-D-2F

(f) 0R-D-2F

(g) 2R-D-2

(h) 1R-D-2

(i) 0R-D-2

Figure 4.5: xR-D-2anion compounds. Colors are C: grey, O:red, N:blue, F: green, P:purple and
H:not shown. rotaxanes are colored in full red in order to distinguish them from the atoms in the
dumbbell.
with the 2PF−
6 counter anion (Figure 4.3a), we can see that the skeleton is very similar to the one
obtained for the 2R-D-2I system and derivatives. However, when we use the F− counter anion for
this family of compounds we see that the rotaxane-rotaxane distance is the more affected. This is
correlated to the thermodynamics and to the electron density as we will see below. In the same
manner, we calculate the optimized structures for the R’ family and we found similar trends. The
structures where 2PF−
has been used. On
6 were used (Figure 4.3b) resemble the ones where I
the other hand, the structures were F− is used are more different to those with 2PF−
6 and I . We

calculate the structures with no counter anions but a total charge of +2 to explore the effect of a
homogeneous field versus a counter anion to neutralize the system. It is difficult to quantify the
difference based on pure rotaxane - rotaxane distances or counter anion - NH+
2 site distances so
thermodynamics and electron densities are needed.
Therefore, we also calculate the thermodynamics of these systems and the results are shown
in Figure 4.6. We found that for the 2R-D compounds (R family) the positive cooperativity only

(a) 2R-Dp-2I

(b) 1R-Dp-2I

(d) 2R-Dp-2F

(e) 1R-Dp-2F

(f) 0R-Dp-2F

(g) 2R-Dp-2

(h) 1R-Dp-2

(i) 0R-Dp-2

Figure 4.6: xR-Dp-2anion compounds. Colors are C: grey, O:red, N:blue, F: green, P:purple and
H:not shown. rotaxanes are colored in full red in order to distinguish them from the atoms in the
dumbbell.
occurs when the counter anions PF−
6 or I is used. In other words we get more negative free energy

when the second rotaxane ring is added than with the first one. However, when the anions F− are
used, the positive cooperativity disappears as it shown in Figure 4.7. This phenomenon happens in
gas phase and solvated phase. Therefore the counteranion should be playing a central role in the
positive cooperativity for the R family. For the 2R-Dp compounds (R’ family) there was never a
positive cooperativity with the PF−
6 counter anion and this remains for I , F and no counter anion

(field of +2) as it can be observed in Figure 4.6 and at the bottom of Figure 4.7.
In order to investigate further the role of the counter anion, we calculate the Electrostatic potential (ESP) and the Mulliken Charges for these systems. Then we use these charges to calculate the
dipole moments. The results are shown in Figure 4.7. The results obtained from ESP charges are
similar to the ones obtained with Mulliken charges however we use the ESP results in this discus-

58
Table 4.6: ∆Ggas and ∆Gsolv with respect to isolated rotaxanes rings and dumbbell. All the units
are in kcal/mol.
Compound

∆Hgas

∆Ggas

∆Gsolv

1R-D-2I
2R-D-2I
1R-D-2F
2R-D-2F
1R-D-2
2R-D-2

-37.0
-79.0
-37.8
-39.3
-114.1
-88.4

-22.0
-53.8
-22.8
-14.1
-99.1
-63.3

-1.5
-54.9
-20.4
-21.4
-46.3
-44.1

1R-Dp-2I
2R-Dp-2I
1R-Dp-2F
2R-Dp-2F
1R-Dp-2
2R-Dp-2

-74.3
-32.9
-29.7
-32.5
-89.1
-85.0

-59.3
-7.7
-14.6
-7.3
-74.0
-59.9

-45.1
-6.5
-16.9
-2.5
-40.7
-37.6

a) Gas phase
Free Energy (kcal/mol)

R family (gas phase)

-20.0

No Cooperativity

-40.0
-60.0
Rx_D_2PF6
Rx_D_2F

Free Energy (kcal/mol)

0.0

b) Solvated phase

Positive
Cooperativity

-40.0

R' family (gas phase)

No Cooperativity

-60.0
Rx_Dp_2PF6
Rx_Dp_2F
-80.0

-20.0

No Cooperativity
-40.0
-60.0

Rx_D_2PF6

Positive
Cooperativity

Rx_D_2F

Free Energy (kcal/mol)

-20.0

R family (Solvated phase)

-80.0

0.0

0.0
-20.0
-40.0
-60.0

R' family (Solvated phase)

No Cooperativity

No Cooperativity
Rx_Dp_2PF6
Rx_Dp_2F

-80.0

Figure 4.7: Free energies in the gas phase for (a) gas phase and (b) solvated phase for the R Family:
2R-D-2PF6 and 2R-D-2F (top) and for the R’ Family: 2R-Dp-2PF6 and 2R-Dp-2F (bottom). The
positive cooperativity is only observed with the PF−
6 (or I , not shown) counter anion.
sion. We can observe that the dipole moment (µ) increase as the size of the counter anion increase
for both R and (R’ family of compounds. This is; the dipole moment is related to the size of the
counteranion. This can be visualized better in Figure 4.8. The highest dipole moment is with the
counteranion PF−
6 (µ = 28 Debye) where the electrostatic potential is very well defined by localized

59
charges. On the hand, the dipole decrease when using F− (µ = 14.8 Debye) because the electrostatic
potential is more spread due to the high contact/interaction between this small counter anion and
the -NH+
2 - site. This contact make the ESP charges to go for the first and second -NH2 - from +1.00
and +0.67 (with PF−
6 ) to +0.49 and +0.36 (with F ), respectively. This means that the smaller

counteranion lowers the strength of the interaction between the rotaxane ring and the recognition
site -NH+
2 - by virtue of lessening the charge on N, which then cause the disappearances of the positive effect even if there is still rotaxane - rotaxane interaction. We must note that the -NH+
2 - serves
as a site where the rotaxane can form by imine bond formation. The same effect happens for the
R’ family of compounds, the dipole moment is larger for the counter anion PF−
6 (µ = 24.9 Debye)
than with F− (µ = 5.8 Debye) as it is shown in Figure 4.8b.
Table 4.7: Dipole moments (µ, /Debye) obtained from Electrostatic potential (ESP) charges and
Mulliken charges. The ESP and Mulliken charges have been normalized.
µ from ESP (/Debye)
ESP charges for N
Compound

Total

1st -NH+
2-

2nd -NH+
2-

2R-D-2PF6
2R-D-2I
2R-D-2F
2R-D-2

25.4
18.1
13.4
0.1

11.7
9.5
6.3
-1.7

-0.2
-2.8
-0.2
-0.2

28.0
20.6
14.8
1.7

1.00
0.58
0.49
0.40

0.67
0.65
0.36
0.23

2R-Dp-2PF6
2R-Dp-2I
2R-Dp-2F
2R-Dp-2

16.7
11.1
3.0
1.0

17.8
9.8
4.8
0.1

-5.0
-0.2
-1.3
0.5

24.9
14.8
5.8
1.2

0.82
0.73
0.45
0.37

0.51
0.42
0.32
0.21

µ from Mulliken (/Debye)

Mullikan charges for N

Compound

Total

1st -NH+
2 ’-

2nd -NH+
2 ’-

2R-D-2PF6
2R-D-2I
2R-D-2F
2R-D-2

26.0
20.6
14.5
4.0

16.3
13.5
10.2
2.8

-0.4
-2.5
-0.2
-0.2

30.7
24.8
17.7
4.9

0.98
0.98
0.96
0.97

0.97
0.97
0.95
0.95

2R-Dp-2PF6
2R-Dp-2I
2R-Dp-2F
2R-Dp-2

16.0
11.7
2.9
2.6

22.5
14.1
9.4
5.4

-5.4
-1.2
-0.3
0.3

28.1
18.4
9.8
6.0

1.00
0.98
0.95
0.96

0.99
0.98
0.97
0.96

Thus the role of the counter anion is to control the charge population on the -NH+
2 - recognition
site which determines the interaction with the rotaxane ring. Then the larger (softer) the counter
anion the less interaction with the recognition site and the more interaction between -NH+
2 - and
the rotaxane ring will be. To the best of our knowledge this is the first time this effect have been
observed.

2R-D-2PF6
Dipole = 28.0 D

2R-D-2F
Dipole = 14.8 D

2R-D-2PF6
Dipole = 24.9 D

2R-D-2F
Dipole = 5.8 D

Figure 4.8: Dipole moments (µ) from ESP charges obtained for the (a) R Family (2R-D-2PF6 and
2R-D-2F) and for the (b) R’ family (2R-Dp-2PF6 and 2R-Dp-2F)

4.4

Conclusions

In general, all FFs studied (Dreiding and OPLS) give poor representation of the thermodynamics
but acceptable representation of the geometries. On the other hand the QM method gives a better representation of the pi-pi interactions as well as a more consistent and physically meaningful
thermodynamics.
The distance between the rotaxanes rings should be optimal for them to interact and this origin of
the positive cooperativity in the template-directed formation of these rotaxane/dumbbell complexes.

61
The rotaxane-rotaxane distance in the R family is of 4.0 Å, this is close to the optimal value of 3.6 Å.
On the other hand, this distance is 5.0 Å for the R’ family making this interaction to be negligible.
Thus the efficiency for the template directed synthesis is tuned by controlling the distance between
recognition sites.
Most importantly, we found that the role of the counter anion is to tune the charge population
on the -NH+
2 - recognition site so that the larger (softer) the counter anion the more charge on the
recognition site and the more interaction with the rotaxane ring is obtained. The interaction with
the recognition site serves as the first directed template mechanism (clipping) for the formation of
the rotaxane rings. This has many implications for the future synthesis of rotaxanes because we
predict that we can control the positive cooperativity by changing the charge population on the
recognition site by tuning the softness of the counter anion. Thus we can control the efficiency of
future directed synthesis of rotaxanes for the clipping mechanism by using different degree of softness
for the counter anion.

Chapter 5

Design of New Models for the
Oxygen Evolving Complex
Jose L. Mendoza-Cortes, Robert Nielsen, Jacob Kanady, Emily Y. Tsui, Theodor Agapie, William
A. Goddard III

5.1

Introduction

Photosystem II is a homodimer where photosynthetic water oxidation occurs.[41] Each monomer
contains 20 subunits with a total molecular mass of 350 kDa. Besides the protein subunits, there are
other cofactors such as four manganese atoms, three to four calcium atoms (one of which is in the
Mn4 Ca cluster) and others such as chlorophylls and β-carotenes.[41] Water oxidation is catalyzed by
a center containing the Mn4 Ca cluster, which is known as the Oxygen Evolution Complex (OEC).
The OEC is one of nature’s capacitors. It couples successive one-electron reductions of an adjacent
chlorophyll center (known as P680 ) to four-electron oxidation of water to dioxygen.[42] At a fundamental level, the chemical reactions taking place are shown in Figure 5.1. First, the most reduced
OEC state is oxidized four units by P+
680 , giving a state that can be characterized as OEC(+4) or
S4 . The S4 state reacts with water to produce dioxygen (Figure 5.1a). However, the path that the
OEC undergoes to reach this virtual OEC(+4) is not well understood and it has been a matter
of debate.[42] On the other hand, there is a consensus that the oxidation of the OEC is stepwise;
each of the oxidation steps are shown in Figure 5.1b. Each oxidation state of the OEC is known as
S-state or Storage-state (Sn ) with S4 being the most oxidized and S0 the most reduced state. The
transition from S4 to S0 is the most important and more controversial step because it is when the
water is converted to dioxygen.
Many mechanisms have been proposed for the transition from S4 to S0 but almost all of them
proposed the need for high oxidation state for Mn, such as Mn(IV) or even Mn(V).[43] This is
consistent with the necessary transfer of 4e− to the OEC from the water oxidation. This transition,

63
however, has proven to be challenging to observe because it happens very quickly, but some progress
have been made in observing S3 to S0 but not the S4 itself.[44, 45, 46]

hν=1.82 eV

e- + P680+

4 P680
OEC + 4 P680+

OEC+4 + 4 P680

OEC+4 + 2H2O

OEC + O2 + 4H+

OEC + 4 P680+

OEC+4 + 4 P680
hν

O2
2H2O

Asp342

H2O H2O Asp170
Ca O O OHx
O Mn OHx
Mn
His
Mn
332
Mn
Glu333

OEC

P680+

2H2O

Glu189

Ala344

P680

+ 4H+ + 4e-

P680

P680+
hν

P680

P680+

S2
P680

P680+

Glu354

hν

Figure 5.1: (a) Fundamental chemical reactions that take place in the production of O2 that start
with the conversion of solar energy (hν) to an electron and a hole in the chlorophyll center called
P680 . (b) The catalytic cycle of the Oxygen-evolving complex (OEC) is shown where every oxidation
is defined as a S-state (Sn ). (Inset) The full description of the OEC is shown.

Me
O O

Mn
Mn

O O
Mn

N N

O O
Mn

TAB-H3

Figure 5.2: Complexes synthesized in the Agapie group containing (left) a Mn3 Ca and (right) a Mn4
cubane. Notice how the Ca in Mn3 at the top have been substituted by one Mn to give Mn4 .
A molecular model of the Mn4 Ca cluster would allow study of the electronic structures involved
in all the oxidation states of the OEC. The synthesis of such a biomimetic compound can be attained
by designing ancillary ligands. One such approach performed by the Apapie group was able to obtain

64
a Mn3 Ca complex. It is the first example where the Ca atom has been incorporated with Mn into
a cubane that resembles the OEC (Figure 5.2). They were also able to synthesize an all Mn cubane
Mn4 . This opens the possibility of studying the role of the Ca in the oxidation states of the Mn.
Thus in this work we validate a methodology to reproduce and predict the reduction potential
of the biomimetic model for the OEC using the rigid ligand 1,3,5-triarylbenzene spacer which incorporates six pyridine and three alcohol groups (TAB-H3 ) shown in Figure 5.2. We then can use this
method to design new compounds that structurally and electronically resemble to a high degree the
most oxidized state of the OEC.

5.2

Methodology

Quantum Mechanics (QM) Nonperiodic QM calculations were carried out using the B3LYP,[47, 48]
M06 and M06-L[7] hybrid DFT functionals with the Jaguar code.[9] Here we used the 6-31G**
for C, H, O, N while and LACVP**[10] basis set for Mn and Ca as implemented in Jaguar. All
geometries were optimized with B3LYP and using the analytic Hessian to determine that the local
minima have no negative curvatures (imaginary frequencies). The vibrational frequencies from the
analytic Hessian were used to calculate the zero-point energy corrections at 0 K. Solvent corrections
were applied using the single point self-consistent Poisson-Boltzmann continuum solvation model as
implemented in the PBF module1[29] in the Jaguar code.

5.3

Results and Discussion

5.3.1

Validation of the Computational Methodology: Geometry

In order to validate our methodology to predict and reproduce the properties of these compounds,
we compare the X-ray diffraction (XRD) coordinates with the minimized structures obtained from
QM calculations.
We first calculated the optimized structure with our QM method of the CaMn3 O4 -Full ligand
compound as it is shown in Figure 5.3a. We measured the deviation of the experimental structure
by virtue of the root mean square (RMS). The larger the RMS between the experimental structure
and the geometry obtained from QM calculations, the worse the methodology. For this compound
which has 147 atoms, we found a RMS of 0.417 Å. This means that we can reproduce the geometry
of the compound with the entire ligand within 1.0 Å of accuracy. We found the biggest difference
in the atoms of the tetrahydrofuran bound to the Ca. There are also some small differences in
the unbound pyridines of the full ligand. These are atoms that are unlikely to participate in the
important processes of this compound. In other words, it is very plausible that most of the chemistry
will be happening in the core CaMn3 O4 , thus accuracy in this area is most important. Thus we

65
calculate the RMS on the core and the first coordination shell of this cluster; 20 atoms. The
comparison of positions between experimental and the calculated geometry give us an RMS of 0.114
Å. This can be broken down to RMS of 0.007 Å for the comparison of bonds and RMS of 0.384◦ in
the estimation of bond angles. This gives us confidence that our QM methodology can reproduce
the geometry of the CaMn3 O4 -Full ligand compound.
Next, we use our QM methodology to calculate the optimized structure of the Mn4 O4 -Full ligand
as it is shown in Figure 5.3b. We found that when comparing the position of the 134 atoms between
the experimental and the QM structure, the RMS is 0.530 Å. The main difference between these
structures is again between the unbound pyridines. When comparing only the Mn4 O4 cluster and
the first coordination shell between the experimental and QM structure it is found an RMS of 0.086
Å. This is composed from the estimation of bonds with an RMS of 0.012 Å and RMS of 0.060◦
for the estimation of bond angles. In general, the estimation of the general structure for the Mn4
is slightly worse than for the CaMn3 case, however when estimating the core cluster the reverse
happens.

Full system
RMS = 0.417 A

Full system
RMS = 0.530 A

Cubane structure
RMS = 0.114 A
RMS (bond) = 0.007 A
RMS (angle) = 0.384o

Cubane structure
RMS = 0.086
RMS (bond) = 0.012 A
RMS (angle) = 0.060o

Figure 5.3: Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light
blue, O; red, C; grey, H; white) and theory (black) using the full ligand. We show the root mean
square (RMS) to compare all the atoms in the structure (top) and the cubane (bottom).

Full system
RMS = 0.348 A

Full system
RMS = 0.292 A

Simplified Ligand
RMS = 0.125 A
RMS (bond) = 0.007 A
RMS (angle) = 0.397o

Simplified Ligand
RMS = 0.093 A
RMS (bond) = 0.012 A
RMS (angle) = 0.074o

Figure 5.4: Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light
blue, O; red, C; grey, H; white) and theory (black) using the simplified ligand. We show the root
mean square (RMS) to compare all the atoms in the structure (top) and the cubane (bottom). The
structures with this simplified ligand are almost identical to the ones obtained with the full ligand
(Figure 5.3).
However, we need to calculate many properties of these compounds such as the vibrational modes
and having to do this for 147 or 134 atoms is too expensive computationally. We postulate that the
TAB ligand, although serving to support the metallic cluster, should not participate in the important
electrochemical reactions. Thus we simplified our compound by removing the four benzene rings at
the bottom and the three unbound pyridines. In addition we fix the carbon that bridges the oxo and
bound pyridine in order to mimic the presence of the stiffness of the full TAB ligand. The results
are shown in Figure 5.4. The first simplification was done on the CaMn3 O4 containing compound
as it is shown in Figure 5.4a. By comparing the position of atoms between the geometry obtained
from experiments with the one obtained from the simplified ligand, we obtained a RMS of 0.348 Å.
This is a smaller number than the one obtained from QM with the full ligand because there are less
atoms. In the case of the simplified ligand we have 84 atoms while with the full ligand we treated

67
147 atoms. Since we are most interested in the estimation of the metallic core, we compared the
geometry between this core including the first coordination shell, and the RMS obtained is 0.125 Å.
In a more detailed fashion, this is a RMS of 0.007 Å for the estimation of bonds and RMS of 0.397◦
for the estimation of angles. This is basically the same accuracy as with the full ligand model.
We performed a similar simplification for the Mn4 O4 containing compound as it is shown in Figure
5.4b. When comparing the structure from experiment and the one obtained with this simplified
ligand, we found a RMS for the position of the atoms of 0.292 Å. This is smaller than with the
full ligand due to the smaller number of atoms being compared. With the full ligand we treat 134
atoms while with this simplification on the ligand we only need to handle 71 atoms. In this case, we
are also interested in how accurate we can predict the geometry of the Mn4 O4 cluster and the first
coordination shell, since we believe most of the electrochemical processes occur there. By comparing
the experimental and the computational geometry of the cluster obtained with the simplified ligand
we obtained an RMS of 0.093 Å for the estimation of the geometry. The RMS is 0.012 Å for
estimation of bonds and the RMS is 0.074 ◦ for the estimation of angles. This is practically the
same as with the full ligand. With the simplified ligand we obtain a better estimation of the geometry
for the Mn4 case than for the CaMn3 structure, including when only taking into account the cluster
and its first coordination shell.
Thus, the models with the simplified ligand gives an accurate description of the geometry observed
in experiments and speeds up our calculation by reducing the number of atoms to be treated to almost
a half.

5.3.2

Validation of the Computational Methodology: Redox Potentials

We also calculated the redox potential with our QM calculations and then compared the results
to the ones obtained experimentally. We started by calculating the redox potential obtained for
the CaMn3 O4 containing compound (Table 5.1). The potentials obtained with B3LYP and M06
contains ZPE, vibrational and solvent terms applied to the model with the simplified ligand. We see
that B3LYP gives a good estimation of the redox potential when dimethylacetamide (DMA) is used.
However it is off almost 0.2 V when dimethylformamide (DMF) is used. On the other hand, M06
gives the best estimation of potential for both cases with a difference of 0.1 V with DMA and of 0.03
V with DMF. The addition of a new electron affects the geometry of the [MnIV 3 CaO4 ] compound
as it is shown in Figure 5.5. The extra electron reduces one of the MnIV to MnIII , and this electron
populates one of the eg orbital that affects the bond distance along an arbitrary z -axis. These bonds
are the Mn3 -O8 and the Mn3 -O16 bonds as it is shown in Figure 5.5. The magnitude of the changes
is the following: the oxidized compound has a Mn3 -O8 bond distance of 1.91 Å, while the reduced
one have a bond distance of 2.38 Å. The same elongation happens for the Mn3 -O16 , the oxidized
species has a bond distance of 1.93 Å, while the reduced one has a bond distance of 2.27 Å. In other

68
words, the oxidized species have bond distances at least 0.33 Å shorter than the reduced compound
along an arbitrary z -axis.
Table 5.1: Oxidation/reduction potentials for the Mn3 CaO4 compound with respect to ferrocene/
ferrocenium. Solvents: dimethylacetamide (DMA) and dimethylformamide (DMF).
Mn3 Ca Compound

Solvent

E◦ redox /V
Exp

E◦ redox /V
B3LYP

E◦ redox /V
M06

[MnIV 2 MnIII CaO4 ]/[MnIV 3 CaO4 ]
[MnIV 2 MnIII CaO4 ]/[MnIV 3 CaO4 ]

DMA
DMF

-0.94
-0.89

-1.07
-1.16

-0.84
-0.92

O16
Mn3
O8

Figure 5.5: Oxidation/reduction for the Mn3 CaO4 compound. Color code: Ca; magenta, Mn; light
blue, O; red, C and H; black.
Next we calculated the redox potential for the compound containing the Mn4 O4 cluster. The
results are shown in Table 5.2. In this case, B3LYP still gives a poor estimation of the experimental
redox potential with a difference of at least 0.17 V. On the other hand, M06 gives a closer estimation
of the potentials with a difference of at most 0.06 V. The experimental redox potential for the
couple [MnIV 2 MnIII 2 O4 ]/[MnIV 3 MnIII O4 ] is 0.29 V, while M06 predicts 0.35 V. The next redox
pair; [MnIV 2 MnIII 2 O4 ]/[MnIV MnIII 3 O4 ] gives an experimental redox potential of -0.70 V, while
M06 predicts -0.67 V. These redox processes have geometrical changes associated. The structural
changes can be observed in Figure 5.6. In the reduction process, the addition of one electron to
the [MnIV 3 MnIII O4 ] compound, populates one of the eg orbitals, elongating the Mn-O bond along
an arbitrary z -axis. This elongation happens in the bonds between Mn1 -O5 and Mn1 -O12 . The

69
oxidized species has a bond distance for Mn1 -O5 of 1.92 Å and for Mn1 -O12 of 1.99 Å. The reduced
complex increases these bonds by more than 0.24 Å. The Mn1 -O5 bond increases to 2.41 Å while the
Mn1 -O12 bond increases to 2.23 Å. In the further reduction another of the MnIV centers is reduced
to MnIII and one of its eg orbitals is populated, changing the bond distance along that axis (Figure
5.6). This time the modified bonds are Mn2 -O7 and Mn2 -N19 . The changes are as follows: Mn2 -O7
bond distance increase from 1.85 Å to 2.21 Å when reduced, while the Mn2 -N19 increases from 2.07
Å to 2.29 Å.
Table 5.2: Oxidation/reduction potentials for the Mn4 O4 compounds with respect to ferrocene/
ferrocenium. Solvent: dimethylacetamide (DMA).
Mn4 Compound

Solvent

E◦ redox /V
Exp

E◦ redox /V
B3LYP

E◦ redox /V
M06

[MnIV 2 MnIII 2 O4 ]/[MnIV 3 MnIII O4 ]
[MnIV 2 MnIII 2 O4 ]/[MnIV MnIII 3 O4 ]

DMA
DMA

0.29
-0.70

0.11
-0.93

0.35
-0.67

O12

Mn1
O5

Mn2
N19

Figure 5.6: Oxidations/reductions for the Mn4 O4 compound. Color code: Ca; magenta, Mn; light
blue, O; red, N; dark blue, C and H; black
Thus we have validated our QM methodology by reproducing the experimental redox potential
for these systems. We were also able to determine how the redox processes affects the geometry of
the structure by reducing the MnIV atoms to MnIII .

5.3.3

Prediction of New Models that Resemble the OEC Both Structurally and Electronically

Unfortunately the molecular models described by the Agapie group do not produce O2 . However
they were able to prove that the presence of a Ca center facilitates the formation of highly oxidized
MnIV species at lower potentials (>1V more negative when comparing MnIV 3 CaO4 and MnIV 4 O4 ,
Table 5.1 and Table 5.2). The highly oxidized MnIV centers have been proposed to be necessary in
the catalytic process because the compound needs to receive 4 electrons in the last step.[43] However,
the main difference with the biological OEC is a fourth dangling manganese in the same plane as
the other Mn of the cubane (Figure 5.1), thus we can improve the model compound by finding a
way to put that fourth Mn in the already proposed model and determine if we can observe a highly
oxidized Mn species.
Table 5.3: Bond distances for the fourth Mn shown and its first coordination shell as it is shown in
Figure 5.7.
CaMn4 -NH2
CaMn4 -bipy
CaMn4 -acac
Type
Bond (Å) Type
Bond (Å) Type
Bond (Å)
Mn4 -O1
Mn4 -O2
Mn4 -O3
Mn4 -N5
Mn4 -O6
Mn4 -O7

2.28
2.31
2.02
2.49
2.23
2.26

Mn4 -O1
Mn4 -O2
Mn4 -O3
Mn4 -O5
Mn4 -N6
Mn4 -N7

2.27
1.94
1.75
2.38
2.14
2.14

Mn4 -O1
Mn4 -O2
Mn4 -O3
Mn4 -O5
Mn4 -O6
Mn4 -O7

2.02
2.19
1.81
2.17
2.13
1.96

The first model we created was modifying the linker in order to have a binding group on the side.
We decided to modify one of the unbounded pyridines and create a point of extension CH2 NH2 that
can host the fourth Mn center. This is shown in Figure 5.7a. We also added another oxygen, O3 , in
order to complete the coordination shell of the fourth manganese (Mn4 ). The electronic state of this
compound shows that we have three MnIV and one MnII which resembles S1 of the biological OEC.
The bond distances for this fourth manganese and its first coordination shell is shown in Table 5.3.
All of the bond distances are too long in all axes, which is larger than 2 Å. We also found that the
geometry for the central Mn4 is not octahedral but a distorted trigonal bipyramidal with the oxygen
O1 from the carboxylate occupying a site that can be described as one of the faces of the pyramid.
This suggests that putting a point of extension on the ligand might constrain the system too much
and the binding of the fourth manganese can be unstable.
We decided to keep the original ligand but using another additional ligand that can bind a fourth
Mn. Thus we use the bipyridine (bipy) molecule as it is shown in Figure 5.7b. Besides the addition
of the bipyridine ligand and the fourth Mn (Mn4 ) we also add another oxo oxygen, O3 . We complete
the coordination shell of the added Mn with H2 O. By analyzing the electronic state of this compound
we found that there are two MnIV and two MnIII , similar to S1 of the biological OEC. The bond

s=5/2
Mn+2

s=3/2
Mn+4

OH2

H2O

O1 O

H2N

N O
Mn

H2O

Mn4

O6
N5

CaMn4-NH2

OH2 Me

O O

s=4/2
Mn+3
s=4/2
Mn+3
s=3/2
+4
Mn

s=3/2
Mn+4

OH2

N7
Mn4

O3 O5

CaMn4-bipy

c)
OH2 Me

O O

s=4/2
Mn+3

s=3/2
Mn+4

OH2

O7
Mn4

O3 O5

CaMn4-acac
Figure 5.7: New models for the OEC that includes the fourth Mn giving a CaMn4 O4 type cluster;
(a) CaMn4 -NH2 , similar to S1 (b) CaMn4 -bipy, similar to S1 and (c) CaMn4 -acac, similar to S2 .
Color code: Ca; magenta, Mn; light blue, O; red, N; dark blue, C; black and H; grey
distances for the fourth Mn and surrounding atoms are shown in Table 5.3. We can see that we have
two long bonds along an arbitrary z -axis and four short bonds in the xy plane which is consistent
with MnIII and one populated eg orbital. Therefore this system is not constrained and the neutral
state resembles one of the steps in the OEC catalytic cycle.
Finally, we designed another molecule with the acetylacetonate (acac) ligand. Because acac has

72
a formal charge of -1, we can modify the electronic structure of the CaMn4 compound and at the
same time coordinate the fourth Mn as it is shown in Figure 5.7c. We found that the electronic
state of this model gives three MnIV and one MnIII , which resembles the S2 state of the biological
OEC. The fourth Mn has an octahedral environment with two short bond along the z -axis (O3 and
O7 ) as it is shown in Table 5.3. This compound does not show constraints in the fourth manganese
or the bridging oxygen (O3 ) which suggest that its synthesis can be viable. This CaMn4 with the
acac in the equatorial position can also have another isomer where the acac binds along the z -axis
in the site where the water is bound, giving the axial isomer. Our calculations show that the axial
isomer is 10 kcal/mol less stable than the equatorial isomer shown in Figure 5.7c.
Although in all our new models we only add one extra dangling Mn, there is not an obvious
reason to think that other two extra dangling Mn cannot be added due to the symmetry of the
ligand and metal cluster.

5.4

Conclusions

We have validated a QM methodology that can reproduce the geometries and redox potential of
the system described by Agapie et al. We found that in this redox process, the MnIV atoms gets
reduced to MnIII and the extra electron populates one of the eg orbitals which elongates the bonds
along the z -axis of the MnIV .
Using this methodology we have designed new molecules with the MnIV 4 CaO4 architecture.
These new models have oxidation states that are similar to the S1 and S2 states of the biological
OEC. We have accomplished these different electronic states by modifying the original host ligand
or by adding common linkers such as bipyridine or acetylacetonate. Thus we have proven that we
can obtain compounds that resemble the OEC both structurally and electronically.

Chapter 6

Methane Storage in Metal-Organic
Frameworks and Covalent-Organic
Frameworks
In this chapter we validate our theoretical methodology by comparing our results with experimental
measurements (COF-5 and COF-8). We describe the sorption mechanism for CH4 and developed a
first principle based van der Waals Force Field for the interaction of Covalent Organic Frameworks
(COFs) that was extended to Metal-Organic Frameworks (MOFs).[49] Then we proceed to use the
this methodology to design new types of materials with optimal characteristic for methane delivery
at room temperature. We found that Two new frameworks, COF-103-Eth-trans and COF-102-Ant,
are found to exceed the DOE target of 180 v(STP)/v at 35 bar for methane storage. [50]

6.1

Adsorption Mechanism and Uptake of Methane (CH4 ) in
Covalent-Organic Frameworks: Theory and Experiment

Reproduced with permission from American Chemical Society, Copyright 2010. Jose L. MendozaCortes, Sang Soo Han, Hiroyasu Furukawa, Omar M. Yaghi, and William A. Goddard, III J. Phys.
Chem. A, 2010, 114 (40), pp 10824 - 10833. .

6.1.1

Introduction

Although gasoline is the current fuel of choice for personal transportation because of its low-cost and
the fuel supply structure, it generates pollutants by combustion and evaporation, including nitrogen
oxides, sulfur oxide, carbon monoxide, and traces of carcinogens chemicals.[51] This has motivated
the search for alternative routes toward new energy sources. Methane is a good candidate for an
alternative fuel because it is inexpensive with clean-burning characteristics.[52] Moreover, the huge
reserves of natural gas (NG) (>95% CH4 , with some ethane, nitrogen, higher hydrocarbons, and

74
carbon dioxide)[52] around the world are comparable to the energy content of the worlds petroleum
reserves. However, to utilize this CH4 , inexpensive means of transporting and storing are required.
Since methane has a critical temperature of 191 K and critical pressure of 46.6 bar, it cannot be
liquefied at room temperature, increasing the cost of its transportation.[53] Attempts to overcome
this disadvantage include
• storing methane as liquefied natural gas (LNG, at ∼112 K) or compressed natural gas (CNG,
at 200 bar),[54]
• converting methane to oxygenates such as methanol or higher hydrocarbons such as ethane,[55,
56, 57] and
• storing in porous materials.[58]
Among these alternatives, we believe that storing methane via adsorption on porous materials
is the most promising near-term route because it allows operation at reasonable pressure (1-300
bar) and temperature (77-298 K) and does not require extra energy input for conversion to higher
hydrocarbons or methanol.
Recently, the new covalent-organic frameworks (COFs) family of porous materials was reported,
based on boronic acid building blocks (Figure 6.1).(9-12)[59, 60, 61, 62] COFs are held together by
strong covalent bonds between light elements such as B, C, O, H, and Si. They have high surface
areas (as high as 6450 m2 /g), large pore volumes (as high as 5.4 cm3 /g), and the lowest densities
for any known crystalline material (as low as 0.17 g/cm3 ),[61] all of which are prerequisites for high
uptake of methane (Table 6.1). In principle, an immense number of COFs using various building
units and various numbers of points of extension and functionality to attain various topologies could
be synthesized and tested for methane adsorption. Such empirical processes have been effective,
but we explore here the alternate procedure in which theory and computation is used to predict
the most promising candidates, followed by experimental synthesis and characterization only on the
most promising cases. Of course, this is only possible if the results from the theory and computation
are sufficiently reliable that one can with confidence reject low performance systems without the
need for experiment. Grand canonical Monte Carlo (GCMC) provides the accuracy required to
predict accurate adsorption isotherms. However, GCMC requires a force field (FF) accurate for
predicting the structure of the COF and for predicting the weak intermolecular interactions with
CH4 . The covalent bonds of the framework for COF systems are well treated by generic FF such as
Dreiding[25] and UFF,[11] and by more specialized FF such as OPLS.[40] However, these FF do not
generally provide the accuracy required to predict adsorption isotherms.[63] GCMC coupled to these
generic FF have been used to reproduce experimental isotherms reported by our group in some 2DCOFs[64] and 3D-COFs[65] finding disagreements between our experiments and this theory of 10%

75
and 25%, respectively. The same approach has been used to study MOF-5, and they were compared
to experiments and the absolute error ranges from +5 to -16%.[66, 67, 68] (19-21) Here it is essential
to account for the van der Waals (vdW) attraction (London dispersion) and electrostatic interactions
that dominate the interaction of CH4 with surfaces. The vdW terms have been a problem because
the powerful density-functional theory (DFT) methods underlying most quantum mechanics (QM)
calculations today are notoriously inaccurate for vdW.[69, 70] Consequently, we focused here on
developing and validating the vdW part of the force field using QM methods (MP2) expected to be
accurate.

Figure 6.1: Molecular structures of building units used for COF synthesis (outside black box) and
their COF formation reactions (green box, boroxine; blue box, ester)
In this work, we predict the methane uptake for five 2D-COFs (COF-1, COF-5, COF-6, COF-8,
and COF-10) and four 3D-COFs (COF-102, COF-103, COF-105, and COF-108), as shown in Figure
6.2. However, a better adjective for 2D- is two-periodic-COFs and for 3D- is three-periodic-COFs.
These predicted isotherms are in excellent agreement with our experimental results (within 2%) for
the two systems for which the experimental data show that the pores of the structures have been
completely cleaned (COF-5 and COF-8 up to 85 bar), validating our computational methodology.
Then we use this method to show that COF-102 and 103 are excellent materials for practical methane
storage.

76
Table 6.1: Pore size (P Size ), surface area (SA ), pore volume (VP ), and density of the
Framework without guest molecules (ρ) for the studied COF seriesa
material

P Size , Å

SA , m2 g−1

VP , cm3 g−1

ρ, g cm−3

topology

space group

COF-1
COF-5
COF-6
COF-8
COF-10
COF-102
COF-103
COF-105
COF-108

27
11
16
35
12
12
19
20,11

1230
1520
1050
1320
1830
4940
5230
6450
6280

0.38
1.17
0.55
0.87
1.65
1.81
2.05
4.94
5.4

0.91
0.58
1.03
0.71
0.49
0.42
0.38
0.18
0.17

gra
bnn
bnn
bnn
bnn
ctn
ctn
ctn
bor

P 63 /mmc
P 6/mmm
P 6/mmm
P 6/mmm
P 6/mmm
I43d
I43d
I43d
P 43m

P Size was calculated by placing a sphere in the center of the largest cavity and measuring
its diameter considering the van der Waals radii of atoms in the framework. SA and
VP were estimated from rolling an Ar molecule with diameter of 3.42 Å[71] over the
frameworks surface.

6.1.2

Methodology

6.1.2.1

Force Field

For geometry optimization, we used the quadruple-ζ valence basis (QZV) supplemented with polarization functions from the cc-pVTZ basis, which is denoted as QZVPP. To develop the FF to
be used in describing the interactions of methane with the COF (CH4 -COF) and the interaction
between methane molecules (CH4 -CH4 ), we used QM at the MP2 level with the approximate resolution of the identity (RI-MP2).[72, 73, 74] Quantum mechanical calculations were performed using
the Turbomole code. The auxiliary-QZVPP basis set was used for the RI-MP2 calculations.[75] We
did not include excitations out of the 1s core orbital in the MP2 calculation.
The binding energies between CH4 -CH4 and CH4 -COFs were corrected using basis-set superposition error (BSSE) by the full counterpoise procedure (eq 6.1).
CP
Einteraction
= Esuper −

i=1

Emiopt +

i=1

(Emif − Emi∗

(6.1)

Where the Ems represent the energies of the individual monomers. The subscripts opt and f
denote the individually optimized monomers and those frozen in their supermolecular geometries
and the asterisk (∗) denotes monomers calculated with ghost orbitals.[76]
Using the accurate RI-MP2 results, we developed FF parameters for nonbonded interactions
between CH4 -CH4 and CH4 -COFs where for the functional form the Morse potential (eq 6.2) was
used. Here the parameter D is the well depth, r0 is the equilibrium bond distance, and α determines
the stiffness (force constant).
rij
rij o
UijM orse (rij ) = D eα(1− r0 ) − 2e− 2 (1− r0 )

(6.2)

Figure 6.2: Atomic connectivity and structure of crystalline products for (a) 2D-COFs and (b) 3DCOFs. Unit cells are shown in blue lines. Atom colors: C, black; O, red; B, pink; Si, yellow; H, blue
It is more common to use Lennard-Jones (LJ-12-6) and exponential-6 (exp-6) functional forms
for such studies,[25] because it is believed that the long-range form should have 1/R6 character.
However, our experience is that LJ-12-6 and exp-6 have inner walls that are too stiff and that the
region of true 1/R6 character is only at much longer distances than relevant here. Thus, we believe
that the Morse function is the most suitable for studying gas adsorption in porous frameworks.
For the electrostatic interactions, we used the atomic charges (C -0.43820 and H +0.10955) of
methane from our QM calculations. For the charges of the COFs framework we used the QEq
charge equilibration method.[12]
6.1.2.2

QM Determination of the vdW Force Field Parameters

The parameters (D, α, and r0 in eq 6.2) were developed to fit QM results. Since all COF systems
considered here are composed only of B, C, H, O, and Si, we developed 13 sets of interaction

78
parameters:
• CCH4 -CCH4 , HCH4 -HCH4 , CCH4 -HCH4
• CCOF -CCH4 , CCOF -HCH4 , HCOF -CCH4 , HCOF -HCH4
• OCOF -CCH4 , OCOF -HCH4 , BCOF -CCH4 , BCOF -HCH4
• SiCOF -CCH4 , SiCOF -HCH4
To obtain these parameters, we considered four different geometrical configurations for each cluster: CH4 -CH4 , C6 H6 -CH4 , B3 O3 H3 -CH4 , and Si(CH4 )4-CH4 (Figure 6.3) as well as the interaction
with the edges. [77]
Table 6.2: Nonbonded FF parameters developed to fit the RI-MP2 calculationsa
term
CCH4 -CCH4
HCH4 -HCH4
CCH4 -HCH4
CCOF -CCH4
HCOF -CCH4
OCOF -CCH4
BCOF -CCH4
CCOF -HCH4
HCOF -HCH4
OCOF -HCH4
BCOF -HCH4
SiCOF -HCH4
SiCOF -CCH4

D/kJ mol−1

3.21×10
1.34×102
2.18×101
2.09×101
3.67×103
2.02×101
1.95×101
4.79×101
3.67×103
3.85×101
3.84×101
4.58×101
3.58×101

r0 /Å

3.92
3.13
3.46
4.23
3.25
3.59
4.11
3.08
3.26
2.55
3.28
4.06
4.78

12.7
11.4
11
13.2
12
11.3
12.3
9.07
12
8.99
11.7
7.19
16.5

The function form (Morse) is given in eq
6.2. D is the well depth, r0 is the equilibrium bond distance, and a determines
the force constant. Each parameter has
been rounded to three significant figures.

Our RI-MP2/QZVPP calculation finds that the energy for CH4 binding (E bind ) to the face of
the organic linker for the most stable configuration is higher than when it interacts with the edge;
also the equilibrium distance (Req ) to the face is shorter. The face E bind of CH4 -C6 H6 is 7.0 kJ
mol−1 with Req equal to 3.7 Å, while the edge E bind is 3.8 kJ mol−1 and Req is 5.0 Å. Also, the face
E bind for CH4 -B3 O3 H3 is 5.2 kJ mol−1 and Req is 3.4 Å, whereas its edge E bind is 1.5 kJ mol−1 and
Req is 4.9 Å.
The energy as a function of distance from QM was calculated near the equilibration distance
for each type of interaction and fitted to eq 6.2 using larger weights at the equilibrium distances
(insets in Figure 6.3). The predominant configurations interactions for the clusters are D3d for
CH4 -CH4 , ANTI for C6 H6 -CH4 , SYN for B3 O3 H3 -CH4 , and ANTI2 for Si(CH4 )4 -CH4 . Our new

Figure 6.3: Comparison of the optimized FF energies with QM (MP2-RI) for four configurations:
(a) CH4 -CH4 ; (b) C6 H6 -CH4 ; (c) B3 O3 H3 -CH4 ; (d) Si(CH4 )4-CH4 . FF results are shown as dashed
lines while the QM results are shown by empty symbols. Each configuration has four plausible
geometrical structures shown to the right, where C atoms are brown, B pink, O red, Si yellow, and
H white. Configurations interacting through the edges are not shown. The insets show the accuracy
in fitting to the equilibrium distance. Data plotted here as the BSSE corrections are included in the
Supporting Information.
FF parameters (Figure 6.2) reproduce well these binding energies and the QM energy profile (Figure
6.3). We validated the FF for CH4 by calculating the CH4 equation of state at various temperatures
(260-400 K) and pressures (1, 10, and 100 bar, see Supporting Information) and by comparing the
sorption isotherms to our experimental results for two COFs.
Table 6.3: Most-stable interaction geometries for clusters considered in
this worka
interaction

geometry

r0 /Å

QM/kJ mol−1

FF/kJ mol−1

CH4 -CH4
C6 H6 -CH4
B3 O3 H3 -CH4
Si(CH4 )4 -CH4

D3d
ANTI
SYN
ANTI2

3.710
3.657
3.352
4.401

1.61
7.01
5.16
4.44

1.59
6.83
5.22
4.28

r0 is the equilibrium bond distance defined as the distance between
the barycenter of every molecule.

80
6.1.2.3

GCMC Procedure

To determine methane storage capacity in COFs, we used the GCMC method with the ab initio based
FF developed herein. At each step of the GCMC, one of four events (translation, rotation, creation,
and annihilation of methane molecules) is applied using the Monte Carlo criteria for acceptance.
Details can be found elsewhere.[78, 79]
To obtain an accurate measure of methane loading, we constructed 3 000 000 configurations to
compute the average loading for each thermodynamic condition. The equilibrium conditions were
verified for every loading curve.
6.1.2.4

Structural Characteristics of COFs

These simulations used the experimental structures of 2D-COF (COF-1, COF-5, COF-6, COF-8,
and COF-10) and 3D-COF (COF-102, COF-103, COF-105, and COF-108) shown in Figure 6.2. The
surface area, pore volume, density, and pore aperture of studied COFs are summarized in Figure
6.1.[71]
There are two classes of 2D-COFs, one in which the layers are eclipsed and the other with them
staggered.
• COF-1 has an underlying graphite topology (gra) given by the“ABAB” stacking sequence of
its layers with interlayer spacing of 3.35 Å, leading to the P 63 /mmc space group. This leads
to compartments with pore apertures of 7 Å.[59]
• In contrast, COF-5, COF-6, COF-8, and COF-10 have a boron-nitride (bnn) topology with
an“AAA” stacking sequence of layers and P 6/mmm space group.(9, 10)[59, 60] The pore
diameters for these COFs are controlled by the building blocks (Table 6.1).
For the 3D-COFs, the simplest two topologies plausible from the connectivity of these building
units are the carbon-nitride (ctn) and boracite (bor) topologies.[80, 81]
• COF-102, COF-103, and COF-105 have the ctn topology with I43d I43d space group. The
pore structures for these materials are similar with pore diameters varying from 12 to 19 Å.[82]
• COF-108 has the bor topology with the P 43m space group leading to two classes of pores
with diameters of 11 and 20 Å.

6.1.3

Results and Discussion

6.1.3.1

Comparison Between Theoretical and Experimental Methane Adsorption

To validate our FF and simulation procedure, we additionally compare the predicted and experimental methane uptakes for COF-5 and COF-8, the two systems for which we had already confirmed

81
to be properly activated. This was done by comparing the measured pore volume with Ar at low
pressure and the measured pore volume from He at high pressure (see Supporting Information). It
is very important to note that if solvent molecules remain in the pore or COF framework or are
partially decomposed, it is not possible to obtain an accurate measure of the adsorption. Indeed,
this is the value of the simulations, in that adsorption performance can be obtained prior to confirming proper activation. Furukawa et al.[83] reported that there are some COFs that still need to
be further activated, a possible solution could the CO2 method developed by Nelson et al.[84] The
GCMC-predicted total methane adsorption isotherms for COF-5 and COF-8 at 298 K based on the
new FF were converted to obtain the excess isotherms because total uptakes are not experimentally
accessible.[85]
Figure 6.4 compares the excess isotherms in gravimetric unit (wt %) from simulations and experiments. Here wt % = (mass of gas) × 100/[(mass of framework) + (mass of the gas)]. The
predicted excess methane uptake in COF-5 is 11.3 wt % at 80 bar, in excellent agreement with
the experimental value of 11.1 wt % at 78 bar. Similarly, the predicted excess uptake in COF-8 of
10.6 wt % at 80 bar is very close to the experimental result of 10.3 wt % at 78 bar. These results
validate our theoretical methodology for these large pore materials; indeed, COF-5 can be classified
as mesoporous while COF-8 is microporous. This indicates that our FF provides a good estimation
of the COF-methane interaction at 298 K. This validation of our simulation procedures allows us to
determine the performance of the other COF systems, providing a guide to determine the optimal
materials for methane uptake.

Figure 6.4: Predicted (open triangles) and experimental (closed circles) methane isotherms at 298
K in excess uptake gravimetric units (wt %): (a) COF-5; (b) COF-8. The total predicted uptake is
shown by open squares.

82
6.1.3.2

Gravimetric Methane Uptake in Other COFs

The predicted gravimetric methane uptakes in other COFs at 298 K are shown in Figure 6.5.
To show superior capability of several COFs over MOFs, we have also included the experimental
and theoretical methane uptake of MOF-177, which have not been reported in the literature yet.
MOF-177 has been a benchmark for the MOFs compounds because of the high surface area (4700
m2 /g)[85] and the large amount of exposed edges of the organic ligands that has been suggested
to be the reason of the high permance for gas adsorption, as well as its microporosity.[86] The
simulated methane adsorption isotherms of the MOF-177 are compared to the experimental data,
giving a good agreement as for COFs where the combination rules have been used as well as our
accurate parameters previous developed for Zn (see Supporting Information).[87] As expected, all
COFs show type I for total and excess isotherms, with profiles that depend strongly on the materials.
The highest total gravimetric methane uptake was found in COF-108 (41.5 wt %) and COF-105 (40.5
wt %), followed by COF-103 (31.0 wt %), COF-102 (28.4 wt %), MOF-177 (25.9%), COF-10 (19.6
wt %), COF-8 (15.9 wt %), COF-6 (12.3 wt %), COF-5 (16.9 wt %), and COF-1 (10.9 wt %) all
at 100 bar. This is in disagreement with a recent report by Lan et al.[88] where it is shown that
at 100 bar the total gravimetric uptake is 54.39% for COF-105 and 54.68% for COF-108. This is
an overestimation of 31% with repect to our values. This might be due to the fact that only one
configuration was used for the organic linker-CH4 interaction and the CH4 -CH4 parameters were
not obtained with the same methodology as the other parameters.
In terms of excess methane uptake (the quantity measured experimentally), the best at 100 bar
are the 3D-COFs [COF-105 (27.6 wt %), COF-103 (26.6 wt %), COF-108 (24.2 wt %), and COF102 (23.8 wt %)] followed by MOF-177 (22.8%) and 2D-COFs [COF-10 (12.2 wt %), COF-5 (11.7
wt %), COF-6 (11.1 wt %), COF-1 (10.9 wt %), and COF-8 (10.7 wt %)]. Most COFs have much
smaller excess/total uptake ratios, generally in inverse proportion to the free volume (see Supporting
Information): 0.81 for COF-5, 0.95 for COF-6, 0.81 for COF-8, 0.77 for COF-10, 0.89 for COF-102,
0.90 for COF-103, 0.76 for COF-105, and 0.71 for COF-108 and 0.92 for MOF-177. However, COF-1
shows an unusual behavior. It has the best performance below 30 bar, with a total uptake amount
very close to the excess uptake with no additional adsorption above 30 bar. The reason is that
COF-1 has parallel exposed faces of boroxine rings spaced at 12 Å (Figure 6.2) and part of the
benzene rings inside the pores. This leads to saturation at lower pressure and low total uptakes.
The pores in COF-1 have small diameters (7 Å) and are isolated due to the “ABAB” stacking
sequence; therefore, the COF-1 might have kinetically inaccessible regions. However, the GCMC
simulation assumes that any points within the simulation cell can be accessed so that our results
for the case of COF-1 might overestimate the adsorption observed experimentally. This implies that
the difussion rate of methane in the COF-1 pores is not very high.
In sorption experiments, the absolute adsorbed amount can be estimated by using eq 3,[85]

Figure 6.5: Predicted gravimetric methane isotherms at 298 K: (a) total and (b) excess uptake
isotherms. We have also validated our calculations for MOF-177 with experiments and these are
included for comparison.

Ntotal = Nexcess + Vp × ρbulk

(6.3)

where Nexcess is the excess mass, Vp is the pore volume, Ntotal is total adsorbed amount of
methane, ρbulk is the bulk density of methane. Using eq 6.3, we recalculated the total uptake
based on the experimental excess isotherms and experimental methane density (see Supporting
Information). Calculated total uptakes from eq 3 are greater than simulated ones over the entire
range of pressure. The error is <10% below 50 bar, but it is >20% for COF-1 at 100 bar. The reason
is that the deviation is not negligible in the high-pressure region and for smaller pore COFs, since
eq 3 does not compensate for the volume of adsorbed guests. Thus although eq 6.3 is convenient for

84
a rough estimate of total uptake from experimental data, it can lead to an error in estimating total
uptake, especially at high pressure.
6.1.3.3

Adsorption Mechanism of Methane in COFs

At cryogenic temperatures (below 20 K), entropic effects in gas adsorption are not significant, so
that the specific adsorption sites of guest molecules can be observed with diffraction experiments.[89]
The change in electron density is related to the strength of the adsorbent-adsorbate interaction since
the electron density reflects the occupancy of the adsorption sites. However, at room temperature,
such diffraction experiments do not provide clear-cut location of the guest molecules due to thermal
disorder.[90] Therefore, the average of the snapshots obtained from the GCMC simulations provide
new insights into the methane adsorption behavior in COFs.
Figures 6 and 7 show the average of all snapshots for every COFs under each thermodynamic
condition. Figure 6.6 shows that the COFs with the larger pores (COF-5, 8, 10) are not filled
completely even at 100 bar, although their excess isotherms show saturation, while COF-6 reaches
saturation at 60 bar. Another smaller pore material, COF-1, reaches saturation at 40 bar since
it can only store three methane molecules per pore (see Supporting Information). The average
of the GCMC snapshots show that the joint of two edges is more populated than the center of
the pore at higher pressures. Surprisingly, we find that adsorption in 2D-COFs can even occur at
room temperature with the coexistence of layer formation and pore filling. The formation of some
pattenrs at higher pressures suggest the formation of a second layer for those pores that can hold
them; however, a third layer is not observed even for COF-10.
Unlike 2D-COFs, the adsorption sites of 3D-COFs can be on the surface of aromatic and boroxine
rings. Figure 6.7 shows that the layer formation and pore filling mechanism is again present even
though we are dealing with topologically different compounds. The average of the GCMC steps
shows that sites that are more populated are those where two edges converge. A similar trend was
observed for COF-108, although it has two different kinds of pores.
6.1.3.4

Isosteric Heat of Adsorption

The adsorption enthalpy is one of the most important parameters to evaluate the performance of
COFs, in addition to surface area and pore volume. We calculated the Qst for COFs from their
total uptake isotherms (Figure 6.8a). These Qst values do not depend strongly on the pressure (i.e.,
adsorbed amounts of methane); however, we do see some interesting trends. We expect the COFmethane interaction to decrease with increasing adsorption of methane, since the stronger binding
sites would be occupied first.[91] Indeed, this is the case for COF-5, COF-10, COF-105, and COF108 (group A). However, the Qst values for COF-1, COF-6, COF-8, COF-102, and COF-103 (group
B) increase directly with pressure. We interpret this phenomenon as related to the pore diameters

Figure 6.6: Ensemble average from the GCMC steps for methane adsorption in 2D-COFs at various
pressures. Atom colors are the same as in Figure 6.2; the average of the methane gas molecules is
shown in blue. The accessible surface is shown in purple and was calculated using the vdw radii of
every atom of the framework and the methane kinetic radii: (a) COF-10, pore diameter = 35 Å; (b)
COF-5, pore diameter = 27 Å; (c) COF-8, pore diameter = 16 Å; (d) COF-6, pore diameter = 11
Å.
because the space is not getting wasted, this suggests that interaction of framework methane is
more effective than in the bulk gas. This assumption is supported by the larger Qst values of the
COF-methane versus methane alone (Figure 6.8a). Thus group B (Psize below 18 Å) have an steady
increase in the Qst values as more methane is added to the structure, while group A (Psize above 18
Å) have a decrease in Qst values at higher pressure; i.e., there is more space so methane can interact
more, as in the bulk (see Figure 6.8a). MOF-177 could be classified in group B since it has a Psize
of 10.8 Å and VP of 1.55 cm3 /g.[86] Although it seems that the desirable pore diameter should be
smaller than 18 Å, it is not always necessary to design narrow pore materials, because large Qst
values could have a negative impact on both heat management and diffusion rate in practical use.[92]

Figure 6.7: Ensemble average of methane molecules at different pressures: (a) COF-103; (b) COF105; (b) COF-108. Atom colors: C, gray; O, red; Si, yellow; B, pink. The average of the methane
gas molecules is in blue. The accessible surface was calculated as in Figure 6.6. COF-102 has the
same sorption profile as COF-103 and it is not shown.
In this sense, we believe that COF-102 and COF-103 having reasonable pore diameters and their
Qst values place them are among the promising materials. From the relation of Qst with VP we
can find that the best materials for methane adsorption (COF-102, COF-103, and MOF-177) are
found at around 1.53 cm3 /g and 10.6 kJ/mol, suggesting a maximum value of performance for these
connectivities and chemical composition (Figure 6.8b).

Figure 6.8: (a)Predicted Qst values for COFs as a function of pressure. We have added the calculated
values for MOF-177 for comparison. (b) VP versus Qst for COFs. There are two groups, based on
the structural analysis: 2D-COFs (-1, -5, -6, -8, -10), which laid in a line with the same slope. Also
the 3D-COFs (-102, -103, -105, -108) have a common line. Both lines coincide at VP ∼ 1.53 cm3 /g
and Qst ∼ 10.6 kJ/mol.

87
6.1.3.5

Delivery Amount in COFs

In practical applications of porous material for gas storage, the delivery amount (that is, the difference in the amount adsorbed at 100 bar vs the amount, e.g., at 5 bar) is the important quantity.
Although the delivery amount can be measured experimentally,[93, 94] it is not easy to predict
delivery amounts from excess isotherms, rather one needs total uptake isotherms. However, the
simulations lead directly to this value. We choose 5 bar as the releasing pressure of cylinders and
compare estimated delivery amounts to the targets set by the U.S. Department of Energy (DOE): release 180 L at standard temperature and pressure (STP), defined as 298 K and 1.01 bar, of methane
per liter of storage vessel (Figure 6.9). The standard temperature and pressure in the DOE targets
are 298 K and 1 atm. However, in the field of chemistry, one usually chooses 273 K and 1 atm as
STP, so that all volumetric uptake is converted to the volume at 298 K.[95]
We see that COF-1 reaches the DOE target in a total volumetric uptake basis (195 v(STP)/v at
30 bar), but the delivery amount is very poor (42 v(STP)/v at 30 bar), making it a bad candidate
for practical applications of methane storage. We predict that COF-102 and COF-103 perform
very nicely in both total uptake (255 and 260 v(STP)/v at 100 bar) and delivery amount (229 and
234 v(STP)/v at 100 bar), suggesting that they are suitable for practical applications of methane
storage. This results from a combination of factors such as small pore diameter, high surface area,
low density, and high pore volume.

6.1.4

Concluding Remarks

To predict reliable methane adsorption isotherms, we developed FFs on the basis of accurate ab
initio calculations for interactions of methane with COF subunits involving C, O, B, Si, and H. We
confirmed that these calculations predict methane adsorption isotherms for COF-5 and COF-8 in
good agreement with experiment. This validates that ab initio based FF can be used to obtain
accurate predictions of gas adsorption isotherms. And the developed FF can be effectively used to
design new materials prior to experiments.
From our GCMC trajectory, we found the multilayer formations coexist with the pore filling
mechanism. We find that a pore diameter (∼12 Å), large pore volume (∼5 cm3 /g), and a high
surface area (>5000 m2 /g) can lead to large volumetric methane uptakes. We also demonstrate
that a high Qst value can improve the initial slope for the isotherm. However, this behavior reduces
the delivery amount of methane, which is more important for practical applications. There may
be the misconception that a weak binding energy will necessarily result in poor methane storage
capacity. However, we find that the volumetric uptake and the total uptakes in COF-102 and
COF-103 outperform other 2D and 3D-COFs at high pressure, even the benchmark MOF-177. The
high delivery/storage amount ratios for these COFs again support the importance of reasonable Qst

Figure 6.9: Predicted volumetric methane isotherms at 298 K for COFs: (a) total uptake isotherm
and (b) delivery uptake isotherm (the difference between the total amount at pressure p and that at
5 bar). Here the black dashed line indicates the uptake for free CH4 gas. MOF-177 uptake is added
for comparison.
values. These results indicate the value of having an additional fused aromatic ring, because the
methane molecules interact strongly with the faces of the aromatic or boroxine ring and weakly to
the edges.
This study focused on representative crystalline COFs that have been structurally characterized.
These results suggest that crystalline framework structures composed of triazines or triphosphorines
instead of the boroxine rings might lead to improved properties.

6.2

Design of Covalent Organic Frameworks for Methane
Storage

Reproduced with permission from American Chemical Society, Copyright 2011. Jose L. MendozaCortes, Tod A. Pascal, and William A. Goddard, III J. Phys. Chem. A, 2011, 115 (47), pp 13852
- 13857.

6.2.1

Introduction

Crystalline microporous materials systems such as the metal-organic frameworks (MOF) and covalent
organic frameworks (COF) are valuable for trapping enormous amounts of gases such as H2 , CO2 ,
and CH4 at modest pressures,[49, 83, 85, 96, 97, 98, 99] due to their outstanding porosity. Thus
COF-105 has a surface area of 6450 m2 /g (equivalent to 1.4 American football fields per gram) and
COF-108 has a pore volume of 5.4 cm3 /g with the lowest density crystalline material known (0.17
g/cm3 ).[59, 60, 61, 100, 101] We are interested in COFs because they contain light elements (B, C,
O, H, and Si). Such materials could be useful in automotive applications (storing CH4 rather than
gasoline[52]) and in CH4 capture to prevent this greenhouse gas for getting into the atmosphere, of
critical importance because methane is 21 times more effective in trapping heat in the atmosphere
than CO2 .[102]
We are also interested in the delivery amount of gas rather than the excess uptake because
delivery is more important for industrial application. We define the delivery amount as the difference
in the total amount adsorbed at certain pressure compared to the base pressure of the system, for
example, atmospheric pressure.[49] Much effort has been focused on reaching the DOE target of
storing methane at 35 bar, because this is the pressure in natural gas pipelines. However, current
commercial tanks can now hold pressures up to 250 bar, and hence we are interested in which
frameworks are useful in this pressure range. Here we use virtual screening of candidate materials to
discover new designs for COFs that can produce better CH4 delivery methane uptake than current
materials.
Our previous results showed that small pore diameter plus a high content of accessible aromatic
rings give a heat of adsorption (Qst ) suitable for binding CH4 at 298 K.[49] On the other hand, too
low a pore diameter leads to quick saturation at low pressures, as was found for COF-1. We also
found[49] that methane-methane interactions are important in achieving good sorption performance
with increasing pressure. On the basis of these lessons, we designed 15 new COFs containing alkyl
substituents that we expected to take advantage of these interactions.
We based the new designs on building blocks with a 3,4-connectivity, shown previously to yield
carbon-nitride (ctn) and boracite (bor) topologies.[61, 80, 81] Figure 6.10 shows the building block
used for this study as well as the chemistry of the condensation reactions. Scheme 6.2.1 summarizes

ctn

bor

HO Si OH
OH

Condensation types

Figure 6.10: Building blocks used in this study for designing new COFs. The inset shows the types
of condensation.
the topologies and the kind of substituents used for the frameworks.
This paper is organized as follows. Section describes the details about the methodology used
for each simulation. It also includes the criteria used for the topological design of the new COFs.
Section presents the results about the volumetric delivery performances as well as Qst values of our
compounds versus representatives COFs and MOFs without open metal sites (COF-102, COF-103,
COF-105, COF-108, COF-202, MOF-177, and MOF-200). We also discussed the comparison of our
results with previous studies. Finally, section summarizes our main findings.

6.2.2

Methodology

6.2.2.1

Force Field

Nonbonding terms. Previously we developed a force field for nonbonded interactions (vdW-FF)
of COFs and CH4 based on quantum mechanics (QM) calculations at the MP2-IR/QZVPP level
expected to be accurate for London dispersion forces (van der Waals attraction). We validated this
FF with the CH4 equation of state at various temperatures (260-400 K) and pressures (1, 10, and

91
Type

Name

topology

X=C

COF102

ctn

X=C

CH2 CH3

COF102-Et-H

ctn

X=C

CH(CH 3 )2

COF102-iPr-H

ctn

X=C

(CH 2) 2CH3

COF102-Pr-H

ctn

X=C
X=C

C(CH3 )3

Reactants

COF102-tBu-H

ctn

C(CH3 )3

C(CH 3) 3

COF102-tBu-tBu

ctn

X=C

CH 3

COF102-Me-Me

ctn

X=Si

CH 3

COF103-Me-Me

ctn

X=C

N/A

COF102-Ant

ctn

X=C

N/A

COF102-Eth-trans ctn

X=Si

N/A

COF103-Eth-trans ctn

5+1

X=Si

CH3

COF105-Me-Me

ctn

5+1

X=C

COF108

bor

5+1

X=C

(CH 2) 5CH3

COF108-nHex-H

bor

5+1

X=C

CH3

COF108-Me-Me

bor

5+3

X=C

N/A

COF105-Eth-trans ctn

6+1

X=C

COF202

ctn

6+4

X=C

COF212

ctn

Scheme 6.2.1: Reactions Involving the New COFs. The first column shows the building blocks used
and the second column shows the type of condensation undergone. Note that between COF-102 and
COF-103 analogs the only difference is the central atoms of the tetrahedral, C and Si, respectively
100 bar) and with experimental loading curves.[49] This vdW-FF was used to calculate the loading
curves.
Covalent Terms. For this work we are interested in studying the stability of the frameworks
using molecular dynamics (MD). Thus we have combined our vdW-FF with the covalent terms from
the DREIDING force field[25] for use in the MD studies.
6.2.2.2

Electrostatic Interactions

We described the electrostatic interactions using used the Mulliken charges from QM for the CH4
molecule (C, -0.43820; H, +0.10955) and the QEq (charges equilibration) charges for the framework.
[12]
6.2.2.3

Grand Canonical Monte Carlo

We used grand canonical Monte Carlo (GCMC) simulations to calculate the loading curves for these
frameworks. Here we use our vdW-FF with QEq charges for the framework and QM charges for
the CH4 . At each pressure we considered 3 000 000 GCMC steps and tested that convergence was
attained in each simulation. Every GCMC step allows four possible events: translation, rotation,
creation, and annihilation each at equal probability.[78, 79] We used the GCMC code as implemented
in Cerius2.

92
6.2.2.4

Molecular Dynamics

To test the stability of the compounds, we performed molecular dynamics (MD) simulations using
the LAMMPS simulation engine with a 1 fs time step.[103] We used the combined force field (vdWFF plus Dreiding) to treat the interactions. The long-range electrostatics were treated using the
particle-particle particle-mesh Ewald[104] technique, with a real space cutoff of 10 Å and an accuracy
tolerance of 10−5 . For each MD simulation we started with the equilibrium geometry from 500 steps
of conjugated gradient (CG) minimization (cell coordinates and atom positions) followed by 10 ps of
N V T dynamics to heat the system from 10 to 298 K. Finally, we ran N P T dynamics at 1 atm and
298 K for 7.5 ns from which we collect all relevant data. The temperature damping constant was
0.1 ps, and the pressure damping constant was 2.0 ps. The equations of motion used are those of
Shinoda et al.,[105] which combine the hydrostatic equations of Martyna et al.[106] with the strain
energy proposed by Parrinello and Rahman.[107] The time integration schemes closely follow the
time-reversible measurepreserving Verlet integrators derived by Tuckerman et al.[108]
6.2.2.5

Topological Consideration in the Design of COFs

For the design of the 3,4 frameworks we used only the ctn (I43d space group) and bor (P 43m
space group) topologies because they have been shown to be the most stable.[61, 80, 81] To build
each structure, we used the corresponding space group and add the irreducible representation of the
ligand into it. None of the ligands produces lower symmetry frameworks.
We minimize these frameworks with CG for 500 steps, which always led to convergence. During
the design of COF-102- Eth-trans, COF-103-Eth-trans, and COF-105-Eth-trans, we found that
the cis version is incompatible with these constraints and that the framework is unstable after
minimization, leaving the trans isomer as the only choice. The optimized structures coordinates are
reported in the Supporting Information.

6.2.3

Results and Discussion

6.2.3.1

Delivery Volumetric Uptake in Designed COFs

The DOE goal for methane storage is 180 v(STP)/v at 35 bar. Here, v(STP)/v denotes the volume
of methane per volume of system, where STP is the standard temperature and pressure of 298
K and 1.01 bar.[95] Only two materials have been reported to satisfy the methane uptake DOE
requirements at 35 bar: Ni-MOF-74 and PCN-14. In the experimental reports, 1 atm and 273 K
were used as the standard units. Thus, Ni-MOF-74[109] reached 190 excess v(273 K, 1 atm)/v
and PCN-14[110] reached 220 excess v(273 K, 1 atm)/v, the latter measured at 290 K. To make a
fair comparison in the following discussions, we multiply these experimental quantities by 1.09 (or
298/273) to get our defined STP. Therefore, after conversion, we obtain 207 v(STP)/v for and Ni-

93
MOF-74 and 240 v(STP)/v for PCN-14.
The representative MOF-177,[86] which is now in industrial production for automotive applications, [111] achieves only 91 excess v(STP)/v at 35 bar. The excess and total uptakes are summarized
in Table 6.4, where we used standard definitions for these quantities.[85, 112] We use only experimental uptakes for PCN-14 and Ni-MOF-74 because our vdW-FF does not deal yet with open metal
sites.
The results for the delivery amount of methane for our four best new designs for up to 35 bar are
shown in Figure 6.11, whereas the performance for the remaining 11 systems are in the Supporting
Information. At 35 bar (in v(STP)/v delivery units) the best performers are
COF-103-Eth-trans (192 ± 4), exceeding the DOE target,
COF-102-Ant (180 ± 3),
COF-102-Eth-trans (172 ± 3), and
COF-105-Eth-trans (110 ± 2).
Thus COF-103-Eth-trans stores 5.6 times as much as bulk CH4 at the same pressure (bulk CH4
reaches 34 ± 1). All our designed COFs have superior performance to previously reported COFs
and MOFs, such as COF-102 (137 ± 3), MOF-177 (112 ± 2), and MOF-200 (81 ± 2).
The new materials were designed for best performance at 35 bar. At higher pressures, the trend
in performance (at 300 bar and in v(STP)/v delivery units) changes: COF-105-Eth-trans (350 ± 7),
COF-103-Eht-trans (328 ± 7),
COF-102-Eht-trans (306 ± 6), and
COF-103-Ant (258 ± 5).
Therefore, at 300 bar, COF-105-Eth-trans stores 1.3 times as much as an empty container (bulk
CH4 takes 263 ± 3). Other good performers over the range of 1-300 bar are shown in the Supporting
Information. For example, at 300 bar, COF-103 reaches 352 ± 7 delivery v(STP)/v, followed by
COF-105 (327 ± 7), COF-108 (318 ± 6), COF-212 (310 ± 6), COF-105-Met-Met (308 ± 6), and
COF-108-Met-Met (302 ± 6). We see that some of these new designs perform better than the
archetypal frameworks: COF-102 (340 ± 7), MOF-177 (336 ± 7), and MOF-200 (321 ± 6). Figure
6.11 shows that COF-102-Ant performs comparable to bulk CH4 container at 300 bar whereas under
35 bar it approaches the DOE target.
Our results show that attaching alkyl substituents such as -CH3 , -CH2 CH3 , -CH2 CH2 CH3 , CH(CH3 )2 , -C(CH3 )3 , or -(CH2 )5 CH3 to the benzene rings does not increase the binding over having
the simple H substituent. Among alkyl-substituted benzenes, the type of isomer matters because the
one with higher surface area performs better, in particular when propyl (2590 m2 /g) and isopropyl
(1420 m2 /g) are compared. The propyl substituent has a higher uptake when compared to isopropyl
because more atoms are available to interact with a sorbent molecule and gives higher surface area
even though they have the same components.

Figure 6.11: CH4 uptake for the best COF performers. The delivery amount using a base pressure
of 1 bar is reported. The best performers at 35 bar are shown along with some that perform best at
300 bar. Solid lines indicate published compounds.
6.2.3.2

Isosteric Heat of Adsorption

Our calculated Qst values are shown in Figure 6.12. These trends can be understood from a comparison of COF-1, COF-102-Ant, and COF-103-Eth-trans (Table 6.4). COF-1 has the highest Qst
among COFs, but it is saturated by 40 bar, giving the poorest delivery uptake. COF-102-Ant outperforms COF-1 despite a smaller Qst value due to the higher and V P . Finally, COF-103-Eth-trans
is the best performer due to its balance of mild Qst , high S A and high V P .
High Qst (>20 kJ/mol) at low pressures and low S A and V P lead to low delivery amount. The
same analysis was done for PCN-14 and Ni-MOF-74 where experiments found high Qst (30.0 and
20.2 kJ/mol, respectively, at nearly 0 bar) but poor S A (1753 and 1033 m2 /g, respectively) and V P
(0.87 and 0.54 cm3 /g, respectively). Thus we expect that PCN-14 and Ni-MOF-74 will saturate by
100 bar, consistent with their experimental sorption isotherm curves trend. We did not simulate
PCN-14 and Ni-MOF-74 in this study because we have not yet developed a FF to deal with the

95
Table 6.4: Isosteric heat of adsorption (Qst ), surface area (S A ), pore volume (V P ), and uptake of
the framework series at 298 K (Where Tot = total, Exc = excess, and Del = delivery)a
material

Qst
(kJ/
mol)

SA
(m2 /
g)

VP
(cm3
g−1 )

Tot

CH4
[v(STP)/v]
at 35 bar

Exc

PCN14[110]
Ni-MOF74[109]
COF1
COF102
COF102-Ant
COF102-Eth-trans
COF103-Eth-trans
COF105-Eth-trans
MOF177
MOF200
Pure CH4

30
20.2
25.1
10.5
18.4
13.1
13.3
9.3
9.6
7.9

1753
1033
1230
4940
2720
4640
4920
6350
4800
5730

0.87
0.54
0.38
1.81
0.75
1.2
1.36
3.62
1.93
4.04

251b(230c )
218b(200c )
196
143
215
184
206
114
116
84
35

240b(220c )
207b(190c )
196
120
200
166
187
86
91
54

CH4
[v(STP)/v]
at 35 bar

Del

CH4
[v(STP)/v]
at 35 bar

Del

145
137
180
172
192
110
112
81
34

150
340
258
306
328
350
336
321
263

CH4
[v(STP)/v]
at 300 bar

Qst values are reported as an average from 1 to 300 bar. S A and V P were estimated from rolling
an Ar molecule with diameter of 3.42 Å6 over the frameworks surface. The GCMC predicts
an uncertainty of 2% in our reported uptakes but for clarity it is not shown. For PCN14 and
Ni-MOF74 we use the experimental Qst at low pressure (nearly zero coverage).[109, 110] The
S A and V P for PCN-14 and Ni-MOF-74 were also obtained from literature.
We have converted the experimental uptake (273 K, 1 atm) to our STP units (298 K, 1.01 bar)
by multiplying by the factor 1.09 to get a better comparison.
Experimental value (273 K, 1 atm).[109, 110]

open metal sites, which are an important feature in these compounds. The trends in performance
at higher pressure are also shown for archetypal MOF-177 and MOF-200, which have lower Qst of
9.7 ± 0.5 and 8.0 ± 0.2, respectively. However, the higher S A (4800 and 5730 m2 /g, respectively)
and V P (1.93 and 4.04 cm3 /g, respectively) give them an advantage at pressure beyond 100 bar.

In this work we are focused on getting the best performance in delivery units and this requires
a low interaction methane-COF in the low-pressure range. In other words, we want to get a low
Qst at low pressure. We have succeeded in obtaining this behavior for COF-102-Eth-trans and
COF-103-Eth-trans by using the tiny vinyl link, as demonstrated by the shape of their Qst curves,
which are similar to that of COF-102 but more marked for the entire pressure range. Eventually,
methane-methane interactions compensate to show moderate Qst . This is opposite to the Qst profile
of COF-102-Ant where the link being used gives a high interaction at low loading (Figure 6.12).
Therefore, our new designs using vinyl linkers present a new way to maximize delivery uptake,
which is different from the approach of using fused phenyl rings.
6.2.3.3

Stability of COFs

Recently, it was suggested[113] that COF-108 and even COF-102 might collapse due to instability of
the frameworks; however, the same study suggested that for COF1 the “AA” conformation is more

Figure 6.12: Heat of adsorption calculated for the compounds in Figure 6.11. The results for the
remaining compounds are in the Supporting Information.
stable than the experimentally observed “AB” conformer.[113] Therefore, we decided to study the
stability of our newly designed COFs with MD simulations. Our results show that cell parameters
of our new COFs change only slightly (0.130-0.142%) throughout the entire dynamics while the cell
angles stayed at 90◦ (orthorhombic) as shown in Table 6.5 and Figure 6.13.
For comparison, we also performed MD on the characteristic MOF-5 because it is very well
documented experimentally that the lattice parameters change from 25.670 to 25.910 Å over a
temperature range of 3.5-300 K but remain stable under these conditions.[89, 114, 115] We find that
MOF-5 has a change of 0.219% in the lattice parameters, larger than our new COFs (Table 6.5).
This indicates that our new COFs and the experimental COFs are stable without guest molecules
at 298 K and 1 atm.

97
Table 6.5: MD statistics for the frameworks obtained at 298 Ka
material

COF-102
COF-103
COF-108
COF-102-Ant
COF-102-Eth-trans
COF-103-Eth-trans
COF-105-Eth-trans
MOF-5

27.444
27.86
28.917
27.759
19.82
20.371
37.043
24.286

lattice (Å)

std dev (%)

0.0268 (0.098)
0.0280 (0.101)
0.0402 (0.139)
0.0389 (0.140)
0.0274 (0.138)
0.0290 (0.142)
0.0483 (0.130)
0.0533 (0.219)

Exp

lattice (Å)

27.177
28.248
28.401

25.790 (0.46%)b

The standard deviation was calculated after 10 ps. All these frameworks
have a cubic lattice.
The experimental lattice value for MOF-5 is taken as the median of most
representative experimental conditions reported (the average for these
experiments is 25.833 Å). For comparison we show in parentheses the
percentage from upper and bottom bounds.[89, 114, 115]

Figure 6.13: Lattice parameter variations obtained from MD for several COFs. The lattice parameters are in Angstroms (Å) and time in nanoseconds (ns). COF-103 and COF-105-Eth-trans are not
shown; the statistics are summarized in Table 6.5.
6.2.3.4

Comparisons to Previous Computational Studies

previous computational report about sorption of CH4 on MOFs showed that increasing the number
of fused benzene rings increases the Qst value.[66] However, they reported that their empirical vdW

98
attraction terms led to errors of 5.7-9.9% greater than experiments. This study did not report the
stability of their designed compound IRMOF-993, and experimentalists attempted to synthesize the
proposed IRMOF-993 but could only create the analog PCN-13. The synthesized framework has
the same components but a different topology with a smaller pore size (almost half of the originally
proposed MOF-993).[116] MOF-993 was reported to be topologically stable on the basis of studies of
Snurr et al.;[66] however, it was found by experimentalists not to be thermodynamically accessible.
Even so, these studies showed that enhancement of CH4 storage at pressures below 35 bar on MOFs
can be attained by increasing the Qst value by putting fused rings into the framework, assuming the
structure is stable. Our study shows that this is also the case for CH4 in COFs; however, we found
that this is a poor strategy if we want to obtain a good delivery uptake at higher pressures and it
does not help beyond 250 bar.
To avoid such problems, we performed MD calculations on our proposed topological stable frameworks to show that they are also dynamically stable. Our current study shows that enhancement of
the CH4 delivery amount can by attained reducing the interaction at low-pressure of methane-COF
while also demonstrating stability of the proposed frameworks. We found that this behavior is opposite to that of putting fused benzene rings when looking at the interaction profile over the entire
pressure range.

6.2.4

Concluding Remarks

In summary, we have also shown two ways to produce improved absorbents for higher delivery
methane up to 35 bar: by using skinny ligands to minimize the methane-COF interaction in the lowpressure range (COF-102-Ethtrans and COF-103-Eth-trans) and by increasing the heat of adsorption
(COF-102-Ant).
We also found that the performance at 300 bar can be improved by frameworks with larger pore
volumes and surface areas. Our results show that attaching systematically alkyl substituents to the
benzene rings does not increase the binding over having a simple -H substituent. These conclusions
should apply also to metal-organic frameworks and zeolite imidazolate frameworks.

Chapter 7

Clean Energy (H2) Storage in
Metal-Organic Frameworks and
Covalent-Organic Frameworks
In this chapter I describe my work on the design of new Covalent-Organic Frameworks (COFs)
and Metal-Organic Frameworks (MOFs) in order to store H2 . In the first section we validate our
methodology by comparing our results with the experimental uptake of the latest MOFs and COFs.
We then propose to metalate the frameworkss with Li, Na or K in order to obtain a higher H2 uptake.
For the gravimetric delivery amount from 1 to 100 bar, we find that eleven of these compounds reach
the 2010 DOE target of 4.5 wt % at 298 K. The best of these compounds are MOF200-Li (6.34) and
MOF200-Na (5.94), both reaching the 2015 DOE target of 5.5 wt % at 298 K. Among the undoped
systems, we find that MOF200 gives a delivery amount as high as 3.24 wt % while MOF210 gives
2.90 wt % both from 1 to 100 bar and 298 K. However, none of these compounds reach the volumetric
2010 DOE target of 28 g H2 /L. The best volumetric performance is for COF102-Na (24.9), COF102Li (23.8), COF103-Na (22.8), and COF103-Li (21.7), all using delivery g H2 /L units for 1-100 bar.
These are the highest volumetric molecular hydrogen uptakes for a porous material under these
thermodynamic conditions.
In the second section we use accurate quantum mechanical (QM) methods to find the H2 binding
energy to six different common organic linkers as well as their metalated analogs (60 compounds).
Precious transitions metals (Pd, Pt) give comparable energies to first row transition metals (Sc to
Cu). We report that metalating certain linkers can give the desired binding energy (>10kJ/mol and
<15.3 kJ/mol) to reach the maximum delivery amount for the DOE targets. We also show a new
route for metalating organic linkers with the use of metallic Pd(0) and we prove that this reaction
is favorable, with the new compound serving as a site for chemisorption and physisorption of H2 .
With these results we propose that these linkers and transition metals can be used to create the
next generation of H2 storage porous materials

100

7.1

High H2 Uptake in Li-, Na-, K- Metalated CovalentOrganic Frameworks and Metal-Organic Frameworks at
298 K

7.1.1

Introduction

A current major obstacle to molecular hydrogen (H2 ) as an alternative source of energy is the
difficulty of storage at operational temperatures. The U.S. Department of Energy (DOE) has set
the 2010 targets of 4.5 wt % and 28 g/L at room temperature (and 5.5 wt % and 40 g/L for
2015).[117, 118] Many materials have been proposed that might approach these demanding goals.
Chemisorption of H2 in solid systems can lead to the required capacities; however chemisorption
generally leads to interaction energies that are too strong (>30 kJ/mol) compounded by additional
barriers that lead to very slow kinetics. On the other hand, physisorption generally has good
kinetics (no barrier), but the net bonding is too weak (interaction energy <10 kJ/mol) for substantial
storage at room temperature.[119] The discovery of robust microporous covalent organic frameworks
(COFs)[59, 61, 100] and metal-organic frameworks (MOFs)[86, 101, 114] have brought excitement
that these systems might lead to a solution to this problem due to their (1) high surface area:
MOF210 has the world record in Brunauer-Emmett-Teller (BET) surface area of 6240 m2 /g, and
Langmuir surface area of 10400 m2 /g;[101] (2) low density: 0.17 g/cm3 for COF108, the lowest for
a crystalline material,[61] while 0.22 g/cm3 for MOF200;[101] and (3) high porosity: as high as 3.59
cm3 /g for MOF200, 3.60 cm3 /g for MOF210, 1.81 for COF102 and 2.05 for COF103.
However, these compounds show a poor uptake of H2 at room temperature due to the weak
interactions between the frameworks and H2 . As a way to obtain higher interaction energies we
proposed metalating MOFs, such as MOF5[120] and MOF177,[121] with Li and we showed that this
could increase the uptake sufficiently to achieve up to 5.5 wt % excess H2 at 300 K.[121]
In the current study, we report the excess and delivery sorption curve from 1 to 100 bar at room
temperature for the latest generation of MOF and COFs, including the Li-, Na-, and K-metalated
analogs. We also calculate the thermodynamics for the formation of the alkaline species in the gas
phase and in tetrahydrofuran (THF), including the possibility of clustering and adducts (Li-benzene
vs Li-Li), to explore the plausibility for the experimental synthesis under room temperature. We
then propose that metalating the new COFs and MOFs with alkali metals (Li, Na, and K) can
dramatically increase the binding energy and, thus, the H2 uptake.
For this study, we used FF parameters developed from accurate quantum mechanics (CCSD(T)

101
and MP2) for describing the physisorption of H2 onto the alkali-aromatic complex adducts. We then
used GCMC based on this first principles FF to calculate the loading curves of H2 versus pressure
at room temperature. These simulations demonstrate that the metalated versions of these materials
can achieve the major DOE gravimetric targets for 2010 and even 2015. We report H2 uptake using
total, delivery, and excess units resulting from metalating the highest surface areas (S A ) and the
highest pore volume (V P ) frameworks with Li, Na, or K, as well as the pristine analogs. This includes
the latest generation of COFs (COF102, COF103, and COF202) and MOFs (MOF177, MOF180,
MOF200, MOF205, and MOF210), which physical properties are summarized in Table 7.1.
Table 7.1: Properties of the frameworks used in this work: surface area (S A ), pore volume (V P ),
and density (ρ)a
material

SA,
m2g-1

V P,
cm3g-1

ρ,
g cm-3

material

SA,
m2g-1

V P,
cm3g-1

ρ,
g cm-3

COF102
COF103
COF202
MOF177
MOF180
MOF200
MOF205
MOF210
COF102-Li
COF103-Li
COF202-Li
MOF177-Li
MOF180-Li
MOF200-Li
MOF205-Li
MOF210-Li

4940
5230
4500
4800 (4500)
5940
5730 (4530)
4630 (4460)
5570 (6240)
5360
5500
4250
5100
6440
6480
5270
6130

1.81
2.05
1.37
1.93 (1.89)
3.5
4.04 (3.59)
2.21 (2.16)
3.61 (3.60)
1.65
1.85
1.25
1.74
3.26
3.69
3.39

0.42
0.38
0.54
0.43
0.25
0.22
0.38
0.25
0.44
0.38
0.54
0.39
0.26
0.23
0.4
0.26

COF102-Na
COF103-Na
COF202-Na
MOF177-Na
MOF180-Na
MOF200-Na
MOF205-Na
MOF210-Na
COF102-K
COF103-K
COF202-K
MOF177-K
MOF180-K
MOF200-K
MOF205-K
MOF210-K

4930
5090
3950
4710
6010
6020
4950
5610
4380
4800
3570
4220
5630
5600
4340
5140

1.35
1.54
1.09
1.49
2.92
3.17
1.75
3.05
1.1
1.27
0.94
1.27
2.6
2.73
1.5
2.73

0.5
0.46
0.59
0.46
0.28
0.26
0.44
0.28
0.56
0.52
0.64
0.51
0.31
0.29
0.49
0.31

The values in parentheses were reported in the literature.[101]S A and V P were estimated
from rolling an Ar molecule with a diameter of 3.42 Å [71] over the frameworks surface.

7.1.2

Computational Details

7.1.2.1

Quantum Mechanics Calculations and Development of the Parameters for
Nonbond Interactions

To develop FF parameters for the nonbonded interactions between H2 and MOF/COFs, we used
DFT/M06[122] with the 6-311G**++ basis set calculations as implemented in Jaguar[9] to determine
the locations and numbers of Li, Na, or K atoms on the aromatic linkers. We then used these
geometries to calculate the binding energies from accurate quantum mechanical methods (CCSD(T)
and MP2) which are capable of accurately describing the London dispersion forces The FF were
then fitted to these QM energies and geometries.

102
We use the Morse potential (eq 7.1), which we found to describe well the nonbond interaction of
H2 . The Morse function involves three parameters: the well depth D, the equilibrium bond distance
r0 , and the stiffness α.
rij
rij o
UijM orse (rij ) = D eα(1− r0 ) − 2e− 2 (1− r0 )

(7.1)

Our experience is that the Morse function gives a slightly better description than exponential6, which performs much better than Lennard-Jones 12-6 potential.[123, 124] Table 7.2 shows the
parameters used for this work.[96, 120, 125]
Table 7.2: Nonbonded FF parameters used for this
study based on MP2 for Li and CCSD(T) for Na and
Ka
term

D, kJ mol−1

r0 , Å

HH2 -HH2
HH2 -CCOF/MOF
HH2 -HCOF/MOF
HH2 -ZnCOF/MOF
HH2 -OCOF/MOF
HH2 -BCOF/MOF
HH2 -SiCOF/MOF
HH2 -LiCOF/MOF
HH2 -NaCOF/MOF
HH2 -KCOF/MOF

7.60 10-2
4.22 10-1
3.63 10-3
5.21 10-1
1.05 10-1
2.02 10-1
4.61 10-1
9.03
5.73
2.71

3.57
3.12
3.25
2.76
3.32
3.49
3.53
2.02
2.49
3.13

10.7
12
12
13.4
12
10.6
14.2
7.13
7.71
8.04

7.1.2.2

The function form (Morse) is given in eq 7.1. D
is the well depth, r0 is the equilibrium bond distance, and α determines the force constant.[120,
96, 125]

Valence Bond Force Field

The equilibrium structures of the pristine MOFs and COFs used in this study were optimized with
the Dreiding force field[25] starting with the reported experimental structures. We have shown that
the resulting structures are in very good agreement with experiment.[120, 96] The coordinates of
the optimized metalated structures are shown in the Supporting Information.
7.1.2.3

Grand Canonical Monte Carlo Loading Curves

We used the first principles based force field described above in grand canonical Monte Carlo
(GCMC) ensemble simulations. Here for each temperature and pressure, we constructed 3,000,000
configurations to compute the average loading for which we observed convergence was obtained.
Every GCMC step allows four possible events, translation, rotation, creation, and annihilation, each
at equal probability. We used the GCMC code as implemented in Cerius2. The structures of the

103
optimized frameworks are shown in Figure 7.1.

10 Å

OO
O Zn
Zn O
O Zn
Zn O

COF102-Li

Si
OO O
B B
OO O
Si

MOF177-Li

COF103-Li
Si

COF202-Li

MOF200-Li

Li, Na, K

MOF210-Li

Figure 7.1: Structures of the Li-doped COFs and MOFs studied in this work. Hydrogen atoms have
been omitted for clarity.

7.1.3

Results and Discussion

7.1.3.1

Nature of the Chemical Bond for the Li-Benzene (Li-Bz) Systems

To investigate the plausibility on the formation of Li-Bz adduct, we calculated their thermodynamics from quantum mechanics in the gas phase and in tetrahydrofuran (THF). Nonperiodic QM
calculations were carried out using the B3LYP[47, 48] and M06[122] hybrid DFT functionals with
the Jaguar code.[9] Here we used the 6-31G**++ and 6-311G**++ basis sets. All geometries were
optimized using the analytic Hessian to determine that the local minima have no negative curvatures
(imaginary frequencies). The vibrational frequencies from the analytic Hessian were used to calculate
the zero-point energy corrections at 0 K (Tables 7.3 and 7.4). To explore the solvation, we consider
two different approaches explicit THF and implicit THF (for which we used the Poisson-Boltzmann

104
continuum approximation; with = 7.6, R0 = 2.52 Å).[28] When we compared the binding energy
for the Li-Li compounds, we found that M06 is closer than B3LYP to the CCSD(T) calculations
(Figure S1). The results for the thermodynamics at 298.15 K and 1.01 bar are shown in Figure
7.2. We observed that, in the gas phase, the Li-Bz is not thermodynamically favorable; however,
MO6 predicts that the Li-Bz-Li compound is favorable in the gas phase with respect to Li(g) and
Bz(g). This observation prompted us to calculate the thermodynamics in THF since this might help
to stabilize the polarized Li species and, therefore, have a favorable thermodynamics under these
conditions. As predicted, we can see from Figure 7.2, if we are able to form Li(g) as well as Bz(g)
and dissolve them in THF, we will observe the formation of Li-Bz adduct is thermodynamically
favorable (∆G = -22.4 kcal/mol). Although such an experimental setup might be difficult, a good
approximation could be attained by dissolving Li(s) and Bz(l) in THF at very low concentrations.
On the other hand, Tacke[126] has shown experimentally and theoretically that when concentrated
quantities of Bz and Li in THF are used at 77 K; C-H activation occurs and Li-Ph + Li-H compounds are formed. In a related work, they also showed that the formation of R-Li· · ·Bz adducts (R
= H, CH3 , and Ph) is possible when R-Li is used as the source for Li.[127] This suggests that the
concentration of Bz and Li, as well as the source of Li is key to obtain the structures here proposed
and also confirms that Li clustering is not a major issue.
Table 7.3: Electronic energy for the optimized systems using different basis sets (6-31G**++ and
6-311G**++) and different functionals (M06 and B3LYP) is presenteda
M06/6-31**++

M06/6-311**++

B3LYP/6-31**++

B3LYP/6-311**++

compound

ESCF
(kcal/
mol)

BSSE
(kcal/
mol)

ESCF
(kcal/
mol)

BSSE
(kcal/
mol)

ESCF
(kcal/
mol)

BSSE
(kcal/
mol)

ESCF
(kcal/
mol)

BSSE
(kcal/
mol)

1Li
2Li
Bz
Li-Bz
Li-Bz-Li

-4696.9
-9416.2
-145624.2
-150323.8
-155032.6

N/A
0.1
N/A
0.3
1.1

-4696.8
-9418.2
-145653.8
-150353.6
-155066.2

N/A
N/A
0.3
0.9

-4700.7
-9421.7
-145747.5
-150449.1
-155153.2

N/A
0.1
N/A
0.4
0.7

-4700.9
-9422.6
-145777.4
-150479.6
-155188.3

N/A
0.1
N/A
0.5
0.5

We also show the basis set superposition error (BSSE)[129] for the addition of a Li atom.
In a remarkable work, Krieck et al.[128] have been able to synthesized the (THF)3 Na(µ-ν 6 -C6 H3 -

2,4,6-Ph3 ) and (THF)4 K(µ-ν 6 -C6 H3 -Ph3 ), see inset of Figure 7.2. They were able to characterize
these compounds by crystallography. This report shows that these systems can be synthesized but
more remarkable it is the fact that the linkers used are the building blocks of MOF-177 and the
precursor of MOF-200.
An interesting question to ask is where the electron goes once the Li-Bz adduct is formed. We
calculated the HOMO and LUMO for these species and the results are shown in Figure 7.3. The
molecular orbital diagram shows that the HOMO-LUMO gap narrows when THF is used (Figure
7.3a). The HOMO shows that the electron remains in the Li in the gas phase; however, if explicit

105

Thermodynamics at 298.15 K and 1.00 atm
Gas Phase
ΔG° M06 [B3LYP]
Free energies, kcal/mol

Bz(g)

Li---Bz---Li (g)
+10.0
[+17.2]

Li(g)

Li(s)

Li(g)

-34.9
[-24.6]

Bz---Li(g)
+2.7
[+2.9]

-18.5
[-14.8]

Bz---Li (s)

-19.6[-17.6]

Bz(g)

Li---Bz---Li (s)

-35.8[-32.4]

-11.2
[-0.5]
ΔG°

Li-Li (g)

Solvation Phase
ΔG° M06 [B3LYP]
Free energies, kcal/mol

-32.8
[-22.3]
ΔG°

-24.5
[-20.7]

-22.4
[-18.4]

Bz(s)

Li-Li(s)

Li(s)

-2.4 [-2.3]

Li(s)

Li(g)
0.0 [0.0]
6-311G**++ basis set

6-311G**++ basis set
(s)=Implicit Solvation, THF

Recent compunds reported by Krieck et al.

Figure 7.2: Calculations of the thermodynamics for the Li species were obtained using M06/6311G**++ and B3LYP/6-311G**++. We defined the following quantities as gas G298K = E SCF +
E ZPE + H TOT - T ×S TOT , and solv G298K = E SCF + E SOLV + E ZPE + H VIB + 6RT - T (0.5 S TOT +
0.5 S TOT ). All the numerical data is shown in Tables 7.3 and 7.4. (Inset) 1, 2, and 3 are experimental
compounds reported by Krieck et al.[128].
Table 7.4: Zero-point energy (ZPE), vibrational enthalpy (Hvib ), total enthalpy (Htot ), vibrational entropy (Svib ), total entropy (Stot ), and solvation energy (Esolv ) obtained for the different
compounds for 298.15 Ka
M06
ZPE

B3LYP
M06
ZPE
Hvib Htot

B3LYP

compound

Hvib Htot Svib Stot Svib Stot Esolv Esolv
(kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/ (kcal/
mol) mol) mol) mol) mol) mol) mol) mol) mol) mol) mol mol

1Li
2Li
Bz
Li-Bz
Li-Bz-Li

0.5
62.8
62.7
58.9

0.5
63.1
63.1
59.9

0.2
2.6
2.7

0.2
1.6
3.1

1.5
2.3
3.4
3.9
5.4

1.5
2.3
3.3
5.1

M06

1.2
4.5
21
29.4

33.9
47.2
64.2
75.7
81.6

B3LYP

1.2
4.4
17.9
26.4

33.9
47.2
64.1
84.9
78.7

M06

-2.4
-19.6
-35.8

B3LYP

-2.3
-17.6
-32.4

ZPE energy corrections were obtained from the vibrational frequencies using the respective
functional.

or implicit THF is used, the electron is transferred the benzene ring (Figure 7.3b). This suggests
that the transfer of electron is promoted by the solvent as expected.
A very important question for experimentalists is how to remove the THF from inside the struc-

106
ture in case it is strongly coordinate to the alkaline metal. The approach discussed so far uses
an implicit model approximation (Poisson-Boltzmann continuum approximation) and this approach
takes into account the entire accessible surface area of the Li-Bz adduct but it does not consider
explicit THF molecules for the calculation. Therefore, we have performed M06/6-311**++ calculations to study how strongly the explicit oxygen of THF can coordinate with the Li from the Li-Bz
adduct. We found that the free energy for this case is in the order of ∆G = -1.0 kcal/mol compared
to the Li-Bz (implicit THF). Thus, if the THF is coordinated to the Li-Bz adduct, it can be removed.
The M06 functional predicts that in gas phase the Li-Bz-Li would be stable while the Li-Bz would
unstable by 2 kcal. This is still within the level of accuracy for current DFT approach. However,
B3LYP and M06 predict that 1 THF is necessary to stabilize the Bz-Li system if necessary.
A promising method to remove solvents from MOFs structures have been published by Hupp et
al.[84] This method uses supercritical CO2 to activate the frameworks. They reported a spectacular
1200% uptake increase in some cases. This has been proven to lead to the successful activation
in MOF-200, for example.[101] This method can be potentially used for the removal of THF since
the molecules of THF are not strongly coordinated to the Li-Bz adduct as we have shown in our
calculations. The supercritical CO2 can be ultimately use to remove the most THF molecules and
this approach could be tuned to avoid removing also the Li.
7.1.3.2

Gravimetric Uptake

We calculated the total wt% (see SI) gravimetric uptake of the frameworks at 298 K, which we used
to estimate the delivery amount; this is the difference in the amount adsorbed at 100 bar versus a
basis, say, 1 or 5 bar. The delivery amount is difficult to estimate experimentally;[93, 94] however,
it is very important for practical applications because it allows us to estimate the maximum amount
that can be obtained if we unload the gas to, for example, ambient temperature and pressure.
Figure 7.4a shows the gravimetric delivery amount using 1 bar as the basis for pure and Li,
Na, and K metalated COFs and MOFs. Here we see that the Li-metalated cases have a better
performance than the Na-metalated cases, while Na-analogs lead to better performance than the Kcases. We can see that from 1 to 100 bar, 11 compounds reach an uptake higher than the 2010 DOE
gravimetric target of 4.5 wt %: MOF200-Li (6.34), MOF200-Na (5.94), COF102-Li (5.16), MOF180Li (5.16), MOF180-Na (4.91), MOF210-Li (4.80), COF103-Li (4.75), COF102-Na (4.75), COF103-Na
(4.72), MOF210-Na (4.68), and MOF205-Li (4.58). From these compounds, only MOF200-Li and
MOF200-Na reach an uptake over 5.5 wt % delivery. It is interesting to note that pure MOF200
gives a delivery amount as high as of 3.24 wt %, while MOF210 gives 2.90 wt % both at 100 bar
and using 1 bar as the basis.
Figure 7.4b shows the gravimetric delivery amount using 5 bar as the basis at 298 K. Under these
units, metalated cases lead to a different trend, with the uptake for Na-metalated > Li-metalated

107
phase
a) GasB3LYP

Implicit THF
B3LYP

LUMO-Implicit

Explicit THF
B3LYP
LUMO-Explicit

Gas phase
M06

Implicit THF
M06

Explicit THF
M06

LUMO-gas

LUMO-Implicit

LUMO-Explicit

HOMO-Implicit

HOMO-Explicit

LUMO-gas
HOMO-Explicit
-.1

HOMO-gas

HOMO-Implicit

-.1

-.3

HOMO-gas

-.3

HOMO orbitals/M06

HOMO orbitals/B3LYP
HOMO-gas

HOMO-Implicit

HOMO-Explicit

HOMO-gas

HOMO-Implicit

HOMO-Explicit

c)
d=1.90 A
Li ch=-0.16
(-0.10)

Li ch=+0.48
(+0.77)

d=2.50 A

d=1.97 A

Li ch=+0.16
(+0.53)
d=1.76 A

Mulliken Charges (Electrostatic Charges)
B3LYP

Li ch=-0.01
(-0.03)
d=2.74 A

d=1.90 A
Li ch=+0.66
(+0.81)
d=2.09 A

Li ch=+0.01
(+0.16)
d=1.76 A

Mulliken Charges (Electrostatic Charges)
M06

Figure 7.3: (a) Molecular orbital (MO) diagram for Li-Bz system. Units for the vertical axis are
Hartrees. (b) Highest occupied molecular orbital (HOMO) for the Li-Bz for the gas phase, for the
implicit THF and for explicit THF obtained from M06 and B3LYP. Atoms colors are C, green; H,
white; and Li, pink. The colors of the orbitals yellow and dark blue represent an arbitrary positive
and negative sign. (c) Mulliken and electrostatic charges for Li-Bz (g), Li-Bz (implicit THF), and
Li-Bz (explicit THF)
> K-metalated at pressures higher than 30 bar. Therefore, the best performance for gravimetric
delivery (5-100 bar) is for MOF200-Na (5.25 wt %), followed by MOF200-Li (4.90 wt %), COF102Na (4.75 wt %), COF103-Na (4.71 wt %), and MOF210-Na (4.11 wt %). This shows another way
to tune the properties to attain better delivery amounts for different basis (1 vs 5 bar). It is also
worthwhile to highlight that, even with 5 bar as basis and 100 bar as the limit, pure MOF200 and
pure MOF210 have a delivery amount of 3.11 and 2.77 wt %, respectively.
A possible explanation for this behavior is shown in Figure 7.5, where we plot V P versus wt%
delivery amount using 1 and 5 bar as the delivery basis for all COFs. For this figure, MOFs

108
were omitted for clarity, but the following discussion also applies (see Figures S19 and S20). Figure
7.5a,b shows that performance at higher pressures depends on the basis used to estimate the delivery
amount. We found that the gravimetric uptake depends generally in higher degree on the V P than
on the S A (Figure S21 vs S22), the same was suggested independently for the H2 uptake in zeolitic
imidizolate frameworks.[125] We also observed that the pore volume decreases as the size of the
metalated atoms increases. Thus, the V P is bigger for the pure framework > Li-metalated > Nametalated > K-metalated.
Figure 7.5a shows that when using 1 bar as the basis, the Li-metalated COFs gives a better
delivery uptake at every pressure (10, 30, 50, 80, and 100 bar). Thus, at every coordinate, the
uptake is higher for the Li-cases, with the difference getting smaller at 100 bar.
Figure 7.5b shows the delivery uptake with 5 bar as the basis, where we can see that at 10 bar
the Li cases barely exceed the Na cases, and at 30 bar and above, the Na-analogs overcome any
other counterparts. The K cases start performing closer to the Na cases with increasing pressure,
while performing almost as good as the Li cases at 100 bar.

Figure 7.4: Delivery gravimetric uptake obtained for the studied COFs and MOFs, also the metalated analogs with Li, Na, and K are shown.
MOF180 and MOF205 as well as the metalated cases are reported in the SI. In (a), we show the delivery amount using 1 bar as the basis, while in
(b) we show the delivery amount using 5 bar as the basis. The error bars at each calculated point are shown, while on some cases they are too small
to fit inside the symbols.

109

110
We conclude that at lower pressure (1-10 bar) the Li cases perform better because the slope of
the curves (uptake vs V P at constant pressure) is larger than the others, while the slope of the Na
cases starts becoming larger than the Li cases as the pressure increases above 30 bar. Finally, the
slope of the curves for the K cases starts becoming as large as the Na cases at 100 bar. In other
words, the Li cases perform better in the range of 1-10 bar, while Na cases perform better in the
range of 30-100 bar, and by extension, the K cases should perform better above 100 bar using 5
bar as the basis, all due to the dependence of their H2 affinity at different pressures. This explains
why Na cases leads to better performance than the Li cases above 30 bar; the higher performance
obtained from 1 to 10 for the Li cases is diminished by removing the uptake up to 5 bar due to the
basis. By extension, we can argue that the K cases will perform better than the Na cases above 100
bar.
We also calculated the excess gravimetric amount[85, 130] in wt% at 298 K. In the case of the
pristine frameworks at 100 bar, we obtained the best performance for MOF177 with 0.87 excess wt%,
followed by COF103 with 0.55 and MOF200 with 0.54. In our previous work, we compared the results
from theory and experiment for different pristine MOFs and COFs to validate our methodology.[96,
120, 121].
For the metalated compounds at 100 bar and 298 K, we obtained the best results for MOF200-Li,
with 4.87 excess wt% units, followed by COF102-Li, with 4.84, and by COF103-Li, with 4.68. We
found that for this pressure range the Li-metalated cases have a better performance than the Na
analogs, which have better performance than the K-metalated frameworks. Using the same general
principle given for delivery gravimetric units, but for this case the delivery basis is 0 bar, we expect
the Na-based frameworks will eventually outperform the Li cases, but at a pressure beyond 100 bar,
as Figures S14 and S15 suggest.
In a related work, we reported that IRMOF-2-96-Li reaches 5.6 excess wt% at 100 bar and 298
K,[121] while IRMOF-1-30-Li reaches 5.16 excess wt% at 100 bar and 298 K.[120] However, for
application purposes, the delivery amount is the important unit because it determines the usable
amount and here we have proven high excess amount uptake does not guarantee a high delivery
amount at different basis.
7.1.3.3

Volumetric Uptake

We also calculated the total, excess, and delivery amount based on volumetric units (g H2 /L) for
all these compounds (Figure 7.6).
For the delivery volumetric amount, we found almost the same behavior as with delivery gravimetric units. When using the basis of 1 bar, the Na analogs overcome the Li analogs at pressures
beyond 50 bar. The best performers at 100 bar and 298 K are COF102-Na with 24.9, followed by
COF102-Li with 23.8, COF103-Na with 22.8, COF103-Li with 21.7, and MOF177-Na with 21.4, all

111
b)
K-cases
Na-cases
Li-cases
Pristine

Figure 7.5: We show the correlation of pore volume (V P ) vs wt% delivery for different COFs: pristine
(dotted line), COF-Li (double dotted line), COF-Na (continuous line), and COF-K (dashed line).
In (a) 1 bar is used as the basis, while in (b) it is 5 bar. Different colors represent different pressures.
using delivery g H2 /L units.
On the other hand, when using the basis of 5 bar, the Na-based frameworks overcome the Li
analogs at 20 bar. Also, the K-analogs overcome the Li-analogs at around 100 bar (at 60 bar in the
case of MOF210) as we predicted it for the gravimetric uptake. At 100 bar and 298 K, we found
the best performers are COF102-Na with 21.6, followed by COF103-Na with 19.8, MOF177-Na with
18.2, COF102-K with 17.2, and COF102-Li with 17.1, using delivery g H2 /L units and basis equal
to 5 bar.
For the excess volumetric amount at 100 bar and 298 K, we found the best performers are
COF102-Na with 23.3, followed by COF102-Li with 22.2, then COF103-Na with 20.6, COF103-Li
with 19.8 and MOF177-Na with 19.5, with excess g H2 /L units. This is the same trend as the
volumetric delivery amount using 1 bar as the basis. These new frameworks perform better than
the best previously reported materials; MOF-C16-Li[120] (or IRMOF-1-16-Li) at 100 bar and 300
K reaches 17.3 excess g H2 /L, while IRMOF-2-54-Li[96] reaches 19.2 excess g H2 /L at the same
thermodynamic conditions.
None of these compounds reach the volumetric 2010 DOE target of 28 g H2 /L, but the closest
compounds to this quantity are COF102-Na and COF103-Na with 24.9 and 22.8 delivery g H2 /L
from 1 to 100 bar (while 21.6 and 19.8 delivery g H2 /L from 5 to 100 bar) at 298 K, respectively.
These are to the best of our knowledge the highest molecular hydrogen uptake for a porous material
in volumetric units under these thermodynamic conditions. Therefore, if a high delivery volumetric
uptake is to be targeted, these results still suggest that high S A and V P are both important, where
it should be remembered if V P is too large it could lead to a waste of space.

Figure 7.6: Delivery volumetric uptake obtained for the pristine, Li-, Na-, and K-metalated COFs and MOFs are shown. In (a) we used 1 bar as the
basis, while in (b) we used 5 bar as the basis. The error bars at each calculated point are shown, and in some cases, they are too small to fit inside
the symbols. Bulk H2 is shown for comparison.

112

113
Current analyzed COFs composed mainly of aromatic rings (COF102 and COF103) perform
better in volumetric units than analyzed MOFs because for the former most of the atoms are
accessible to interact with H2 . In contrast, these MOFs with Zn clusters in their structures have
zinc and oxygen atoms that are partially inaccessible (see inset of Figure 7.1). Also, a special case
is COF202, where the t-butyl group used in the formation of the borosilicate has four carbons and
one silicon atom per cab group that are partially unreachable as well (see Figure 7.1). This is, the
more partially or totally inaccessible atoms the framework has, the worst performance in volumetric
units, because these atoms that occupy space are not used to interact with H2 .
7.1.3.4

Isosteric Heat of Adsorption

We also calculated the isosteric heat of adsorption (Qst ) of these systems at 298 K. The unmetalated
systems remain flat around 3.5-5 kJ/mol, while the Li-metalated cases vary from 13 to 21 kJ/mol, the
Na-metalated cases are between 10 and 17 kJ/mol, and K-metalated frameworks window corresponds
to 8-10 kJ/mol (see Figure 7.7). From these results we observe that a flat curve of Qst with high
absolute value is better for the delivery amount (this is of course aside from the ideal Qst curve of
increasing interaction at higher pressure). This is because for the delivery amount we do not want
strong interaction energy at low pressure (below 1 or 5 bar), because this will bind a large number
of molecules that will be difficult to remove after a cycle. For example, when discharging from 100
to 1 bar, the molecules absorbed from 0 to 1 bar will not be used. This can be seen in the Li cases,
where they have the highest total uptake amount, but when we analyzed delivery units, they were
overcome by the Na cases, which have a flatter Qst curve. The K cases have a flatter curve than the
Na analogs; however, the absolute Qst value for Na cases is higher, therefore, they perform better
than K-based frameworks at a pressure below 100 bar. This is another explanation for why the
Na cases perform better at these delivery pressure ranges; Li cases bind too strongly to molecular
hydrogen at lower pressure, while Na cases bind softer, resulting in a higher delivery amount. While
K cases have a flatter surface, which is optimal for charge/discharge purposes, its absolute value is
too low to compete with the Na cases. Therefore, this study suggests that the next generation of
frameworks targeting hydrogen adsorption with high delivery amount should have a flatter Qst , and
the absolute value should be at least as high as 15 kJ to reach the DOE gravimetric targets.
7.1.3.5

Adsorption Mechanism of Molecular Hydrogen

The multiple configurations that the H2 framework needs to explore at room temperature in the
sorption process prompt us to analyze the mechanism from the ensemble average rather than single
snapshots (Figures 7.8,7.9,7.10). After averaging the ensemble of all configurations, we found that
the single layer mechanism is predominant for the metalated frameworks, while the pore filling
mechanism appears after the sites surrounding the alkaline metals have been covered. On the other

114

Figure 7.7: Heat of adsorption obtained for the pristine COFs and MOFs, as well as the analogs
metalated with Li, Na, and K. MOF180 and MOF205 as well as for the metalated cases are reported
in the SI. Top plots show the error bars at each calculated point, and in the bottom plots, the error
bars are too small to fit inside the symbols.
hand, for pristine COFs and MOFs, the pore filling mechanism is predominant, while there are not
clear evidence about the formation of single layers. Previous works on the topic did not address the
problem of the mechanism of hydrogen adsorption at room temperature; however, it is important
to discern if there is a characteristic mechanism because it provides a validation for which physical
model can be used to represent each sorption curve. In this case, we have proved at the atomistic
level, we can use the Langmuir model for metalated frameworks, while the BET model can be applied
for pristine compounds both at low saturation uptakes. Although the connectivity and the topology
of all these frameworks differ, the profile of the sorption at different pressures remains similar in all
of them.

Figure 7.8: We show the ensemble average of molecular hydrogen for COF102 (bottom) and COF102Li (top) at 298 K. Atom colors are C, gray; O, red; and B, pink; the average of molecular hydrogen
is shown in green. COF103 and COF103-Li have the same mechanism as COF102 and COF102-Li,
and they are not shown.

115

Figure 7.9: We show the ensemble average of molecular hydrogen for MOF177 (bottom) and
MOF177-Li (top) at 298 K. Atoms colors are Zn, purple; C, gray; O, red; and the average of
molecular hydrogen is shown in green. MOF200, MOF180, and MOF210 have a similar mechanism
to MOF177 and they are not shown; the same applies to their metalated analogs.

Figure 7.10: We show the ensemble average of molecular hydrogen for MOF205 (bottom) and
MOF205-Li (top) at 298 K. Atom colors are the same as in Figure 7.9.
7.1.3.6

Comparisons to Previous Computational Studies

Subsequent to our work showing the Li-doped MOFs could lead to substantial H2 adsorption at
room temperature,[120] Blomqvist et al.[131] used the generalized gradient approximation to density
functional theory by using the projector augmented wave (PAW) method to confirm our results for
Li-MOF5. However, if it is assumed that two Li atoms per benzene ring could be stable (one in each
face), then a corrected DFT functional for vdW interactions should be used such as M06, because
a function such as B3LYP would predict otherwise (Figure 7.2). Recently, Cao et al.[132] reported
the uptake on COF102-Li and COF103-Li using force field parameters obtained from DFT/PW91.
However, it is well-known that this level of DFT does not account for the London dispersion, so these

116
results likely underestimate the reversible binding.[122, 133] Therefore, these FF parameters have
a lower quality than our CCSD(T) and MP2 calculations to estimate the dispersion interactions.
This probably explains why they find a lower value for COF102-Li, with 4.25 effective wt% uptake,
while from our calculation, we obtain 4.42 effective wt% (what is called in the literature effective
amount[112] is what they define as excess amount), even though they report two Li atoms per
benzene-BO2 unit, while we report only one.

7.1.4

Concluding Remarks

We have calculated the gravimetric and volumetric uptake for the latest generation of COFs and
MOF, as well as their Li-, Na-, and K-metalated analogs. We also calculated the thermodynamics
for the formation of the Li-Bz adduct and found that its formation is favorable when THF is used.
We found that for the gravimetric delivery amount from 1 to 100 bar, eleven compounds reach
the 2010 DOE target of 4.5 wt %, while only two compounds reach the 2015 DOE target of 5.5 wt
% (MOF200-Li and MOF200-Na).
However, none of these compounds reach the volumetric 2010 DOE target of 28 g H2 /L, but the
closest compound to this quantity is COF102-Na, with 24.9 delivery g H2 /L. In general, an increase
in porosity (or pore volume) of MOFs or COFs leads to an increase in the gravimetric H2 uptake but
decrease in the volumetric H2 uptake. This can be seen when comparing MOF-200 and COF-102.
The best gravimetric H2 uptake is found in MOF-200 analogs, where pore volume is larger than
any other MOFs and COFs considered here; however, the best volumetric H2 uptake is found in the
COF-102 analogs, which have one of the smallest pore volumes. Therefore, to increase volumetric
uptake, it is better to consider MOFs or COFs with low pore volume (of around 1.8, but smaller
than 2 cm3 /g) at the expense of reducing the gravimetric uptake.
n summary, we recommend three ways to improve both gravimetric and volumetric delivery units:
(a) by creating compounds with high S A with all the atoms to be accessible, (b) by controlling the
V P to get the best compromise of used space (smaller V P leads to better volumetric delivery, while
bigger V P leads to a better gravimetric delivery), and (c) by aiming for a flat Qst curve, which can
be obtained when several strong sorption sites exist. According to the present work, a constant Qst
value at least 15 kJ/mol should be obtained in order to reach the DOE gravimetric goal.

117

7.2

Dependence of the H2 Binding Energies Strength on the
Transition Metal and Organic Linker

Jose L. Mendoza-Cortes, Hiroyasu Furukawa, Omar M. Yaghi, William A. Goddard III, 2012

7.2.1

Introduction

A current major obstacle to molecular hydrogen (H2 ) as an alternative source of energy is the
difficulty of storage at opera tional temperatures. The U.S. Department of Energy (DOE) has set
the 2015 targets of 5.5 wt % and 40 g/L at 233-358 K and 3-100 bar (and ultimate 7.5 wt %
and 70 g/L).[117, 118, 134] Among the most promising routes to obtain this goal is physisorption
because is fully reversible and has fast kinetics at desired condi tions. However, current materials
have been able to attain <10 kJ/mol at ambient conditions and this decays as the sorption sites get
saturated.[121, 135] Thus, sorption sites that are able to ac commodate more H2 molecules and have
a stronger affinity for H2 are needed. We and others have found that this necessary to keep a constant
heat of adsorption (Qst) as the loading increase and to be efficient for the loading/unloading cycle,
which are requirements for materials to attain the DOE targets.[135, 58] There have been several
theoretical studies that try to put stronger interactions between H2 and the material host, however
they still have to be synthesized.[120, 115, 136, 137]
We have speculated that using transition metal sites in the structures of porous materials can
reach this goal.[138, 139] Our trials have been focusing in using precious late transition metals
(TM) such as Pd. In this paper we show that it is not necessary to use such precious and heavy
TM to obtain good binding energies with H2 . We report the binding energy of 4 H2 interacting
with 60 compounds (6 linkers with 12 different transition metals). We found that early TM (Sc
to Cu) can attain the same strength of interactions as precious late transition metals (Pd and
Pt). We also report that the square planar coordination geometry is not necessary to obtain many
strong interactions because the tetrahedral geometry gives similar affinity. This is maybe because
we are dealing with mainly long range interactions and the local geometrical environments is not
determinant as in the covalent bond formation. We focus on the ligands (building blocks) used for
synthesizing porous materials since it is easier to calculate the binding energy to these smaller species
and at the fundamental level, there is not a significant difference with the extended structure.
7.2.1.1

Types of Interactions for H2

There are several interactions that H2 can have with other atoms, molecules or solids, which are
dispersion, electrostatics and orbital interactions.[140, 2] The nature and magnitude of these interactions are shown in Table 7.5 and Figure 7.11. The existence of each of these interactions can allow

118
us to tune the ∆H ◦ bind to obtain the optimal value.
Table 7.5: Different interactions H2 can have with other entities that can be
used to tune the ∆H ◦ ads
Interaction

Energy dependence

Charge - quadropole
Charge - induced dipolea
Dipole - induced dipolea
Dispersion
Orbital interaction

Typical values (kJ/mol)
∼3.5 [140]
∼6.8 [140]
∼0.6 [140, 141]
∼5-6 [58]
∼20-160 [2, 142, 143, 144]

1/r
1/r4
1/r5
1/r6
< vdW radii

If a strong external field is present; a dipole can be induced in H2 if a strong
external field is present.

Non covalent interaction

Orbital interaction

δ+

Charge Quadropole

δ−

δ+

dxz

δ+
δ−

Dipole Induce dipole*

δ+

δ−
δ+

δ−

-11.7 eV
[M]

δ−

δ+
δ+
δ−

δ+

[M]---H2

H-H bond distance

δ+

δ−
δ+
δ−
δ+

δ+

Dispersion

L L
L M
LL

δ−

σ∗

δ−

Charge Induce dipole*

+2 eV

δ−

0.75 Å

0.8-1.0 Å

True H2
complex

1.0-1.3 Å

Elongated H2
complex

1.3-1.6 Å

>1.6 Å

compressed
dihydride

dihydride

reversibility of H2 binding

Figure 7.11: Interactions H2 can have; noncovalent interactions and orbital interactions. The molecular orbital diagram and the H-H bond distances (from crystallography and NMR) are adapted from
reference [2]. (*) A strong external field is needed to create a dipole in H2 .
Non covalent interactions (electrostatic and dispersion) have a typical ∆H ◦ ads value of less than
10 kJ/mol while orbital interac tion have values larger than 20 kJ/mol.
The first non-zero multipole moment for H2 is the quadrupole moment due to their non-spherical
nature and this interaction is responsible for most interactions in bulk H2 . However if other species
interact with H2 , other electrostatic interactions can appear such as charge - quadrupole. If a strong
external field is applied, then a dipole can be induced in H2 and generate other interactions such
as charge - induced dipole and dipole - induced dipole.[140, 141] The charge - H2 interactions are
difficult to appear because we need unscreened coulombic interactions which are rarely present in

119
many systems, although some examples have been discovered in the so called open metal sites.[145]
The other ubiquitous non covalent interaction is dispersion, and this is responsible for the interaction
of H2 with carbonaceous materials such a graphite and carbon nanotubes.[58]
Orbital interactions require either a very high pressure of 490 GPa[146] or d-orbitals of transitions
metals (TM) to appear.[2, 142, 143, 144] The use of the d-orbital of TM is the most obvious choice
because of the constraint of using up to 100 bar of pressure. The orbital interactions have different
magnitude depending on the TM and the ligands used, and ultimately affect the H-H bond. The
more the H-H bond elongates the higher the interaction and the less reversible the binding is (Figure
7.11 and Table 7.5).
We need all these different kind of interaction in order to obtain strong interactions with H2 but
without modifying the H-H bond length significantly in order to obtain reversibility. For example
combinations of charge - quadrupole, dispersion as well as orbital interactions can give us the interaction ion - H2 and ligands - H2 in a range 0.4-35 kJ/mol by changing the charge on the ligand
or the ligand itself.[140] Thus ligands that bind to transition metals can have different binding sites
and by designing the counteranion, we can obtain different kinds of strong enough interactions with
H2 .
7.2.1.2

Langmuir Theory and the Optimal Enthalpy

In this paper we consider the single layer approximation of the Langmuir model to get an estimation
of the optimal en thalpy needed for maximum delivery. Previous work done by Bathia et al.,[58] has
shown that this approximation is a good estimation for the H2 sorption on porous materials such
as graphite and carbon nanotubes. This is an acceptable first order approximation because H2 is a
small molecule and the H2 - H2 interactions are not very important.
With the Langmuir theory we can determine the uptake (n) and we can determined the necessary
properties to get the delivery amount (D):[147]

D(K, Pmax , Pmin =

KPmax nm
KPmin nm
1 + KPmax
1 + KPmin

(7.2)

where K is the equilibrium constant from the Langmuir theory at certain temperature, Pmax and
Pmin are the maximum and minimum pressure of the delivery and nm is the adsorption capacity of
the material. The maximum delivery amount can be found by finding the optimal K. Thus from
∂D/∂K = 0, the optimal value is K opt =1/( Pmax Pmin ).[58, 147, 148]

Therefore, from K opt =(e∆S /R )(e∆H /RT )/P0 , where ∆S0 is the entropy change, ∆H 0 is the
enthalpy change and the reference pressure, P0 = 1 bar, we obtain the optimal binding value;
RT
∆H opt = T ∆S +
ln

Pmax Pmin
P02

(7.3)

120
Bathia et al. reported that for various porous adsorbents a typical value for the H2 adsorption
is ∆S0 ≈ -8R.[58] Assuming this ∆S0 value for the temperatures range of the DOE targets, we can
estimate the optimal values for ∆H ◦ opt for a homogenous material (same type of binding site).

In Table 7.6, we show the optimal values calculated for the 2015 DOE goals. We are going to
focus on the Fuel Cell (FC) delivery condition for 3/100 atm delivery limits but the same arguments
can be applied to the Internal Combustion Engine (ICE) case. At 233K the optimal enthalpy change
(∆H ◦ opt ) is equal to -10.0 kJ/mol. On the other hand at 358K the ∆H ◦ opt = -15.3 kJ/mol. A
second order approximation is undergoing.
Table 7.6: DOE targets for H2 storage system for light-duty vehicle and the
estimation of the optimal ∆H ◦ ads under these conditions using the Langmuir
model
Storage parameter

Units

2015

System gravimetric capacity
System volumetric capacity
Min/Max delivery temperature
Min/Max delivery pressure FCa
(This work ) FCa
Min/Max optimal ∆Hopt

kg(H2 )/kg(System)
kg/m3
atm
kJ/mol

0.055
40
233/358
3/100
-10.0/-15.3

FC = fuel cell

In order to show how ∆H ◦ affects the delivery amount we plot the different uptakes at 298K
in Figure 7.12. We can see how the optimal value strength of 12.8 kJ/mol at 298K offers the best
enthalpy of adsorption for the delivery amount for the range from 3 to 100 bar. The maximum
delivery value calculated with these assumptions is of 0.709 (Table 7.7).

Figure 7.12: We show the normalized uptake (n/nm = uptake/sorption capacity) for three different
temperature conditions (left: 233K, center: 298K, right: 358K) using the Langmuir model and ∆S◦
= -8R. We can see that the magnitude ∆H ads have a strong effect on the amount that can be
delivered between 3 and 100 bar, i.e., a small value (3 kJ/mol) gives poor uptake and poor delivery,
a large value (25 kJ/mol) gives high uptake but poor delivery. The ideal ∆H ads gives both a high
uptake and high delivery.
Therefore, using these premises we embark ourselves in finding new ligands that can have a
binding energy between 10 and 15.3 kJ/mol in order to get the optimal delivery amount for the
DOE targets (233/358 K) by exploiting all the different types of interactions that the H2 can have.

121
Table 7.7: Delivery amount obtained using ideals
∆H ◦ ads and different temperatures
Temperature(/K)

∆H ◦ opt
(/kJ mol-1)

Deliverya
(3 to 100 bar)

233
298
358

-10
-12.8
-15.3

0.709
0.709
0.709

7.2.2

We have normalized the Delivery amount usKPmin
KPmax
− 1+KP
ing D(K, Pmax , Pmin /nm = 1+KP
max
min
where the maximum delivery is close to 1.

Computational Details

To estimate the interactions between H2 and the different linkers (with and without TM), we used
the M06[122] hybrid DFT functionals that contains corrections for dispersion interactions as implemented in the Jaguar code.[9] Here we used the 6-31G**++ basis set for the light elements. For
the TM we used the Los Alamos LACVP**++ electronic core potential which includes relativistic
corrections.[10] The unrestricted open shell procedure for the self-consistent field calculations was
used for all spin states. All geometries were optimized using the analytic Hessian to determine that
the local minima have no negative curvatures (imaginary frequencies). The vibrational frequencies
from the analytic Hessian were used to calculate the zero-point energy correction at 0 K.
For our calculations we used the following nomenclature,
∆H ◦ bind = ∆H ◦ host+H2 − ∆H ◦ host − ∆H ◦ H2

(7.4)

Where ∆H ◦ bind is the binding enthalpy of H2 to the host, and it represents our estimation of
∆H ◦ ads . ∆H ◦ host is the enthalpy of the host or linker and ∆H ◦ H2 is the enthalpy of the free H2 .
From here on, we use the term binding energy instead of binding enthalpy.
We first find the ground state for a given spin (s) according to the oxidation for the TM. For our
cases we studied the most common oxidation state of the TM. We also explore the most favorable
geometry given the electronic spin state; Tetrahedral (Tet) versus Square Planar (Sqr) when applicable or Trigonal bipyramidal (Tbi) versus Square pyramidal (Spy). The other geometries studied
depending on the number ligands are Octahedral (Oct) and Pentagonal bipyramidal (Pbi). Therefore we used the first row transition metals from Sc to Cu because we consider they should be light
and abundant. We also include Pd(II) and Pd(0) for comparison.
For the nucleophilic transition metals, we explore:
* Sc(III), geometry = Spy, Tbi with s = 0;
* Ti(IV), geometry = Oct with s = 0;
* V(V), geometry = Pbi with s = 0;

122
* Cr(III), geometry = Spy, Tbi with s = 1/2, 3/2;
While for the electrophilic transition metals, we studied:
* Mn(II), geometry = Tet, Sqr with s = 1/2, 3/2, 5/2;
* Fe(II), geometry = Tet with s = 0, 2/2;
* Co(II), geometry = Tet, Sqr and s = 1/2, 3/2;
* Ni(II), geometry = Tet, Sqr with s = 0,2/2;
* Cu(II), geometry = Sqr with s = 1/2;
* Pd(II) and Pd(0), geometry = Sqr with s = 0;
All the geometries and their energies are contained in the supplementary information. Pd is
studied to get a comparison to precious metals. The geometry that we show is the ground state
along with the spin state and all the ∆H ◦ bind are calculated based on these structures. When the
Square and Tetrahedral structure converge to the same coordinates (or Trigonal bipyramidal and
Square pyramidal), only one of them is presented. For the V(V) case, we found that the metal does
not bind to the linker but interacts mostly by columbic interactions.

7.2.3

Results and Discussion

7.2.3.1

Current Linkers Used in Porous Frameworks

With the objective of generating sites for metalation we have developed new COFs with the imine
and hydrazide linkage.[149, 150] Also we have post-modified MOFs in order to have metals on the
bridging ligands.[138, 139] Figure 7.13 summarize the linkers where we have purposely created sites
to host metals on it. We also show the bipyridine ligands commonly used for the synthesis of MOFs
and recently also in COFs.

BBH

BPY

BPYM

PIP

PIPE

PIA

Figure 7.13: Connectivity developed in linkers used for COFs and MOFs where sites for metalation
are present. The pink circle indicates the sites where transition metals can be placed.
Ligand Containing the Hydrazide binding group.

123
The first linker we calculate the binding energies for is the hydrazide containing linker; (E)N’-benzylidenebenzohydrazide (BBH) shown in Figure 7.13. Our synthetic efforts have produced
two Covalent Organic Frameworks with this connectivity which denominated COF-42 and COF43.[150] In the spirit of knowing which transition metal would have the best binding energy to H2 ,
we calculate the interactions of such compounds using first row transition metals (Sc to Cu) as
well as Pd. While Pd is a heavy precious metal, we wanted to explore if the square predominant
geometry can have an effect given the closed shell electronic nature of this metal. Thus we include
the Pd(II)Cl2 case. The numerical results are shown in Table 7.8 and plotted in Figure 7.14.
Table 7.8: Binding energies (∆H ◦ bind ) obtained for the ground state of linker BBH and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln + H2 . The H-H
bond of isolated H2 is 0.741 Å
Linker =
BBH

Geom
for M

Spin
(s)

n H2

∆H ◦ bind
(kJ/mol)

H-H bond
(Å)

Linker
+ Sc(III)Cl3
+ Ti(IV)Cl4
+ V(V)Cl5
+ Cr(III)Cl3
+ Mn(II)Cl2
+ Fe(II)Cl2
+ Co(II)Cl2
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pd(II)Cl2

N/A
Spy
Oct
Oct
Spy
Tet
Tet
Tet
Tet
Sqr
Sqr

3/2
5/2
2/2
3/2
2/2
1/2

1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4

-6.16, -6.13, -6.08, -6.05
-12.2, -12.1, -11.9, -11.6
-12.7, -12.6, -12.5, -12.4
-11.7, -10.9, -10.4, -9.60
-17.6, -12.5, -12.2, -11.5
-20.1, -13.1, -13.0, -12.8
-12.4, -12.3, -12.3, -12.3
-14.0, -13.2, -12.8, -12.3
-16.5, -16.3, -14.9, -14.0
-14.0, -13.8, -13.6, -12.4
-12.3, -12.0, -11.4, -11.3

0.745, 0.745, 0.745, 0.744
0.745, 0.745, 0.745, 0.743
0.745, 0.745, 0.745, 0.744
0.747, 0.746, 0.746, 0.745
0.747, 0.746, 0.745, 0.744
0.748, 0.747, 0.746, 0.746
0.748, 0.748, 0.748, 0.748
0.749, 0.748, 0.747, 0.747
0.747, 0.747, 0.746, 0.744
0.746. 0.746, 0.745, 0.744
0.746, 0.746, 0.745, 0.745

The first H2 interacts strongly with the metal but it does not form a hydride.

Cln

TM
Cl

(E)-N'-benzylidenebenzohydrazide
BBH+TMCln

Figure 7.14: Different binding energies ∆H ◦ bind at 298K obtained for BBH ligand interacting with
four physisorbed H2 . We have focused on isoelectronic TM. PdCl2 is shown for comparison. The
error bars estimate the different configurations. Mn(II), Cr(III) and Ni(II) show strong interactions
with the first H2 but there is no evidence of formation of hydride (Table 7.8).
We found that the ligand BBH alone does not interact strongly with the hydrogen molecule

124
(∆H ◦ bind = -6.16, -6.13, -6.08 and -6.05 kJ/mol for the 1st to 4th H2 , respectively). However,
we found that if this ligand is bound to the TM, this interaction energy increases. Also, all of
studied TM interacting with H2 have the correct energy to maximize the delivery amount for the
temperature range needed by the DOE.
For all these cases, Sc to Cu and Pd(II), the H2 does not bind chemically to the TM. We found
strong interaction between the first H2 with Cr(III), Mn(II) and Ni(II) but there is no evidence for
the formation of hydride due to the still short H-H bond and the small value of the energetics. For
the case of BBH-Cr(III)Cl3 , the first H2 interacts strongly with the Cr(III)Cl3 center forming an
octahedral environment Cr(III)Cl3 L2 (η 2 -H2 ), where L2 represents the two binding sites of ligand
BBH. This first H2 has ∆H ◦ bind = -17.6 kJ/mol while the H-H bond is 0.747 Å. The Cr-H2 is long
to be considered a true chemical bond; 2.57 and 2.58 Å. This quasi-complex BBH-Cr(III)Cl3 (η 2 -H2 )
then serves as the host for other physisorbed H2 with values of ∆H ◦ bind = -12.5, -12.2 and -11.5
kJ/mol for the 2nd to 4th H2 , respectively. The H-H bond distance for these physisorbed H2 are
0.746, 0.745, 0.744 Å, which are comparable to the isolated H2 (0.741 Å).
The other strong interaction with the first H2 occurs when using BBH-Mn(II)Cl2 . The first H2
forms a quasi-complex Mn(II)Cl2 L2 (η 2 -H2 ) with a distorted trigonal bipyramidal environment for
the Mn(II) where L2 represents the two binding sites of ligand BBH and with the η 2 -H2 occupying
the equatorial positions. The ∆H ◦ bind = -20.1 kJ/mol and the H-H bond for this first H2 is of 0.748
Å, which shows there is no hydride formation. This also can be observed by the Mn-H2 distances
which are 2.48 and 2.49 Å. This shows that the strong interactions comes from dispersive forces and
presumably to some coulombic interaction between the Mn(II)Cl2 and the quadrupole moment of
H2 . This quasi-complex formed by BBH-Mn(II)Cl2 (η 2 -H2 ) then interacts with more H2 to a smaller
degree. The strength of the interaction with the 2nd , 3rd and 4th H2 is -12.5, -12.2 and -11.5 kJ/mol,
respectively. This is consistent with a short H-H bond of 0.747, 0.746 and 0.746 Å, respectively, on
these H2 .
The third compound with a strong relative interaction with H2 is the BBH-Ni(II)Cl2 . The first
H2 interacts strongly with the tetrahedral center formed by Ni(II)L2 Cl2 where L2 represents the
two binding sites of ligand BBH. The strength for this interaction is ∆H ◦ bind = -16.5 kJ/mol and
the H-H bond for this H2 is of 0.747 Å. For this case there is no η 2 -H2 binding to the metal center.
Instead we found that the H2 interacts mainly with the Cl− ligand, this is observed because of the
Cl− H2 distance of 2.86 and 3.60 Å, which are shorter than the Ni(II)-H2 distances (3.90 and 4.50
Å). For this case, there is a second H2 that interacts strongly with the BBH-Ni(II)Cl2 center, which
is located on the opposite side of the ligand. The interaction strength is very similar to the first H2
as it can be observed with the ∆H ◦ bind = -16.3 kJ/mol and the H-H bond of 0.747 Å. The distance
for the Ni(II)-2nd H2 are 2.89 and 3.63 Å, while the Ni-H2 distances are longer (3.49 and 4.02 Å).
This suggests that the same kind of interaction observed for the 1st H2 occurs in the 2nd H2 . The

125
3rd and 4th H2 interacts less strongly with the Ni(II)L2 Cl2 as it can be observed by the values of
∆H ◦ bind = -14.9 and -14.0 kJ/mol, respectively. The H-H bonds distance for these physisorbed H2
are 0.746 and 0.744 Å. This is an example of how the counter anion, in this case Cl− , can work as
center where the H2 can interact strongly.
The rest of the TM studied exhibits a very similar behavior with ∆H ◦ bind that ranges from
11-14 kJ/mol for the 1st -4th interacting H2 (Table 7.8 and Figure 7.14). These TM; Sc(III), Ti(IV),
V(V), Fe(II), Co(II), Cu(II) and Pd(II) which have Cl as the counter anion, exhibit H-H bond for
the interaction with H2 in the range of 0.743-0.749 Å. All these elements have different coordination
shell (Square pyramidal, Octahedral, Tetrahedral and Square planar) but similar ∆H ◦ bind which
suggests that the interactions with H2 do not depend strongly on the geometry that the TM adopts.
These elements also have different oxidation states and the interaction strength is still in similar
range, this also supports the hypothesis that the long range interactions depends poorly on the TM,
oxidation state and geometry of the coordination shell when there is not η 2 -H2 interaction.
The case of the Fe(II) and Co(II) are puzzling because they have the largest H-H bond distance
for the interacting H2 but they have the energetics in the normal range of -14 to -12 kJ/mol. For
the compound BBH-Fe(II)Cl2 where the coordination geometry for the TM is tetrahedral, we have
∆H ◦ bind = -12.4, -12.3, -12.3 and -12.3 kJ/mol for the 1st to 4th H2 , respectively. And the H-H
bond corresponds to each distance 0. 748 Å. A similar behavior occurs for the BBH-Co(II)Cl2
case, where the ∆H ◦ bind = -14.0, -13.2, -12.8 and -12.3 kJ/mol and the H-H bond is 0.749, 0.748,
0.747, 0.747 Å, for the 1st to the 4th interacting H2 , respectively. These compounds combined with
the BBH-Mn(II)Cl2 and the BBH-Ni(II)Cl2 cases which also have tetrahedral geometry for the
TM, strongly propose that the TM tetrahedral generates the most distortion for the interacting H-H
bond.
The square geometry for the TM can be observed for the cases of BBH-Cu(II)Cl2 and BBHPd(II)Cl2 . The interaction strength for these cases is also ordinary, on the range of -14 to -11 kJ/mol
for the four interacting H2 . There is also not a big distortion in the H-H bond, with this distance
ranging from 0.744 to 0.746 Å. Contrary to what we should expect, the square geometry does not
give a better interaction for more H2 bounded to the complex. For example, for BBH-Cu(II)Cl2 ,
the first H2 bind with ∆H ◦ bind = -14.0 kJ/mol while the interaction strength drops for the 4th H2
to ∆H ◦ bind = -12.4 kJ/mol. The same behavior is observed for the BBH-Pd(II)Cl2 complex. The
first H2 bind with ∆H ◦ bind = -12.3 kJ/mol while the interaction strength drops to ∆H ◦ bind = -11.3
kJ/mol for the 4th H2 . This supports the hypothesis that the geometrical coordination for the TM
does not determinant the strength of the interactions with H2 when there is not η 2 -H2 interaction.
In the case BBH-V(V)Cl5 , there is only a coordination with the O from the C=O of the BBH
but not with the N of the imine. This can be observed by the long N-V of 3.93 Å, and the short O-V
distance of 2.29 Å. However the V(V) is coordinated to the five Cl− with a distance of 2.125, 2.208,

126
2.213, 2.218, and 2.290 Å. This complex has an octahedral geometry with ∆H ◦ bind = -11.7, -10.9,
-10.4 and -9.6 kJ/mol. The other compounds with octahedral geometry is BBH-Ti(IV)Cl4 where
both coordination sites of BBH are used. The strength of the interaction with H2 is ∆H ◦ bind =
-12.7, -12.6, -12.5 and -12.4 kJ/mol which is similar to the V(V) analog. In both cases the H-H bond
distance is around 0.745 Å. At the beginning of these studies we speculated that the octahedral
geometry would hindrance the interaction of the TM with the H2 , however this interaction is still
comparable to those interaction obtained from tetrahedral and square geometry.
While we focused on the ground state for the TM interacting with H2 , we also explore the effect
of having other spin for the same oxidation state. The first example is BBH-Mn(II)Cl2 , where we
found the ground state to be s = 5/2. However, if s = 1/2 would be synthesized, the interaction
with H2 will drop by 8 and 1 kJ/mol (∆H ◦ bind = 12.3 and 12.1 kJ/mol) for the 1st and 2nd H2 ,
respectively. The second example we study is the case of BBH-Co(II)Cl2 where the ground state
was found to be s = 3/2, however if the s = 1/2 were synthesized, the interaction with H2 would
fall by more than 1 kJ/mol (∆H ◦ bind = 13.0 and 12.8 kJ/mol) for the 1st and 2nd H2 . A similar
trend occurs for BBH-Ni(II)Cl2 , where we found that the ground state is s = 2/2 but if the s =
0 were synthesized, the interaction to H2 would decrease by more than 3 kJ/mol (∆H ◦ bind = 12.8
and 12.8 kJ/mol for the 1st and 2nd H2 , respectively). For the Ni case, the geometry for s = 2/2
is tetrahedral while for s = 0 is square planar, therefore contrary to what should be expected even
when the square environment can have a closer interaction than the tetrahedral case, the tetrahedral
case interacts more strongly with H2 due to their unpaired spin electrons.
Although the difference in energy is minimal, we can say that in general the high spin TM interact
more strongly with H2 than the slow spin analog. In all our cases the high spin was the ground
state and this correspond to a Tet or Oct geometry however the Ni(II) low spin correspond to Sqr
geometry and still gets less energy interaction with H2 . These observations suggest once again that
geometrical difference in the coordination sphere influences to a lesser degree than the spin state for
this kind of long range interactions.
Ligand containing the Imine binding group.
Our efforts to synthesis other kinds of COFs lead us to the developed the imine connectivity.[149]
In this case the main linker used for the synthesis is (E)-2-((phenylimino)methyl)phenol (PIP). While
the acid-basic conditions can varied we also explored the binding energy to H2 of the un-protonated
analog of this linker; (E)-2-((phenylimino)methyl)phenolate (PIPE). We studied the same TMs; Sc
to Cu as well as Pd(II) for comparison between early transition metals and rare-earth elements. The
results for the protonated and un-protonated linkers are shown in Table 7.9 and Figure 7.15.
The PIP and PIPE ligands do not interact strongly with the H2 . Our calculations show that
PIPE interacts more strongly than PIP with H2 . PIP have ∆H ◦ bind = -5.96, -5.92, -5.90 and
-5.88 kJ/mol for the 1st to the 4th interacting H2 . On the other hand, PIPE have ∆H ◦ bind = -9.25,

127
Table 7.9: Binding energies (∆H ◦ bind ) obtained for the ground state of linkers PIP and PIPE
and different number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln + H2 .
The H-H bond of isolated H2 is 0.741 Å
Linker =
PIP

Geom
for M

Spin
(s)

n H2

∆H ◦ bind
(kJ/mol)

H-H bond
(Å)

Linker
+ Sc(III)Cl3
+ Ti(IV)Cl4
+ V(V)Cl5
+ Cr(III)Cl3
+ Mn(II)Cl2
+ Fe(II)Cl2
+ Co(II)Cl2
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pd(II)Cl2

N/A
Spy
Oct
Oct
Spy
Tet
Tet
Tet
Tet
Sqr
Sqr

3/2
5/2
2/2
3/2
2/2
1/2

1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4

-5.96, -5.92, -5.90, -5.88
-12.7, -12.3, -12.1, -11.9
-11.6, -11.4, -11.3, -10.5
-11.0, -10.9, -10.5, -10.2
-20.2, -11.6, -11.0, -11.9
-19.5, -13.0, -12.9, -12.5
-12.9, -12.9, -12.7, -12.4
-14.2, -13.9, -12.4, -12.2
-11.9, -11.9, -11.7, -11.7
-16.2, -16.1, -15.2, -13.4
-13.4, -13.2, -12.7, -11.7

0.745, 0.745, 0.745, 0.744
0.746, 0.745, 0.744, 0.744
0.745, 0.744, 0.744, 0.743
0.745, 0.745, 0.745, 0.744
0.747, 0.745, 0.745, 0.744
0.748, 0.747, 0.746, 0.745
0.747, 0.747, 0.746, 0.746
0.746, 0.746, 0.744, 0.743
0.746, 0.745, 0.744, 0.743
0.746, 0.746, 0.746, 0.744
0.746, 0.745, 0.745, 0.744

Linker =
PIPE

Geom
for M

Spin
(s)

n H2

∆H ◦ bind
(kJ/mol)

H-H bond
(Å)

Linker
+ Sc(III)Cl3
+ Ti(IV)Cl4
+ V(V)Cl5
+ Cr(III)Cl3
+ Mn(II)Cl2
+ Fe(II)Cl2
+ Co(II)Cl2
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pd(II)Cl2

N/A
Spy
Oct
Oct
Spy
Tet
Tet
Tet
Tet
Sqr
Sqr

3/2
5/2
2/2
3/2
2/2
1/2

1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4

-9.25, -9.16, -9.08, -8.90
-12.8, -12.7, -12.3, -12.2
-12.9, -12.7, -12.6, -12.0
-11.8, -11.6, -11.1, -10.8
-16.6, -13.1, -13.0, -12.6
-16.4, -13.9, -13.8, -13.7
-14.9, -14.8, -14.0, -13.7
-14.4, -14.1, -14.1, -13.7
-14.6, -14.5, -14.2, -13.5
-15.7, -15.4, -14.0, -13.8
-14.5, -14.5, -13.6, -13.2

0.747, 0.747, 0.746, 0.745
0.746, 0.746, 0.745, 0.745
0.746, 0.745, 0.745, 0.745
0.745, 0.745, 0.745, 0.744
0.747, 0.746, 0.746, 0.746
0.749, 0.749, 0.749, 0.748
0.748, 0.747, 0.746, 0.746
0.747, 0.747, 0.745, 0.745
0.748, 0.747, 0.747, 0.744
0.747, 0.747, 0.746, 0.746
0.746, 0.746, 0.746, 0.745

The first H2 interacts strongly with the metal but it does not form a hydride

-9.16, -9.08 and 8.90 kJ/mol for the 1st to the 4th interacting H2 , this is more than 3kJ/mol stronger
than the neutral analog. This is expected since unscreened coulombic interactions give around 3.5
kJ/mol of additional interaction with the quadrupole moment of H2 (Table 7.5).
All of the ground states configurations were used to determine the interactions with H2 . The
interaction with H2 is only stronger for the negative ligand alone, since this trend is not universal
when a TM is bound to the PIPE ligand, presumably because the negative charge of the O- is
transferred to the TM center and there is no longer an effective negative charge (Table 7.9 and
Figure 7.15).
We found that almost all the compounds of the form PIP+TM(n)Cln or PIPE+TM(n)Cln do
not bind chemically to the first H2 . However we found that the Cr(III), Mn(II) and Cu(II) cases
interact strongly with the first H2 . For example the complex PIP-Cr(III)Cl3 interacts with the 1st
H2 giving ∆H ◦ bind = -20.2 kJ/mol. The analog case PIPE-Cr(III)Cl3 gives a ∆H ◦ bind = -16.6
kJ/mol. In both of these cases, the geometry for the TM is Square pyramidal and the first H2 binds

128

Cln

(E)-2-((phenylimino)methyl)phenol
PIP+TMCln

Cln

Cl
(E)-2-((phenylimino)methyl)phenolate
PIPE+TMCln

Figure 7.15: Different binding energies ∆H ◦ bind at 298K obtained for the PIPE ligand interacting
with four physisorbed H2 . PdCl2 is shown for comparison. The error bars estimates the different
configurations. Mn(II), Cr(III) and Cu(II) show strong interactions with the first H2 but there is
no evidence of formation of hydride (Table 7.9).
to the bottom of the pyramid forming an octahedral environment for the TM where there is a η 2 -H2
interaction. In the case of PIP-Cr(III)Cl3 (η 2 -H2 ) the Cr-H2 distance is 2.488 and 2.502 Å. For
analog PIPE-Cr(III)Cl3 (η 2 -H2 ) the Cr-H2 distance is longer with 2.525 and 2.544 Å. These ligandCr(III)Cl3 (η 2 -H2 ) complexes then serves as the host for the following 2nd to 4th H2 . The strength
for these latter H2 is around 11 to 13 kJ/mol with an H-H bond of 0.745-0.746 Å, with a slightly
stronger interaction for the PIPE case.
In a similar fashion the PIP-Mn(II)Cl2 complex interacts strongly with the 1st H2 with ∆H ◦ bind
= -19.5 kJ/mol, while PIPE-Mn(II)Cl2 gives ∆H ◦ bind = -16.4 kJ/mol. In the case of the PIP complex the H2 forms a PIP-Mn(II)Cl2 (η 2 -H2 ) where the geometry is a distorted trigonal bipyramidal
with the η 2 -H2 and the binding sites of the PIP ligand occupy the equatorial positions while the Cl−
occupies the axial positions. The distances for the Mn-H2 are 2.65 and 2.67 Å. The same geometry
and type of interaction is obtained for the negative analog link that forms PIPE-Mn(II)Cl2 (η 2 -H2 ).
The distances for the Mn-H2 are 2.66 and 2.67 Å, which are similar to the PIP case. The following

129
2nd to 4th H2 binds with a weaker ∆H ◦ bind of around -13.9 to -12.5 kJ/mol. The H-H bonds in all
these interactions ranges from 0.745 to 0.749 Å.
The other TM that has a strong interaction with the first H2 is Cu(II). In this case, we observe
that the 2nd H2 also interacts as strong as the 1st one. The PIP-Cu(II)Cl2 interacts with the 1st
and 2nd H2 with ∆H ◦ bind = -16.2 kJ/mol and -16.1 kJ/mol, respectively. This is the same scenario
for the complex PIPE-Cu(II)Cl2 with ∆H ◦ bind = -15.7 kJ/mol and -15.4 kJ/mol for the 1st and
2nd H2 , respectively. In any of these interactions there is no evidence for η 2 -H2 . The distances for
the Cu-1st H2 in the PIP-Cu(II)Cl2 are 2.785 and 3.182 Å, while for the Cu-2nd H2 the distances
are 3.438 and 3.963 Å. This shows the asymmetry of this interaction. On the other hand, the
distances for the Cu-1st H2 in the PIPE-Cu(II)Cl2 case are 2.87 and 3.31 Å, while for the 2nd H2 ,
the distances are 2.93 and 3.49 Å. In this case, the square planar geometry for the Cu is distorted.
For the next H2 interacting with these complexes the ∆H ◦ bind ranges from -15.2 to -13.4 kJ/mol.
In general also the H-H bond is not perturbed significantly since the range for the distances are
from 0.744 to 0.747 Å. Thus the square planar geometry for this ligand has a preference because the
interaction with H2 is mild but the interaction strength does not drops drastically for the subsequent
H2 . The geometries for the Mn(II) and Cu(II) are Tetrahedral and Square planar, respectively, and
the stronger interaction is for the Tetrahedral geometry when compared to the square geometry, as
in the BBH ligand.
The other TMs have mild interactions with H2 , the ∆H ◦ bind ranges from -14.9 to -10.2 kJ/mol.
This is the ideal range for maximum delivery under the assumption presented in this work, and our
results suggest that any of the TMs presented here with their respective oxidation state should give
optimal delivery amount of H2 . In general the tetrahedral and square planar geometry for the TM
gives the stronger interaction followed by the Square pyramidal and Octahedral geometry.
In most of the cases the TM coordinates to the PIP or PIPE ligand. However the V(V) does
not coordinate with the PIP ligand and it weakly coordinates to the O in the PIPE ligand. In
the formation of the interaction between PIP and V(V), the bonds are too long to be considered
coordination bonds, the values for the V-O and V-N distances 3.53 and 3.81 Å. This makes the
V(V)Cl5 complex to have a quasi-square pyramidal geometry. A similar case happens for the PIPEV(V)Cl5 where the V(V) coordinates this time waekly to the O- of the PIPE ligand. The distance
for the V-O and V-N are 1.77 and 3.86 Å. The interaction of the V(V)Cl5 complex with the O of
the PIPE, makes the geometry of the TM to be octahedral. Both cases (PIP V(V)Cl5 and PIPEV(V)Cl5 ) have the lowest interaction with H2 , since their values ranges from ∆H ◦ bind = -11.8 to
-10.2 kJ/mol. This is probably because of the screened coulombic charge for the V(V)Cl5 and the
poor dispersion interaction that the octahedral geometry offers. The H-H bond length is not out
of the ordinary, which can be observed by the constant values of 0.744 and 0.745 for all the four
interacting H2 .

130
In general the negatively charged PIPE compounds have more interaction than the neutral
analog PIP analogs except when the TM is bound directly to the negatively charged species and
this TM is highly electrophilic. This makes the charged to be screened and then there will not
be a strong charge quadrupole interaction. We also found that with these two linkers, all the
TM falls in the ideal range of 10-15 kJ/mol interaction for maximum delivery uptake, thus if the
gravimetric uptake needs to be optimized, we can use the lighter version of TM. We corroborated
that the tetrahedral geometry in general gives slightly stronger interaction than the square geometry.
And these geometries give slightly stronger interaction than the square bipyramidal followed by the
octahedral geometry. This will serves for future design as a way to tune the H2 interaction.
Ligand containing the Imine-Pyridine binding groups.
Our efforts to generate metalation sites include the (E)-N-(pyridin-2-ylmethylene)aniline (PIA)
ligand which we used in a MOF to create metalation sites.[139] We explored for this linker the same
TMs; Sc to Cu as well as Pd(II). The results are shown in Table 7.10 and Figure 7.16.
Table 7.10: Binding energies (∆H ◦ bind ) obtained for the ground state of linker PIA and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(n)Cln + H2 . The H-H
bond of isolated H2 is 0.741 Å
Linker =
PIA

Geom
for M

Spin
(s)

n H2

∆H ◦ bind
(kJ/mol)

H-H bond (Å)

Linker
+ Sc(III)Cl3
+ Ti(IV)Cl4
+ V(V)Cl5
+ Cr(III)Cl3
+ Mn(II)Cl2
+ Fe(II)Cl2
+ Co(II)Cl2
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pd(II)Cl2

N/A
Spy
Oct
Oct
Spy
Tet
Tet
Tet
Tet
Sqr
Sqr

3/2
5/2
2/2
3/2
2/2
1/2

1, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1a, 2, 3, 4
1a, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4

-7.57, -7.53, -7.48, -7.40
-15.2, -12.3, -11.7, -10.9
-11.9, -11.6, -10.9, -10.0
-10.9, -10.8, -9.78, -8.33
-18.5, -12.5, -10.9, -10.3
-15.7, -12.8, -12.7, -12.5
-14.0, -14.0, -14,0, -13.9
-13.8, -13.6, -13.6, -13.4
-14.3, -14.2, -14.1, -14.1
-13.9, -13.6, -13.5, -13.2
-12.8, -12.8, -11.9, -11.9

0.746, 0.746, 0.745, 0.744
0.747, 0.745, 0.745, 0.743
0.745, 0.745, 0.744, 0.743
0.747, 0.747, 0.745, 0.745
0.747, 0.745, 0.744, 0.744
0.748, 0.747, 0.746, 0.746
0.747, 0.747, 0.746, 0.746
0.746, 0.746, 0.746, 0.745
0.747, 0.746, 0.746, 0.746
0.746, 0.746, 0.745, 0.744
0.745, 0.745, 0.745, 0.744

The first H2 interacts strongly with the metal but it does not form a hydride.

As in the other cases we found TM that interacts strongly with the 1st H2 trough a η 2 -H2
interaction. For the first time in this series we found this interaction for the Sc(III)Cl3 type complex.
The 1st H2 forms a PIA-Sc(III)Cl3 (η 2 -H2 ) complex with a ∆H ◦ bind of -15.2 kJ/mol. The TM has
an octahedral geometry with the η 2 -H2 occupying one of the sites. The distances for the Sc-H2 are
2.77 and 2.81 Å, while the H-H bond is 0.747 Å. The following 2nd to 4th H2 interact less strongly
with this psedo-complex which is observed from ∆H ◦ bind = -12.3, -13.3 and -12.7 kJ/mol. The H-H
bond is also not distorted (0.745, 0745 and 0.743 Å, for 2nd to 4th H2 , correspondingly).
The other case where the TM interacts strongly with the first H2 forming a η 2 -H2 complex is
Cr(III). This interaction forms the PIA-Cr(III)Cl3 (η 2 -H2 ) complex where the Cr(III) forms an octahedral coordination center. The ∆H ◦ bind for this interaction is -18.5 kJ/mol. The bond distances

131

Cln

(E)-N-(pyridin-2-ylmethylene)aniline
PIA+TMCln

Figure 7.16: Different binding energies ∆H ◦ bind at 298K obtained for the PIA ligand interacting
with four physisorbed H2 . We have focused on isoelectronic TM. PdCl2 are shown for comparison. The error bars estimate the different configurations. Mn(II), Cr(III) and Sc(II) show strong
interactions with the first H2 but there is no evidence of formation of hydride (Table 7.10).
for the Cr-H2 are 2.54 and 2.53 Å, which are shorter than the Sc(III) case. The next H2 binds less
strongly with ∆H ◦ bind = -12.5, -10.9 and -10.3 kJ/mol for the 2nd to 4th H2 , respectively. This is
a drastic drop for the ∆H ◦ bind . It is expected since now an octahedral geometry is being form and
this coordination shell for the TM is the one that has the least binding energy towards H2 .
The last TM in this series that interacts strongly with the first H2 is Mn(II). The strength
of this interaction is ∆H ◦ bind = -12.3 kJ/mol and forms PIA-Mn(II)Cl2 (η 2 -H2 ). The TM gets
transformed from a tetrahedral coordination shell to a distorted trigonal bipyramidal with the η 2 H2 in the equatorial position. The Mn-H2 distance is 2.70 Å, for both H2 which show the symmetry
of the interaction. The H-H bond is 0.748 Å. The following H2 interacts less strongly with ∆H ◦ bind
= -12.8, -12.7 and -12.5 kJ/mol for the 2nd to 4th H2 , respectively. The H-H bond is not significantly
affected in these interactions since the bonds range from 0.747 to 0.746 Å.
All the other TM have an interactions in the ideal ∆H ◦ bind range of 10-15 kJ/mol, and the V(V)
is in the limit. The results shown in Table 7.10 suggest the same trends as in the other ligands,
when comparing the geometry of the TM. This is that the stronger interactions in general are for
the tetrahedral coordinations shell, followed closely by the square planar geometry. Then the next
geometry that gives strong interaction with H2 is the square pyramidal coordination shell, and at
the end, the octahedral geometry gives the worst interaction with H2 .
In V(V) case, there is not a coordination interaction between the PIA ligand and the V(V)Cl5
cluster. This can be deducted because of the long V-N distances which are 3.39 and 3.90 Å. The
V(V)Cl5 adopts distorted square pyramidal geometry, however the PIA occupies a site making this
coordination shell a distorted octahedral. The interactions with H2 are the worst in this series with
∆H ◦ bind = -10.9, -10.8, -9.78 and -8.33 kJ/mol for the 1st to the 4th H2 , respectively. The second

132
worst performance is for the other octahedral geometry and in this case there is a true coordination
bond forming the PIA-Ti(IV)Cl4 complex. The strength of interaction for this complex is ∆H ◦ bind
= -11.9, -11.6, -10.9 and -10.0 kJ/mol for the four H2 by order of interaction.
From this ligand we have confirmed that the tetrahedral geometry for the coordination shell gives
the stronger interactions with H2 , followed closely by the square planar case. Then, the next strong
interaction is given by the square pyramidal geometry and finally the octahedral coordination shell
gives the worst interaction with H2 .
7.2.3.2

Proposed Linkers Based on Experimental Crystal Structures

We speculated that the square geometry was essential to obtain the maximum number of interacting
H2 with the linker versus tetrahedral or other geometry. Thus, we search the Cambridge Structural
Database (CSD) for square geometry for TM with pyridine ligands. We were focused on these
ligands because we believe they can be an easy metalation sites in a framework (Figure 7.13). We
found the various numbers of synthesized compounds in the literature with these restrictions. This
type of interaction sites are analogous to the COF synthesized with triazine linkage.[151]
Ligand containing the bipyridine group.
The first linker we studied with this approach was the 2,2’-bipirydine (BPY). Using the crystal
structures we calculated the H2 binding energy for all these TM; Ni(II)[152], Cu(II)[153], Pt(II)[154]
and Pd(II)[155]. We include Pt(II) to have another comparison besides Pd(II) for precious late transition metal and also because Pt(II) in this coordination environment is ubiquitous in coordination
chemistry. The results are shown in Table 7.11 and Figure 7.17.
Table 7.11: Binding energies (∆H ◦ bind ) obtained for the ground state of linker BPY and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(II)Cl2 + H2 . The H-H bond
of isolated H2 is 0.741 Å
Linker =
Geom Spin n H2
∆H ◦ bind
H-H bond
BPY
for M (s)
(kJ/mol)
(Å)
Linker
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pt(II)Cl2
+ Pd(II)Cl2

N/A
Sqr
Sqr
Sqr
Sqr

1/2

1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4

-5.33, -5.18, -4.90, -4.78
-10.9, -10.1, -8.83, -7.64
-14.7, -13.3, -13.0, -11.7
-11.4, -11.1, -10.9, -10.4
-9.89, -9.86, -9.81, -9.78

0.745, 0.744, 0.744, 0.744
0.746, 0.746, 0.745, 0.745
0.746, 0.746, 0.744, 0.744
0.744, 0.744, 0.744, 0.744
0.747, 0.747, 0.747, 0.746

The BPY ligand alone does not interact strongly with H2 . The ∆H ◦ bind ranges from -5.33 to
-4.78 kJ/mol, which is the usual strength for interaction with an organic linker. The H-H bond
distance for the H2 are also in the usual range with 0.745, 0.744, 0.744 and 0.744 Å, for the 1st to
the 4th H, respectively. However we increase this interaction by adding TM to the binding sites of
this linker.
The best results are for the BPY-Cu(II)Cl2 complex with ∆H ◦ bind = -14.7, -13.3, -13.0 and

133

2,2'-bipyridine
BPY+TMCl2

Figure 7.17: Different binding energies ∆H ◦ bind at 298K obtained for the BPY ligand interacting
with four physisorbed H2 . We have focused on isoelectronic TM. The error bars estimate the different
configurations.
-11.7 kJ/mol. This is in the ideal range for maximum delivery H2 for the 233/358 K under our
current assumptions. The H-H are 0.746, 0.746, 0.744 and 0.744 for the 1st to 4th interacting H2 ,
this indicates that the H-H bond is not significantly distorted. The next best performance was
the BPY-Pt(II)Cl2 complex. We found that the ∆H ◦ bind is slightly better than the Pd(II) case,
as we explain below. For the 1st to the 4th H2 , we found that ∆H ◦ bind = -11.4, -11.1, -10.9 and
-10.4 kJ/mol, respectively. All the H-H bond for these H2 are the same; 0.744 Å. We calculate the
∆H ◦ bind for the BPY-Ni(II)Cl2 in a square planar geometry, although the most common geometry
is tetrahedral for this case. Our intention was to compare the square geometry among different
elements. Our results under for this geometry is ∆H ◦ bind = -10.9, -10.1, -8.83 and -7.64 kJ/mol. We
observe a drastic drop in the binding energy when the number of H2 increase, which is not desirable
for a material in real application. Finally, the BPY-Pd(II)Cl2 complex gives a worst performances
with ∆H ◦ bind in the range of -9.89 to -9.78 kJ/mol for the 1st to the 4th H2 , respectively.
Thus, except for the Ni(II) case, all the other TM have a constant ∆H ◦ bind over the first four
H2 , which is desirable for a host in real applications, and also the interactions are slightly larger
than 10 kJ/mol. We show again the utility of metalation as a way to improve the interaction with
H2 .
Ligand containing two bipyridine groups.
The first linker we studied with this approach was the 2,2’-bipirimidine (BPYM). Using the
crystal structures we calculated the H2 binding energy for all these TM; Ni(II)[156], Cu(II)[157],
Pt(II)[158] and Pd(II)[159]. In this case we studied the effect of having an extra TM in the same
ligand and if this effect is somehow additive. The results are shown in Table 7.12 and Figure 7.18.
The BPYM alone does not have strong interactions with H2 , which is shown by the ∆H ◦ bind

134
Table 7.12: Binding energies (∆H ◦ bind ) obtained for the ground state of linker BPYM and different
number of physisorbed H2 . We also show ∆H ◦ bind for the linker + TM(II)Cl2 + H2 . The H-H bond
of isolated H2 is 0.741 Å
Linker =
Geom Spin n H2
∆H ◦ bind
H-H bond
BPYM
for M (s)
(kJ/mol)
(Å)
Linker
+ Ni(II)Cl2
+ Cu(II)Cl2
+ Pt(II)Cl2
+ Pd(II)Cl2

N/A
Sqr
Sqr
Sqr
Sqr

1/2

1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4
1, 2, 3, 4

-5.85, -5.74, -5.52, -5.23
-10.3, -10.3, -10.2, -10.2
-14.4, -14.2, -14.0, -13.7
-11.5, -11.3, -11.0, -10.6
-12.5, -12.5, -12.1, -12.1

0.745, 0.745, 0.745, 0.745
0.748, 0.748, 0.747, 0.746
0.746, 0.746, 0.746, 0.746
0.746, 0.746, 0.746, 0.746
0.745, 0.745, 0.745, 0.745

Cl
TM

2,2'-bipyrimidine
BPYM+TMCl2

Figure 7.18: Different binding energies ∆H ◦ bind at 298K obtained for the BPYM ligand interacting
with four physisorbed H2 . We have focused on isoelectronic TM. The error bars estimate the different
configurations.
= -5.85,-5.74, -5.52 and -5.23 kJ/mol, which is slightly higher than the BPY ligand. Also the H-H
bonds are slightly higher with all the bonds being 0.745 Å. We then calculate the binding energy
with other TM and we found that we the interaction strength is improved.
The best performance is for the BPYM-Cu(II)Cl2 with a ∆H ◦ bind = -14.4, -14.2, -14.0 and
-13.7 kJ/mol, with all the H-H bond being the same; 0.746 Å. The next best performance is for
BPYM-Pd(II)Cl2 complex with ∆H ◦ bind = -12.5, -12.5, -12.1 and -12.1 kJ/mol, for the 1st to
the 4th H2 respectively. The compound BPYM-Pt(II)Cl2 has the third best performance where
∆H ◦ bind for the 1st to the 4th H2 is in the range of -11.5 to -10.6 kJ/mol for the first four H2 .
Finally the BPYM-Ni(II)Cl2 case we have ∆H ◦ bind in the range of -10.3 to -10.2 for the first 4 H2 .
Once again, we explored the square planar geometry for Ni(II) in order to compare among the same
geometry, even when it is more common to find Ni(II) in the tetrahedral geometry.
We found that the additive effect for more ∆H ◦ bind given that two TM are close to each other
was only found for the case of PdCl2 , while in the other cases we did not see this effect clearly. It
is possible that more configurations need to be explored. The compound that offers the stronger

135
interaction with H2 is the Cu(II)Cl2 for both ligands.
7.2.3.3

Alternative Strategy to Metalate COFs and MOFs

Until now we have explored the reaction of metal salts such as Pd(CH3 CN)2 Cl2 , PdCl2 and Cu(BF4 )2
with the organic linker,[138, 139] however another strategy is to react metallic atoms such as Pd(0)
with the same ligands. This would create metallic center in the structure where the H2 can interact
strongly with.
We found that the reaction of any of the linkers described in this work reacts with Pd(0) exothermically as it can be seen in Figure 7.19. The most exothermic reaction is between Pd(0) and the
PIPE ligand (∆Hr◦ = -100.8 kJ/mol, ∆G◦r = -68.4 kJ/mol), presumably because this is the only
ligand with a formal negative charge. In terms of neutral species, the most favorable interactions
are for the ligands that contains the most nitrogen atoms, thus the most exothermic interaction is
between Pd(0) and BBH, followed by Pd(0) and BPY which binds the Pd(0) to two N atoms. The
linkers that interact the least strongly are PIP followed by BBH, each with only one N binding
site and one OH binding site. The equilibrium between PIP and the PIPE ligand was studied
trough the calculation of the pKa obtained with our ab-initio quantum mechanical methods.[160]
We obtained that the pKa is equals to 8.7 in water which indicates that the PIP ligand is basic and
that at normal neutral conditions in water, the PIP does not dissociates to create PIPE and H+ .
It is important to study this equilibrium because the X-ray studies very rarely can determine if the
H is in the structure or not, and it is more difficult when powder X-ray structure determinations is
used.
We then proceed to study the reactivity of these Linker-Pd(0) complexes interacting with H2 .
The results are shown in Figure 7.20 and Table 7.13. As we can observe there are chemical reactions
between the first H2 and all of the Linkers-Pd forming species that can be considered hydrides due to
the H-H bond length and the energetics. The energetics for these reactions range from ∆Hr◦ = -53.5
kJ/mol (for BBH-Pd) to ∆Hr◦ = -106 kJ/mol (for PIPE-Pd). In a similar manner the H-H bond
length ranges from 0.855 to 1.806 Å, with the shortest bond being for the least energetic reaction
(BBH-Pd + H2 ) and the largest H-H bond for the most energetic reaction (PIPE-Pd + H2 ). The
ligands in between have energetics that not necessarily correlates with the energetics, this is for
examples the next strong reaction is the formation of PIA-Pd with ∆Hr◦ = -96.1 kJ/mol and the
H-H bond of 0.868 Å, however the next reaction gives longer bonds but still smaller energetics for the
reaction. PIP-Pd creates ∆Hr◦ = -91.7 kJ/mol and H-H bond of 0.869 Å, followed by BPYM-Pd
with ∆Hr◦ = -80.7 kJ/mol and H-H bond of 0.870 Å, (this ligand in particular host two Pd per linker
and the 2nd H2 binds with ∆Hr◦ = -80.5 kJ/mol with H-H bond of 0.869 Å), followed by BPY-Pd
with ∆Hr◦ = -77.1 and H-H bond of 0.871 Å. This shows that the H-H bond is sensitive to the
energetics but also that the H-H bond with our methodology might have an error in the estimation

136

Pd (g)

G= -62.6
H= -94.6
kJ/ mol

Pd(g)

G= -41.7
H= -73.2
kJ/mol

-O
NH

Pd
Pd(g)

G= -38.8
H= -71.8
kJ/ mol

Pd(g)

G= -51.5
H= -86.9
kJ/mol

Pd(g)

Pd N

-O
G= -68.4
H= -100.8
kJ/mol

pKa = 8.7

W ater

Pd N

-O

H+

Figure 7.19: Alternative option for metalating the linkers using metallic Pd(0). Our calculations
show that all these reactions are favorable, and therefore it should be a viable mode for putting
metals inside extended structure. Note that in the reaction from PIP to PIPE, we did not consider
a counter cation for PIPE; this makes the reaction with H+ extremely favorable. The inset shows
the calculated pKa for PIP/PIPE.
of the bond in the order of 0.003 Å, but it still sensitive enough to capture this direct correlation
of H-H bond to the strength of ∆Hr◦ . In the paper by Kubas,14 the range for a true H2 complex
is given as 0.8 to 1.00 Å, while the elongated H2 complex is estimated as the H-H bond distance
from 1.0 to 1.3 Å. However our calculations show energetics for the formation of hydrides and H-H
bond around 0.9 Å, while the only long bond is of 1.8 Å, for the PIPE-Pd. This discrepancy can
be resolved by trusting the energetics of our QM method but considering our distances for H-H
bond obtained from QM shorter than those described by Kubas. This can be seen in the following
comparison, Kubas used the value of the isolated H-H of 0.75 Å, while our QM method found this
value to be 0.741 Å.
Another evidence for the formation of hydride is the short H-Pd bond in all these linkers. The
distances for the Pd-H bond in the PIPE-Pd-H2 complex are 1.566 and 1.564 Å. We then obtained
longer Pd-H bond distances for the PIA-Pd-H2 complex with 1.722 and 1.717 Å. The PIA-Pd-H2
complex gives Pd-H bond distances of 1.729 and 1.724 Å, these distances are longer than the PIPE
ligand. The distances for the Pd-H bonds in the BPYM-Pd2 -H2 complex are 1.713 and 1.712 Å,

137
Table 7.13: Binding energies (∆H ◦ bind ) obtained for the ground state of all linkers (BBH, PIP,
PIPE, PIA, BPY, and BPYM) + Pd shown in Figure 7.19 reacting with different number of
H2 . For each case the spin is 0. The H-H bond of isolated H2 is 0.741 Å
Linker-Pd

Geom
for M

n H2

∆H ◦ bind
(kJ/mol)

H-H bond
(Å)

BBH-Pd
PIP-Pd
PIPE-Pd
PIA-Pd
BPY-Pd
BPYM-Pd

Sqr
Sqr
Sqr
Sqr
Sqr
Sqr

1a- 5
1a- 5
1a- 5
1a- 5
1a- 5
1a- 5

-53.5, -12.6, -12.5, -12.0, -12.1
-91.7, -13.7, -13.6, -13.6, -13.1
-106, -14.8, -14.2, -13.8, -13.8
-96.1, -13.7, -13.0, -12.7, -12.0
-77.1, -11.4, -11.4, -11.0, -10.9
-80.7, -80.5, -14.5, -14.5, -13.2

0.855, 0.749, 0.748, 0.747, 0.744
0.869, 0.749, 0.748, 0.748, 0.744
1.806, 0.748, 0.747, 0.747, 0.744
0.868, 0.749, 0.747, 0.747, 0.743
0.871, 0.746, 0.745, 0.743, 0.743
0.870, 0.869, 0.748, 0.748, 0.748

The first H2 react chemically and forms a linker-Pd-H2 that resembles a hydride formation due
to the energetics involved.

Pd
L=BBH, PIP, PIPE,
PIA, BPY, BPYM

Figure 7.20: (left) Our calculations showed that Pd(0) binds to the different linkers studied here.
(Right) The plot shows the energetics when the H2 interacts with the compounds formed with
Pd(0) shown in Figure 7.19. The first H2 forms a hydride converting the Pd(0) into Pd(II). The
subsequent H2 interacts strongly by physisorption with the formed Pd(II)H2 . BPYM shows two
H2 bound chemically because it has two Pd per linker.
while for the second H2 in the BPYM-Pd2 -2H2 complex, the distance for the analog bonds are
1.713 and 1.713 Å. Then we have the BPY-Pd-H2 complex with both Pd-H bond distances of 1.715
and 1.713 Å. Finally the bond distances for the Pd-H in the BBH-Pd-H2 complex are 1.729 and
1.723 Å. This trend suggest that the longer the Pd-H bond the least energetics for the formation
of the linker-Pd-H2 (with the PIA-Pd-H2 complex not quite following this trend, perhaps because
the N in the pyridine ring makes this bond longer than the rest due to the pi electrons from the
aromatic ring). For all these cases we found that the singlet is the final electronic ground state of
the linker-Pd-H2 complex and all the geometries are square planar.
Once the first H2 is bound chemically to the linker-Pd system, the new complexes linker-Pd-H2
serves as the host that interacts with other H2 . We show the energies for these other 4 H2 in Table
7.13. In general the energies are very similar to the energies obtained for the physisorbed H2 of the

138
other ligands with transition metals and chlorines as the counter anion. This indicates that even
when we have square planar geometries that allow more H2 to interact with the metallic center, we
do not obtain much gain, however the new concept of using the same coordinated metallic center
for chemisorption and physisorption allows us to explore new types of hydrogen uptake.
A very important phenomenon happens when we absorb H2 into BPY versus BPYM. While
BPY has one site for hosting the Pd(0), the BPYM ligand has two sites and it turns out that the
binding of the H2 is stronger for the BPYM-Pd2 -2H2 com-plex than with BPY-Pd-H2 suggesting
a cooperative interactions caused by having two Pd in the same ligand. This is the same effect
observed for Pd(II)Cl2 , this suggest that late transition metals have this property but we have not
observed in early TM. The physisorbed H2 to BPYM-Pd2 -2H2 have a stronger binding energy of
around 14.5 kJ/mol while the analogs for the BPY-Pd-H2 are around 11.4 kJ/mol. The same trends
is observed when we analyzed the H-H bond; this bond distance is longer for the BPYM-Pd2 -2H2
(around 0.748 Å) that for the BPY-Pd-H2 case (around 0.745 Å). This is an effect not observed
for the other cases and gives us a hint for using mult-binding sites for metals such as the BPYM,
rather than the single-site binding sites such as the BPY. The overall gain is bigger when the metals
are in the same ligand.

7.2.4

Concluding Remarks

We showed early TM (Sc to Cu) gives similar and superior van der Waals interactions than precious
TM (Pd and Pt), therefore suggesting the viability for real applications.
We found high spin TM interacts more strongly with H2 than the low spin analog. Another
characteristic correlated with the spin state, is that we found that the tetrahedral geometry in
general gives slightly stronger interaction than the square geometry. And these geometries give
slightly stronger interaction than the square bipyramidal followed by the octahedral geometry. In
general the negatively charged compounds have more interaction than the neutral analog analogs
except when the TM is bound directly to the negatively charged species and this TM is highly
electrophilic. This makes the charged to be screened and then there will not be a strong charge
quadrupole interaction. The role of the ligand is also cooperative, since we observe that the Chlorine
ligand interacts with the H2 , presumably due to charge-quadrupole interactions. Our results shows
that most of the TM used falls in the ideal range of 10-15 kJ/mol interaction for maximum delivery
uptake, thus if the gravimetric uptake needs to be optimized, we can use the lighter version such as
the early TM. Among all studied the spins states, ligands and TM, bound to the Chlorine ligand,
we found that they do not form hydrides when interacting with one H2 but sometimes there is a
strong affinity with the first H2 forming a η 2 -H2 interaction. This will serves for future design as a
way to tune the H2 interaction.
This study also suggest that an material with heterogeneous sorption sites might be useful when

139
a drastic change of temperature occurs in the environment since different ∆H ◦ ads values between
10-15.3 kJ/mol will help the delivery amount. However if the system is maintained at the same
temperature, then a homogenous material is the best option.
We also showed an alternative way of metalating the linkers of common COFs and MOFs, which
is by using Pd(0). Our results showed that the formation of the complex linker-Pd(0) is favorable for
all the linkers studied. When these complexes interact with H2 , the first H2 forms a hydride with the
Pd creating a linker-Pd-H2 complex. The following H2 interacts by non-covalent interactions forces
(dispersion and coulombic) with the formed linker-Pd-H2 complex. This new route shows a new
form of using the coordinated transition metal as site for chemisorption and physorption, opening
the door to new types of H2 uptake. We also showed that having two metals in the same ligand
gives a cooperative interaction with H2 , this can be observed for the cases of BPY-Pd-H2 and the
BPYM-Pd2 -2H2 complexes.
With our results we predict that by metalating the existing COFs or MOFs with light or late TM
with a tetrahedral or square geometry we will obtain a binding energy for optimal delivery amount
of H2 . We also predict that if nucleophilic TM is used and it has a square pyramidal or octahedral
geometry which is accessible to interact with H2 , then the ∆H ◦ bind will also increase.
We believe that these results are of fundamental importance for the development of the next
generation of H2 storage porous materials. We are currently developing the Force Field for the most
promising TM candidates.

A.1

All QM Calculations

Quantum Mechanical Calculations and Geometries
on the Formation of Molecular Machines

Appendix A

140

H(gas)
-6.25912E+04
-7.18457E+03
-5.90200E+05
-9.95162E+05
-8.96625E+05
-7.85625E+05
-1.95169E+06
-7.70993E+05
-1.89183E+06
-1.78082E+06
-2.94690E+06
-1.76627E+06
-2.88703E+06
-2.77607E+06
-3.94215E+06
-2.76152E+06
-1.01694E+06
-9.05930E+05
-2.07199E+06
-8.91317E+05
-2.01213E+06
-1.90117E+06
-3.06723E+06
-1.88657E+06
-3.00732E+06
-2.89636E+06
-4.06244E+06
-2.88182E+06

Compound
F−
I−
PF61R
D-2F
D-2I
D-2PF6
D-2
1R-D-2F
1R-D-2I
1R-D-2PF6
1R-D-2
2R-D-2F
2R-D-2I
2R-D-2PF6
2R-D-2
Dp-2F
Dp-2I
Dp-2PF6
Dp-2
1R-Dp-2F
1R-Dp-2I
1R-Dp-2PF6
1R-Dp-2
2R-Dp-2F
2R-Dp-2I
2R-Dp-2PF6
2R-Dp-2
-6.26022E+04
-7.19727E+03
-5.90224E+05
-9.95221E+05
-8.96676E+05
-7.85676E+05
-1.95175E+06
-7.71044E+05
-1.89192E+06
-1.78092E+06
-2.94699E+06
-1.76636E+06
-2.88715E+06
-2.77619E+06
-3.94227E+06
-2.76165E+06
-1.01699E+06
-9.05981E+05
-2.07204E+06
-8.91368E+05
-2.01222E+06
-1.90126E+06
-3.06732E+06
-1.88666E+06
-3.00745E+06
-2.89649E+06
-4.06256E+06
-2.88194E+06

G(gas)
-6.26928E+04
-7.25915E+03
-5.90268E+05
-9.95229E+05
-8.96687E+05
-7.85718E+05
-1.95177E+06
-7.71203E+05
-1.89194E+06
-1.78095E+06
-2.94703E+06
-1.76648E+06
-2.88719E+06
-2.77623E+06
-3.94231E+06
-2.76175E+06
-1.01700E+06
-9.06021E+05
-2.07207E+06
-8.91508E+05
-2.01224E+06
-1.90129E+06
-3.06735E+06
-1.88678E+06
-3.00747E+06
-2.89653E+06
-4.06260E+06
-2.88204E+06

G(solv)

Table A.1: Free energies in gas and solvated phase including quantum corrections. The solvent used is CH3 CN. Units:kcal/mol

141

-6.25938E+04
-7.18823E+03
-5.90217E+05
-9.95510E+05
-8.96967E+05
-7.85967E+05
-1.95204E+06
-7.71334E+05
-1.89252E+06
-1.78152E+06
-2.94759E+06
-1.76696E+06
-2.88807E+06
-2.77711E+06
-3.94319E+06
-2.76256E+06
-1.01728E+06
-9.06271E+05
-2.07233E+06
-8.91658E+05
-2.01282E+06
-1.90186E+06
-3.06792E+06
-1.88726E+06
-3.00836E+06
-2.89740E+06
-4.06348E+06
-2.88285E+06

I−
PF61R
D-2F
D-2I
D-2PF6
D-2
1R-D-2F
1R-D-2I
1R-D-2PF6
1R-D-2
2R-D-2F
2R-D-2I
2R-D-2PF6
2R-D-2
Dp-2F
Dp-2I
Dp-2PF6
Dp-2
1R-Dp-2F
1R-Dp-2I
1R-Dp-2PF6
1R-Dp-2
2R-Dp-2F
2R-Dp-2I
2R-Dp-2PF6
2R-Dp-2

E, scf

Compound
0.00000E+00
0.00000E+00
1.20070E+01
3.28599E+02
3.24753E+02
3.24753E+02
3.24753E+02
3.24753E+02
6.56066E+02
6.56066E+02
6.56066E+02
6.56066E+02
9.85690E+02
9.85690E+02
9.85690E+02
9.85690E+02
3.24753E+02
3.24753E+02
3.24753E+02
3.24753E+02
6.56066E+02
6.56066E+02
6.56066E+02
6.56066E+02
9.85690E+02
9.85690E+02
9.85690E+02
9.85690E+02

ZPE
0.00000E+00
0.00000E+00
2.08100E+00
1.70370E+01
1.41130E+01
1.41130E+01
1.41130E+01
1.41130E+01
3.44260E+01
3.44260E+01
3.44260E+01
3.44260E+01
5.16350E+01
5.16350E+01
5.16350E+01
5.16350E+01
1.41130E+01
1.41130E+01
1.41130E+01
1.41130E+01
3.44260E+01
3.44260E+01
3.44260E+01
3.44260E+01
5.16350E+01
5.16350E+01
5.16350E+01
5.16350E+01

Hvib
2.61845E+00
3.65542E+00
4.45100E+00
1.94070E+01
1.64830E+01
1.64830E+01
1.64830E+01
1.64830E+01
3.67960E+01
3.67960E+01
3.67960E+01
3.67960E+01
5.40050E+01
5.40050E+01
5.40050E+01
5.40050E+01
1.64830E+01
1.64830E+01
1.64830E+01
1.64830E+01
3.67960E+01
3.67960E+01
3.67960E+01
3.67960E+01
5.40050E+01
5.40050E+01
5.40050E+01
5.40050E+01

Htot
0.00000E+00
0.00000E+00
1.02720E+01
1.19796E+02
1.13238E+02
1.13238E+02
1.13238E+02
1.13238E+02
2.77676E+02
2.77676E+02
2.77676E+02
2.77676E+02
3.89058E+02
3.89058E+02
3.89058E+02
3.89058E+02
1.13238E+02
1.13238E+02
1.13238E+02
1.13238E+02
2.77676E+02
2.77676E+02
2.77676E+02
2.77676E+02
3.89058E+02
3.89058E+02
3.89058E+02
3.89058E+02

Svib
3.69456E+01
4.26061E+01
7.85360E+01
1.97765E+02
1.70006E+02
1.70006E+02
1.70006E+02
1.70006E+02
3.17215E+02
3.17215E+02
3.17215E+02
3.17215E+02
4.30516E+02
4.30516E+02
4.30516E+02
4.30516E+02
1.70006E+02
1.70006E+02
1.70006E+02
1.70006E+02
3.17215E+02
3.17215E+02
3.17215E+02
3.17215E+02
4.30516E+02
4.30516E+02
4.30516E+02
4.30516E+02

Stot

-9.70695E+01
-6.81235E+01
-5.61219E+01
-2.05595E+01
-2.02911E+01
-5.18886E+01
-3.43250E+01
-1.68734E+02
-2.30938E+01
-3.65654E+01
-4.64984E+01
-1.21114E+02
-3.84228E+01
-4.57423E+01
-4.53417E+01
-1.10013E+02
-1.99386E+01
-4.95869E+01
-4.11532E+01
-1.49998E+02
-2.74249E+01
-4.06581E+01
-3.39980E+01
-1.21905E+02
-3.06199E+01
-4.74455E+01
-4.66618E+01
-1.07737E+02

E(solv)

Table A.2: Electronic Energy (E,scf), Zero Point Energy (ZPE), Solvation energy for CH3 CN (Esolv). Units:kcal/mol

142

-9.95162E+05
-2.89325E+05
-6.75272E+05
-8.20194E+05
-1.99035E+06
-1.99032E+06
-1.28450E+06
-1.67048E+06
-1.81540E+06

1R
Bz(OCH3)2
-NH2- site
-NH2’- site
1R-1R
1R’-1R’
1R-Bz(OCH3)2
1R-NH2- site
1R-NH2’- site

-1.99045E+06
-1.99044E+06
-1.28458E+06
-1.67055E+06
-1.81548E+06

-9.95221E+05
-2.89353E+05
-6.75304E+05
-8.20231E+05

G(gas)

-1.99047E+06
-1.99045E+06
-1.28458E+06
-1.67057E+06
-1.81549E+06

-9.95229E+05
-2.89348E+05
-6.75316E+05
-8.20239E+05

G(solv)

E, scf
-9.95510E+05
-2.89436E+05
-6.75361E+05
-8.20336E+05
-1.99105E+06
-1.99102E+06
-1.28496E+06
-1.67092E+06
-1.81589E+06

Compound

1R
Bz(OCH3)2
-NH2- site
-NH2’- site

1R-1R
1R’-1R’
1R-Bz(OCH3)2
1R-NH2- site
1R-NH2’- site

6.58173E+02
6.56478E+02
4.33114E+02
4.11047E+02
4.62013E+02

3.28599E+02
1.04135E+02
8.07760E+01
1.31735E+02

ZPE

3.66040E+01
3.46260E+01
2.35260E+01
2.41510E+01
2.68440E+01

1.70370E+01
4.08000E+00
5.70600E+00
7.90500E+00

Hvib

3.89740E+01
3.69960E+01
2.58960E+01
2.65210E+01
2.92140E+01

1.94070E+01
6.45000E+00
8.07600E+00
1.02750E+01

Htot

2.58352E+02
2.74323E+02
1.64741E+02
1.76566E+02
1.95686E+02

1.19796E+02
2.34762E+01
3.60639E+01
5.62807E+01

Svib

3.35071E+02
3.20944E+02
2.42929E+02
2.42304E+02
2.63315E+02

1.97765E+02
9.39090E+01
1.08914E+02
1.25741E+02

Stot

-2.83913E+01
-4.45452E+01
-1.63825E+01
-2.55056E+01
-2.78585E+01

-2.05595E+01
-5.95564E+00
-2.32889E+01
-1.93427E+01

E(solv)

Table A.4: Electronic Energy (E , scf), Zero Point Energy (ZPE), Solvation energy for CH3 CN (Esolv). Units:kcal/mol

H(gas)

Compound

Table A.3: Free energies in gas and solvated phase including quantum corrections. The solvent used is CH3 CN. Units:kcal/mol

143

144

A.2

Geometries for the R Family (2R-D-2PF6 , 1R-D-2PF6 ,
2R-D-2PF6 ) and for the R’ Family (2R-Dp-2PF6 , 1RDp-2PF6 , 2R-Dp-2PF6 )

A.2.1

2R-D-2PF6 -M06L

201
2R-D-2PF6-M06L

6.65680

13.70690

7.19040

8.77290

14.71850

3.05630

11.12290

2.53230

9.23700

11.54530

2.32320

4.50430

11.26060

11.17400

6.57730

10.77290

10.85820

5.69690

10.61740

10.91800

7.35690

13.07910

6.72760

6.94840

12.52050

6.56410

6.08110

12.40160

6.64030

7.74060

6.71560

13.13430

8.48340

7.02580

12.08170

8.44270

5.70650

13.19790

8.89030

7.40790

13.68010

9.13850

7.51370

15.07350

2.52230

7.06910

15.92340

3.05670

6.80950

14.23180

2.55550

7.69190

15.35450

1.48410

10.01820

1.65090

9.16010

9.21760

2.06520

8.53380

9.65340

1.53180

10.17990

10.30910

0.67100

8.75960

12.10430

2.83790

3.31010

11.91940

3.91510

3.20460

11.61470

2.30800

2.49350

13.18820

2.66300

3.26160

7.80380

13.71210

6.46580

7.67680

14.21460

5.16340

145

6.69820

14.54830

4.83950

8.79270

14.26390

4.33620

10.03640

13.80450

4.79350

10.88120

13.79630

4.10880

10.14090

13.29610

6.07930

9.03300

13.25780

6.93560

9.13610

12.82770

7.92710

11.42050

12.65760

6.52850

11.73280

12.96340

7.53520

12.24350

12.85300

5.83330

12.55020

10.45630

6.73380

13.03090

10.84220

7.63780

13.17500

10.73090

5.87680

12.27150

8.97530

6.80050

11.71940

8.66690

5.90100

11.61830

8.76060

7.65860

13.53370

8.13560

6.91870

14.21610

8.25650

6.06670

14.09740

8.33220

7.83850

14.08770

5.63670

7.06880

14.61770

5.78480

8.01020

14.78990

5.75050

6.23930

13.29990

4.35800

7.01690

12.70190

3.87630

8.17170

12.91800

4.31060

9.14400

11.70830

2.89170

8.06670

11.34340

2.38400

6.82360

10.56060

1.64430

6.70550

11.98450

2.85830

5.67240

12.96830

3.83960

5.75940

13.41300

4.27490

4.87240

12.11740

10.57900

9.92590

14.01750

12.49770

9.04670

14.86780

13.55770

6.59740

14.29110

12.11260

4.25670

12.42110

10.18540

3.50890

146

9.84780

10.51390

4.11440

8.60720

9.86260

6.57560

9.57260

10.57140

9.11780

13.48030

10.55760

10.31000

13.97990

9.93520

9.55710

13.60790

10.05350

11.27990

14.09950

11.93490

10.33820

13.59430

12.59230

11.06420

15.15280

11.84950

10.66290

14.72640

13.71340

8.96850

15.81050

13.53040

9.07600

14.42830

14.39210

9.78580

14.43590

14.38180

7.65560

13.35500

14.58940

7.56610

14.95190

15.35810

7.62890

14.65240

14.18990

5.35620

15.21980

15.13540

5.29330

13.58550

14.44980

5.23060

15.08860

13.27540

4.24930

14.99260

13.80500

3.28610

16.15380

13.00900

4.37140

14.56050

11.30900

3.12860

15.63980

11.07900

3.06010

14.29550

11.86230

2.21440

13.80040

10.00640

3.24610

13.95630

9.39530

2.34360

14.17630

9.42210

4.09500

11.64430

10.68970

2.50500

12.08660

10.95190

1.20880

13.10440

10.72250

0.91570

11.20640

11.46470

0.25930

11.57000

11.66740

-0.74390

9.88120

11.71630

0.59090

9.19800

12.13680

-0.14030

9.43000

11.41270

1.86790

8.39620

11.59940

2.14560

147

10.28830

10.88010

2.83300

8.67950

9.97640

4.16790

8.11460

9.75390

3.25700

8.03140

9.56170

5.40440

6.81550

8.86820

5.29080

6.41950

8.64400

4.30670

6.17310

8.45730

6.44680

5.24330

7.89830

6.39560

6.74480

8.77050

7.67030

6.28540

8.47750

8.60720

7.95610

9.48080

7.68440

8.49260

9.88100

8.97870

7.90120

9.56280

9.84300

9.86350

10.97930

10.42930

8.86880

11.36600

11.33380

7.83370

11.35720

11.00220

9.18190

11.75940

12.62820

8.39180

12.05760

13.30950

10.50890

11.76080

13.03790

10.77120

12.05390

14.05030

11.51960

11.38500

12.15670

12.54370

11.36050

12.51090

11.20790

11.00460

10.85200

13.90950

6.68080

10.10760

15.97070

8.45160

9.30530

16.93550

9.52790

6.92050

16.27640

8.00840

4.62630

14.27220

6.19280

3.84310

11.64150

6.53900

4.34280

10.30670

6.03910

6.79220

11.31650

6.71090

9.33200

15.26120

6.53270

10.50930

15.71550

5.89180

9.74620

15.33100

6.00420

11.46950

16.02250

7.83620

10.57110

15.60550

8.51470

11.33590

148

17.06530

7.62150

10.86380

16.74770

9.62920

9.26470

17.81900

9.38310

9.35430

16.49310

10.29180

10.11130

16.48490

10.34700

7.97050

15.40890

10.57860

7.86240

17.01000

11.32020

7.97280

16.70600

10.11010

5.66330

17.28180

11.04830

5.54790

15.64090

10.38160

5.54130

17.13090

9.13260

4.60370

17.09400

9.62500

3.61550

18.17600

8.82210

4.77070

16.48000

7.19560

3.49370

17.54070

6.90330

3.40030

16.21980

7.75780

2.57970

15.64960

5.94040

3.62790

15.80260

5.28980

2.75520

15.97280

5.38290

4.51350

13.50550

6.58670

2.77550

13.98300

6.74970

1.47500

15.02180

6.54830

1.23770

13.12080

7.16780

0.45970

13.51250

7.29570

-0.54580

11.78390

7.42630

0.73520

11.10450

7.77830

-0.03510

11.30010

7.22930

2.02140

10.25800

7.43010

2.24440

12.13720

6.78660

3.05010

10.46270

6.01580

4.38570

9.93750

5.72050

3.47060

9.72520

5.76290

5.61770

8.42740

5.24070

5.50220

7.99510

5.09840

4.51590

7.71760

4.96710

6.66340

6.70240

4.58460

6.61430

149

8.31860

5.21770

7.88910

7.79620

5.05890

8.82820

9.61370

5.75880

7.90360

10.20340

6.07560

9.20030

9.61220

5.76530

10.06910

11.65150

7.10300

10.63730

10.67210

7.52640

11.54160

9.63960

7.57030

11.21410

11.00220

7.90380

12.83580

10.21480

8.23460

13.50600

12.32880

7.85870

13.24380

12.60580

8.14060

14.25600

13.32760

7.46030

12.35420

14.35510

7.42010

12.69820

13.00020

7.09970

11.04750

6.75150

6.95370

11.03650

7.55380

5.54810

11.27740

7.66180

7.68330

12.17950

6.02430

8.39750

10.73200

7.91330

7.35590

9.90930

5.89380

6.27020

9.82800

5.62790

6.56200

12.11590

7.34140

6.93290

2.09960

6.58400

8.38980

2.17540

8.15770

5.51130

2.08990

8.39640

7.55740

1.02260

8.35280

7.43980

3.32350

6.36660

6.43440

0.92310

6.33070

6.35230

3.24200

150

A.2.2

1R-D-2PF6 -M06L

137
1R-D-2PF6-M06L

5.83900

12.45040

6.35920

8.38000

14.66560

3.01660

10.99290

2.06900

9.17710

11.13640

2.39280

4.44260

10.86820

10.95550

6.50740

10.75640

10.68170

5.52830

10.06860

10.52490

7.01770

12.74070

6.60360

7.10790

12.26380

6.54070

6.17420

11.98570

6.39940

7.79040

5.79040

11.62200

7.51520

6.35370

10.69450

7.36860

4.73720

11.39320

7.67280

6.19230

12.13640

8.39460

7.17670

14.98770

2.34410

6.52480

15.61640

2.96360

6.62530

14.08550

2.05200

7.46740

15.53920

1.45050

9.94210

1.13250

9.05120

9.08160

1.56120

8.51980

9.64570

0.86810

10.06640

10.26420

0.22670

8.52130

11.53630

3.08220

3.27040

11.27810

4.14660

3.31680

10.98390

2.62620

2.45050

12.61630

2.98360

3.09210

7.06120

12.80410

5.91210

7.06440

13.54860

4.72300

6.10900

13.77550

4.26620

8.27000

13.95190

4.16480

9.48460

13.61040

4.78080

10.41540

13.92310

4.31730

9.46310

12.88500

5.96310

151

8.25760

12.47500

6.55070

8.26380

11.91470

7.48000

10.75110

12.45570

6.59690

10.80520

12.68920

7.66180

11.62270

12.87640

6.08770

12.11720

10.34170

7.06470

12.06500

10.48500

8.14630

12.96850

10.90160

6.66120

12.11930

8.87860

6.67510

12.22480

8.78350

5.58560

11.13660

8.46270

6.93450

13.17780

8.00490

7.33660

14.17780

8.13420

6.91040

13.23000

8.15380

8.42150

13.74510

5.50370

7.21900

14.21870

5.60370

8.19600

14.49110

5.67240

6.43700

12.97120

4.22260

7.05900

12.45400

3.59550

8.18410

12.71050

3.93260

9.18300

11.49770

2.58270

8.02290

11.08320

2.19500

6.75470

10.32350

1.43930

6.59450

11.63310

2.82110

5.62740

12.58670

3.82770

5.76970

12.96740

4.36510

4.90820

13.79180

5.61260

10.47120

15.70350

7.49910

9.67490

16.41800

9.14480

7.44400

15.63510

8.23090

4.94740

13.68070

6.47780

4.05400

11.08870

6.53440

4.69940

9.98830

5.89190

7.27390

11.27320

6.24430

9.76790

15.17410

5.40330

10.70170

15.50000

4.80630

9.84370

152

15.34260

4.79880

11.60470

15.98220

6.67840

10.78660

15.76190

7.22990

11.71490

17.05260

6.40740

10.82390

16.41490

8.71260

9.78140

17.50180

8.53010

9.72720

16.21280

9.18990

10.75620

16.00780

9.65910

8.68890

14.91270

9.81090

8.70430

16.47190

10.64300

8.87840

16.12200

10.02770

6.39140

16.68230

10.97350

6.49340

15.04580

10.28630

6.39540

16.46360

9.35970

5.08980

16.31120

10.07180

4.26010

17.52660

9.06520

5.08000

15.81880

7.58860

3.70720

16.88580

7.36870

3.52790

15.47700

8.24040

2.88560

15.05080

6.29040

3.74210

15.17010

5.73830

2.80030

15.44270

5.66020

4.54770

12.82670

6.82050

3.03390

13.22530

7.09000

1.72590

14.27400

7.07210

1.45090

12.26760

7.36680

0.74910

12.59380

7.57050

-0.26650

10.91610

7.37640

1.07240

10.15850

7.57410

0.32160

10.51650

7.11170

2.37580

9.45870

7.11130

2.62180

11.45720

6.82610

3.37240

9.96850

5.90890

4.84370

9.39610

5.56430

3.98000

9.36110

5.58260

6.12810

8.10840

4.94870

6.07860

153

7.64350

4.74760

5.11610

7.48140

4.63090

7.27470

6.50410

4.15800

7.27320

8.12560

4.93780

8.46430

7.67550

4.71230

9.42770

9.38260

5.55630

8.41980

10.05790

5.84060

9.68130

9.44980

5.66730

10.58180

11.72570

6.56460

11.05690

10.91230

7.22610

11.98280

9.93630

7.56710

11.65380

11.36270

7.50050

13.26830

10.71980

8.03440

13.96080

12.63540

7.09630

13.65240

12.99260

7.28220

14.66090

13.47550

6.46240

12.73810

14.46220

6.14090

13.05340

13.04260

6.22700

11.43440

9.21700

9.71590

9.48350

8.55400

8.27250

9.79070

9.47840

10.00530

11.04210

9.91470

11.16670

9.07090

10.69450

9.02340

9.33010

8.99450

9.45010

7.83490

7.77280

10.43980

9.52840

6.96990

5.49780

2.29980

5.61750

6.36010

2.11290

8.37180

4.64190

2.53540

7.74570

6.41480

1.19180

7.47340

6.55380

3.48000

6.51980

4.44150

1.16580

6.26330

4.59160

3.46920

154

A.2.3

0R-D-2PF6 -M06L

73
0R-D-2PF6-M06L

5.40420

14.15650

5.39050

7.20230

12.44640

1.34410

9.15690

1.13250

8.23790

8.85350

2.82370

3.80800

9.31390

10.52530

6.18790

9.36310

9.71410

5.55130

8.33460

10.61550

6.46770

10.29440

6.49520

7.46750

9.74610

6.59990

6.60840

9.66020

6.26190

8.25480

5.50570

14.35770

6.78650

5.54770

13.40480

7.32980

4.60760

14.89870

7.08150

6.38940

14.95480

7.04530

6.05890

12.91740

0.65510

5.96180

14.00740

0.73460

5.14140

12.44980

1.03340

6.20120

12.64200

-0.38900

8.38690

0.01650

7.84270

7.39580

0.31730

7.47930

8.27200

-0.60290

8.73170

8.88860

-0.56400

7.05730

9.09220

3.87260

2.88550

8.64600

4.81490

3.22210

8.62900

3.56150

1.94950

10.16460

4.03780

2.72310

6.41600

13.48920

4.78420

6.26680

13.31990

3.40150

5.37570

13.72150

2.93450

7.25270

12.65850

2.67830

8.39230

12.15060

3.32450

9.13370

11.61230

2.74640

8.52680

12.32890

4.69020

155

7.54360

12.99860

5.43990

7.68770

13.15960

6.50480

9.70730

11.76990

5.42140

10.08940

12.47380

6.16760

10.52240

11.46500

4.76520

10.15290

10.23880

7.40160

9.95860

11.06020

8.09630

11.19050

10.31410

7.07030

9.82810

8.87790

8.00890

8.86910

8.52440

7.61240

9.66760

8.97040

9.08330

10.90840

7.81670

7.77140

11.54880

8.06200

6.92190

11.51080

7.67540

8.67070

11.26780

5.36680

7.26030

11.77450

5.21910

8.21210

11.97750

5.70970

6.50580

10.50730

4.15660

6.81310

10.17490

3.16930

7.72690

10.46430

3.24220

8.77080

9.42570

2.06500

7.29140

9.00290

1.97610

5.96970

8.41920

1.14030

5.60310

9.32520

2.99890

5.06780

10.08210

4.09450

5.47660

10.35260

4.88730

4.78620

9.52280

6.41320

11.02350

8.81500

4.96890

11.09380

8.33640

7.10610

11.85730

10.25050

7.87740

10.82170

10.40350

6.12870

12.33310

10.70880

5.76470

10.05510

8.66480

6.72440

9.59530

10.65360

8.13750

3.94910

9.70440

9.36510

3.42820

11.53290

6.95610

4.63970

156

11.74780

8.40800

2.82100

11.38680

9.22720

4.96580

9.85220

7.07260

3.05370

9.50020

7.91590

5.18550

157

A.2.4

2R-Dp-2PF6 -M06L

208
2R_Dp_2PF6

7.18400

6.68280

12.04600

6.05960

7.87550

11.89320

8.32140

5.50790

12.13170

8.08940

7.65210

12.98840

6.41390

6.08320

13.32560

7.96340

7.30060

10.71550

6.29980

5.73800

11.03460

6.17990

5.97110

2.86630

4.78940

6.74660

3.28510

7.59150

5.22700

2.50690

6.59230

7.24380

1.93140

6.94310

6.72070

4.14320

5.43760

5.24470

1.63870

5.79090

4.75220

3.88300

2.60860

11.11480

7.81140

3.01100

12.49330

3.28010

11.36110

2.45850

9.17750

10.93980

2.63740

4.44160

7.70190

12.09140

6.47670

7.50300

11.34690

5.75480

7.48780

11.67370

7.40700

12.62580

7.04630

6.96300

11.93900

6.96190

6.17640

12.09130

6.85330

7.84590

3.18200

10.95510

9.09580

4.09040

10.33970

9.05780

2.43040

10.45060

9.70280

3.43080

11.92220

9.55280

1.76260

11.88870

3.00790

0.95170

12.34980

3.58690

1.78050

10.81240

3.22390

1.57640

12.04040

1.94450

10.37270

1.44780

9.20930

158

9.42690

1.79550

8.77300

10.21750

1.20750

10.26090

10.69720

0.54610

8.67340

11.24540

3.27370

3.21430

10.96880

4.33630

3.22290

10.65880

2.76000

2.45340

12.31470

3.19100

2.97250

3.37570

11.70770

6.86190

2.78610

11.78540

5.59250

1.79220

11.37320

5.46600

3.48650

12.37780

4.54840

4.77830

12.88230

4.75650

5.32630

13.29050

3.91100

5.35580

12.77900

6.01370

4.65480

12.20970

7.08470

5.13830

12.12060

8.05250

6.76750

13.23540

6.22580

6.87750

13.90530

7.08590

7.15930

13.75150

5.34310

9.11280

12.53900

6.39950

9.21770

13.38330

7.08380

9.24930

12.94780

5.39300

13.17550

8.42060

7.02870

13.88190

8.52860

6.19580

13.76470

8.47840

7.95260

13.65580

5.96920

6.80440

14.35280

6.07730

7.63720

14.18640

6.18170

5.87190

12.93370

4.65300

6.78610

12.59920

4.02920

7.97910

12.95070

4.41030

8.93320

11.69330

2.95910

7.95860

11.15950

2.50400

6.75710

10.43580

1.69880

6.71000

11.53740

3.12460

5.55950

12.43090

4.19140

5.56380

159

12.66460

4.73290

4.65550

8.76690

13.20120

9.44200

8.48930

15.53050

7.84740

8.42200

16.04760

5.14170

9.24270

13.94360

3.45040

9.06390

11.24840

3.51000

6.80080

10.26400

4.45590

6.47260

9.50720

7.13200

7.05800

11.12170

9.34620

9.69300

14.27480

9.45200

10.42140

14.02680

8.67260

10.23580

14.31980

10.40490

9.05620

15.60850

9.13540

8.28760

15.87610

9.88000

9.83410

16.39160

9.17340

8.06940

16.78660

7.36340

8.93030

17.47460

7.30330

7.32770

17.24520

8.03960

7.45720

16.61050

5.99930

6.56060

15.96760

6.05380

7.12020

17.59440

5.62770

7.93840

15.89370

3.82740

7.66320

16.86970

3.39050

7.02810

15.26650

3.81370

9.01220

15.25610

2.99040

8.69170

15.23900

1.93410

9.93580

15.85710

3.04670

10.19820

13.27380

2.66170

11.19480

13.74030

2.76090

9.91780

13.36070

1.60070

10.29580

11.82020

3.11230

10.77300

11.21770

2.32370

10.91700

11.73850

4.01060

8.06650

11.11770

2.59210

8.19150

11.38430

1.22960

9.14840

11.67790

0.81430

160

7.09700

11.21960

0.38370

7.20880

11.43730

-0.67470

5.87710

10.77950

0.88410

5.01910

10.66690

0.22920

5.76560

10.46580

2.23130

4.82320

10.10610

2.63550

6.85190

10.60870

3.09770

6.07940

9.24610

4.77220

5.57930

8.63800

4.01420

5.94790

8.77000

6.14480

5.29410

7.54670

6.36410

4.89870

6.99790

5.51630

5.22650

7.05320

7.65730

4.74810

6.10010

7.86480

5.79680

7.78730

8.68760

5.78510

7.43750

9.71260

6.38870

9.01970

8.37840

6.81370

9.86290

9.48950

6.82920

9.37100

10.46790

7.14990

11.87990

10.52130

6.36020

11.60330

11.64420

5.69110

10.74730

11.61070

6.41150

12.40140

12.77920

5.78620

12.16520

13.63400

7.25930

13.50090

12.80330

7.30790

14.13930

13.68050

8.05030

13.80580

11.69760

8.70550

14.66830

11.74130

8.00120

13.00640

10.55660

14.02500

6.41440

9.97450

16.01790

8.05640

8.88160

16.51600

9.34180

6.40750

15.37260

8.23100

4.09250

13.09010

6.73230

3.55910

10.66260

6.78140

4.69360

9.93320

5.95190

7.28190

161

11.37260

6.62360

9.59590

15.40420

6.14100

10.14670

15.65950

5.47080

9.31830

15.58400

5.59480

11.08310

16.27540

7.37210

10.08590

16.08970

8.04230

10.94170

17.33250

7.05690

10.14620

16.85340

9.18500

8.75500

17.89860

8.87480

8.58640

16.83510

9.78510

9.68150

16.37610

10.04250

7.61890

15.32090

10.32630

7.78580

16.96220

10.97930

7.60100

16.10550

10.12620

5.31430

16.70960

11.04880

5.24220

15.05080

10.43660

5.43130

16.25190

9.33080

4.04950

16.01540

9.98350

3.19100

17.29420

8.99100

3.92580

15.24160

7.62810

2.82790

16.21990

7.29270

2.43920

14.84160

8.35900

2.10460

14.33620

6.42750

2.95970

14.19560

5.94510

1.98170

14.79830

5.69470

3.63140

12.08600

7.23780

2.77510

12.23720

7.65820

1.45470

13.20710

7.61670

0.97100

11.12910

8.11110

0.73360

11.26400

8.42940

-0.29640

9.87020

8.13700

1.32240

8.99570

8.47300

0.77240

9.71690

7.70550

2.63520

8.73510

7.70790

3.10040

10.81050

7.24700

3.37470

9.62660

6.04050

4.89740

162

8.98260

5.72520

4.07060

9.20860

5.58480

6.21720

8.03560

4.82000

6.31060

7.47530

4.58290

5.40950

7.59230

4.44320

7.57180

6.67410

3.87350

7.68560

8.32080

4.83680

8.68640

7.98660

4.62540

9.69840

9.49540

5.57770

8.49050

10.26390

5.97110

9.66420

9.83620

5.67040

10.62550

11.92080

7.00260

10.83420

11.11260

7.46670

11.87540

10.04400

7.55800

11.70830

11.66090

7.80940

13.10470

11.00760

8.16290

13.89610

13.02940

7.68160

13.30550

13.47160

7.93270

14.26540

13.85640

7.22860

12.27760

14.91900

7.11610

12.46140

13.31130

6.90280

11.03770

12.09040

9.46180

6.96280

12.43840

10.81140

6.84310

11.46370

11.79060

6.70900

10.10590

11.45250

6.67260

9.75730

10.11310

6.81760

10.73510

9.13540

6.97650

13.48890

11.09960

6.84460

11.75810

12.83410

6.59900

8.71290

9.80890

6.79190

10.41730

8.10270

7.08930

163

A.2.5

1R-Dp-2PF6 -M06L

144
1R_Dp_2PF6

9.81150

7.60240

10.98440

8.31060

7.82930

11.58480

11.28450

7.36930

10.28140

10.26100

9.07510

11.46710

10.31150

6.91550

12.34290

9.30740

8.26060

9.53480

9.33700

6.14290

10.37600

8.84370

6.05240

3.93390

7.21760

6.06100

3.75780

10.46530

6.07260

4.22240

8.86320

7.66020

3.63820

8.64050

6.39590

5.56320

9.08450

5.73680

2.37600

8.78890

4.47220

4.28620

2.59060

10.46380

7.20330

3.13980

12.42580

2.90310

7.61890

1.93340

8.86150

10.06300

1.76390

4.78810

7.43730

12.12140

6.36790

7.17580

11.40240

5.64990

7.28030

11.65550

7.28270

10.55800

6.49700

7.61890

9.97270

6.33720

6.77950

9.94710

6.89760

8.34650

3.12230

10.18440

8.48480

4.11700

9.72480

8.41440

2.43020

9.48460

8.95330

3.19660

11.08930

9.10310

2.02900

11.68630

2.44120

1.10770

11.96170

2.97130

2.19130

10.60580

2.55110

1.92270

11.92630

1.38290

6.88200

0.80890

8.43240

164

6.33590

1.01060

7.50120

6.16940

0.58900

9.22770

7.52880

-0.06440

8.27420

11.01740

2.34430

3.91360

10.76250

3.38340

3.68230

10.98770

1.74720

3.00210

12.02870

2.29610

4.34040

3.31310

11.29370

6.40650

2.82260

11.43640

5.10030

1.92590

10.89190

4.82910

3.50720

12.24310

4.19840

4.68120

12.90490

4.58610

5.25090

13.45940

3.84480

5.14990

12.75470

5.88250

4.46580

11.95970

6.81150

4.88180

11.82460

7.80550

6.50060

13.28610

6.25610

6.52780

13.79420

7.22670

6.90480

13.96470

5.50010

8.88060

12.47780

6.24260

9.07350

13.26020

6.97800

8.99900

12.90760

5.24520

11.62610

7.50840

7.29100

12.16700

7.09040

6.43650

12.28460

7.54060

8.15990

11.13350

5.19040

8.12900

11.19730

5.29710

9.21100

12.14570

5.13610

7.71900

10.32930

4.00980

7.68820

9.31860

3.49260

8.48760

9.08890

3.91930

9.45790

8.59100

2.38840

8.02330

8.86880

1.82280

6.78390

8.31780

0.97510

6.39480

9.87920

2.37020

5.98410

10.62010

3.45830

6.43590

165

11.38370

3.91230

5.81290

8.65220

13.45640

9.34030

7.90770

15.79780

7.98490

6.90300

16.58500

5.46430

7.47120

14.76480

3.40620

7.87090

11.96960

3.18430

6.46900

10.07030

4.46630

6.68270

9.41570

7.21550

7.04790

11.27320

9.29970

9.48770

14.60430

9.29560

10.13250

14.43960

8.42620

10.13520

14.65580

10.18160

8.72610

15.89720

9.12430

8.10960

16.12310

10.01050

9.45510

16.72130

9.02370

7.17650

16.98810

7.78480

7.85830

17.82370

7.55230

6.62490

17.26040

8.70160

6.19720

16.79600

6.66310

5.53450

15.93850

6.87890

5.55170

17.68960

6.59080

6.02410

16.37920

4.38370

5.44120

17.29230

4.16730

5.29910

15.58130

4.62350

6.81900

15.99610

3.16790

6.13300

15.90650

2.30810

7.55680

16.77860

2.92450

8.00530

14.22600

2.22050

8.74270

14.91250

1.76770

7.19910

14.08540

1.48170

8.70240

12.92260

2.53610

9.14500

12.49920

1.62460

9.51920

13.10490

3.24180

6.96240

11.28320

2.42650

6.76070

11.48590

1.06250

7.35270

12.21130

0.51770

166

5.79950

10.74800

0.37610

5.65400

10.92710

-0.68510

5.02810

9.80600

1.04440

4.25800

9.24900

0.51940

5.24750

9.58290

2.39680

4.63620

8.86680

2.93910

6.22730

10.28700

3.10490

6.33060

8.86280

4.89040

6.15510

8.03190

4.19770

6.42730

8.47740

6.29110

6.24110

7.12230

6.60340

6.07130

6.41310

5.80030

6.36600

6.71200

7.92260

6.26880

5.66400

8.19180

6.65780

7.66720

8.88280

6.82090

7.40170

9.92230

6.79720

9.00690

8.48390

7.03690

10.00420

9.52170

7.19660

9.59740

10.52890

7.09430

12.08660

10.44320

6.31110

11.80100

11.56560

5.64810

10.94100

11.51800

6.34910

12.59880

12.70180

5.72390

12.35890

13.55590

7.19500

13.69870

12.72990

7.25240

14.32650

13.61410

7.97470

14.01590

11.61990

8.63930

14.87040

11.67110

7.91480

13.23370

10.46750

11.03250

8.84710

6.98450

10.98180

9.84090

7.96340

10.32330

11.03610

7.70380

9.71700

11.25560

6.46530

9.80040

10.27260

5.47490

10.45510

9.07600

5.73360

11.40010

9.65060

8.94770

167

10.23030

11.78510

8.48640

9.31780

10.42550

4.51140

10.48690

8.30330

4.97310

168

A.2.6

0R-Dp-2PF6 -M06L

80
0R_Dp_2PF6

5.85140

15.08870

8.50220

1.32500

14.45010

7.20960

13.33310

0.63400

7.01450

15.48120

4.71570

5.87090

5.43870

10.81460

5.42190

4.87070

10.38390

6.15930

6.28880

11.08830

5.96610

10.29560

5.52400

6.91490

10.91390

6.24590

6.47740

10.07760

4.91350

6.12310

7.21370

14.68380

8.41830

7.31820

13.60490

8.56430

7.72950

15.21380

9.21810

7.65310

14.97370

7.45500

0.92870

15.33400

8.23970

1.34270

16.33950

8.09120

1.23820

14.96730

9.22650

-0.15910

15.38190

8.19680

14.44470

-0.07090

6.49930

14.59670

0.13800

5.43280

14.22110

-1.12930

6.63170

15.36650

0.17620

7.04150

15.43870

6.13490

5.76180

14.57280

6.46650

5.18250

16.35570

6.41880

5.24700

15.42310

6.60520

6.75360

4.98260

14.49280

7.65980

3.63350

14.81230

7.86700

3.39340

15.50270

8.66620

2.65640

14.21820

7.07830

3.01240

13.29880

6.08020

2.22910

12.83230

5.49060

4.35470

13.01050

5.87560

169

5.35420

13.61760

6.64140

6.39390

13.34500

6.50250

4.75020

12.01510

4.83140

5.46310

12.42910

4.10970

3.88610

11.64350

4.27290

5.81540

9.77690

4.38660

6.32730

10.32840

3.59200

4.87760

9.38520

3.98160

9.04310

6.15600

7.45870

9.36880

6.78300

8.29620

8.43850

5.34330

7.87190

11.04470

4.77080

7.98600

10.32780

4.08540

8.44740

11.31190

5.52800

8.73070

12.24090

4.04720

7.45600

12.26110

2.65860

7.46280

11.43450

2.07500

7.85660

13.38580

1.99030

6.95780

14.45380

2.70890

6.43550

15.32840

2.22580

6.01720

14.40850

4.11030

6.42140

13.31600

4.78850

6.95780

13.26390

5.86970

6.92220

8.26220

6.97640

6.48160

8.82630

8.11760

5.91170

8.04410

8.97480

5.16120

6.68200

8.72150

4.98890

6.13090

7.54900

5.50230

6.92150

6.67790

6.24200

9.87340

8.35230

6.06590

8.49250

9.87400

4.74680

5.07300

7.33660

5.36280

6.48030

5.78250

6.67400

7.01490

10.53680

8.63190

6.52830

9.86800

10.00720

7.49310

11.22860

7.14670

170

8.03440

11.54010

9.37910

8.18630

9.43230

8.44710

5.83280

11.65260

8.69580

5.98920

9.57060

7.76010

11.77290

7.00400

3.97600

10.97210

8.40350

3.83860

12.53660

5.59560

4.25420

13.18750

7.75640

3.78830

11.89150

7.31390

5.66370

11.62720

6.68730

2.41340

10.34340

6.23800

4.30900

171

Appendix B

Generalization of the Sorption
Process with Multilayers for
Non-Self-Interacting Atoms and
Molecules
Jose L. Mendoza-Cortes, 2012
In this section a formulation to generalize the sorption process of any gas in any framework is
developed. The only restriction is the topology or connectivity of the framework. The parameters
needed are the interaction energies of the guest molecule to the framework. Such parameters will be
reported elsewhere based on DFT calculation. In this paper we only present the formal derivation
of the statistical mechanics of the process and the case of H2 sorption in any framework is studied.

B.1

Given a Topology

The following derivation of the sorption process is solely restricted by the topology and it is focused
in a H2 gas. By the topological constraint we mean the connnectivity in the 3D dimensional space
of periodic structure.
An example is shown below:

B.2

Determine the Occupancy

The topology is going to determine the number of absorption sites that we are going to have for our
system. For our model we use connection that have the same width/distance in every direction this
can be applied to any other model. This can be easily seen in the following picture.

172

Figure B.1: Topological constrain

Figure B.2: Determination of number of adsorption sites

B.3

Gibbs Ensemble

In the following subsection we will explain how every step is derived and how we can build the
Langmuir theory and the Brunauer-Emmett-Teller (BET) theory with this model. At the end we
will see that the restrictions imposed by these two theories are overcomed, which are monolayer for
the the Langmuir theory and infinite layers for the BET case.
We make the following definition and assumptions based on the postulates above:
• Equivalent sites B
• The system has N molecules distributed in B sites
• there are not interaction between molecules
• The lattice may be one-, two-,three- periodic

173
• Let the relation between V and B be V = B × α

B.3.1

Monolayer Theory

Using the the Gibbs ensamble (also known as Grand Canonical distribution) we have

Ξ(µ, τ )

∞ X

N =0 S(N )

exp[(nµ − S(N ) )/τ ]

[S(N ),N =0]

exp[(nµ − S(N ) )/τ ]

(B.1)

Where,
• [S(N ), N = 0] is for all states of the system for all number of partciles
• S(N ) = each S depends on the number of particles. S(N ) is the energy of the state S(N ) of
the exact N = particle Hamiltonian.
Now we can calculate the thermal average number of particles by

S,N N exp[(nµ − S(N ) )/τ ]

hN i =

(B.2)

that combining with
∂Ξ
1X
N exp[(nµ − S(N ) )/τ ]
∂µ

(B.3)

S,N

we obtain:

hN i =

τ ∂Ξ
∂ log Ξ
=τ
Ξ ∂µ
∂µ

(B.4)

From the definition of λ = exp µ/τ we have
hN i
∂ log Ξ
=λ
∂λ

(B.5)

Now taking into account the assumption from the Langmuir theory as two energy states for each
particle as shown in the following figure
E=ε

E=0

Figure B.3: Assumption from Langmuir theory

174
Then we can derive the partition function as
Ξ = 1 + λ exp

−

(B.6)

Using this result into eq B.5 we have:

hN i

λ exp(−/τ )
1 + λ exp(−/τ )
λ−1 exp(/τ ) + 1

(B.7)

Multilayer Theory
In the following sections the multilayer theory generalization is shown and the special case of the
BET theory is shown to be an special case as well as the Langmuir theory.
Given that a gas molecule can be absorbed on each site B, with partition function j1 that can
named “first layer”. Also that this first molecule can be used as a site for another for a “second
layer” molecule and so on. The partition funtion for these other second and beyond molecules is
j∞ . If given N total number of molecules and N1 are in the first layer and N ∗ are in higher layers
(more details can be found elsewhere [161][162]).
Using the grand canonical partition function, we have

Ξ(B, µ, T ) =

exp[(N µ)/kτ ]Q(N, B, T )

N ≥0

=1 +

B!(j1 exp(µ/(kT )))N1
N1 !(B − N1 )!(N1 − 1)!

N1 =1

(N1 + N ∗ − 1)!(j∞ exp(µ/(kT )))N

N ∗!

N ∗ =0

(B.8)
And

Ξ(B, µ, T ) =

N1 =0

B!(y)N1
= (1 + y)B
N1 !(B − N1 )!

(B.9)

where we have defined,

j1 exp(µ/kT )
1 − j∞ exp(µ/kT )

(B.10)

175
Using again
N = kT

∂ log Ξ
∂µ

(B.11)
T,B

and applying it to eqn. B.9 we have
cx
(1 − x + cx)(1 − x)

(B.12)

given c = jj∞
and x = j∞ exp(µ/kT ). This is also known as the BET adsorption isotherm

equation.

B.3.2

Restricted Multilayer Theory

If the adsorption is restricted to n layers,

Ξ(B, µ, T ) =

N1 X
N2

Nn−1

...

N1 =0 N2 =0 N3 =0

Nn =0

B!
(B − N1 )!N1 !

N1 !
(N1 − N2 )!N2 !
Nn−1 !(cx)N1 xN2 +...+Nn
(Nn−1 − Nn )!Nn !

(B.13)

Summing in turn over Nn , Nn−1 , . . ., N1 we find

Ξ = [1 + cx(1 + x + x2 + . . . + xn−1 )]B

1 − xn
= 1 + cx
1−x

(B.14)

Using this into eqn. B.11 we find the BET equation for restricted adsorption
cx[1 − (n + 1)xn + nxn+1 ]
(1 − x)(1 − x + cx − cxn+1 )

(B.15)

This equation is more general since

n=∞

cx
(1 − x + cx)(1 − x)

(B.16)

176
the BET equation, and

n=1

j1 exp(µ/kT )
1 + j1 exp(µ/kT

(B.17)

the Langmuir equation.

B.4

Hydrogen Molecule Case

For the hydrogen gas we assume ideal behaviour, therefore

λ=

nq
τ nq
kB T nq

(B.18)

and
nq =

B.4.1

Mτ
2πh̄2

3/2

M kB T
2πh̄2

3/2
(B.19)

Monolayer Theory in H2

If we apply these assumptions to eqn. B.7 we get the Langmuir equation for H2

hN i

(nq τ /p) exp(/τ ) + 1
(nq τ ) exp(/τ ) + p
p/p0
(nq τ ) exp(/τ )/p0 + p/p0

(B.20)

where p0 = 1 bar. The results are plotted in fig. B.4.
A more complete plot can be seen in fig. B.5 It can bee seen that for ∆H = 20 KJ/mol the
delivery amount has the largest value.
These results can be compared to those published by Bhatia and Myers [58], they reached a close
result but there is an underestimation of the entrophy, The result obtained by them can be seen in
the fig. B.6.

B.4.2

Multilayer Theory in H2

In order to obtain the j1 and j∞ the procedure illustrated in fig. B.7 was used.
In the following sections no interaction between H2 molecules are considered.

177
Langmuir theory for H2 (our generalization)
0.9
Δn – H2 delivery between 5 and 100 bar

0.8

N /Nmax

0.7
0.6

ΔHads = 3 kJ/mol

← Δn25 kJ/mol

0.5

ΔHads = 15 kJ/mol
ΔHads = 25 kJ/mol

0.4
0.3
0.2
← Δn15 kJ/mol

0.1
0 5 10

100

P/P0 (bar)

Figure B.4: Isotherms of H2 uptake using our generalization
Langmuir theory for H2 (our generalization)
← Δn30 kJ/mol

0.9

Δn – H2 delivery between 5 and 100 bar

0.8

N /Nmax

0.7
0.6

← Δn25 kJ/mol

0.5

← Δn20 kJ/mol

0.4

ΔHads = 3 kJ/mol
ΔHads = 15 kJ/mol

0.3

ΔHads = 20 kJ/mol

0.2
← Δn15 kJ/mol

0.1

ΔHads = 25 kJ/mol
ΔHads = 30 kJ/mol

0 5 10

100

P/P0 (bar)

Figure B.5: Isotherms of H2 uptake using our generalization
Langmuir theory for H2 (Bhatia et al.)

← Δn25 kJ/mol

0.9
0.8

Δn – H2 delivery between 5 and 100 bar

N /Nmax

0.7
0.6

ΔH = 3 kJ/mol

← Δn15 kJ/mol

0.5

ΔH = 15 kJ/mol
ΔH = 25 kJ/mol

0.4
0.3
0.2
0.1

← Δn3 kJ/mol

0 5 10

100

P/P0 (bar)

Figure B.6: Isotherm of H2 uptake using the theory by Bhatia and Myers

= e−1 /kT ∼
= e−∆Hads /kT

(B.21)

−∆Hads
/kT

(B.22)

=e
= e−∞ /kT ∼

178
ε2=ε3=ε4=...=ε∞

ε1

Figure B.7: Assumption for the multilayer theory

∆Hads /kT

Surface · · · H2

(B.23)

∆Hads
/kT

H 2 · · · H2

(B.24)

This can also be observed in fig. B.8

Figure B.8: Assumption for the multilayer theory
We performed ab initio quantum mechanics to investigate the interaction of the H2 molecules
with different building blocks for potential COFs. We decided to use density functional theory
(DFT) at the M06 level which has been shown to predict accurately interaction energies for non
covalent interactions including that of H2 . We used the algorithm as implemented in Jaguar 7.0
using the effective core potentials (ECP) for heavy atoms and 6-31G basis set for the outermost core
orbitals when the atoms are not described by ECP. This is also known as LACVP**++ . Some of
the models are shown in fig. B.9.
Thefore using this interaction energy into Eq B.15 we can, in principle, calculate the sorption
isotherm of any framework composed given the ligand. This will be useful to know a priori if a lot
of resources are to be invested in synthesizing certain porous material.

179

L1
L2

L1
M2
L2

H ads

H ads
M=Co, L1 =Cl, L 2=H 2O

A 15.8

M1=M2 =Pt, L 1,L2 ,L 3,L4 =Cl

G 16.9

M=Ni, L 1=Cl, L2 =Cl

B 14.0

M1=M2 =Co, L1 ,L 2,L3 ,L 4=Cl

E 15.0

M=Pt, L 1=Cl, L2 =Cl

C 13.7

M1=M2 =Ni, L 1,L2 ,L 3,L4 =Cl

F 14.4

M=Cu, L 1=Cl, L2 =Cl

9.8

H ads

H ads
12.1

I 13.3

Fe F

Model

L1
M L2
L3

Hads

H ads

M=Ni, L 1=Cl, L2 =Cl

N 17.0

M=Cr, L 1=L2 =L 3=Cl

10.3

M=Zn, L1 =Br, L2=Br

J 15.6

M=Cr, L 1=L2 =L 3=Cl

9.3

M=Cr, L1 =L2 =L 3=Br

8.3

H ads

O Cu N

7.0

Hads

P 17.1

Hads (kJ/mol)

Figure B.9: Models studied with DFT/MO6

B.5

Supplementary Information

B.5.1

NIST Data for H2

NIST have reported the experimental entalphy and entrophy for H2 with respect to standard conditions (298 K, 1 bar) [163].
The data is reported as a empirical formula:

∆H = At +

Bt2
Ct3
Dt4
− +F −H

(B.25)

Ct2
Dt3
− 2 +G
2t

(B.26)

in KJ/mol.
and

S = A log(t) + Bt +
Given:

A = 33.066178
B = -11.363417
C = 11.432816
D = -2.772874
E = -0.158558
F = -9.980797
G = 172.707974
H = 0.000000

180
and t = Temperature(K)/1000.
The results for 298-1000 K are shown in fig. B.10 and fig. B.11.
ΔH298
for H2 (NIST)

[H o − H298.15
] (/(kJ mol−1 )

300

400

500

600

700

800

900

1000

Temperature (/K)

Figure B.10: Experimental data for ∆H of H2
S1bar
for H2 (NIST)

170
165

S o /(J mol K−1 )

160
155
150
145
140
135
130
300

400

500

600

700

800

900

1000

Temperature (/K)

Figure B.11: Experimental data for S◦1 bar of H2

181

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