PREDICTION OF STRUCTURAL AND THERMOCHEMICAL PROPERTIES:
COMPUTATIONAL STRATEGIES FOR SMALL MOLECULES TO PERIODIC
SYSTEMS
By
Zainab H. A. Alsunaidi

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

Chemistry – Doctor of Philosophy
2017

ABSTRACT
PREDICTION OF STRUCTURAL AND THERMOCHEMICAL PROPERTIES:
COMPUTATIONAL STRATEGIES FOR SMALL MOLECULES TO PERIODIC
SYSTEMS
By
Zainab H. A. Alsunaidi
The prediction of thermochemical properties is central in chemistry and is essential in
industry to predict the stability of materials and to gain understanding about properties of
reactions of interest such as enthalpies of formation, activation energies and reaction enthalpies.
Advances in state-of-the-art computing and algorithms as well as high-level ab initio methods
have accounted for the generation of a considerable amount of thermochemical data. Today, the
field of thermochemistry is largely dominated by computational methods, particularly with their
low cost relative to the cost of experiment.
There are many computational approaches used for the prediction of thermochemical
properties. In selecting an approach, considerations about desired level of accuracy and
computational efficiency need to be made. Strategies that have shown utility in the prediction of
thermochemical properties with high accuracy and lower computational cost than high-level ab
initio methods are ab initio composite approaches, or model chemistries, such as the correlation
consistent Composite Approach (ccCA). ccCA has been shown to predict enthalpies of formation
within “chemical accuracy”, which is considered to be 1 kcal mol-1, on average, for main group
elements with respect to well-established experiments.
In this dissertation, ccCA and the commonly used Gn composite methods have been
utilized to establish effective routes for the determination of structural and thermochemical
properties of oxygen fluorides species and for organoselenium compounds. To assess the

reliability of these approaches, enthalpies of formation were calculated and compared to
experimental data. Density functionals have also been employed in these projects to examine
their performance in comparison to experiments as well as to composite methods. The impact of
several thermochemical approaches on the accuracy of the predicted enthalpies of formation via
various computational methods has been also considered such as the traditional atomization
approach and molecular reaction approaches.
Additionally, in this dissertation, the reaction of a direct amination of benzene to produce
aniline on the Ni(111) surface was investigated to identify possible reaction intermediates and to
determine the thermodynamically preferred reaction pathways. The adsorption behaviors and
energetics of all species involved in this reaction are presented. Periodic density functionals were
used to consider this heterogeneous catalytic process. Because DFT is based on the uniform
electron gas model, which in principle resembles the band theory of metallic systems, DFT is
particularly good at modeling metallic systems and thus well suited for the study of
heterogeneous catalysts at the molecular level.

Copyright by
ZAINAB H. A. ALSUNAIDI
2017

This dissertation is dedicated to my husband Uthman and children Riadh, Sahar, and
Yousef.
Thank you for always believing in me.

v

ACKNOWLEDGMENT

I would first like to praise and thank Allah for all the countless blessings and for giving
me the strength and courage to complete this dissertation. The faith in his support, glory, and
mercy has always held me strong.
Upon completion, I would like to acknowledge many people who have been supportive
during my graduate career. First, I would like to thank my research advisor Professor Angela K.
Wilson for continuous support and patience during my PhD study at both the University of North
Texas and Michigan State University. Her mentorship, guidance, motivation, and leadership
have contributed to my growth as an independent scientist. I am very grateful to her for
encouraging me to get publications and to present at conferences. Her words, advice, and actions
have all granted me an incredible academic experience at the U.S.
I acknowledge financial support from the University of Dammam in Saudi Arabia. I
believe that this scholarship has contributed successfully to my personal and academic
development. It also gave me the opportunity to meet and learn from outstanding scientists from
around the world. Without their financial support, none of this would have been possible.
I acknowledge Professor Thomas Cundari for collaboration on the work presented in
Chapter 5 and for his support and enthusiastic sharing of knowledge. I thank my committee
members here at Michigan State University Professor James “Ned” Jackson, Professor Gary
Blanchard, and Professor Katharine Hunt for their time and suggestions. I also thank my former
committee members at the university of North Texas Professor Thomas Cundari, Professor Paul
Marshall, and Professor Mohammad Omary for their time and suggestions during my qualifying
exams.

vi

Thank you to my amazing colleagues in the Wilson group, past and present, for their
continuous sharing of knowledge and techniques. Thank you to Dr. Jiaqi Wang and Michael
Jones for support and helpful conversation. I thank Dr. Kameron Jorgensen, who introduced me
to ab initio composite methods, Dr. Charlie Peterson for fruitful discussion and for help with my
solid state calculations, and Dr. George Schoendorff and Dr. Inga Ulusoy for thoughtful and
interesting discussions. I thank Dr. Deborah Penchoff, for her friendship, many enriching
conversations, and help in managing challenges and stress along the way.
I thank my friends who have been there for me during my Ph.D. work. All of my friends
in Denton have helped me to keep focus and maintain balance through these hectic years. I thank
them for constant cheering and for making our stay in Denton a pleasant experience. The support
from my friends in Saudi Arabia has always been substantial for my success. Their words,
prayers, and encouragement always have been like fuel to continue and to succeed.
I am especially grateful to my immediate family for their love, prayers, words and
encouragements that have been sources of strength and inspiration. I express my greatest
gratitude to my parents, Sajedah and Dr. Husain, for their endless support, prayers, and love, and
who made me what I am today. I am very grateful to my mother- and father-in-law, Khaledah
and Riadh, for their support, love, and encouragement. My deepest gratitude goes to all my
siblings for consistent motivation, support, love, prayers and always believing in me.
Finally, I am endlessly grateful to the love of my life, my husband, Uthman Alhumaidan,
for his patience, understanding, and keeping me calm through all of my stressful challenges.
Your wisdom, genius, kindness, love, and trust have contributed the most in my success. No such
words can describe my gratitude and appreciation. You have been always there for me either to
celebrate a little achievement or to overcome obstacles. I cannot remember any time that you

vii

were disappointed in me even with all of my frustration and absence. Thank you for reminding
me and keeping me involved in my kids’ childhood. Without your support, none of this would
have been possible. To my precious gems Riadh, Sahar, and Yousef, thank you for being such
responsible, supportive, and respectful kids. Thank you for always bringing joy and love to my
life. You are my heroes and my everything.

viii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................................... xii
LIST OF FIGURES ............................................................................................................................. xv
LIST OF SCHEMES.......................................................................................................................... xvii
CHAPTER 1 INTRODUCTION ........................................................................................................... 1
CHAPTER 2 THEORETICAL BACKGROUND ................................................................................. 6
2.1 The Schrödinger Equation .................................................................................................... 6
2.1.1 Born-Oppenheimer Approximation ............................................................................................ 8
2.1.2 Slater Determinant....................................................................................................................... 9
2.1.3 Variational Principle ................................................................................................................. 10
2.2 Ab initio Methods................................................................................................................ 11
2.2.1 Hartree-Fock Approximation .................................................................................................... 11
2.2.2 Post-HF Methods....................................................................................................................... 13
2.2.2.1 Configuration Interaction ...................................................................................... 14
2.2.2.2 Perturbation Theory .............................................................................................. 15
2.2.2.3 Coupled Cluster Theory ........................................................................................ 17
2.3 Density Functional Theory ................................................................................................. 19
2.3.1 Local Density Approximation (LDA) ....................................................................................... 21
2.3.2 Generalized Gradient Approximation (GGA) ........................................................................... 22
2.3.3 Meta-GGA................................................................................................................................. 22
2.3.4 Hybrid- GGA............................................................................................................................. 23
2.4 Basis Sets ............................................................................................................................ 23
2.4.1 Atom-Centered Basis Sets ......................................................................................................... 24
2.4.1.1 Pople Basis Sets .................................................................................................... 26
2.4.1.2 Correlation Consistent Basis Sets ......................................................................... 27
2.4.2 Plane Wave Basis Sets .............................................................................................................. 29
2.4.2.1 Pseudopotentials ................................................................................................... 30
2.5 Composite Methods ............................................................................................................ 30
2.5.1 Gaussian-n (Gn) Theory ............................................................................................................ 31
2.5.2 Correlation Consistent Composite Approach (ccCA) ............................................................... 33
REFERENCES………………………………………………………………………………….……37
CHAPTER 3 DFT AND AB INITIO COMPOSITE METHODS: INVESTIGATION OF OXYGEN
FLUORIDE SPECIES1 ........................................................................................................................ 48
3.1 Introduction ......................................................................................................................... 48
3.2 Computational Methodology .............................................................................................. 54
3.3 Results and Discussion ....................................................................................................... 55
3.3.1 Structures................................................................................................................................... 55
3.3.2 Enthalpies of Formation (ΔH°f, 298) ........................................................................................... 65
3.1 Conclusion .......................................................................................................................... 76

ix

REFERENCES ......................................................................................................................... 78
CHAPTER 4 ENTHALPIES OF FORMATION FOR ORGANOSELENIUM COMPOUNDS VIA
SEVERAL THERMOCHEMICAL SCHEMES ................................................................................. 86
4.1. Introduction ........................................................................................................................ 86
4.2 Computational Details ........................................................................................................ 93
4.2.1 Methods ..................................................................................................................................... 93
4.2.2 Thermochemistry ...................................................................................................................... 94
4.2.2.1 Atomization Approach (RC0) ............................................................................... 94
4.2.2.2 Isodesmic (RC2) and Hypohomodesmotic (RC3) Reaction Schemes .................. 95
4.2.3 Organoselenium Compounds .................................................................................................... 96
4.2.4 Reference Data .......................................................................................................................... 99
4.3 Results and Discussion ..................................................................................................... 102
4.3.1 Atomization Approach Using Composite Methods and B3PW91 .......................................... 104
4.3.2 Homodesmotic Approach Using Composite Methods and B3PW91...................................... 107
4.3.3 Atomization Approach Using Single Point Energies within the ccCA Method...................... 113
4.3.4 Homodesmotic Approach Using Single Point Energies within the ccCA Method ................. 116
4.4 Conclusion ........................................................................................................................ 120
APPENDIX ............................................................................................................................. 124
REFERENCES ....................................................................................................................... 133
CHAPTER 5 TOWARDS A MORE RATIONAL DESIGN OF THE DIRECT SYNTHESIS OF
ANILINE: A DFT STUDY ............................................................................................................... 141
5.1 Introduction ....................................................................................................................... 141
5.2 Computational Details ...................................................................................................... 145
5.2.1 Method .................................................................................................................................... 145
5.2.2. Surface Model ........................................................................................................................ 146
5.2.3 Thermochemistry .................................................................................................................... 147
5.2.4 Method Calibration ................................................................................................................. 148
5.3 Results And Discussion .................................................................................................... 152
5.3.1 Adsorption Geometries and Energies ...................................................................................... 152
5.3.1.1 NH3*, NH2*, NH*, N*, and H*.............................................................................. 152
5.3.1.2 C6H6*, C6H5*, C6H5NH2*, and C6H5NH* .......................................................... 156
5.3.2 Decomposition Reactions ........................................................................................................ 165
5.3.2.1 Decomposition of Ammonia ............................................................................... 165
5.3.2.2 Decomposition of Benzene ................................................................................. 167
5.3.3 Production of Aniline .............................................................................................................. 167
5.3.3.1 Langmuir-Hinshelwood Mechanism .................................................................. 168
5.3.3.2 Rideal-Eley Mechanism ...................................................................................... 169
5.3.4 Desorption of Aniline .............................................................................................................. 170
5.3.5 Density of States...................................................................................................................... 171
5.4. Conclusions ...................................................................................................................... 175
APPENDIX ............................................................................................................................. 176
REFERENCES ....................................................................................................................... 188
CHAPTER 6 CONCLUDING REMARKS....................................................................................... 196
6.1 DFT and Composite Methods Investigations ................................................................... 196
6.1.1 Enthalpies of Formation for Oxygen Fluoride Species via Atomization Approach................ 196

x

6.1.2 Enthalpies of Formation for Organoselenium Compounds via Reactions Schemes ............... 197
6.1.3 Future Interest ......................................................................................................................... 198

6.2 Periodic DFT for the Direct Amination of Benzene on the Ni(111) ................................ 199
6.2.1 Future Interest ......................................................................................................................... 200

REFERENCES ....................................................................................................................... 201

xi

LIST OF TABLES

Table 3.1 Structural parameters of the oxygen fluoride species at different level of theories, bond
lengths are in angstroms and bond angles and dihedral angles in degree. ............................ 56
Table 3.2 The expectation value of the total spin <S2>. ............................................................... 62
Table 3.3 Enthalpies of formation for chlorine oxides and related hydrides. ............................... 67
Table 3.4 Enthalpies of formation for the oxygen fluoride species using M06 and M06-2X paired
with the correlation consistent basis sets. ............................................................................. 68
Table 3.5 Enthalpies of formation for oxygen fluoride species using the different variants of
ccCA method. ....................................................................................................................... 69
Table 3.6 Calculated enthalpies of formation for the oxygen fluoride species using all methods
and the MADs of these methods with respect to the reference data. .................................... 70
Table 3.7 Calculated enthalpies of formation for the oxygen fluoride species using M06 and
M06-2X methods based on B3LYP/aug-cc-pVTZ geometries. ........................................... 74
Table 3.8 Calculated Enthalpies of formation for the oxygen fluoride species using all methods
and the MADs of these methods with respect to the ATcT values. ...................................... 75
Table 4.1 The definition of the homodesmotic reaction schemes according to Wheeler.57,58 ...... 91
Table 4.2 Experimental and estimated enthalpies of formation in kcal mol-1 for organoselenium
compounds.a,b ...................................................................................................................... 101
Table 4.3 Calculated enthalpies of formation (in kcal mol-1) for the elemental products and
reactants of organoselenium compounds via the atomization approach (RC0). ................. 102
Table 4.4 Calculated enthalpies of formation (in kcal mol-1) for the hydrocarbon fragments via
the atomization approach (RC0). ........................................................................................ 103
Table 4.5 Calculated enthalpies of formation (in kcal mol-1) for target organoselenium molecules
via atomization approach (RC0). ........................................................................................ 106
Table 4.6 Calculated enthalpies of formation (in kcal mol-1) for target molecules via the
isodesmic approach (RC2). ................................................................................................. 110
Table 4.7 Calculated enthalpies of formation (in kcal mol-1) for target molecules via the
hypohomodesmotic approach (RC3). ................................................................................. 111
xii

Table 4.8 Overall differences between RC0, RC2, and RC3 using composite methods and
B3PW91. ............................................................................................................................. 112
Table 4.9 Calculated enthalpies of formation (in kcal mol-1) for target organoselenium molecules
via the atomization approach (RC0) using the specified level of theory at the B3LYP/ccpVTZ geometry.a ................................................................................................................ 114
Table 4.10 Calculated enthalpies of formation (in kcal mol-1) for target organoselenium
molecules via isodesmic reaction approach (RC2) using the level of theories specified in the
table, at the B3LYP/cc-pVTZ geometry.a ........................................................................... 117
Table 4.11 Caculated enthalpies of formation (in kcal mol-1) for target organoselenium molecules
via hypohomodesmotic reaction approach (RC3) using the level of theories specified in the
table, at the B3LYP/cc-pVTZ geometry.a ........................................................................... 118
Table 4.12 Overall differences between RC0, RC2, and RC3 using the level of theories specified
in the table.a......................................................................................................................... 119
Table 5.1 Bond dissociation energies (BDE) of gaseous molecules in kcal mol-1. .................... 149
Table 5.2 Adsorption energies (Ead) for ammonia and benzene adsorbed on a Ni(111) surface in
kcal mol-1. ........................................................................................................................... 151
Table 5.3 Adsorption sites and adsorption energies (Ead) (in kcal mol-1) for NHx (x = 0 - 3)
species and H adsorbed on a Ni(111) surface. .................................................................... 153
Table 5.4 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed NHx (x = 1 3) species, adsorbed N, and adsorbed H. ............................................................................ 155
Table 5.5 Vibrational frequencies (in cm-1) of free and adsorbed NH3, NH2, and NH. ............. 156
Table 5.6 Adsorption sites and adsorption energies (Ead) (in kcal mol-1) of the aromatic species
adsorbed on a Ni(111) surface. ........................................................................................... 157
Table 5.7 Bond lengths (r) in Å of free and adsorbed benzene and phenyl. ............................... 162
Table 5.8 Bond lengths (r) in Å and bond angles (a) in degrees of free and adsorbed aniline and
anilide. ................................................................................................................................. 163
Table 5.9 C-H, C-C, C-N, and N-H vibrational frequencies (in cm-1) of gas phase and adsorbed
C6H6, C6H5, C6H5NH2, and C6H5NH. ................................................................................. 164
Table 5.10 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the adsorption and
decomposition reactions of ammonia on the Ni(111) surface, all in kcal mol-1.a ............... 166

xiii

Table 5.11 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the adsorption and
decomposition reactions of benzene on the Ni(111) surface, all in kcal mol-1.a................. 167
Table 5.12 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the proposed reaction
processes of the production of aniline on the Ni(111) surface, all in kcal mol-1.a .............. 169
Table 5.13 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the desorption reaction
of aniline on the Ni (111) surface, all in kcal mol-1.a .......................................................... 170
Table 5.14 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed benzene and
phenyl. ................................................................................................................................. 183
Table 5.15 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed aniline and
anilide. ................................................................................................................................. 184
Table 5.16 Calculated vibrational frequencies of gas phase and adsorbed aromatic species,
in cm-1. ................................................................................................................................ 185

xiv

LIST OF FIGURES

Figure 3.1 B3LYP/aug-cc-pVTZ structures of the oxygen fluoride species included in this study.
............................................................................................................................................... 64
Figure 4.1 Selenium-containing elemental reactants and products. ............................................. 97
Figure 4.2 Isodesmic (RC2) reaction schemes. ........................................................................... 98
Figure 4.3 Hypohomodesmotic (RC3) reaction schemes. ............................................................ 98
Figure 4.4 The mean absolute deviations (MADs) of the calculated enthalpies of formation using
three thermochemical schemes, RC0, RC2, RC3, with composite methods and single point
energy calcuations utilized within ccCA methodology. ..................................................... 123
Figure 4.5 The optimized structures for organoselenium molecules at the B3LYP/cc-pVTZ level
of theory. a. Dimethyl selenide. b. Dimethyl diselenide. c. Divinyl selenide. d. Diethyl
selenide. e. Diethyl diselenide. f. Diisopropyl selenide. g. Dipropyl selenide. h. Dibutyl
selenide ............................................................................................................................... 125
Figure 5.1 Adsorption structure of ammonia (a) and benzene (b) on the Ni(111) surface. (*)
Indicates an adsorbed molecule. ......................................................................................... 151
Figure 5.2 Adsorption sites of NH2 (a), NH (b), N (c), and H (d) on the Ni(111) surface.
(*) Indicates an adsorbed molecule..................................................................................... 154
Figure 5.3 Adsorption sites of phenyl (a), aniline (b), and anilide (c) on the Ni(111) surface.
(*) Indicates an adsorbed molecule..................................................................................... 160
Figure 5.4 A top view of aniline adsorbed on the p(3x3) surface unit cell of Ni(111) on bridge
site A (a), on the p(5x5) surface unit cell on bridge site B (b), and a side view of aniline
adsorbed on the large 5x5x4 Ni(111) slab model. .............................................................. 161
Figure 5.5 The local density (LDOS) of N in NH (a), N (b), and Ni (d) in NH/Ni(111) system and
the density of states (DOS) of clean Ni(111) surface (c). ................................................... 174
Figure 5.6 Spin density of the NH/Ni(111) system. ................................................................... 174
Figure 5.7 Lattice constant convergence test for bulk fcc Ni using variable Ecutoff and fixed kpoints (9x9x9). The DFT-optimized lattice constant is 3.52 Å .......................................... 177
Figure 5.8 K-points convergence test for the Ni(111) surface using two values of Ecutoff (400 and
500 eV). The optimal set of k-points for our systems is 5x5x1. ......................................... 177
xv

Figure 5.9 Energy cut off convergence test for the Ni(111) surface using 5x5x1 k-points. The
optimal energy cut off for our systems is 400 eV................................................................ 178
Figure 5.10 Adsorption sites and adsorption energies (Ead) of NH2 adsorbed on an fcc site (a),
and NH2 adsorbed on an atop site (b) of the Ni(111) surface. (*) Indicates an adsorbed
molecule. ............................................................................................................................. 179
Figure 5.11 Adsorption sites and adsorption energies (Ead) of C6H5 adsorbed on an hcp site (a),
and C6H5 adsorbed on a bridge site (b) of the Ni(111) surface. (*) Indicates an adsorbed
molecule. ............................................................................................................................. 179
Figure 5.12 The local density of states (LDOS) of N in NH2 (doublet) (a), N (b), in NH2/Ni(111)
system. ................................................................................................................................ 180
Figure 5.13 The density of states (DOS) of clean Ni(111) surface (a) and the local density of
states (LDOS) of Ni in NH2/Ni(111) system (b). ............................................................... 181
Figure 5.14 Spin density of the NH2/Ni(111) system. ................................................................ 182

xvi

LIST OF SCHEMES

Scheme 5.1 Synthesis of aniline. Adapted from Reference 1. .................................................... 142
Scheme 5.2 The proposed direct route of the production of aniline. .......................................... 143
Scheme 5.3 The overall modeled reaction for the direct production of aniline. ......................... 144
Scheme 5.4 The Ni(111) surface model. .................................................................................... 146
Scheme 5.5 Possible reactions pathways for the production of aniline and the change in the
reaction free energies for each process. ................................................................... 171

xvii

CHAPTER 1 INTRODUCTION

Computational chemistry is a rapidly growing field of chemistry that uses fundamental
physics, mathematics, and computer simulation to investigate chemical systems. Advances in
high computing performance have played an important role in improvements in computational
methods and algorithms that, in turn, facilitate the elucidation of complex chemical systems,
such as solids, biological macromolecules, polymers, and ionic liquids. Information such as
electronic structure, reactivity of atoms and molecules, thermochemical and spectroscopic
properties, just to name a few, can all be reliably provided from high-level theoretical
calculations. This information helps chemists to gain in-depth understanding of a particular
chemical problem and develop and design new reactions or systems. Computational applications
also aid in interpreting available experimental measurements and provide predictions for
systems/properties that are unknown or unexplored, or that are difficult to address
experimentally. Nowadays, applications in critical areas such as anti-cancer drugs, energy
development, astronomy, and green chemistry have been explored theoretically.
Two main classes of computational chemistry methods are molecular mechanics and
electronic structure methods and within each class are numerous approaches. Each family of
approaches differs in the type of approximation, attainable accuracy, and computing resources
required (disk space, time, and memory). Knowing the applicability and limitations of a theory
allow suitable methods to be selected for a given chemical problem while taking into account the
system size, the target accuracy, the available computing resources, and the property of interest.
Molecular mechanics (MM) are classical mechanics approaches that solve for Newton’s
equations of motion using pre-determined empirical force fields to describe potential energy

1

surface (PES). MM are highly useful approaches for providing molecular and thermodynamic
properties of large molecules, as large as >10000 atoms, such as enzymes, from a macroscopic
perspective. These approaches are used intensively in biochemical research. The reliability of a
MM calculation depends on how accurate the empirically derived force fields are and how
suitable/transferable they are for a system of interest and on the correct sampling of the phase
space.
Electronic structure methods, on the other hand, are quantum mechanical approaches that
are based on solving the time-independent Schrödinger equation and are increasingly important
in chemistry, physics and material science. They can be categorized into three classes: ab initio
molecular orbital (MO) theory, density functional theory (DFT), and semi-empirical methods.
Both semi-empirical and ab initio methods are wave function based; however, unlike ab initio
methods, semi-empirical methods, as expected from the name, use fitting parameters typically
derived from experimental data (e.g. enthalpy of formation, ionization potentials, structural
parameters, and dipole moments) to compensate for approximations made to the quantum
mechanical model, such as neglecting two-electron integrals, i.e. electron correlation is
approximated using empirical parameters. Although semi-empirical methods are computationally
faster compared to ab initio methods, and can be applied to systems containing >1000 atoms,
they are less accurate than ab initio methods and their accuracies are dependent on the
experimental database for which they were parameterized.
In this dissertation, ab initio molecular orbital (MO) theory and density functional theory
(DFT), discussed in more detail in Chapter 2, were employed to investigate systems spanning
from small inorganic molecules to larger organic compounds to extended periodic systems. The
aim is to utilize various computational approaches and strategies to predict accurate (within “or
2

near “chemical accuracy”) thermochemical properties and to evaluate the performance of these
methods relative to experiment, where available. Another aspect of this work is to use density
functional theory as well as statistical thermodynamic to identify and study possible adsorbed
intermediates involved in a heterogeneous reaction process.
Ab initio methods are developed from first principles (physical constants), i.e. do not use
empirically obtained force fields or parameters, and use several approximations to solve for the
many-body Schrödinger equation. If these approximations are small in magnitude (such as in
Configuration Interaction (CI)), accurate solutions to the Schrödinger equation can be achieved
yet at high computational cost. These less approximated methods can be only applied to small
molecules. Density functional theory, however, can be applied to larger systems (~100 - 1000
atoms) at a moderate computational cost, i.e. DFT scales as N4, where N represents the number
of basis functions. DFT solves for the Schrödinger equation in terms of the total electron density
instead of a wave function. The solution for the Schrödinger equation provides a real numerical
value of the energy of a system and its electron distribution. Calculating the second derivative of
the energy (Hessian matrix) with respect to atomic positions determines force constants and
vibrational frequencies. This information allows predicting thermochemical properties including
enthalpies of formation, bond dissociation energies, ionization potentials, and electron affinities.
There are strategies that have been established to address the accuracy and high
computational cost demands of high-level ab initio methods. For example, a number of ab initio
composite approaches,

or model chemistries, have been developed for predicting

thermochemical properties with accuracies that mimic those possible from high-level ab initio
methods, such as coupled cluster with single, double, and perturbative triple excitations
(CCSD(T)), but with reduced computational cost. Composite methods utilize a series of steps
3

combining lower level methods and basis sets to replicate results with higher-level methods.
Gaussian-n (Gn) composite methods and the correlation consistent Composite Approach (ccCA)
both are discussed in Chapter 2 and were utilized in Chapter 3 and Chapter 4.
Understanding the utility of theoretical methods for predicting energetic properties of
various classes of molecules is important, and can lead to the development of effective strategies
for future studies. In Chapter 3, composite methods including ccCA, G3, and G3B3 are utilized
for the prediction of enthalpies of formation (∆ ° ′ ) for oxygen fluoride species, which is

compared to reliable experimental data. In addition, the performance of several density
functionals including M06 and M06-2X, for determining structures and ∆ ° ′ of the same set of

oxygen fluorides also was examined. The set includes fluorides, difluorides, dioxides, trioxides,
and the corresponding hydrides. These molecules have been a great challenge for the
computational community particularly due to the unusual geometry of molecules such FOO and
FOOF.
The research in Chapter 4 includes the prediction of accurate enthalpies of formation for
a set of organoselenium compounds using several thermochemical schemes via composite
methods and density functionals. Selenium compounds play a substantial role in organic
synthetic reactions, in the semiconductor industry, and in biochemistry. Thermochemical

properties, particularly ∆ ° ′ , are of great importance in providing predictions and insight

about chemical reactions including molecular stability, reaction enthalpy, and bond dissociation
energy. Isodesmic and hypohomodesmotic reaction schemes have been developed to cancel
errors arising from differential correlation effects and size extensivity (which will be discussed
herein), which, in turn, can result in a better prediction of ∆ °
4

as compared with the

conventional atomization approach.
In Chapter 5, plane-wave DFT is employed to investigate possible reaction mechanisms
for the direct amination of benzene on the Ni(111) surface. The direct amination of benzene to
produce aniline is of significant interest from a green chemistry perspective, although, it is very
challenging because of the strong C-H bond of benzene and the N-H bond of ammonia. In this
research, a full detailed study of this reaction including adsorption behaviors (structures,
energetics, frequencies, electronic interactions) of all species on the Ni(111) surface and
thermochemical properties is done and suggestions of reliable computational models are
provided. The study uses the PBE and PBE-D3 functionals to determine adsorption structures
and energetics for a variety of adsorption systems including adsorbed NHx species and adsorbed
aromatic species to consider possible reaction intermediates relevant to the direct amination of
benzene. Statistical thermochemistry is employed to calculate reaction enthalpies and reaction
free energies of the proposed reaction pathways between imide and benzene. The study also aims
to compare and correlate a heterogeneous Ni(111)–imide model with the corresponding
homogenous nickel-imide model for the C-H amination reaction. In Chapter 6, all of the research
projects are summarized and future interests are discussed.

5

CHAPTER 2 THEORETICAL BACKGROUND

2.1 The Schrödinger Equation
In quantum mechanics, electrons are described using a wave function (Ψ). The wave
function conveys all information of the state of the system and can be used with an operator to
measure an observable property of a given system. A cornerstone wave equation of quantum
mechanics is the non-relativistic time-dependent Schrödinger equation,1–6 Eq. 2.1,
−

where

ℏ

Ψ , ,

=

Ψ , ,

is the Hamiltonian operator (the energy operator), Ψ , ,

(2.1)
is the wave function of

electronic coordinates, nuclear coordinates, and time, respectively. equals to √−1, and ℏ equals
to ℎ ⁄ 2 , where ℎ is the Planck’s constant. The time-dependent Schrödinger equation describes
how a wave function Ψ , ,

for a system evolves with time when governed by a Hamiltonian.

In other words, it describes the dynamics of a given system and provides the probability
distribution of the state of the particle at each time.
In quantum chemistry, many applications are concerned with obtaining the constant
energy of stationary states, i.e. standing waves that have no time dependence, of a chemical
system. Hence, the non-relativistic time-independent Schrödinger equation, Eq. 2.2, is widely
used, which can be derived from Eq. 2.1 using the separation of variables principle in which the
wave function is factored into a function that depends only on spatial coordinates and a function
that depends only on time. The time-independent Schrödinger equation, Eq. 2.2, is employed in
this dissertation and will be referred to as the Schrödinger equation henceforth. It is a second
order differential equation in electronic and nuclear coordinates. The Schrödinger equation is
6

also an eigenvalue equation, where the Hamiltonian operator (H) is applied to a wave function
,

(

) that describes the chemical system to give the total energy (E) of that system.7
,

=

,

(2.2)

The Hamiltonian is shown in Eq. 2.3 in atomic units and is expressed as the sum of the
kinetic energy ( ) and potential energy ( ) operators of N electrons (i and j) and M nuclei (A and
B) within a system:
%

1

1

%

%

%

1
1
∇/$
3/
1
$
= − ! ∇# − !
−!!
+ !!
| / − #|
2)*))+ 2
0/ ())))*)
7 # − 87
()*)+
()
)))+ ()
#&'
/&'
/&' #&'
#&')
89#
))*)
)))+
,-

1

,2

1

3/ 3:
+!!
| / − :|
())))*))))+
/&' :9/

52-

5--

(2.3)

522

where MA is the mass of the nuclei, 3/ and 3: are the charges of nuclei A and B, respectively.

|

/

− # | is the distance between an electron and a nucleus, 7 # − 8 7 is the distance between two

electrons, |

/

−

:|

is the distance between two nuclei, and ∇$ is the Laplacian operator. The

first two terms represent the kinetic energy operator of the electrons ( ; ) and the nuclei ( < ). The

following terms correspond to the potential energy operator of the attraction between electrons
and nuclei (

<; ),

the repulsion between electrons (

;; ),

and the repulsion between nuclei (

<< ).

8

The Schrödinger equation, Eq. 2.2, elucidates that certain energy levels (eigenvalues) are
allowed for a given system and correspond to wave functions that are the stationary state
solutions (eigenfunctions) of this given system. The wave function itself is not measureable,
however it can be squared (

∗

) to give the probability, |

$ |of

finding an electron within a

given region in space, according to Max Born,9 i.e. it can describe the electron density of the
7

system. The integral of |
normalized wave function.

$|

over all the volume space >? must be equal to one for a
@|

$|

>? = 〈 | 〉 = 1

(2.4)

2.1.1 Born-Oppenheimer Approximation
The Schrödinger equation cannot be solved exactly except for one electron systems such
as hydrogen atom or hydrogenic cations. Thus, solving for the total energy for multi-electron
systems requires the use of approximations due to the many body problems arising from the
correlation of the motion of many electrons in the Schrödinger equation. One fundamental
approximation is based on the fact that the masses of the nuclei are much larger than the mass of
the electrons, which, in turn, means that the nuclei move more slowly than the electrons for a
given kinetic energy. Thus, the nuclei can be considered fixed with respect to the motion of the
electrons. This is the essence of the so-called Born-Oppenheimer approximation10 that allows a
decoupling of the nuclear and electronic motions. With the assumption that the electrons move in
the field of fixed nuclei, the Hamiltonian can be reduced to an expression independent of the
nuclear motion8 as shown in Eq. 2.5,
;C;D

%

1

%

%

%

1
3/
1
= − ! ∇$E − ! !
+!!
| / − #|
2)*))+ ())))*)
7 # − 87
()
)))+ ()
#&'
/&' #&'
#&')89#
))*)
)))+
,-

52-

5--

(2.5)

where the kinetic energy term of the nuclei ( < ) is zero when applying the Born-Oppenheimer
approximation. The repulsion between the nuclei (

<< )

becomes a constant that is obtained

classically via Coulomb’s law. Since constant terms in an operator do not have an effect on the
wave function, the (

<< )

term is not included in the electronic Hamiltonian. When the electronic

8

Hamiltonian (
is obtained

;C;D )

is applied to a wave function, the electronic Schrödinger equation, Eq. 2.6,

;C;D

where

;C;D

=

;C;D

;C;D

;C;D

is obtained from a separation of variables from

(2.6)
,

.

The addition of the potential energy of the repulsion of nuclei (
;C;D

energy

results in the total energy
FGF

=

FGF
;C;D

<< )

to the electronic

of the system, as shown in Eq. 2.7.
1

1

3/ 3:
+!!
| / − :|
())))*))))+
/&' :9/
522

(2.7)

2.1.2 Slater Determinant
The electronic wave function

;C;D

in the electronic Schrödinger equation (Eq. 2.6)

must be a product of both the spatial and spin functions in order to fully describe an electron. As
fermions, electrons cannot share the same set of quantum numbers, i.e. they must obey the Pauli
exclusion principle.11,12 Furthermore, the electronic wave function is required to be
antisymmetric with respect to the interchange between spatial or spin functions. To achieve both
conditions a determinant can be utilized to construct an antisymmetric wave function which was

introduced first by Slater.13 For an N-electron system x' , x$ , … , x% occupying N spin orbitals
(J# , J8 , … , J% (2.8), the Slater determinant satisfies the requirement of an antisymmetric wave

function,

9

Ψ x' , x$ , … , x%

where

'

√%!

J# x'
1 J# x$
MM
=
⋮
√K!
J# x%

J8 x'
J8 x$
⋮
J8 x%

⋯
⋯
⋱
⋯

J% x'
J% x$ M
M
⋮
J% x%

(2.8)

is a normalization factor. The rows in a Slater determinant represent electrons and the

columns represent spin orbitals. The interchange between two electrons (two rows) or two spin
states (two columns) changes the sign of the determinant. In addition, if the same electron
occupies the same spin orbital, then two columns will be equal and the determinant is zero.8

2.1.3 Variational Principle
The variational principle states that for a well-behaved wave function the expectation
value of the Hamiltonian must result in an energy
ground state energy (
energy.

Q)

) that is greater than or equal to the exact

of that system, as shown in Eq. 2.9, i.e. there is a lower bound to the

=

〈Ψ7H7Ψ〉
≥
〈Ψ|Ψ〉

Q

(2.9)

The wave function Ψ here is a trial wave function and the expectation value is the resultant
trial energy

. For a normalized wave function, the denominator 〈Ψ|Ψ〉, as mentioned earlier,

equals 1 and thus the energy

will equal to 〈Ψ7H7Ψ〉.

The variational principle allows the determination of the best wave function that gives the
most accurate energy, i.e. the lowest energy of a given system. The more parameters the trial
wave function contains, the closer the trial energy is to the exact ground state energy.

10

In order to solve the Schrödinger equation, approximate forms of the electronic
Hamiltonian, termed methods, are used in combination with basis sets, which are mathematical
functions used to construct the wave function. There are now several methods utilized for this
purpose, such as ab initio methods, semiempirical methods, and density functional theory (DFT).
Here the focus is only on the ab initio and density functional methods.

2.2 Ab initio Methods
Ab initio means “from the beginning,” indicating that these calculations are based on
quantum mechanics, physical constants, and laws of physics without reference to empirical data
or parameters. The lack of experimental parameters makes ab initio methods flexible to apply to
different systems and problems without showing any degree of bias. Various ab initio methods
have been developed based on the type of approximation employed to solve the Schrödinger
equation.

2.2.1 Hartree-Fock Approximation
The Hartree-Fock (HF) approximation14–18 is among the simplest ab initio methods and is
often the first approximation made when solving the Schrödinger equation for multi-electron
systems. It can be used to provide a well-defined starting point for more advanced wave function
based methods. The electron-electron repulsion in HF theory is computed using the mean-field
approximation that treats the motion of each electron in an average potential field of other
electrons. The Hartree-Fock wave function ΨTU is a single Slater determinant and for an N

electron system occupying N spin orbitals (J# , J8 , … , J% is
11

ΨTU = |J' J$ ⋯ J% V

(2.10)

The variational principle is used to select the “best” spin orbitals that will give the lowest energy
when using the HF equation, Eq. 2.10. The eigenvalue HF equation can be written as

where J#

WX# J#

= Y# J#

(2.11)

represents the one-electron orbital wave function, Y# is the energy of that orbital,

and WX# is the Fock operator of the form

<ZDC;#

1
3/
WX# = − ∇$# − !
+ [ TU
| / − #|
2

(2.12)

/&'

The first two terms in the Fock operator, Eq 2.12, represent the one-electron core

Hamiltonian ℎ# , which consists of the kinetic energy of the electron and the potential energy of
the attraction between the electron and nuclei, respectively. [ TU

corresponds to the effective

potential of the interaction of the ith electron with the average charge density of the rest of the
electrons, and is called the Hartree-Fock potential. The HF potential depends on the coulomb and
the exchange potentials that are generated from the interaction of one-electron with the field of
the remaining electrons. Because this term depends on all other electrons, an iterative scheme
must be used to solve the HF equation in order to obtain optimized orbitals and their energies.
This can be achieved by using the self-consistent field (SCF) methods.
The solutions to the HF equation are a set of optimized molecular orbitals (MOs) that are
constructed from the linear combination of the one-electron atomic orbitals (LCAO). The HF
limit can be obtained by using an infinite set of basis functions (that construct the one-electron

12

atomic orbitals) and it provides the lowest energy accessible for the ground state energy of a
system when electron correlation is a mean field correlation.
The HF approximation accounts for ~99% of the total energy of a system,19 the
remaining ~1% energy, which is due to the electron-electron correlation beyond the mean field
approximation, is critical for describing the chemistry of a given problem.20 The electron
correlation energy (
(

;]^DF )

DG\\ )

is defined as the difference between the exact energy of a system

and the HF energy (

TU ).
DG\\

=

;]^DF

−

TU

(2.13)

2.2.2 Post-HF Methods
To obtain more accurate information of a chemical system, post-HF methods have been
developed to account for the electron correlation energy. Examples of these methods include
configuration interaction (CI), Møller-Plesset perturbation theory (MPn), and coupled cluster
theory (CC). The electron correlation energy can be accounted for by mixing in excited state
determinants in addition to the HF Slater determinant to improve the quality of the wave
function. The linear combination of the HF wave function and the excited state determinants
results in a new trial energy that is lower than the HF energy and approaches to the exact energy
when using a variational method, such as CI and CC. This multi-determinant wave function can
be written as
Ψ = _Q Φab + ! _# Φ#
#&'

13

(2.14)

where _Q is the coefficient of the HF wave function ΦTU and it depends on the normalization of

the wave function. The _# coefficients define the weight of each excited state determinant Φ#

into the wave function.

2.2.2.1 Configuration Interaction
The CI method is similar to the HF method where both utilize the variational principle.
However, instead of using a single Slater determinant in the HF approximation, CI defines the
wave function (Ψcd as a linear combination of the possible determinants arising from excitations

from the reference state. Typically, the reference state is the Slater determinant corresponding to

the ground state HF wave function Φab , though faster convergence to the exact energy

sometimes can be obtained using other reference wave functions. The possible excitations can be
grouped as single (S), double (D), triple (T), etc., excitations from the reference state up to n-

tuple excitations, where n is the number of electrons. If the CI expansion (Eq. 2.15)20 is not
truncated, then the method is called Full Configuration Interaction (Full-CI).
Ψcd = _Q Φab + ! _e Φe + ! _f Φf + ! _g Φg + ⋯ = ! _# Φ#
e

f

g

#&Q

(2.15)

In Equation 2.15, _# is the coefficient corresponding to each configuration and each _# is

a variational parameter that is varied to minimize the total energy. Full CI provides the “exact”
non-relativistic solution of the Schrödinger equation within the Born-Oppenheimer

approximation for the working basis. When a complete basis set is used, the method is called
Complete CI and the truly exact non-relativist energy is obtained.
The computational cost of Full CI increases dramatically as the number of orbitals
increases, to which the Full CI becomes impractical. A binomial coefficient, shown in Eq. 2.16,

14

can be used to provide the number of determinants required for a system with K number of
orbitals and N number of electrons
h

2i
2i !
j=
K
K! 2i − K !

(2.16)

Because of the high computational scaling of the Full CI method, it is usually truncated to
include only certain number of the possible excited state determinants. For example, CIS only
includes the ground state wave function and the singly excited determinants. CISD includes the
singly and doubly excites determinants as well as the ground state wave function, and so on.
These truncated CI methods, although can be computational feasible, they are size inconsistent
methods. If the energy calculated from the sum of energies of two individual atoms is equal to
the energy calculated when these two atoms are at infinite distance from each other, i.e. they are
non-interacting, then the method is size consistent.8

2.2.2.2 Perturbation Theory
Another non-variational method for recovering correlation energy is many-body
perturbation theory (MBPT). The MBPT concept is to use a well-defined approximate solution to
Schrödinger equation to a certain chemical problem as a reference and then add a correction to
this reference as a perturbation. The assumption is that the approximate solution that is used as
the zeroth order Hamiltonian and wave function should be close to the exact solution, i.e. the
perturbation must be small if the perturbation expansion series is to be convergent.
Mathematically, MBPT defines the full Hamiltonian operator ( ) of a system as a sum of two
parts, a reference, unperturbed zeroth order Hamiltonian

Q

and a perturbation Hamiltonian

k ′ , where k defines the level of perturbation (correction), Eq. 2.17.
15

=

Q

+k ′

(2.17)

In addition, the perturbed wave function is expanded in the form
<

Ψ = ΨQ + ! k# Ψ#

(2.18)

#&'

and the total energy will be in the form
<

E = EQ + ! k# E#

(2.19)

#&'

One commonly used form of perturbation theory is the Møller-Plesset (MPn) perturbation
theory.21 The MPn perturbation theory uses the sum over the one-electron Fock operator, defined
in Eq. 2.12, as the zeroth order Hamiltonian

Q

and the Hartree-Fock determinant as the zeroth

order wave function ΨQ . The Fock operator double counts the average electron-electron term

〈

;; 〉,

thus the perturbation Hamiltonian, which represents the remaining correlation, becomes8,20
=

where the

−

Q

= 〈

;; 〉 −

2〈

;; 〉

=−〈

;; 〉

(2.20)

is the full electronic Hamiltonian.

The wave function and the energy can then be expanded in Taylor series. The eigenvalue
equation of the ith eigenfunctions when the perturbations is added can be written as
Q

+ k ′ ! k< Ψ# <
<&Q

= ! k< E# <
<&Q

! k< Ψ# <

<&Q

where n represent the order of the perturbation to the zeroth order energy

(2.21)
Q

. The first-order

energy correction returns the Hartree-Fock energy, i.e. it does not include electron correlation
beyond HF theory. The most commonly used MPn method is the second-order energy correction

16

(MP2) method, which only involves perturbation of double excitation states and accounts for
about 80-90% of correlation energy.20 The energy of the second order correction has the form22
GDD p#\

MP$ = ! !

#q8 ^qo

^o
^o
〈ΦQ |H′|Φ#8
〉〈Φ#8
|H′|ΦQ 〉
Q

−

^o
#8

(2.22)

where and r refer to occupied orbitals, _ and s refer to virtual orbitals. ΦQ is the HF wave
^o
function and Φ#8
is the doubly excited wave function.

2.2.2.3 Coupled Cluster Theory
Coupled cluster theory (CC)23–26 is similar to the CI method in that it uses the HF wave
function as a starting point to construct the CC wave function that includes excited state
determinants (e.g. S, D, T, Q, etc.). The CC wave function ( Ψcc ), Eq. 2.23, includes an

exponential cluster operator , defined in Eq. 2.24 and Eq. 2.25, that acts on the reference wave
function ΦQ to generate all possible excitation states,

Ψtt = u , ΦQ

u, = 1 +

'

+h
+

$

1
2!

=

+

1
2!

$

$

+

'
'

$

+

$

j+h

1
2!

'

$

+ ⋯+
v
$

+

+

(2.23)

%;C;D

' $

1
4!

'

+

x

1
3!

+ ⋯

(2.24)
'

v

j+

x

+

v '

(2.25)

where ΦQ is the HF wave function. The first term in Eq. 2.24 is the HF determinant. Single
excitation states are generated by

',

double excitation are generated by

17

$

and

'

$

, triple

v,

excitations are generated by

' $,

'

and

v

#

. All

are connected operators while the

remaining other operators are called disconnected operators (products of connected operators),
such as

'

$

and

' $.

Examples of the excitations are shown below, where is the amplitude

which is analogous to the _# coefficient of the CI method. Eq. 2.26 and Eq. 2.27 are two
examples of single and double excitations, respectively, using connected operators. Eq. 2.28, on
the other hand, represents triple excitations using disconnected operators.
' |ΨQ V

GDD p#\

= !!
#

^

GDD p#\

1
!!
$ |ΨQ V =
4
#8 ^o

'

GDD p#\

1
!!
$ |ΨQ V =
4

#8{^oD

^
#

|Ψ#^ V

^o
#8

|Ψ#^8o z

^ oD
# 8{

|Ψ#^8o{D z

(2.26)

(2.27)

(2.28)

⋯

The utilization of the disconnected operators in the CC methods allows the generations of
all possible excitation configurations of each type of excited determinant. It is the cluster
operator that makes the CC theory an outstanding computational method and superior over the
CI method. In fact, it is the inclusion of the disconnected cluster operators that accounts for the
faster convergence to the exact energy of the CC expansion compared to the CI expansion.
Moreover, it is also the disconnected cluster operators that make a truncated CC expansion size
extensive in contrast to a truncated CI expansion.
Perhaps the most widely used coupled cluster method is the CCSD(T), which includes
single and double excitations and a perturbative inclusion of triple excitations. CCSD(T) in

18

conjunction with sufficiently large basis functions can usually provide accurate energetics within
± 1 kcal mol-1 deviation from experimental data for the light main group species that are
dominated by a single determinant.20
Although the post-HF methods yield more accurate energetics than HF alone, these
methods can be computationally intensive. The HF method scales as N4, where N is the number
of basis functions. The cost of post-HF methods typically increases exponentially or even
combinatorially. While the minimal scaling of the correlation methods (post-HF methods) is N5
as in MP2, it can be as high as NN! as in the Full CI. CCSD and CCSD(T), on the other hand,
scale as N6 and N7, respectively. MP3 and MP4 scale as N6 and N6, respectively. As the
computational scaling of an ab initio method increases, the computational cost in terms of
memory, CPU time, and disk space increases. Thus, achieving a balance between efficiency and
accuracy is often important particularly for large chemical systems.

2.3 Density Functional Theory
Density functional theory (DFT)27–29 is a common electronic structure method that is used
in physics, chemistry, and material science to study chemical and physical related problems.
DFT scales roughly the same as HF, (N4), but with a pre-factor that is dependent of the density
functional employed. The advantage is that DFT accounts for electron correlation energy
typically at a lower computational cost than post-HF methods. Modern DFT has been developed
based on two theorems: the Hohenberg-Kohn30 and the Kohn-Sham31 theorems, in which both
rely on the fact that there is a unique relationship between the electron density and the ground
state energy.30,31 Thus, all properties of a given system can be calculated as a function of the

19

electron density |

, which is the square of the wave function integrated over N-1 electron

coordinates, Eq. 2.29. In ab initio methods, the wave function depends on the 3N coordinates of
each of n-electrons (can be 4N if electron spin is taken into account), while in DFT the electron
density is only a function of the three dimensions of space, i.e. |
|

%-€-•

= K ! @ |Ψ
#&'

' , $, ⋯ , %

|$ > $ >

= W }, ~, • .

v⋯> %

(2.29)

In the Kohn-Sham (KS) theory, the kinetic energy is calculated from an N independent
non-interacting electron system that is constructed from a single determinant wave function of a

‚|ƒ for a fully interacting

fully interacting system.31 The total Kohn-Sham DFT energy
system is defined as in Eq. (2.30)20

where

„ ‚|ƒ

‚|ƒ =

„ ‚|ƒ

+

<; ‚|ƒ

+ …‚|ƒ +

†t ‚|ƒ

is the kinetic energy of the non-interacting electrons,

(2.30)

<; ‚|ƒ

is the potential energy

of the attraction between the nuclei and the electrons, …‚|ƒ is the Coulomb term representing the
electron-electron repulsion, and

†t ‚|ƒ

is the exchange-correlation energy that accounts for all

the remaining terms of the electron-electron interactions, e.g. the kinetic energy caused by
interacting electrons. The DFT energy expression, Eq. (2.30), is within the Born-Oppenheimer
approximation as there is no nuclear kinetic energy and the internuclear repulsions are still
solved classically.
The exchange-correlation energy

†t ‚|ƒ

is a functional of the electron density and can be

divided into two approximate functionals; the exchange functional (
same-spin electron interactions and the correlation functional (
mixed-spin electron interactions as

20

† ‚|ƒ

t ‚|ƒ

corresponding to the
corresponding to the

†t ‚|ƒ

=

† ‚|ƒ

+

t ‚|ƒ

(2.31)

Because the exact form of the exchange-correlation functional is unknown, a variety of
approximations of the

†t

formulations have been developed. These approximations can be

categorized into two main classes: the local density approximation (LDA), which utilizes local
functionals that depend only on the electron density | and the generalized gradient

approximation (GGA) that uses gradient-corrected functionals that depend not only on the
electron density | but also on its gradient ( ∇‡ ). Perdew42 presented a hierarchy of DFT

functionals and named it the “Jacob’s Ladder” of DFT, which includes LDA (first rung), GGA
(second rung), meta-GGA (third rung), hybrid-GGA (fourth rung), and double hybrid GGA (fifth
rung). The most commonly used functionals are LDA up to the hybrid GGA, which will be
introduced herein.

2.3.1 Local Density Approximation (LDA)
The LDA32 is the simplest approximation in which the density is treated locally as a non-

interacting uniform electron gas. In LDA, the density is defined as | = K/ , where N is the
number of electrons and V is the volume of the gas. This form of electron density is only used in

the LDA. Generally, since electrons have spin ‰ or spin Š, LDA is replaced by the local spin

density approximation (LSDA). In LSDA, the total electron density | is replaced by the spin

electronic density, |‹ and |Œ . The LSDA approximation generally provides better molecular

geometries and vibrational frequencies than the HF approximation; however, it tends to

overestimate the chemical bonding.33 The LDA approximation is commonly used in solid-state

21

physics for studying metals where the electron density varies slowly.34 One of the commonly
used LSDA functionals is VWN.35

2.3.2 Generalized Gradient Approximation (GGA)
Since in LDA the electron density is treated as a local property that does not reflect the
spatial variation in densities, the GGA method36–41 corrects for this shortcoming by including the
electron density and its first derivative ∇‡ . One of the commonly used GGA corrected

exchange functionals is B88 developed by Becke36 in which a correction parameter is added to

the LDA exchange energy. GGA corrected correlation functionals were also developed, such as
the LYP38 functional and the P8642 functional. Because the exchange-correlation energy is
comprised from two terms, the exchange and the correlation terms, the gradient-corrected
exchange functional can be combined with the gradient-corrected correlation functional. The
most widely used combinations are BLYP,36,38 PBE,40,41 and BP86.36,42 The PBE functional is a
non-empirical functional and has numerous applications on metallic systems largely because it
correctly describes the slowly varying electron densities of metals.

2.3.3 Meta-GGA
Additional improvement over the GGA method is the meta-GGA (MGGA) approach in
which more inhomogeneity property is added to the electron density by including the second

derivative of the electron density ∇$ | and/or, local kinetic energy density ?| . These

additional terms can offer a better performance than LDA and GGA particularly in the

22

description of chemical interactions. TPSS43 and M06-L44 are commonly used meta-GGA
functionals.

2.3.4 Hybrid- GGA
In DFT, the description of the exchange energy suffers from the self-interaction problem
that arises from the spurious interaction of an electron with itself. The idea in hybrid functionals
is to use the Hartree-Fock exact exchange in addition to the Kohn-Sham correlation. This can
help improve the performance of the exchange functional of the DFT. However, the inclusion of
100% of the HF exchange term can in some cases worsen the performance of the functional
because it can result in a poor description of the total exchange-correlation hole of DFT.
Combination of HF exchange with DFT exchange, however, largely improves the description of
molecularly properties.33,45 Two types of the hybrid functionals are developed. The first one is
the hybrid GGA (HGGA) in which the HF exchange function is added to a pure GGA functional.
B3LYP is one of the most popular hybrid-GGA functional containing 20% of HF
exchange.33,38,46 In addition, B3PW91 is another popular hybrid-GGA functional that also
includes 20% of HF exchange.33,47 The other type of hybrid functional is hybrid MGGA
(HMGGA). In this type, a percentage of HF exchange energy is added to the MGGA functional.
The Minnesota functionals M06, M062X, and M06-HF are all useful HMGGA functionals,48 in
which M06 contains 27%, M06-2X contains 54%, and M06-HF contains 100% HF exchange.

2.4 Basis Sets
In the previous sections, the focus was on using several computational methods, such as
ab initio methods and density functional theory, to approximate the Hamiltonian operator in the

23

Schrödinger equation. However, the accuracy of all the methods depends on the number and
quality of the basis functions (basis sets) that are used to describe the wave function. Basis sets
are basically vectors that are used to define a certain region of space. In quantum chemistry,
basis sets are mathematical functions that describe the molecular orbitals (MOs) and can be
expanded as a linear combination of atomic orbitals or basis functions (J\ Eq. (2.32),
•# = ! Ž\# J\
\

(2.32)

where • represent a MO and Ž\# are the weighting coefficients indicating the relative importance
of each basis function (or atomic orbital) J\ .

A finite number of basis functions is always used in conjunction with an electronic

structure method to construct the wave function ( Ψ ) which is used as a solution to the

Schrödinger equation. This finite set can be a source of error in the calculation and is usually
referred to as incomplete basis set error. Types of basis sets commonly used are atom-centered
basis sets, such as the Pople basis sets49–52 and the correlation consistent basis sets developed by
Dunning and coworkers.53–59 These basis sets are constructed using basis functions localized in a
region of space. Another kind of basis set is constructed with plane waves. Plane waves are
delocalized basis function basis sets that are usually used for describing periodic systems, such
as crystals.60

2.4.1 Atom-Centered Basis Sets
The atomic orbital basis sets are sets of localized functions used to construct atomic
orbitals. The linear combination of these atomic orbitals produces the MOs of a given system.

24

Two types of these basis sets have commonly been used: Slater-type orbitals (STOs)7,61 and
Gaussian-Type orbitals (GTOs)62–64.
STOs are developed to resemble the hydrogen atomic orbitals and are expressed as:
Ψ r, θ, ϕ = K ’C“ θ, ϕ

<”'

u ”•\

(2.33)

where K is the normalization factor and ’C“ is the angular function and is defined by the angular
– and magnetic — quantum numbers. is the distance between the electron and the nucleus

and ˜ is the principle quantum number. ™ is the exponent and it determines the spatial extent
of the function, i.e. small ™ gives diffuse functions while large ™ gives tight function. STOs can

successfully describe short range and long range behavior to correctly describe the cusp at the
nucleus and the tail, respectively. While STOs correctly describe these regions, electronic
integrals cannot be solved analytically and thus must be computed numerically. This results in
additional computational expense while also making the quality of the computed results
dependent on the size of the integration grid.
Alternatives to STOs are GTOs which have the following functional form:
Ψ r, θ, ϕ = K ’C“ θ, ϕ

where the radius exponent here is squared u ”•\

š

$<”$”C

u ”•\

š

(2.34)

compared to the exponent in the STOs u ”•\ .

This formulation is easier to compute than the STOs since integrals over GTOs have analytic

solutions. However, the performance of the GTOs at the cusp and the tail of a radial function is
poor. GTOs have a zero gradient at the r=0 rather than a cusp in addition to decaying too slowly
in the tail region. To improve the performance of the GTOs, multiple GTOs are used in a linear
combination to reproduce the shape of STOs. This requires many functions, thus contracted

25

GTOs are often used to minimize the computational expense. As the number of GTOs included
in the linear combination increases, the description of the atomic orbital using the GTOs become
more accurate.
A minimal basis set is the smallest number of basis functions that can describe all
electrons of an atom, i.e. one function per atomic orbital. For example, the minimal basis set of
hydrogen is one basis function representing the 1s atomic orbital. For the carbon atom, and other
first row elements, the minimal basis set includes two functions for the 1s and 2s orbitals and
three functions for the px, py, and pz. Although the minimal basis set can describe atomic orbitals,
it is not enough to describe the molecular orbitals where atomic orbitals can undergo distortion.
Furthermore, minimal GTO basis sets cannot reproduce the cusp and tail regions correctly. To
overcome this shortcoming, additional basis functions can be added to the valence orbitals since
they are essential for chemical bonding. These basis sets are called split-valence basis sets. To
illustrate, a double-™ basis set has two GTO functions for each valence orbitals, a triple-™ basis
set has three GTO functions for each valence orbitals, and so on.

2.4.1.1 Pople Basis Sets
Pople and coworkers49–52 developed the Gaussian split-valence basis sets that employ the
contracted GTOs concept. A general notation of a Pople double-™ basis set is X-YZG, where X
represents the number of the primitive GTOs used to construct the contracted GTO for core
orbitals. YZ represent the number of primitive GTOs used to make two contracted GTOs for the
valence orbitals. For Pople triple-™ basis set, a number will be added to the split valence function
to show how many primitive GTOs used to make the third contracted GTO for the valence
orbital, e.g. X-YZTG. Common examples of the Pople double-™ basis set are 6-31G, 6-21G, 4-

26

31G, 3-21G, etc. and Pople triple-™ basis set can be written as 6-311G. Polarization functions can
be added to the basis set to better describe distortion or polarization that occurs when a bond is
formed. In order to allow for this polarization, the angular momentum of the polarizing function
must increase by one compared with the type of function being polarized, e.g. p-functions to
polarize s-functions, d-functions to polarize p-functions, etc. These functions are represented by
an asterisk “*” as in 6-31G*. They also can be denoted by adding d or p, such as 6-31G(d,p), in
which a set of d functions are added to non-hydrogen atoms and a set of p functions are added to

the hydrogen atom. Diffuse functions that have small ™ exponents are added to account for long

range interaction, such as if an electron is far away from the nucleus as happens in anionic

systems. Diffuse functions are represented as a plus sign “+” as in 6-31+G which means s and p
functions are added to non-hydrogen atoms.

2.4.1.2 Correlation Consistent Basis Sets
The correlation consistent (cc) basis sets introduced by Dunning and coworkers53–59 were
designed in order to systematically and predictably recover the correlation energy of the valence
electrons by increasing the number of the basis functions per atoms.56 Specifically, these basis
sets built on the idea that functions recovering same amount of correlation energy are added to
the same shell. The correlation consistent (cc) basis sets are denoted as cc-pVnZ, where pV
indicates polarized valence functions, Z is zeta, and n is related to the number of functions used
to describe the valence orbitals. The n also can be an indication of the maximum angular
momentum function contained within the basis set. The zeta level differs for different values of
n. The values of n can be D(2), T(3), Q(4), 5, and 6 and so on. For example, for first row atoms,
in which the minimal basis set is 2s1p, the cc-pVDZ set includes 3s2p1d, where a d polarized

27

function is added. The cc-pVTZ includes 4s3p2d1f, where the second d and the first f recover the
same amount of correlation energy. The cc-pVQZ includes 5s4p3d2f1g, in which the third d, the
second f, and the first g recover the same amount of correlation energy. The reason for the
inclusion of these higher basis functions is to systematically recover more correlation energy of a
molecule.
The systematic recovery of the correlation energy built in these basis sets allows for the
extrapolation of the correlation energy to the complete basis set (CBS) limit where the error
arising from the use of a finite basis set vanishes, yet the intrinsic error from the chosen method
remains. Various extrapolation techniques estimate the CBS limit, including the Peterson
extrapolation scheme65 and the Schwartz extrapolation scheme.66 Further discussion of the
extrapolation schemes of the correlation consistent basis set is presented in Section 2.5.2.
Additive basis functions such as diffuse functions (aug)54,57 and polarized core-valence
correlating functions (CV)56,59 can also be added without affecting the convergent behavior of
the basis sets, such as aug-cc-pCVTZ. The diffuse functions are often added to help describe
long-range interactions, while the polarized core-valence correlating functions are used when the
subvalence or core electrons are included in the correlated method in addition to the electrons in
the valence space. Additionally, a relativistic re-contraction of the Hartree-Fock set of functions
is often used in conjunction with relativistic calculations.67 This re-contraction often provides
faster convergence of the relativistic wave function as well as aiding in optimization to the
correct electronic state.

28

2.4.2 Plane Wave Basis Sets
Plane wave (PW) basis sets are basis sets used to describe valence electrons in extended
systems, such as solids and crystals, and are used in conjunction with periodic boundary
conditions (PBC). Since the valence electrons in periodic systems behave as free electrons, using
the atom-centered basis sets to describe these systems is impractical. Rather, plane wave basis
sets are used and are delocalized across the entire periodic system. The discrete energy levels
vanish in periodic systems, thus bands are formed rather than localized atomic and molecular
orbitals.

For a periodic system, plane wave basis functions u #›œ are used to construct the

periodic wave function Ψ› r , Eq. 2.35. This wave function obeys the Bloch theorem68 that
states that “the eigenfunction of the wave equation for a periodic potential is the product of a

plane wave u #›.œ times a function u› r with the periodicity of the crystal lattice”. Thus, Ψ› r
represents a numerical solution to the Schrӧdinger equation.
Ψ› r = u #›œ

(2.35)

In Eq. 2.35, ž is the wave vector. The size of a plane wave basis set is controlled by the highest

value of the k vector.69 Plane wave basis sets are very large compared with all-electron basis sets.

Since these basis sets are not spatially bound, an energy cut-off has to be set to allow for an SCF
convergence. A common energy cut off value is 200 eV, which corresponds to about 20,000
basis functions depending on the size of the unit cell being modeled.20

29

2.4.2.1 Pseudopotentials
The core electrons in the metallic systems are strongly localized near the nuclei, which in
turn requires a large number of PW functions in order to describe this behavior. Plane wave basis
sets work well in describing the valence electrons in extended systems but are inefficient at
describing core electrons. Since core electrons are not significantly involved in chemical bonding
and reaction, the effect of core electrons can be implicitly described using pseudopotentials,
which smear the nuclear charges and model the effect of the core electrons.
Different types of pseudopotentials have been developed, such as norm-conserving
pseudopotentials,70 ultra-soft pseudopotentials,71 and the projector augmented-wave (PAW)
pseudopotentials.72,73 The PAW method developed by Blӧchl is known to be an efficient method
for predicting the electronic structure of materials because it is capable to include the upper core
electrons as well as the valence electrons in the self-consistent iteration of the Kohn equations. In
the PAW method, the exact wave function of the core electrons is mapped onto an auxiliary
pseudo-wave function in the core region using projectors and retaining the correct nodal
structure of the pseudo-wave function, in contrast, to standard pseudopotentail methods.72

2.5 Composite Methods
In order to reduce the computational cost of high level ab initio calculations, composite
methods or model chemistries have been developed. These methods are constructed of sequential
additive steps of a combination of high level methods with a small basis sets and low level
methods with large basis sets resulting in a high level of accuracy with lower computational cost.
Composite methods that have been developed include the Gaussian-n (Gn) methods by Pople et

30

al.,74–83 the Weizmann-n (Wn) methods by Martin et al.,84–89 the High accuracy Extrapolated Ab
initio Thermochemistry (HEAT) method by Stanton et al.,90–92 the complete basis set (CBS)
methods by Petersson et al.,93–98 and the correlation consistent Composite Approach (ccCA) by
Wilson et al.99–110 Herein the Gn methods and the ccCA are introduced and are used in Chapter 3
and Chapter 4.

2.5.1 Gaussian-n (Gn) Theory
Gaussian-n methods are composite methods that perform sequential ab initio molecular
calculations to predict accurate thermochemical properties at low computational cost. The
original Gn method is the Gaussian-1 (G1) developed by Pople and coworkers74–83 with a target
accuracy of ± 2 kcal mol-1 for compounds containing first-row elements and ± 3 kcal mol-1 for
compounds containing second-row elements.74 The G1 method performs poorly for the
dissociation energies of ionic species, triplet states, some hydrides, and hypervalent species.75
Therefore, a series of developments have been implemented in G1 and other versions of the Gn
theories have been developed including G2,75 G3,78 and G482 with higher target accuracy of ~1
kcal mol-1. In addition, each Gn theory has several variants, for example, the G3 family of
composite methods includes G3(MP2),80 G3B3,79 and G3-RAD.111
The most commonly used version of Gn methods is G3, which is used in Chapter 3 and
Chapter 4 of this dissertation. In G3, a sequence of ab initio molecular orbital calculations is
performed to predict accurate energetics. The following computational steps are used in G3:78
1. Initial geometry optimization and frequency calculations are carried out at the HF/631G(d) level of theory. A scaling factor of 0.8929 is used to correct for the anharmonicity
in the vibrations. These frequencies are used to calculate the zero point energy, E(ZPE).

31

2. Equilibrium geometries are then obtained using the MP2(full)/6-31G(d) level of theory.
This equilibrium structure is used for all the single point energy calculations that follow.
3. A single point energy calculation is performed at the MP4/6-31G(d) level. The energy
obtained from this step is the reference energy of the G3 method.
4. A series of single point energy calculations are carried out at high level of theories and
are used to improve the reference energy as follows:
a. A correction for the correlation effect beyond the MP4 method using the quadratic
configuration interaction method (QCISD(T)),112 ΔE(QCI):

ΔE(QCI) = E[QCISD(T)/6-31G(d)]-E[MP4/6-31G(d)]

(2.36)

b. A correction for diffuse functions, ΔE(+):

ΔE(+) = E[MP4/6-31+G(d)]-E[MP4/6-31G(d)]

(2.37)

c. A correction for higher polarization function, ΔE(2df,p):

ΔE(2df,p) = E[MP4/6-31G(2df,p)]-E[MP4/6-31G(d)]

(2.38)

d. A correction for a larger basis set effect, ΔE(G3large):
ΔE(G3large) = E[MP2(full)/G3large]-E[MP2/6-31G(2df,p)]- E[MP2/6(2.39)
31+G(d)]+E[MP2/6-31G(d)]
5. Atomic spin orbit correction is included, ΔE(SOa).
6. An empirical “high level correction” (E(HLC)) is added to the reference energy to
recover any remaining correlation energy, such as correlation of valence electron pairs

32

and correlation of unpaired electrons in molecules. HLC also aims to minimize the
difference between theory and experiment in the predicted enthalpies of formation and
atomization energies.
7. A combination of the reference energy and all other contribution results in the G3 energy at
0 K, E0(G3):

E0(G3) = E[MP4/6-31G(d)] + ΔE(QCI) + ΔE (+) + ΔE(2df,p) +
(2.40)
ΔE(G3large) +E(HLC) +ΔE(SOa) +E(ZPE)
The goal of the G3 method is to achieve target accuracy within the QCISD(T)/G3Large
level of theory.
G3B3 method79 is similar to G3 in that both perform single point energy calculations at
the same level and procedure but at different structure. The geometry optimization in G3 is at
MP2(full)/6-31G(d) level of theory; in contrast, G3B3 uses the B3LYP/6-31G(d) level of theory
to predict structures and to calculate zero point energy. G3B3 actually was developed for openshell systems where the unrestricted MP2 method, used in G3, suffers from spin contamination
of the HF reference wavefunction.79 The inclusion of the empirical parameters within the HLC
term introduces a bias in the Gn methods.

2.5.2 Correlation Consistent Composite Approach (ccCA)
The ccCA method, developed by Wilson and coworkers,99–110 avoids the use of the
empirical high-level correction (HLC) found in the Gn methods and utilizes the convergence
behavior of the correlation consistent basis sets to eliminate the basis set incompleteness error.
The ccCA method is designed to approach the [CCSD(T,FC1)-DK/aug-cc-pCV∞Z-DK] energy
at a reduced computational cost, which in turn, can achieve the chemical accuracy of 1 kcal/mol
33

of reliable experiments for energetic properties of main group species, on average. The detailed
computational steps in ccCA are as follows:
1. A geometry optimization and frequency calculation are performed at the B3LYP/ccpVTZ. The optimized structure is determined to be a minimum on the potential energy
surface via a Hessian calculation. Harmonic vibrations are scaled by a factor of 0.989 in
order to account for anharmonicity and are used to calculate the zero point
energy,E(ZPE). The equilibrium structure predicted in this step is used for all the single
point energy calculations that follow.
2. A single point energy calculation is carried out at the MP2/cc-pVnZ level, where n= D, T,
and Q and the energies are extrapolated to the CBS limit to obtain the ccCA reference
energy. The HF reference energies (resulted from this step) are extrapolated to the CBS
limit using the Feller extrapolation scheme:113,114
˜ =

Where

TU”t:„

+ Ÿ exp −1.63˜

˜ is the energy at the nth zeta-level of the used basis set,

(2.41)
TU”t:„

is the

extrapolated HF energy to the CBS limit, and B is a fitting variable. The energy resulting
from this extrapolation is the E(HF/CBS).
The MP2 valence correlation energies are then extrapolated using one of the following
extrapolation schemes. One option is the Peterson extrapolation scheme which is a mixed
Gaussian and exponential formula:65
˜ =

t:„

+ Ÿ exp‚− ˜ − 1 ƒ + £ exp‚− ˜ − 1 $ ƒ

34

(2.42)

˜ is the energy at the nth zeta-level of the used basis set,

where

t:„ is

the energy at

the CBS limit, and B and C are fitting parameters. The ccCA variant that utilizes the
Peterson extrapolation scheme is referred to as ccCA-P. Other alternative extrapolation
schemes are the Schwartz extrapolation schemes,66 which are based on the cubic or
quartic inverse power of the highest order angular momentum (–“^] ) function included in

the basis set:

–“^] =

t:„

+

Ÿ

–“^] +

1
2

]

(2.43)

where at x = 3 ccCA is designated as ccCA-S3 and is designated as ccCA-S4 at x = 4.
The energy resulting from this extrapolation is the E(MP2)/CBS.
3. A series of single point energy calculations are carried out at high level of theories and
are used as additive terms that added to the ccCA reference energy. These calculations as
follows:
a. A contribution of a scalar relativistic effect is accounted for using the spin-free
one-electron Douglas-Kroll Hamiltonian at the MP2 level with the corresponding
relativistically re-contracted basis set, ΔE(DK):

ΔE(DK) = E[MP2-DK/cc-pVTZ-DK] – E[MP2/cc-pVTZ]

(2.44)

b. A contribution of the core-core and the core-valence correlation effects is
determined by employing an MP2 calculation that correlates the outer core as
well as the valence in conjunction with a core-valence basis set, ΔE(CV):

35

ΔE(CV) = E[MP2(FC1)/aug-cc-pCVTZ] – E[MP2/aug-cc-pVTZ]

(2.45)

where FC1 indicates that outer core electrons are correlated in addition to the
valence.
c. A contribution of high levels of electron correlation that are not described by MP2
is determined using CCSD(T) with the cc-pVTZ basis set, ΔE(CC):

ΔE(CC) = E[CCSD(T)/cc-pVTZ] – E[MP2/cc-pVTZ]

(2.46)

4. Atomic spin orbit correction is included, ΔE(SOa).
5. Finally, a combination of the reference energy and all other contribution results in the
ccCA energy at 0 K, E0(ccCA):
E0(ccCA) = E(HF/CBS) + E(MP2/CBS) + ΔE(CC) + ΔE(CV) + ΔE(DK) +
(2.47)
ΔE(SOa) + E(ZPE)
Various variants of ccCA have been developed including the ccCA-TM115 for first row
transition metal, the relativistic-pseudopotential (rp)-ccCA108 for transition metals heavier than
3d elements, multireference (MR)-ccCA106 for molecules with multireference characters, and
ONIOM-ccCA107 for large chemical system. Other implementations in ccCA include methods to
decrease the computational cost such as the resolution-of-the-identity (RI)-ccCA105 and the
ccCA-F12.109 All of which have been found to be efficient and accurate, overall, within the target
accuracy.

36

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37

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47

CHAPTER 3 DFT AND AB INITIO COMPOSITE METHODS:
INVESTIGATION OF OXYGEN FLUORIDE SPECIES1
3.1 Introduction
The oxygen fluorides have attracted interest because they can be employed as propellants
in the rocket industry and can be used as strong fluorinating and oxidizing agents. In addition,
oxygen fluorides play a role as intermediates in atmospheric chemistry and are believed to make
a minor contribution to the destruction of ozone.1-6 The source of fluorine in the atmosphere
originates from the decomposition of chlorofluorocarbons (CFCs) and their radical fragments,
but most of the atmospheric fluorine is in the form of hydrogen fluoride (HF). Hydrogen fluoride
is formed from the fast reaction of a fluorine atom with methane and water vapor.5,7 Although
the role of fluorine in ozone depletion is minor, the percentage of fluorine in the atmosphere has
been reported to be increasing with time.8-10 Thus, accurate thermochemical properties are
required for modeling fluorine compounds in the study of atmospheric reactions. Due to the
unstable nature of oxygen fluorides, experimental measurements of the energetic properties have
been limited. Computational approaches can aid in understanding such systems.
Investigating the structural properties of the oxygen fluorides has been a challenge to the
computational chemical community, particularly for FOO and FOOF. The F-O bond in oxygen
fluorides is a covalent bond between two highly electronegative atoms where both atoms contain
lone pair electrons. Therefore, the F-O bond exhibits strong electron lone pair – lone pair
repulsion and can become very long in molecules such as FOO and FOOF (~0.2 Å longer than
the F-O bond in FOF),11,12 requiring consideration of high-level electron correlation methods. In
FOO and FOOF, the O-O bond length is similar to that in the O2 molecule but ~0.2 Å shorter
This entire chapter has reprinted from Z. H. A. Alsunaidi, and A. K. Wilson, “DFT and ab initio composite
methods: Investigation of oxygen fluoride species” Computational and Theoretical Chemistry. 2016, 1095, 71-82,
with permission of Elsevier.

1

48

than the O-O bond length in HOOH.11 The unusual geometry of FOO and FOOF presented a
computational difficulty for electronic structure methods, which led to numerous investigations
of oxygen fluorides using a variety of methods to study their structures and energetic
properties.13-10 Many methods have been unsuccessful in predicting the right structure for oxygen
fluorides, such as FOO, FOOO, and FOOF, with respect to the experimental geometries, as will
be seen in the following sections.
As a full literature review of these efforts is outside the scope of this paper, a number of
significant and recent investigations are highlighted. The FOO structure and enthalpy of
formation (ΔH°f, 298) have been computed by Francisco et al.16 using Møller-Plesset perturbation
theory (MP2, MP3, and MP4), complete active space self-consistent field (CASSCF), and
quadratic configuration interaction [QCISD(T)] in conjunction with Pople’s basis sets. The study
found that all MPn methods underestimated the F-O bond length by > 0.2 Å. QCISD(T)/631G(d) yielded the best FO bond length that is only shorter by 0.002 Å from the experimental
length (expt. re (F-O) = 1.649 ± 0.013 Å,31 where re indicates an equilibrium structure), whereas
the best CASSCF description of the F-O bond length is 0.8 Å shorter than experiment.
Francisco’s study reported an enthalpy of formation at 0 K for FOO of 8.9 ± 3 kcal mol-1 by
using isodesmic and isogyric reaction schemes using QCISD(T)/6-311G(d,p) results.16 Ventura
and Kieninger’s26 study on FOO concluded that B3LYP/6-311++G(3df, 3pd) is a reliable method
to describe structures and predict reaction enthalpies for molecules involving F-O bonds. Studies
by Denis30,32,33 found that the inclusion of the full treatment of the triple excitation [CCSDT
instead of CCSD(T)] overcame the spin contamination problem presented in UCCSD(T), hence
CCSDT predicted an accurate structure and energetics of the FOO molecule. Karton et al.20
reported the ΔH°f, 298 of FOO of 5.87 ± 0.16 kcal mol-1 in excellent agreement with experiment

49

(6.1 ± 0.5 kcal mol-1) using the high-level computationally demanding W4 method.34 A recent
theoretical study by Feller et al.15 obtained a correct structure of FOO using R/UCCSD(T)/augcc-pVTZ level of theory and with a calculated value of ΔH°f, 298 of 6.4 ± 0.7 kcal mol-1 using a
composite approach that is based on coupled cluster theory with up to quadruple excitations. The
difference in the uncertainties estimated by Karton (5.87 ± 0.16 kcal mol-1)20 and Feller (6.4 ±
0.7 kcal mol-1)15 imputes to their different approaches. While W4 estimates uncertainties based
on the performance of a set of 25 small molecules,20 Feller’s approach uses molecule-bymolecule criteria to calculate the estimated uncertainties.15
The structure and the ΔH°f,

298

of FOOF have been studied extensively with a broad

variety of quantum chemical methods. The computational challenge in the FOOF structure arises
from the anomeric delocalization effect that exists in FOOF between the oxygen lone pair and
the antibonding orbital of the F-O bond.29 Although CCSD(T)/aug-cc-pVTZ15 and B3LYP/6311++G(2d)18 can provide a qualitatively correct geometry for FOOF, very few methods used in
previous work reproduced the experimental FOOF structure. In fact, a local density functional
(LDF) paired with numerical and Gaussian basis sets35 and the local SVWN functional paired
with 6-311++G(2d)18 were two methods that predicted the closest re of the F-O bond compared
to experiment, with LDF being superior. LDF predicted F-O and O-O bond lengths that are 0.01
Å and 0.001 Å off from experimental geometries (rs(F-O) =1.575 ± 0.003 Å and rs(O-O) = 1.217
± 0.003 Å),11 respectively. LDF predicted this good description for FOOF likely due to the high
and evenly distributed electron density in FOOF, as justified in Ref. 34. MP2, MP3, and MP4
with different size and type of basis sets, on the other hand, predicted incorrect geometries for
FOOF with respect to experiment, however MP6 at the complete basis set (CBS) limit predicted
an accurate geometry.29 Not only is the structure of FOOF problematic but its ΔH°f, 298 has also

50

been difficult to predict. The calculated ΔH°f,

298

of FOOF using even high-level ab initio

methods has a large deviation from the experimental value reported in the NIST-JANAF
thermochemical table (4.6 ± 0.5 kcal mol-1).36-37 The ΔH°f, 298’s reported by Karton et al.20 is 7.84
± 0.18 kcal mol-1 and 8.21 ± 0.18 kcal mol-1 using W4 energies at the CCSD(T)/cc-pVQZ and
experimental geometries, respectively. The most recent value of the ΔH°f, 298 of FOOF is 6.4 ±
0.7 kcal mol-1 and was calculated using a coupled cluster-base composite approach.15 These are
only a few examples of this large deviation from experiment.
Predicting the conformational structure of FOOO has also been challenging. Frecer
et al.38 investigated the FOOO that formed by F + O3 reaction and found that FO(O)2 is the most
stable structure with F-O being a weak bond (3.671 Å). However, FOOO was observed later as a
stabilized intermediate in dilute mixtures of F2 and O3 in solid argon by FT-IR spectroscopy.39
Based on the reported frequencies of FOOO, it is characterized as a FO-O2 complex, and it
cannot be a weak van der Waals complex,39 which differs from Frecer’s stable structure,38
mentioned above. Quantum chemical studies by Li et al.40 and Peiró-García et al.41 of the F + O3
reaction mechanisms using MP2/6-31G(d) and QCISD/6-311+G(d,p), respectively, also could
not predict the FOOO ground state complex observed experimentally in the argon matrix.39 A
geometry optimization and frequency calculations of FOOO were performed by Roohi et al.25 at
the CCSD/aug-cc-pVDZ, CCSD/6-311+G(d), and QCISD/aug-cc-pVDZ levels of theory.
Roohi’s study25 showed that the planar FOOO with dihedral angle of 0.0o is the most stable
structure, with its calculated frequencies agreeing well with the reported experimental
frequencies.39 No ΔH°f,

298

for FOOO has been previously reported, to our knowledge. The

structure of the corresponding hydride FOOOH has only been studied previously by MINDO42
and by MP2/6-3lG(d).43 As MP2 theory has encountered difficulty for calculating the F-O and

51

the O-O bond lengths, an additional investigation of the FOOOH structure has to be done.
While methods such as CCSDT and QCISD are computationally demanding, ab initio
composite methods have been developed to circumvent the computational demands of such
methods. One such approach, the correlation consistent Composite Approach (ccCA)44-46, is a
method that has been demonstrated to be practical and reliable for the prediction of
thermochemical properties, such as enthalpies of formation, ionization potentials, and electron
affinities. The targeted accuracy of ccCA for main group molecules is to yield a mean absolute
deviation of approximate chemical accuracy, 1 kcal mol-1 at reduced computational cost. This is
in contrast to coupled cluster-based composite methods, which generally strive for a chemical
accuracy of ± 0.24 kcal mol-1, such as the W4 composite method and the approach used by Feller
et al.15 Because the performance of ccCA for a variety of halogen oxides and their related
hydrides has not been examined in detail, it is of our interest to consider the utility of ccCA in
describing oxygen fluorides, such as FOO, FOOF, and FOOO.
Density functionals provide another option, as, overall, functionals have a lower formal
computational scaling than post-HF methods such as CCSD(T) and CCSDT, though DFT
predictions such as for enthalpies of formation, in general, do not reach the accuracies achievable
by composite methods, such as ccCA. Thus, they are system dependent methods and are worth
considering for each system. For example, the Minnesota density functionals M0647 and M062X47 were used by Meyer and Kass,48 in conjunction with the correlation consistent basis sets49-51
to assess their performance for predicting the ΔH°f, 298’s of a set of chlorine oxides and related
hydrides (ClOx and ClOxH, where x =1-4) with respect to the ΔH°f, 298’s of W4 method.34 The
capability of G352 and G3B353 for calculating ΔH°f,

298’s

of chlorine oxides were also

investigated in the same study.48 The main findings from the Meyer and Kass study are that M06

52

ΔH°f, 298’s were found to differ by an average of 1.3 kcal mol-1 from the W4 ΔH°f, 298’s, while
M06-2X resulted in larger error (6.2 kcal mol-1). G3 and G3B3 ΔH°f, 298’s yielded an average
error of 4.6 kcal mol-1 and 6.5 kcal mol-1, respectively. The author attributed the large errors of
G3 and G3B3 ΔH°f,

298’s

to their poor predicted geometries. Although M06 and M06-2X

functionals were examined for the prediction of the ΔH°f, 298’s of chlorine oxides, the capability
of M06 and M06-2X to predict structures and ΔH°f, 298’s has not been assessed for other halogen
oxides. Thus, it is of interest to evaluate these functionals for oxygen fluoride species, as well as
examine the performance of G3 and G3B3 methods for these systems. G3 and G3B3 are used
here, largely, as they were included in the Meyer and Kass study.48 Though G4 is a more modern
method, beginning with an MP4 reference energy is a costly start, and as shown in previous
studies, G4 predicts very similar energies as G3.54-55
In the present study, the reliability of ccCA, G3, and G3B3 for the prediction of the
ΔH°f, 298’s of oxygen fluoride species was evaluated. In addition to these composite methods, the
performance of M06 and M06-2X was also examined for predicting the structures and enthalpies
of formation of oxygen fluoride species. A set of various oxygen fluorides were considered in
this study, including FO, FOO, FOOO, and the related hydrides (FOH, FOOH, and FOOOH) and
difluorides (FOF, FOOF, and FOOOF), where the ΔH°f, 298’s of FOOO and FOOOH have not
been reported previously. The effects of basis set size and spin contamination were also
considered. For comparison, the ΔH°f, 298’s of chlorine oxides and related hydrides have been
provided, whereas full theoretical investigations for chlorine oxides and related hydrides can be
found in the Meyer and Kass study and references therein.48

53

3.2 Computational Methodology
All calculations were performed using the Gaussian 09 software package.56 The hybridmeta-generalized gradient approximation (HMGGA) Minnesota functionals (M0647 and M062X)47 in conjunction with the augmented correlation consistent polarized valence basis sets (augcc-pVnZ), where n = D, T, Q,49-51 were used to optimize the structures of all molecules under
investigation. The tight-d correlation consistent basis set of Dunning et al.,57 aug-cc-pV(n+d)Z,
where n = D, T, Q, were used for chlorine. Frequency calculations were performed to ensure that
the structure is a stationary point. The enthalpies of formation for these structures were
determined at the same level of theory.
ccCA, G3, and G3B3, were also applied to predict the enthalpies of formation. In ccCA,
geometry optimization and vibrational frequencies calculations are performed using B3LYP/augcc-pVTZ.44 The harmonic vibrational frequencies are then corrected using a scale factor of 0.989
as recommended in Ref. 44. The remaining steps in ccCA involve a series of single point energy
calculations performed using the B3LYP/aug-cc-pVTZ geometry (for details see Chapter2
Section 2.5.2). Several variants of ccCA can be used, which vary by the means used to
extrapolate the MP2 energy (MP2/aug-cc-pV∞Z) to the CBS limit.44 ccCA-S3 and ccCA-S4
utilize Schwartz’s inverse cubic and quartic extrapolation scheme, respectively.58 ccCA-P
utilizes Peterson’s mixed Gaussian/exponential extrapolation scheme59 and ccCA-PS3 is an
average of ccCA-P and ccCA-S3. G352 and G3B353 both are composite methods that involve the
same series of single point energy calculations though based upon different geometries (see
Chapter 2 Section 2.5.1). The geometry optimization in G3 is at the MP2(full)/6-31G(d) level of
theory, while G3B3 uses the B3LYP/6-31G(d) level of theory.

54

For open-shell systems (radicals) such as FOO and FOOO, which show a degree of spin
contamination, restricted open shell (RO) calculations are used, i.e. ROM06, ROM06-2X. In
addition, RO-ccCA60 and G3-RAD61 energies were obtained and used to calculate their ΔH°f,
298’s.

Gaussian 0956 was used to determine these energies. The mean absolute deviations (MADs)

of the calculated ΔH°f, 298’s were determined for all of the utilized methods with respect to the
experimental values, unless otherwise noted.

3.3 Results and Discussion
3.3.1 Structures
The structural parameters obtained by M06 and M06-2X for all of the species are listed in
Table 3.1. The optimized structures at the B3LYP/aug-cc-pVTZ, MP2(full)/6-31G(d), and
B3LYP/6-31G(d) levels, which are used for geometry optimizations in ccCA, G3, and G3B3,
respectively, were also considered (shown in Table 3.1). Experimental structural parameters of
FO,22 FOO,31 FOF,12 FOOF,11 and FOH,17 have been reported and were utilized as reference data
to determine the performance of the considered methods. To the authors’ knowledge no
experimental observations have been reported for the geometric parameters of FOOH, FOOO,
and FOOOF. Thus, for these molecules theoretical results from rigorous methods such as
coupled cluster are presented to calibrate the considered methods (CCSD(T)/TZ2P structure for
FOOH,21 CCSD/6-311+G(d) structure for FOOO,25 and CCSD(T)/cc-pVTZ for FOOOF).19

55

Table 3.1 Structural parameters of the oxygen fluoride species at different level of theories, bond lengths are in angstroms and
bond angles and dihedral angles in degree.
FO
Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)
Experimenta

r (FO)
1.332
1.328
1.324
1.329
1.329
1.325
1.351
1.354
1.344
1.354
FOH

Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)
Experimentb

r (FO)
1.408
1.405
1.401
1.401
1.400
1.397
1.430
1.434
1.444
1.4350 ± 0.0031

r (OH)
0.973
0.969
0.966
0.971
0.968
0.967
0.971
0.977
0.979
0.9657 ± 0.0016
FOF

Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ

r (FO)
1.380
1.377
1.374
1.376
1.374

a (FOF)
103.5
103.6
103.7
102.9
103.0

56

a (FOH)
99.1
99.2
99.3
99.3
99.4
99.5
98.6
97.8
97.1
97.54 ± 0.50

Table 3.1 Continued.

M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)
Experimentc

1.371
1.403
1.409
1.423
1.412

103.1
103.9
103.9
102.6
103.1
FOO

Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
ROM06/aug-cc-pVDZ
ROM06/aug-cc-pVTZ
ROM06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
ROM062X/aug-cc-pVDZ
ROM062X/aug-cc-pVTZ
ROM062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)
Experimentd
Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)

r (FO)
1.811
1.752
1.747
1.589
1.580
1.572
2.090
1.520
1.519
1.508
1.500
1.500
1.618
1.571
1.649±0.013
r (FO)
1.447
1.438
1.434
1.419
1.415
1.412
1.470
1.465

r (OO)
1.343
1.346
1.343
1.358
1.361
1.357
1.365
1.376

r (OO)
1.177
1.171
1.170
1.182
1.178
1.178
1.184
1.190
1.187
1.194
1.194
1.191
1.188
1.211
1.200±0.013
FOOH
r (OH)
0.977
0.972
0.970
0.973
0.970
0.968
0.974
0.981

57

a (FOO)
110.7
110.6
110.7
110.6
110.6
110.7
111.2
110.0
110.1
109.9
110.0
110.1
111.2
111.0
111.2±0.36
a (FOO)
105.9
105.9
106.0
105.3
105.4
105.5
106.3
106.1

a (OOH)
104.0
103.9
104.0
103.6
103.6
103.7
103.7
102.9

d(FOOH)
85.5
85.2
85.4
84.6
84.6
84.7
85.0
83.1

Table 3.1 Continued.

MP2(full)/6-31g(d)
CCSD(T)/TP2Ze

1.468
1.481

1.39
1.393

0.981
0.969

105.0
105.4

102.0
101.9

83.1
84.5

FOOF
Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)
Experimentf
Method/Basis set
M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
ROM06/aug-cc-pVDZ
ROM06/aug-cc-pVTZ
ROM06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
ROM062X/aug-cc-pVDZ
ROM062X/aug-cc-pVTZ
ROM062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
ROB3LYP/aug-cc-pVTZ
ROB3LYP/6-31g(d)

r (FO)
1.506
1.494
1.485
1.426
1.420
1.419
1.523
1.497
1.496
1.575±0.003
r (FO)
1.338
1.335
1.331
1.357
1.354
1.350
1.331
1.333
1.327
1.360
1.359
1.356
1.354
1.360
1.379
1.380

r (OO)
1.217
1.219
1.221
1.285
1.289
1.286
1.227
1.266
1.291
1.217±0.003
FOOO
r (FO-O), r (FOO-O)
2.469, 1.196
2.408, 1.191
2.449, 1.189
1.704, 1.192
1.687, 1.189
1.681, 1.188
2.598, 1.191
2.537, 1.187
2.702, 1.187
1.589, 1.204
1.575, 1.205
1.573, 1.203
2.715, 1.204
2.504, 1.211
1.709, 1.201
1.710, 1.214

58

a (FOO)
108.6
108.5
108.6
106.6
106.7
106.8
109.3
108.3
106.9
109.5±0.5
a (FOO), a (OOO)
97.8, 110.8
93.0, 106.5
92.4, 105.9
100.2, 110.1
100.9, 110.5
101.1, 110.7
88.5, 103.4
90.4, 105.6
91.0, 107.8
103.3, 112.1
103.9, 112.4
104.0, 112.5
101.1, 113.8
91.0, 103.3
101.2, 111.2
100.3, 110.2

d (FOOF)
87.2
86.9
87.0
85.9
85.7
85.8
88.1
86.7
85.8
87±0.5
d (FOOO)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Table 3.1 Continued.

MP2(full)/6-31g(d)
CCSD/6-311+G(d)g

1.378

1.745, 1.200

100.5, 111.5

0.0

FOOOH
Method/Basis set

r (FO)

r (FO-O), r (O-OH)

r (OH)

M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)
MP2(full)/6-31g(d)

1.483
1.471
1.466
1.427
1.423
1.421
1.502
1.485
1.481

1.290, 1.427
1.292, 1.428
1.291, 1.424
1.331, 1.406
1.333, 1.407
1.330, 1.403
1.303, 1.461
1.331, 1.454
1.358, 1.450

0.974
0.970
0.968
0.972
0.967
0.968
0.972
0.979
0.981

a (FOO), a (OOO),
a (OOH)
106.5, 109.0, 101.1
106.5, 109.0, 101.1
106.6, 109.1, 101.2
105.3, 107.9, 101.8
105.5, 108.1, 102,1
105.6, 108.2, 102.2
107.3, 109.6, 100.7
106.3, 108.8, 99.9
104.9, 107.5, 99.7

d (FOOO)

d (OOOH)

-85.8
-85.7
-85.6
-84.0
-84.0
-83.9
-87.4
-84.9
-83.2

91.7
91.4
91.8
91.4
90.1
90.3
96.0
89.0
87.0

FOOOF
Method/Basis set
r (FO)
r (OO)
a (FOO), a (OOO)
d (FOOO)
M06/aug-cc-pVDZ
1.419
1.355
106.2, 109.0
± 93.0
M06/aug-cc-pVTZ
1.413
1.355
106.2, 109.1
±92.5
M06/aug-cc-pVQZ
1.410
1.353
106.3, 109.2
±92.4
M062X/aug-cc-pVDZ
1.403
1.360
105.3, 108.1
±90.9
M062X/aug-cc-pVTZ
1.400
1.360
105.7, 108.3
±90.8
M062X/aug-cc-pVQZ
1.399
1.357
105.7, 108.5
±91.0
B3LYP/aug-cc-pVTZ
1.440
1.377
106.6, 109.3
±93.6
B3LYP/6-31g(d)
1.440
1.386
105.8, 108.7
±90.5
MP2(full)/6-31g(d)
1.365
1.340
105.6, 108.2
±90.1
CCSD(T)/cc-pVTZh
1.444
1.385
105.5, 108.3
±91.3
a
b
c
d
e
f
g
Reference 22. Reference 17. Reference 12. Reference 31. CCSD(T)/TZ2P: Reference 21. Reference 11. CCSD/6-311+G(d): Reference25.
h
CCSD(T)/cc-pVTZ: Reference 19.

59

The F-O bond length calculated by M06 and M06-2X for all set of molecules showed a
systematic decrease in length when using the correlation consistent basis set family going from
aug-cc-pVDZ, aug-cc-pVTZ, to aug-cc-pVQZ (Table 3.1). However, this decrease in the bond
length while increasing basis set size does not occur for the O-O bond length as shown in Table
3.1, and can be dependent on the density functional being utilized. Both M06 and M06-2X
underestimated the F-O and O-O bond lengths with respect to the corresponding experimental
values. M06-2X predicted shorter F-O bond lengths and longer FO-O bond lengths than M06.
The average difference between the aug-cc-pVTZ F-O bond lengths and the aug-cc-pVQZ F-O
bond lengths is 0.005 Å for M06 and it is 0.002 Å for M06-2X, and for the FO-O bond length it
is 0.003 Å for both functionals whereas the aug-cc-pVDZ bond lengths are generally longer. Yet,
the M06/aug-cc-pVDZ and M06-2X/aug-cc-pVDZ predicted the closest geometries to the
reference data with average errors in the F-O bond length of 0.032 Å and 0.062 Å, respectively.
Thus, increasing the basis set size will not always give the better structures for the systems under
investigation. For open-shell species, such as FO, FOO, and FOOO, the degree of spin
contamination resulting from the mixing of higher spin states into the wavefunction was
calculated, as high spin contamination results in incorrect geometries and energies. Previous
studies showed a high degree of spin contamination when studying FOO using other methods,
such as MP2.16,26 No spin contamination was found when calculating FO, but it was present
when calculating FOO and FOOO. The expectation values of the total spin, <S2>, are listed in
Table 3.2, where the optimal value for these radicals is <S2> = 0.75. The effect of spin
contamination becomes appreciable as the deviation of <S2> from 0.75 increases, and this
deviation decreases with increasing the size of the basis sets, as shown in Table 3.2. Both UM06
and UM06-2X suffer from spin contamination associated with FOO (small) and FOOO (severe),

60

as shown in Table 3.2. This error was corrected by using the restricted open-shell density
functionals as shown in Table 3.1. ROM06 and ROM06-2X provided better structural parameters
with respect to the reference data for FOO and FOOO than what UM06 and UM062X predicted.
Thus, the ROM06 and ROM06-2X geometries were used later to calculate the enthalpies of
formation. FOOOF was found to exist in two conformers. Both have very similar geometries but
differ in the dihedral angles. One conformer has d(OOOF) = 91.3° and the other one has
d(OOOF) = 82.0°.19 Because the energy difference between the two conformers at the
CCSD(T)/cc-pVTZ level is very small, 0.24 kcal mol-1, with the d(OOOF) = 82.0° conformer
having the lowest energy,19 only one conformer was included in the molecule test set. M06-2X
described the structure of FOOOF better than M06 when compared to the CCSD(T) structure.
Overall the geometries predicted by M06 are in better agreement with the reference data than
M06-2X, although both functionals generally underestimated the F-O and the O-O bond lengths.
Thus, for this set of molecules, doubling the amount of Hartree-Fock exchange from M06 to
M06-2X does not improve the results.
As shown in Table 3.1, the F-O bond lengths obtained by B3LYP/aug-cc-pVTZ are in
very good agreement (MAD of 0.01 Å) with respect to the reference data, with the exception of
the F-O bond distance(s) in FOO and FOOF. The difference in F-O bond lengths is more than
0.01 Å (0.018 Å in FOO and 0.049 Å in FOOF) compared to experimental values. Although
B3LYP/aug-cc-pVTZ did not predict very accurate bond lengths for FOO and FOOF, it provided
a qualitatively correct description of the structures of these two molecules. The capability of
B3LYP to describe the geometries has been noticed previously for some of the oxygen
fluorides.26,35 Quite similarly, the calculated F-O bond lengths at the B3LYP/6-31G(d) level were
in very good agreement with respect to the reference data; however, not only is the F-O bond

61

length underestimated in FOO and in FOOF (by 0.065 Å in FOO and 0.075 Å in FOOF), but also
the F-O bond distance in FOOH was underestimated by about 0.016 Å using B3LYP/6-31G(d) in

Table 3.2 The expectation value of the total spin <S2>.

Molecule

Method/Basis set

<S2>

FOO

M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)

0.756
0.754
0.754
0.782
0.750
0.75
0.75
0.7509

FOOO

M06/aug-cc-pVDZ
M06/aug-cc-pVTZ
M06/aug-cc-pVQZ
M062X/aug-cc-pVDZ
M062X/aug-cc-pVTZ
M062X/aug-cc-pVQZ
B3LYP/aug-cc-pVTZ
B3LYP/6-31g(d)

0.892
0.782
0.782
0.803
0.780
0.807
0.790
0.776

comparison to the reference data. Additionally, when using the 6-31G(d) basis set, the average
error for B3LYP increased from 0.01 Å (obtained when using an aug-cc-pVTZ basis set) to 0.02
Å. Thus, again B3LYP with the small basis set 6-31G(d) is not enough to describe peroxide
systems, such as FOO, FOOF, and FOOH. B3LYP in conjunction with aug-cc-pVTZ also
resulted in the least average error of 0.01 Å (from the reference data) for the O-O bond length
compared to other methods. The effect of spin contamination for open shell systems using
UB3LYP has been tested and the total spin operators <S2> are presented in Table 3.2, for each
level of theory. The <S2> values for FOO show that the use of UB3LYP at either basis set levels

62

does not result in spin contamination, whereas for FOOO, both UB3LYP/aug-cc-pVTZ and
UB3LYP/6-31G(d) levels resulted in large deviation from the optimal value <S2> = 0.75.
Consequently, the ROB3LYP is used to predict the geometry for FOOO, which is in agreement
with the structure predicted by CCSD,25 as shown in Table 3.1. For FOOOF, B3LYP was able to
predict the two conformers with d(OOOF) = 91.3° and with d(OOOF) = 82.0° and the B3LYP FO and O-O bond lengths agree well with the CCSD(T) bond lengths.
The predicted geometries for FOF, FOH, and FOOH by MP2(full)/6-31g(d) agree well
with the reference data within a 0.01 Å difference. However, MP2(full)/6-31g(d) predicted a
0.1 Å shorter F-O bond and a 0.1 Å longer O-O bond for FOOF compared to experimental bond
lengths, this large difference in the bond lengths was also found previously using MP2/631g**.43 Likewise, the F-O and O-O bond lengths predicted by MP2(full)/6-31g(d) for FOOOF
are 0.08 Å and 0.05 Å shorter than CCSD(T) results, indicating that this level of theory is not
enough to describe the peroxide’s geometry. For the open-shell systems FOO and FOOO, the
UMP2 method could not provide converged geometries due to large spin contamination.
As mentioned earlier for FOOOH, no reliable theoretical or experimental geometries
have been reported. Based on the success of B3LYP/aug-cc-pVTZ method in predicting the
FOOOF geometry compared to the CCSD(T)/cc-pVTZ, the B3LYP/aug-cc-pVTZ geometry for
FOOOH is considered as the most reliable structure. For this compound, only one conformer
d(FOOO) = -87.4°) is found to be a stable structure. The B3LYP/6-31G(d) structure of FOOOH
is quite similar to the structure at the B3LYP/aug-cc-pVTZ level, with a large difference of 0.03
Å in the FO-O bond length. M06 and M06-2X generally underestimated the bond lengths of

63

FO

FOO

FOOO

FOF

FOH

FOOF

FOOH

FOOOF

FOOOH

Figure 3.1 B3LYP/aug-cc-pVTZ structures of the oxygen fluoride species included in this study.

64

FOOOH as compared to the B3LYP/aug-cc-pVTZ geometries. MP2 (full)/6-31g(d) predicted
shorter F-O bond length and longer FO-O bond length than the B3LYP/aug-cc-pVTZ.
As a result of the above discussion, M06 and M06-2X are not recommended methods for
predicting the geometries of oxygen fluorides and related hydrides and difluorides. MP2
performed well for most of the closed-shell compounds with the exception of the peroxides. The
geometries obtained by B3LYP/aug-cc-pVTZ, shown in Figure 3.1, result in the lowest deviation
from the reference data among the considered methods. As shown in Figure 3.1, using
B3LYP/aug-cc-pVTZ supports conclusions from previous studies12,17,31 that FOO, FOF, and
FOH are bent with bond angles of 111.2°, 103.9°, and 98.6°, respectively. Different bond angles
indicate that the bond angle opens more as the repulsion between bonds increases. Similarly,
FOOF and FOOH have dihedral angles of 88.2° and 85.0°, respectively, in order to minimize the
repulsion between bonds. FOOOF and FOOOH display a zigzag shape with d(FOOO) = 93.6°,
and d(FOOO) = -87.4°, respectively. In contrast to all the peroxide systems, the stable conformer
of FOOO is when d(FOOO) = 0.0°. Intermolecular dispersion forces might be the cause of the
stable FOOO structure.

3.3.2 Enthalpies of Formation (ΔH°f, 298)
To provide a comparison between the performance of the utilized methods on chlorine
oxide and oxygen fluoride species, the ΔH°f, 298’s of chlorine oxides and related hydrides were
determined using M06/aug-cc-pVQZ, M06-2X/aug-cc-pVQZ, ccCA-S3, G3, and G3B3 and are
listed in Table 3.3 The MADs of the considered methods with respect to experiment for
predicting ΔH°f, 298’s are provided in Table 3.3 as well. These MADs are 1.1 (ccCA-S3), 2.1
(M06), 2.5 (M06-2X), 2.3 (G3), and 3.5 (G3B3) kcal mol-1. The MAD of ccCA-S3 indicates that

65

ccCA is a reliable method in predicting energetics for chlorine oxides. M06 resulted in a MAD
of 2.1 kcal mol-1 for the calculated ΔH°f, 298’s of chlorine oxides, which is 0.9 kcal mol-1 greater
than the MAD (1.2 kcal mol-1) that resulted from the calculations done by Meyer and Kass.48
This small difference arises from the use of a temperature correction approach that reduces the
energy contributed from the low vibrational frequency modes as pointed out in Meyer and Kass
study.48,62 In the present study, however, scale factors of 0.9853 (M06) and 0.9733 (M06-2X)63
were used for the correction of the vibrational frequencies in the computations. The ΔH°f, 298’s
calculated by M06 for chlorine oxides in the present study are in good agreement with the
experimental values with the exception of ClO3, which is known to be problematic for not only
computational methods but also for experiments, as demonstrated by the error bar associated
with the experimental ΔH°f, 298 (± 3 kcal mol-1),64-66 as compared with smaller uncertainties for
many main group species. Only ccCA-S3 and G3 predict the ΔH°f,

298

of ClO3 within the

experimental uncertainty. The ΔH°f, 298’s obtained by G3 are in relatively good agreement with
the experiments (MAD = 2.3 kcal mol-1), yet the ClO2 ΔH°f, 298 predicted by G3 overestimated
the experimental value by ~4 kcal mol-1. Similar to G3, M06-2X achieved a MAD of 2.5 kcal
mol-1, while the MAD for G3B3 was larger (MAD of 3.2 kcal mol-1). Therefore, ccCA results in
the lowest MAD with respect to experiment for the prediction of energetic properties of chlorine
oxides, followed by M06.

66

Table 3.3 Enthalpies of formation for chlorine oxides and related hydrides.
ΔH°f, 298 K (kcal mol-1)
Compd.
ccCA-S3

M06a

M06-2Xa

G3

G3B3

Expt.

ClO

25.3

23.1

23.5

25.9

26.7

24.29 ±0.03b

ClO2

23.9

21.2

26.8

26.8

27.6

22.6 ± 0.3b,c

ClO3

44.0

40.5

50.2

48.3

51.0

46 ± 3d

ClO4

57.7

52.6

65.4

66.0

65.5

-

-19.5
-18.0
-19.3
-17.4
-16.9
-18.4 ± 0.03e
HOCl
3.5
4.6
6.5
6.4
7.3
HOClO
-2.8
-3.9
3.3
2.0
3.8
HOClO2
-0.8
-3.4
5.5
5.6
8.7
HOClO3
1.1
2.1
2.5
2.3
3.5
MAD
a
M06 and M06-2X in conjunction with aug-cc-pV(Q+d)Z for chlorine and aug-cc-pVQZ for oxygen and
hydrogen. bReference 70. cReference 71. dReferences 64-66. eReference 72.

The ΔH°f,

298’s

for all of the oxygen fluoride species included in this study were

calculated using M06 and M06-2X in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and aug-ccpVQZ at 298 K using the atomization energy approach and the results are shown in Table 3.4. A
systematic decrease in the ΔH°f, 298 values as the size of the basis set increases is observed, since
the basis set with larger zeta (ξ) level recovers more energy, as shown in Table 3.4. The
differences between energies determined using M06/aug-cc-pVTZ ΔH°f,

298’s

and those

determined using M06/aug-cc-pVQZ ΔH°f, 298’s is 0.1 - 1.1 kcal mol-1 with an average difference
of 0.5 kcal mol-1, whereas the differences between energies determined using M06-2X/aug-ccpVTZ ΔH°f, 298’s and those determined using M06-2X/aug-cc-pVQZ ΔH°f, 298’s is 0.3 – 1.9 kcal
mol-1 with an average difference of 1.2 kcal mol-1. To evaluate the reliability of the utilized
methods in calculating ΔH°f, 298’s, the following reference data was used: experimental ΔH°f, 298
values for FO, FOO, FOF, FOOF and FOH; the CCSD(T)/ANO4 ΔH°f, 298 value for FOOH; and

67

the extrapolated CCSD(T)/aug-cc-pV(T,Q)Z ΔH°f,

298

value for FOOOF. For FOOO and

FOOOH neither experimental nor theoretical ΔH°f, 298 values are available. The MADs of the
calculated ΔH°f, 298’s with respect to the reference data were computed. Because of the wellknown challenges of FOOF,13,20,21,28 the MAD was also calculated without FOOF. For ccCA, the
ccCA-S3 variant was selected as it results in the lowest MAD for the ΔH°f,

298’s

of oxygen

fluoride species with respect to the reference data as shown in Table 3.5 as compared with the
other ccCA variants.
Table 3.4 Enthalpies of formation for the oxygen fluoride species using M06 and M06-2X paired
with the correlation consistent basis sets.
ΔH°f, 298 K (kcal mol-1)
Compd.

M06

Reference dataa

M06-2X

aDZ

aTZ

aQZ

aDZ

aTZ

aQZ

FO

29.6

28.5

28.1

29.1

28.3

27.5

26.1±2.4

FOH

-16.9

-17.3

-17.7

-16.4

-18.3

-18.6

-23.16±1.2

FOF

12.9

9.7

9.6

11.5

9.6

8.7

5.9±0.5

FOO

10.6

9.5

9.0

18.3

16.0

14.5

6.1±0.5

FOOH

-6.0

-6.9

-7.6

-5.6

-7.6

-8.4

-10.4±1.0b

FOOF

14.1

11.3

11.2

18.6

16.9

15.5

4.6±0.5

FOOO

40.3

37.8

36.7

43.4

43.2

41.3

-

FOOOH

4.9

3.5

2.6

6.2

4.1

2.9

-

FOOOF

35.3

31.5

30.9

34.4

32.7

30.9

26.6c

MAD

6.3

4.4

4.0

7.7

6.0

5.2

5.7
4.0
3.5
6.7
5.0
4.3
MAD w/o
FOOF
aDZ: aug-cc-pVDZ
aTZ: aug-cc-pVTZ
aQZ: aug-cc-pVQZ
a
NIST-JANAF Tables: References 36-37. b CCSD(T)/ANO4: Reference 21. c Extrapolated CCSD(T)/augcc-pV(T,Q)Z: Reference 19.

68

Table 3.5 Enthalpies of formation for oxygen fluoride species using the different variants of
ccCA method.

ΔH°f, 298 K (kcal mol-1)
Compd.
ccCA-P

ccCA-S3

ccCA-PS3

ccCA-S4

Reference dataa

FO

27.3

27.0

27.2

27.3

26.1±2.4

FOH

-21.1

-21.6

-21.4

-21.1

-23.16±1.2

FOF

6.6

6.2

6.4

6.7

5.9±0.5

FOO

8.1

7.5

7.8

8.1

6.1±0.5

FOOH

-11.0

-11.7

-11.3

-10.9

-10.4±1.0b

FOOF

9.4

8.7

9.0

9.4

4.6±0.5

FOOO

31.8d

31.0d

31.4d

31.8d

-

FOOOH

-0.7

-1.6

-1.1

-0.6

-

FOOOF

27.8

26.8

27.3

27.8

26.6c

MAD

1.8

1.4

1.6

1.8

-

MAD w/o FOOF

1.3

0.9

1.1

1.3

-

a

NIST-JANAF Tables: References 36-37. b CCSD(T)/ANO4: Reference 21. c Extrapolated CCSD(T)/augcc-pV(T,Q)Z: Reference 19. dUsing RO-ccCA

The calculated ΔH°f, 298’s of FO by ccCA, M06, M06-2X, G3, and G3B3 are within the
reported experimental uncertainty (± 2.4 kcal mol-1), as shown in Table 3.6. The ΔH°f, 298’s of FO
calculated by G3 and G3B3 are the nearest to the reported experimental value, while the ΔH°f, 298
calculated by M06 deviated the most by 2.0 kcal mol-1, but is still within the experimental
uncertainty. The FO ΔH°f,

298’s

predicted by ccCA is also in very good agreement with

experiment. For FOH, the ΔH°f, 298’s calculated by ccCA is found to be the closest to the reported
experimental value, while G3 and G3B3 provide ΔH°f,

298’s

that are 1.6 and 1.9 kcal mol-1,

respectively, less than the experimental uncertainty. M06 and M06-2X underestimate the ΔH°f,
298’s

of FOH by 5.46 and 4.56 kcal mol-1, respectively, with respect to the experimental value.

69

The ccCA ΔH°f, 298 of FOF is within the experimental error bar. G3 and G3B3 predict ΔH°f, 298’s
of 6.5 and 6.8 kcal mol-1, which are greater than the experimental uncertainty by 0.1 and 0.4 kcal
mol-1, respectively. M06 predicts a ΔH°f,

298

of FOF that is 3.2 kcal mol-1 outside of the

experimental uncertainty, while the ΔH°f, 298 calculated by M06-2X is 2.3 kcal mol-1 outside of
the experimental uncertainty.
Table 3.6 Calculated enthalpies of formation for the oxygen fluoride species using all methods
and the MADs of these methods with respect to the reference data.
ΔH°f, 298 K (kcal mol-1)
Compd.
ccCA-S3

M06a

M06-2Xa

G3

G3B3

Reference datab

FO

27.0

28.1

27.5

26.1

26.5

26.1±2.4

FOH

-21.6

-17.7

-18.6

-20.4

-20.1

-23.16±1.2

FOF

6.2

9.6

8.7

6.5

6.8

5.9±0.5

FOO

7.5e

9.0f

14.5f

7.1g

7.0

6.1±0.5

FOOH

-11.7

-7.6

-8.4

-10.3

-10.2

-10.4±1.0c

FOOF

8.7

11.2

15.5

9.3

8.9

4.6±0.5

FOOO

31.0e

36.7f

41.3f

30.1g

30.1g

-

FOOOH

-1.6

2.6

2.9

0.2

-0.3

-

FOOOF

26.8

30.9

30.9

27.8

27.3

26.6d

MAD

1.4

4.0

5.2

1.5

1.5

-

MAD w/o FOOF

0.9

3.5

4.3

0.9

0.9

-

a

M06 and M06-2X in conjunction with aug-cc-pVQZ. b NIST-JANAF Tables: Reference 36-37.
c
CCSD(T)/ANO4: Reference 21. d Extrapolated CCSD(T)/aug-cc-pV(T,Q)Z: Reference 19. e Using ROccCA. f Using ROM06 and ROM06-2X. g Using G3-RAD.

For FOO, ccCA and G3B3 give ΔH°f, 298’s that are outside the experimental error by 0.9
and 0.4 kcal mol-1, respectively. These results demonstrate the utility of ccCA and G3B3 in
predicting the FOO ΔH°f, 298. G3-RAD, one of the G3 versions developed for open-shell systems,
is used instead of G3 to calculate the ΔH°f, 298’s of the radicals FOO and FOOO. The G3-RAD

70

ΔH°f, 298 of FOO is also in good agreement with experiment. The calculated ΔH°f, 298 for FOO
using ROM06 is above experimental value by 2.9 kcal mol-1, whereas the ΔH°f, 298 calculated by
ROM06-2X is 10.6 kcal mol-1 greater than experiment. This large deviation can be explained by
the poor geometry obtained using these ROM06 and ROM06-2X.
For FOOH, the CCSD(T)/ANO4 ΔH°f, 298 which is -10.4 ± 1.0 kcal mol-1,21 is being used
as a reference value for this molecule. G3 and G3B3 predict ΔH°f, 298’s of FOOH of -10.3 and 10.2 kcal mol-1, respectively, which are in excellent agreement with the CCSD(T) value.
Conversely, the ccCA ΔH°f, 298 value of FOOH is -11.7 kcal mol-1, which is more negative than
the CCSD(T) value by 1.3 kcal mol-1. Based on the fact that oxygen fluoride molecules are
considered highly correlated molecules, accounting for the core correlation correction in the
method is highly important. Thus, ccCA ΔH°f, 298’s can be more accurate than the CCSD(T)
energies because ccCA energies includes core-valence and core-core correction terms, whereas
the reported CCSD(T) results used the frozen-core approximation.21 G3B3 includes the high
level correction term (HLC) in the energy. The HLC is calculated based on empirical parameters
and it is added to the G3 energy to reduce the error between theory and experiment. Without the
HLC the G3B3 ΔH°f, 298 deviates by ~7.0 kcal mol-1 from the CCSD(T) value. M06 and M06-2X
both underestimate the ΔH°f, 298 of FOOH by 2.6 and 1.0 kcal mol-1, respectively. For FOOF, the
ccCA ΔH°f, 298 value lies 3.6 kcal mol-1 outside the error bar of the value reported by NISTJANAF.36,37 G3 and G3B3 predict ΔH°f, 298’s that are greater than experimental error bar by 4.2
and 3.8 kcal mol-1, respectively. M06 and M06-2X give ΔH°f, 298’s larger than experiment by 6.6
and 10.9 kcal mol-1, respectively. Several previous high-level theoretical studies have pointed out
the discrepancy between experimental and calculated ΔH°f,

298’s,

and suggested that the

experiment to be revisited.15,20,21,28 For example, high-level methods predicted ΔH°f, 298 of FOOF

71

of 9.6 ± 0.9 kcal mol-1 (iCAS-CI+Q),15 8.7 ± 2.0 kcal mol-1 (CCSD(T)/ANO4),21 7.84 ± 0.18
kcal mol-1 (W4),20 and 7.3 kcal mol-1 (B3PW91/aug-cc-pVQZ).28 In addition, from this work the
ccCA value of the ΔH°f,

298

of FOOF is 8.7 kcal mol-1. Thus, the ΔH°f,

298’s

provided by

theoretical approaches is between 7-9 kcal mol-1, whereas the experimental value is 4.6 ± 0.5
kcal mol-1. Because of this large and consistent discrepancy, the MAD of the ΔH°f,

298’s

is

calculated with and without FOOF.
RO-ccCA, G3-RAD, ROM06, and ROM06-2X were employed to calculate the ΔH°f, 298
for FOOO and the predicted ΔH°f, 298’s are listed in Table 3.6. Due to the lack of reference data
for FOOO, the ΔH°f, 298 of ccCA for FOOO (31.0 kcal mol-1) is considered the most accurate
based on the previous successes of ccCA in predicting energetic properties (MAD of 1.01 kcal
mol-1 using ccCA-PS3 for main group molecules (G03/05 test set)).44 G3-RAD also predicts a
very close value to the ccCA value (30.1 kcal mol-1). However, including empirical parameters
makes G3-RAD a system-dependent method. Thus, the RO-ccCA value is recommended. The
computed ΔH°f, 298 for FOOO using ROM06 is 5.7 kcal mol-1 greater than the RO-ccCA value.
M06-2X predicts very high ΔH°f, 298’s for FOOO compared to the other methods. For FOOOH,
the calculated ΔH°f, 298’s of ccCA is considered the reference data for the same reason previously
mentioned. The ΔH°f, 298 of ccCA for FOOOH (-1.6 kcal mol-1) is chemically sensible since
formation of hydride is usually exothermic with fluoride lowering its stability. In addition, G3B3
predicts as exothermic ΔH°f, 298 as ccCA, but greater by 1.3 kcal mol-1. G3 and M06 and M06-2X
overestimated the ΔH°f, 298 of FOOOH by 1.8, 4.2, and 4.5 kcal mol-1, respectively, with respect
to the ccCA value. Finally, ccCA successfully predicts the ΔH°f, 298 of FOOOF with only a 0.2
kcal mol-1 deviation from the extrapolated CCSD(T)/aug-cc-pV(T,Q)Z value calculated
previously by Huang et al.,19 where other methods such as G2 and G96PW91/D95(3df) predicted

72

ΔH°f, 298’s that are > 7.0 kcal mol-1 higher than the CCSD(T) value.67 Here G3B3 ΔH°f, 298 is also
in good agreement with the CCSD(T) value, with a deviation of only 0.7 kcal mol-1 between the
two, but G3 ΔH°f, 298 differs by 1.2 kcal mol-1. This difference between G3B3 and G3 results
typically comes from geometry optimization, with MP2 found to be insufficient to describe the
structure of dioxygen fluoride species. M06 and M06-2X again overestimated the enthalpy of
formation of FOOOF by 4.3 kcal mol-1 with respect to the CCSD(T) value.
The MADs of the calculated ΔH°f, 298’s for all the utilized methods with respect to the
reference data were computed and provided in Table 3.6. The MADs of M06 and M06-2X as
shown in Table 3.6 are 4.0 and 5.2 kcal mol-1 (3.5 and 4.3 kcal mol-1 without FOOF),
respectively. Thus, compared to the chlorine oxides in Table 3.3, M06 and M06-2X do not
perform well for oxygen fluoride species. That can be attributed to the poor geometries obtained
by M06 and M06-2X. Because of the deficiencies in the M06 and M06-2X computed
geometries, single point M06 and M06-2X energy calculations were performed using the
B3LYP/aug-cc-pVTZ geometries to examine the performances of M06 and M06-2X for oxygen
fluorides energy calculations. ΔH°f,

298

and MAD’s were calculated and listed in Table 3.7.

However, no improvement is noticed in the M06 and M06-2X ΔH°f, 298’s when using B3LYP
geometries. That supports our conclusion that M06 and M06-2X are not considered reliable
methods to predict structures and energetic properties for oxygen fluorides. G3 and G3B3
(including the G3-RAD values) perform well with MAD’s of 1.5 kcal mol-1 for both methods
(0.9 kcal mol-1 for both methods without FOOF). This performance is expected taking into
account the inclusion of the HLC term in the G3 and G3B3 energy. For example, the G3B3 ΔH°f,
298

of FO without the HLC term is 30.3 kcal mol-1, a value that is greater by 3.8 kcal mol-1 than

the G3B3 ΔH°f, 298 listed in Table 3.6. The MAD of the G3 and G3B3 methods (1.5 kcal mol-1) is

73

much smaller for the oxygen fluorides than for the chlorine oxides (2.3 kcal mol-1 for G3 and 3.5
kcal mol-1 for G3B3), so G3 and G3B3 perform better for oxygen fluorides than for chlorine
oxides. The MAD of ccCA-S3 is 1.4 kcal mol-1 (0.9 kcal mol-1 without FOOF) for oxygen
fluorides and is 1.1 kcal mol-1 for chlorine oxides. This indicates a capability of ccCA to predict
reliable energetic properties for halogen oxides.
Table 3.7 Calculated enthalpies of formation for the oxygen fluoride species using M06 and
M06-2X methods based on B3LYP/aug-cc-pVTZ geometries.

ΔH°f, 298 K (kcal mol-1)
Compd.

B3LYPa//M06b

Reference datac

FO

28.4

27.7

26.1±2.4

FOH

-17.5

-18.5

-23.16±1.2

FOF

10.2

9.3

5.9±0.5

FOO

9.3

15.0

6.1±0.5

FOOH

-6.9

-7.7

-10.4±1.0d

FOOF

11.8

19.9

4.6±0.5

FOOO

34.7

47.5

-

FOOOH

4.9

4.5

-

FOOOF

31.8

32.1

26.6e

MAD

4.5

6.0

-

4.0

4.4

-

MAD w/o FOOF
a

B3LYPa//M06-2Xb

b

B3LYP/aug-cc-pVTZ. M06/aug-cc-pVQZ and M06-2X/aug-cc-pVQZ
NIST-JANAF Tables: Reference 36-37. d CCSD(T)/ANO4: Reference 21.
e
Extrapolated CCSD(T)/aug-cc-pV(T,Q)Z: Reference 19.
c

In addition, a comparison between the calculated ΔH°f, 298’s in this study and the recent
Active Thermochemical Tables (ATcT)68,69 values of the ΔH°f, 298’s of FO, FOH, FOF, FOO,
FOOF, and FOOOF are examined. The ATcT tables use artificial intelligence algorithms to
reduce the uncertainties in the experimentally measured ΔH°f, 298’s by combining experimental

74

and highly accurate theoretical thermochemical data.68,69 As shown in Table 3.8, the
uncertainties of the ATcT values of FO, FOH, FOF, and FOO decreased in comparison to the
NIST-JANAF values (Table 3.6). Thus, to evaluate our methods against the ATcT values, the
MADs of the calculated ΔH°f, 298’s for all the utilized methods with respect to the ATcT values
were computed and provided in Table 3.8. The MADs of ccCA-S3, M06, M06-2X, G3, and
G3B3 were all lowered by 0.5-0.9 kcal mol-1 in comparison with the MADs shown in Table 3.6
(with ccCA-S3 providing the lowest MAD, at 0.6 kcal mol-1). The large difference in the MADs
between NIST-JANAF table and ATcT is likely attributed to the large difference between the
ATcT value of the ΔH°f, 298 of FOOF (8.04±0.09 kcal mol-1) and the NIST-JANAF value (4.6 ±
0.5 kcal mol-1).
Table 3.8 Calculated Enthalpies of formation for the oxygen fluoride species using all methods
and the MADs of these methods with respect to the ATcT values.
ΔH°f, 298 K (kcal mol-1)
Compd.
ccCA-S3

M06a

M06-2Xa

G3

G3B3

ATcTb

FO

27.0

28.1

27.5

26.1

26.5

26.51±0.04

FOH

-21.6

-17.7

-18.6

-20.4

-20.1

-20.85±0.05

FOF

6.2

9.6

8.7

6.5

6.8

5.91±0.06

FOO

7.5e

9.0f

14.5f

7.1g

7.0

5.99±0.06

FOOH

-11.7

-7.6

-8.4

-10.3

-10.2

-

FOOF

8.7

11.2

15.5

9.3

8.9

8.04±0.09

FOOO

31.0c

36.7d

41.3d

30.1e

30.1e

-

FOOOH

-1.6

2.6

2.9

0.2

-0.3

-

FOOOF

26.8

30.9

30.9

27.8

27.3

26.63±1.86

MAD

0.6

3.1

4.7

0.8

0.7

a
d

M06 and M06-2X in conjunction with aug-cc-pVQZ. bATcT: Reference 68-69. c Using RO-ccCA.
Using ROM06 and ROM06-2X. e Using G3-RAD.

75

3.1 Conclusion
The capability of ccCA, G3, and G3B3 for the prediction of the enthalpies of formation
of oxygen fluoride species was evaluated. In addition, the performance of M06 and M06-2X in
conjunction with the correlation consistent basis sets (aug-cc-pVnZ), where n = D, T, Q, was
also examined for predicting the structures and enthalpies of formation of oxygen fluoride
species. An important finding from this study is that though M06 and M06-2X are useful
functionals for many main group species (including chlorine oxides), M06 and M06-2X were
less successful in the prediction of reasonable structures and ΔH°f, 298’s for oxygen fluorides,
oxygen difluorides, and related hydrides. This could be generalized to systems containing F-O
and/or O-O bonds (e.g. peroxides and polyoxides). Geometries predicted by B3LYP/aug-ccpVTZ are generally in good agreement with the listed reference data. When calculating the
enthalpies of formation, ccCA-S3 provides the lowest MAD (1.4 kcal mol-1 with respect to the
reference data; 0.9 kcal mol-1 excluding FOOF) without any parameterized energies. While
ccCA-S3 provides the smallest MAD of the four different CBS extrapolation formulas
considered for this set of molecules, other ccCA variants, such as ccCA-PS3, have been found to
be useful in previous studies.44,45 G3 and G3B3 achieved a MAD that is greater than ccCA-S3 by
only 0.1 kcal mol-1 with respect to the reference data while incorporating an empirical parameter
that is intended to reduce the overall MAD of G3 and G3B3 (or MAD of 0.9 kcal mol-1
excluding FOOF, which is identical to ccCA-S3 in this case). The performance of G3 and G3B3
for chlorine oxides is not as good as for oxygen fluorides. ccCA-S3 predictions of the ΔH°f, 298’s
of both the oxygen fluorides and of the chloride oxides species are in good agreement with the
experimental values. In addition, when comparing the calculated ΔH°f, 298’s to the ATcT values,
ccCA-S3 provides the lowest MAD (0.6 kcal mol-1) in comparison to the other methods included

76

in this study. The enthalpies of formation for FOOO and FOOOH are predicted to be 31.0 and
-1.6 kcal mol-1, respectively, by the ccCA-S3 method. Overall, the use of the correlation
consistent Composite Approach (ccCA) is recommended for such systems, with promise for
other halogen systems and peroxides.

77

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78

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85

CHAPTER 4 ENTHALPIES OF FORMATION FOR ORGANOSELENIUM
COMPOUNDS VIA SEVERAL THERMOCHEMICAL SCHEMES

4.1. Introduction
Organoselenium compounds have been a subject of interest due to their potential
applications in areas including organic synthesis,1,2 green chemistry,3,4 biochemistry,5-8 redox
chemistry,9,10 and synthesis of conducting materials, semiconductors, and optoelectronic
materials.11-15

Organoselenium

reagents

such

as

selenoxide,

carbonyl

selenide,

isoselenocyanates, and selenones play an important role in organic reactions involving
transformation mechanisms and typically result in high yields overall.1,2 The generation of
complex alkenes via the stereospecific syn-elimination of selenoxides is another important and
successful applications of organic selenium compounds.16-18
Although selenium is a chalcogen like oxygen and sulfur, it exhibits quite different
chemistry. The selenium-carbon bond (bond length (r) = 1.98 Å and bond dissociation energy
(BDE) = 55.93 kcal mol-1) is longer and weaker than that of the sulfur-carbon bond (r = 1.81 Å
and BDE = 65.01 kcal mol-1), which, in turn, is longer and weaker than the carbon-oxygen bond
(r = 1.41 Å and BDE = 85.56 kcal mol-1). Organoselenium reagents, as a result, are more active
and involved in wide range of chemical applications than their corresponding organosulfur and
organo-oxygen compounds.19
Insight about the potential utility of organoselenium compounds can be gained, in part,
by knowing about their thermochemical properties including enthalpies of formation, Gibbs free
energies, and bond dissociation energies at certain temperatures. Due to the weak Se-C and SeSe bonds, some organoselenium compounds tend to be relatively unstable during

86

thermochemical measurements. In addition to their instability, toxicity and difficulties in
purification also contribute to the limited availability of thermochemical experimental data for
organoselenium species as well as numerous discrepancies among the available experimental
results.20,21 For example, Voronkov et al.22 reported an enthalpy of formation (∆ °

,$¤¥ )

of

diethyl selenide (C2H5SeC2H5) of -11.78 ± 0.96 kcal mol-1 while Tel’noi et al.23 reported an
∆ °

,$¤¥

of -5.02 ± 0.96 kcal mol-1 for the same molecule. The most recent review of the

thermochemistry of organoselenium compounds was in 2011 by Liebman and Slayden21 in

which they reviewed and assessed the available ∆ °

,$¤¥ ′

of organoselenium compounds that

were mostly reported in three different review publications.22-24
The lack of reliable thermochemical properties of organoselenium species increases the

need for high-level ab initio quantum chemical calculations for the prediction of energetic
properties of organoselenium compounds and for the validation of available experimental data.
Boyd et al.25,26 evaluated the performance of density functionals for the prediction of the
geometries and bond dissociation energies of several biologically relevant organoselenium
compounds with respect to the quadratic configuration interaction (QCISD) in conjunction with
the cc-pVTZ basis set. The authors found that B3PW91 in conjunction with 6-311G(2df,p)
performed the best.25,26 Another study by Maung et al.27 found that MP2/6-311G(d,p) predicted
the most accurate BDE of HSe-H (H2Se) with a deviation of only 0.3 kcal mol-1 off from
experiment, while B3LYP/6-311G(d,p) predicted a BDE that is 4.7 kcal mol-1 higher than the
experimental value. Maung also calculated BDEs of other organoselenium compounds using
several density functionals. Due to the absence of reliable reference data, according to Maung,
no definitive conclusion can be reached from their study,27 although the non-local BHandHLYP
functional was determined to be the most useful choice for the prediction of BDEs of

87

organoselenium compounds at an inexpensive computational cost with respect to its prediction of
the BDEs of HSe-H and H-Se.27 Overall, most of the theoretical applications of quantum
mechanics on organoselenium compounds involved the prediction and evaluation of BDEs rather
than ∆ °

,$¤¥ ′

.25-30

Although QCISD and coupled cluster with single, double, and perturbative triple

excitations (CCSD(T)) have been reliable for predicting energetic properties, it is essential that
the energies are extrapolated to the complete basis set (CBS) limit, i.e. the basis set
incompleteness error is eliminated. However, CBS calculations with highly correlated methods
are computationally demanding in terms of computer time, memory, and disk space. A number
of ab initio composite approaches have been developed for modeling thermochemical properties
with accuracy similar to that possible with CCSD(T)/CBS, but with reduced computational
cost.31-38 Composite methods utilize a series of steps combining lower level methods and basis
sets to replicate results possible with higher level methods. The most commonly used composite
methods are the Gaussian-n (Gn) methods developed by Pople et al.31-34 Other successful
composite methods are the correlation consistent Composite Approaches (ccCA) developed by
Wilson et al.35-41 The Gn methods, detailed in Chapter 2 Section 2.5.2 and elsewhere,42 were
extended to include molecules containing third-row main group elements.34,43,44 The developers
of the Gn methods also introduced molecule sets, such as G3/05 set,45 that can be used to gauge
the utility of computational approaches.
The only selenium-containing compounds in the G3/05 set are SeH and SeH2. The
deviations of the calculated atomization energies with respect to experiments for SeH are 0.1
kcal mol-1 (G2), -1.1 kcal mol-1 (G3), and -0.7 kcal mol-1 (G4), and the deviations for SeH2 are
1.1 kcal mol-1 (G2), 0.9 kcal mol-1 (G3), and 1.1 kcal mol-1 (G4).34,44 The ∆ °
88

,$¤¥

of SeH2 was

computed using G2 and was only 1.1 kcal mol-1 off from the experimental value.46 ccCA,
detailed in Chapter 2 Section 2.5.2 and elsewhere,47 also was applied to the G3/05 training set.37
The deviation of the calculated atomization energies when using ccCA with respect to
experiment was -0.7 kcal mol-1 for SeH and -0.4 kcal mol-1 for SeH2. These deviations were
reduced to -0.2 kcal mol-1 for both molecules when including the theoretical second-order atomic
spin-orbit corrections, calculated by Blaudeau et al.48 using the configuration interaction (CI)
method, to the ccCA energy,37 displaying a superior performance over the Gn methods for these
molecules. The ccCA mean absolute deviation (MAD) for the molecules containing third-row
atoms (Ga-Kr) included in the G3/05 set was 0.95 kcal mol-1 (0.88 kcal mol-1 when the secondorder atomic spin-order corrections was included) for a group of thermochemical properties
including 19 atomization energies (D0), 11 enthalpies of formation (∆Hf), 15 ionization potentials
(IP), 4 electron affinities (EA), and 2 proton affinities (PA).37 The aforementioned examples
illustrate the rigor of these composite approaches.

There has been much less investigation of the ∆ °

,$¤¥ ′

of selenium-containing organic

compounds than for oxygen- or sulfur-containing organic compounds. The most common and
simplest method to determine the ∆ °

,$¤¥ ′

in calculations is through the use of the atomization

energy approach. This approach employs the difference in energy between the target molecule
and its constituent atoms. Although the atomization approach (RC0) has been successfully
applied to predict ∆ °

,$¤¥ ′

using high levels of theory and/or model chemistries, differential

electron correlation effects and size extensivity can be two problems associated with using this
approach. Differential electron correlation effects come from the difference in correlation energy

between the molecules (can involve conjugation, polarization, and strain) and the isolated
atoms.49-51 Size extensivity is the ability of a method to scale linearly with increasing the number

89

of electrons, i.e. the method becomes independent of the size of the system.41,52 Typically, these
two factors become increasingly important as the size of the target molecule is increased.
Additionally, since the atomization approach involves relative energies of a molecule and its
constituent atoms, any error associated with the approximation of the Schrödinger equation (i.e.
Born-Oppenheimer approximation, lack of correlation correction, relativistic effects, and
incomplete basis sets) will not be balanced resulting in an accumulation of errors.41,53 In order to
reduce these errors, molecular reaction schemes such as the isogyric reaction, isodesmic reaction,
and homodesmotic reaction schemes have been developed to calculate thermochemical
properties based on bond interaction energies.54,55 In thermochemical reaction schemes, relative
energies are calculated between the target molecule and its constituent molecules (known as
elemental reactants and products) rather than between the target molecule and its constituent
atoms as is the case when using the atomization approach. This allows for the cancellation of
errors arising from differential electron correlation and size extensivity; thus, in principle, the
isodesmic reaction scheme can provide more accurate energetic properties than the atomization
approach depending on the accuracy of the calculated reaction enthalpy of the bond separation
reaction (BSR) of the target molecule and the experimental ∆ °
molecules.40,41,52,56-58

∆ °

,$¤¥ ′

of the constituent

Wheeler et al.57,58 defined a hierarchy of homodesmotic reactions for the calculation of

,$¤¥ ′

for hydrocarbon compounds. The hierarchy includes: isogyric (RC1), isodesmic

(RC2), hypohomodesmotic (RC3), homodesmotic (RC4), and hyperhomodesmotic (RC5)
reactions.57 As the homodesmotic reactions hierarchy increases from RC1 to RC5, the degree of
error-balanced between reactants and products increases as well as the accuracy of computed
enthalpies. For acyclic, closed-shell hydrocarbons, even low-level computational methods such

90

as Hartree-Fock can provide chemical accuracy when it is used with RC4 or RC5 reaction
schemes.58 The definition of these reaction schemes, according to Wheeler,57,58 are shown in
Table 4.1. In RC1 the number of electron pairs is maintained while in RC2 the number and type
of carbon-carbon are both maintained. Not only the number and the bond type of C-C bonds are
conserved in RC3, but also the hybridization state and the number of carbons with an equal
number of hydrogen atoms attached are both maintained. RC4 and RC5 balance more chemical
interactions than the lower scheme, see Table 4.1. This homodesmotic reaction hierarchy
provides a clear classification and definition of homodesmotic reactions that make it possible to
extend the scheme to a variety of organic molecules including those containing oxygen and
sulfur atoms.
Table 4.1 The definition of the homodesmotic reaction schemes according to Wheeler.57,58
Reaction
scheme
RC1
RC2
RC3

Name

Reaction scheme constraints

isogyric
isodesmic
hypohomodesmotic

The number of electron pairs and unpaired electrons
The number and bond type of carbon-carbon
The number and the bond type of C-C bond, and
The hybridization state of each carbon atom and the number of
carbons with an equal number of hydrogen atoms attached
“The number of each type of carbon-carbon bond [C§¨© −
C§¨© , C§¨© − C§¨š , C§¨© − C§¨ , C§¨š − C§¨š , C§¨š − C§¨ , C§¨ −
C§¨ , C§¨š = C§¨š , C§¨š = C§¨ , C§¨ = C§¨ , C§¨ ≡ C§¨]in reactants
and products, and
The numbers of each type of carbon atom (sp3, sp2, sp) with zero,
one, two, and three hydrogens attached in reactants and
products”
The number of carbon-carbon bond types [ Hv C − CH$ , Hv C −
CH, H$ C − CH$ , Hv C − C, H$ C − CH, H$ C − C, HC − CH, HC −
C, C − C, H$ C = CH, HC = CH, H$ C = C, HC = C, C = C, HC ≡
C, and C ≡ C] in reactants and products, and
The number of each type of carbon atom (sp3, sp2, sp) with zero,
one, two, and three hydrogens attached in reactants and
products”

RC4

homodesmotic

RC5

hyperhomodesmotic

Wilson et al.41 extended this definition to include larger molecules and found that for the
91

ccCA and G3 methods it is necessary to use higher level reaction schemes to gain high accuracy
when calculating the ∆ °

,$¤¥ ′

of aromatic hydrocarbons. However, this statement does not

hold for the G4 method. The ccCA, G3, and G4 methods used in the Wilson study resulted in
MAD’s for the ∆ °

,$¤¥ ′

of aromatic hydrocarbon of 2.88, 1.60, and 1.04 kcal mol-1,

respectively for RC2 and 0.79, 1.55, and 1.78 kcal mol-1, respectively for RC3. These results
show that RC3 is recommended for larger molecules, especially when using ccCA. Engelkemier
and Windus59 extended this hierarchy to calculated ∆ °

,$¤¥ ′

of oxygen-containing organic

molecules and showed the effectiveness of these reaction schemes in the cancellation of errors
and in providing more accurate enthalpies even for large molecules such β-D-glucopyranose-gg.
Jorgensen and Wilson40 published a detailed study of the effect of the hypohomodesmotic

reaction scheme (RC3) when used in combination with ccCA, G3, and G4 for the prediction of
∆ °

,$¤¥ ′

of organosulfur species and compared it with the atomization approach (RC0). In

general, the RC3 reaction scheme did decrease the overall MAD of the ∆ °

,$¤¥ ′

for ccCA, G3,

and G4 as compared to the RC0 approach, though not significantly. For example, the MAD of
the ∆ °

,$¤¥ ′

of organosulfur species computed with ccCA-P is 0.98 kcal mol-1 using RC0 and

0.54 kcal mol-1 using RC3.40 Thus, RC0 is still an effective method when using composite
approaches such as ccCA, G3, and G4,40,41 particularly for light atoms or/and small molecules
but not necessarily for heavy elements or/and large molecules. However, the decrease in the
MAD when using the RC3 scheme compared to the RC0 for the component methods that are
used for the additive terms in the ccCA methodology is very significant (2.39 kcal mol-1 when
using MP2/aug-cc-pVQZ to 78.11 kcal mol-1 when using MP2/aug-cc-pVDZ).40

92

In the present study, the homodesmotic hierarchy is used to predict ∆ °

,$¤¥ ′

for

selenium-containing organic compounds. The effect of RC2 and RC3 schemes on predicting the
∆ °

,$¤¥ ′

of organoselenium molecules via ccCA, G3, G4, and B3PW91/aug-cc-pVTZ is

investigated and compared to RC0 results. Due to the lack of reliable thermochemical properties
of organoselenium species, the molecule set in this study is smaller than for the organosulfur
study,40 mentioned earlier. Additionally, the quality of the experimental ∆ °

,$¤¥ ′

is also

assessed due to the significant discrepancies between the reported experimental results. The
performance of each individual step of ccCA, using RC2 and RC3 schemes, is also discussed.
The study compares trends of the computational approaches used to calculate the ∆ °

chalcogen-containing hydrocarbon molecules (group 16 of the periodic table).

,$¤¥ ′

of

4.2 Computational Details
4.2.1 Methods
All calculations have been carried out using the Gaussian 09 software package.60 The
correlation consistent Composite Approach (ccCA), detailed in Chapter 2 Section 2.5.2 and
elsewhere35,36,38 and has been applied widely in prior studies,40,41,47,61-63 were used to predict the
∆ °

,$¤¥ ′

of organoselenium species. For molecules containing third row atoms (Ga-Kr), the

atomic second-order spin orbit coupling is also added to the total ccCA atomic energies.37 The
valence correlation space includes the 3s, 3p, 4s, 3d, and 4p orbitals for selenium in all single
point energy calculations within the ccCA methodology and the FC1 correlation space include
all the electrons except the 1s electrons for selenium.37

93

The most commonly used composite methods, G344 and G434 were used for comparison.
The hybrid density functional B3PW9164,65 in conjunction with the aug-cc-pVTZ basis set was
also used as it was found to provide accurate geometries and energies for organoselenium
compounds when compared to results obtained using QCISD/cc-pVTZ.26 The ∆ °

,$¤¥ ′

of

organoselenium compounds were also calculated using each level of theory that are components
of the ccCA methodology. The mean absolute deviation (MAD) and the mean signed deviation
(MSD) were both calculated for each method. The geometries and structural parameters of all
molecules of interest are presented in the Appendix. The frequency calculations and the wave
function stability tests were both used to ensure that the predicted closed-shell structures are all a
stable minimum.

4.2.2 Thermochemistry
The ∆ °

,$¤¥ ′

of organoselenium compounds were calculated using ccCA, G3, G4, and

B3PW91 methods. Three thermochemical approaches were used in the calculations of the
∆ °

,$¤¥ ′

: the atomization approach (RC0), the isodesmic reaction scheme (RC2), and the

hypohomodesmotic reaction scheme (RC3).

4.2.2.1 Atomization Approach (RC0)
In this method, the ∆ °

,$¤¥ ′

were computed as follows:

94

∆

,1

298i = ! ˜∆
^FG“°

+·

1

0i − ² ! ˜

,/

298i −

− ² ! ˜·
^FG“°

/

1

^FG“°

0i ¸

298i −

/

/

−

1

−

³´µ ¶

(4.1)

0i ¸¶

The enthalpy of formation of the molecule of interest (M) (∆

,1 )

at 298 K is calculated using

Eq. 4.1. The first term in Eq. 4.1 is the experimental enthalpy of formation of its constituent
atoms (∆

,/ )

at 0K multiplied by n, the number of each type of atom. The recommended

experimental ∆ °

,Q

of the selenium atom, 57.9 kcal mol-1,66,67 was used in this study. Carbon

and hydrogen ∆ ° ,Q ′ are the same as those used in Jorgensen’s study,40 which are 170.11 kcal

mol-1 and 51.63 kcal mol-1,68,69 respectively. The second term is the atomization energy of the

molecule of interest (¹Q = ∑^FG“° ˜

/

−

1

−

³´µ ),

where EA, EM, and EZPE are the total

energies of the constituent atoms, the total energy of the molecule of interest, and the zero point
energy of the molecule of interest, respectively. The energies are calculated at the specified level
of theory. The last two components are the thermal corrections to the enthalpies to account for a
temperature of 298 K for the atoms (experimental) and for the molecule of interest, calculated at
a specified level of theory. The thermal corrections to enthalpies for atoms are 1.32 kcal mol-1 for
selenium,66 0.25 kcal mol-1 for carbon,68 and 1.01 kcal mol-1 for hydrogen.69

4.2.2.2 Isodesmic (RC2) and Hypohomodesmotic (RC3) Reaction Schemes
The ∆ °

,$¤¥ ′

were computed using the RC2 and RC3 reaction schemes as follows:

95

∆

In Eq. 4.2, the ∆

,1

298i =

−

! ∆

»\G¼ZDF

!

\;^DF^<F

−½ !

,1

∆

»\G¼ZDF

,»\G¼.

298i

298i

,\;^DF.

298i −

(4.2)

!

\;^DF^<F

is calculated using the experimental ∆

298i ¾

298i of the elemental reactants

and elemental products, i.e. the constituent molecules, and the calculated enthalpy of the reaction
which is represented by the term ·∑»\G¼ZDF

298i − ∑\;^DF^<F

298i ¸. Elemental

reactants and products are molecules produced from the bond separation reaction (BSR)55 of the
target molecule and they must maintain all of the constraints of each given reaction scheme. The
first step in thermochemical reaction schemes, such as RC2 and RC3, is to define these elemental
reactants and products.

4.2.3 Organoselenium Compounds
A set of eight organoselenium molecules were selected based on the availability of
experimental data. This set contains only carbon, selenium, and hydrogen atoms and consists of
two constituent molecules dimethyl selenide ((CH3)2Se) and dimethyl diselenide ((CH3)2Se2)),
six target molecules divinyl selenide ((CH2=CH)2Se, diethyl selenide ((CH3CH2)2Se), diethyl
diselenide

((CH3CH2)2Se2),

diisopropyl

selenide

(((CH3)2CH)2Se)),

dipropyl

selenide

((CH3(CH2)2)2Se), dibutyl selenide ((CH3(CH2)3)2Se), and selenium dihydride (H2Se). Aromatic
molecules were not included in the set. The ∆ °

,$¤¥ ′

for the set of molecules were calculated

using the RC0, RC2, and RC3 approaches via ccCA, G3, G4, and B3PW91. In order to calculate

96

the ∆ °

,$¤¥

of the aliphatic organoselenium compounds using the RC2 and RC3

thermochemical reaction schemes, Wheeler’s definition57 of RC2 and RC3 was extended to
include selenium-containing elemental reactants and products. That is, for RC2, the number and
the bond type of Se-C and Se-Se bonds was conserved, and for RC3 the number, the bond type,
and the hybridization state of selenium were all conserved. These elemental reactants and
products are provided in Figure 4.1. The proposed RC2 and RC3 reactions are shown in Figures
4.2 and 4.3, respectively. In these reaction schemes, the uncertainties of the reported results are
cumulative. Thus, a potential source of deviations in RC2 and RC3 schemes can come from the
uncertainties associated with the experimental ∆ °
in the proposed reaction schemes.

,$¤¥ ′

of the constituent molecules involved

Figure 4.1 Selenium-containing elemental reactants and products.

97

Figure 4.2 Isodesmic (RC2) reaction schemes.

Figure 4.3 Hypohomodesmotic (RC3) reaction schemes.

98

4.2.4 Reference Data

The available experimental gas phase ∆ °

,$¤¥ ′

of organoselenium molecules were

considered as reference data. Due to the large discrepancies between experiments, the
quantitative structure-property relationship (QSPR) ∆ °

,$¤¥ ′

were also considered for

evaluation purposes. QSPR is a semiempirical method developed to predict chemical and

physical properties, such as ∆ °

,$¤¥ ′

of organic and organometallic compounds, using

numerical descriptors that generated from molecular structures and has been successfully applied
for a variety of organic and organometallic compounds.70-74 Shown in Table 4.2 are all available
reference data categorized by the methods used for measurement.
All the experimental ∆ °

,$¤¥ ′

of organoselenium compounds, provided in Table 4.2,

were determined via thermochemical schemes relative to the selenium dioxide (SeO2)
combustion product. The reason for using the combustion procedure is because SeO2 is the only
metallic oxide that is produced from the burning of selenium and its compounds.24 SeO2 is
soluble in water and to ensure its complete dissolution in water, a high precision measurement,
such as the rotating bomb calorimetry, is often used. While rotating bomb calorimetry is a
preferred experimental method, Batt24 showed very good agreement between static and rotating

bomb measurement of the ∆ °

,$¤¥

of SeO2.

A review by Liebman and Slayden21 of the evaluation of organoselenium compounds

thermochemistry, as well as the ∆ °

,$¤¥ ′

predicted by QSPR74 were both used as a guidance in

evaluating the reference data. Liebman and Slayden21 evaluated the ∆ °

,$¤¥ ′

of

organoselenium compounds reported from two main calorimetric measurements: static bomb
calorimetry performed by Tel’noi23 and rotating bomb calorimetry performed by Voronkov.22

99

Liebman21 used the well-established linear relationship, developed by Rossini et al.,75-77 for the
∆ °

,$¤¥ ′

of a set of homologous organic compounds, such as RZ and R2Z where R is an alkyl

group and Z is a heteroatom to examine the validity of the experimental ∆ °
selenides and to predict unknown ∆ °

found that the experimental ∆ °

,$¤¥

,$¤¥ ′

,$¤¥ ′

of the dialkyl

for other homologous organic compounds. It was

of (CH3)2Se measured by Tel’noi23 using static bomb

calorimetry deviates from the Rossini linear relationship by ~3.12 kcal mol-1 – a deviation that is
too large for reliability.21 An ∆ °

,$¤¥

of -2.39 kcal mol-1 for (CH3)2Se is suggested by Liebman

to be more credible.21 Using the QSPR approach, a value of -1.77 kcal mol-1 is predicted for the

∆ °

,$¤¥

of (CH3)2Se.74 The QSPR ∆ °

,$¤¥ of

(CH3)2Se is near the value suggested by Liebman.

Using the Rossini linear relationship, Liebman validated the ∆ °

,$¤¥ ′

of -11.78±0.96 kcal

mol-1 for (CH3CH2)2Se, -25.81±0.96 kcal mol-1 for ((CH3)2CH)2Se, and -31.50±1.20 kcal mol-1
for (CH3(CH2)3)2Se; all were measured by Voronkov et al.22 using rotating bomb calorimetry.
The ∆ °

,$¤¥

of (CH3(CH2)2)2Se was interpolated from this relationship to have a value of -21.75

kcal mol-1. As shown in Table 4.2, the predicted ∆ °
most similar to those measured by Voronkov et al.22
The experimental ∆ °

,$¤¥ ′

,$¤¥ ′

of these compounds using QSPR are

of dialkyl diselenides exhibit large discrepancies and high

uncertainties, which precludes the potential of applying Rossini’s linear relationship75-77 to these
compounds. Furthermore, no results from QSPR are available for dialkyl diselenids. For
consistency, and since both (CH3)2Se and (CH3)2Se2 are considered constituent molecules, the
∆ °

,$¤¥

of (CH3)2Se2, measured by Tel’noi23 using the same experiment as (CH3)2Se, was

estimated in the same manner as the ∆ °
recommended ∆ °

,$¤¥

,$¤¥

of (CH3)2Se was estimated by Liebman.21 The

of (CH3)2Se2 is ~6.22 kcal mol-1. The experimental ∆ °

100

,$¤¥ ′

of

(CH3CH2)2Se2 and (CH3(CH2)3)2Se2 measured by Tel’noi et al.23 using combustion procedure in
a stationary bomb often are associated with high uncertainties as shown in Table 4.2. Liebman
found that the slope of these two ∆ °

,$¤¥ ′

versus the number of carbon atoms are in reasonable

agreement with the slope for similar corresponding symmetrical n-alkanes.
The experimental ∆ °

,$¤¥ ′

of divinyl selenide shown in Table 4.2 were measured with

the static bomb23 to be 49.71±1.90 kcal mol-1 and with the rotating bomb22 to be 28.44±0.96 kcal
mol-1. The enthalpy of hydrogenation of divinyl selenide using the 49.71±1.90 kcal mol-1 value

and the recommended ∆ °

,$¤¥ of

diethyl selenide (-11.78±0.96 kcal mol-1)21 is -30.71 kcal mol-1

per vinyl group which is very close to the enthalpy of hydrogenation of the corresponding
alkene, 1,4-pentadiene, which is -30.11±0.15 kcal mol-1.78 However, the enthalpy of
hydrogenation using the rotating bomb value (28.44±0.96 kcal mol-1 ) is -20.08 kcal mol-1 per
vinyl group which is much smaller than that of the corresponding alkene. Based on these values
of the enthalpy of hydrogenation of divinyl selenide, the value 49.71±1.90 kcal mol-1 can be
considered more reliable than 28.44±0.96 kcal mol-1. Data shown in bold in Table 4.2 are
considered to be the most reliable and are thus used as reference data in the present work.
Table 4.2 Experimental and estimated enthalpies of formation in kcal mol-1 for organoselenium
compounds.a,b
∆¿°À,ÁÂà ′Ä
(SBC)c

∆¿°À,ÁÂà ′Ä
(RBC)d

∆¿°À,ÁÂà ′Ä
(Estimated)e

∆¿°À,ÁÂà ′Ä
(QSPR)f

(CH3)2Se

4.3±1.90

-

-2.39±1.90

-1.77

(CH3)2Se2

12.91±1.90

-0.72±0.96

6.22±1.90

-

(CH2=CH)2Se

49.71±1.90

28.44±0.96

(CH3CH2)2Se

-5.02±0.96

-11.78±0.96

-

-10.68

(CH3CH2)2Se2

-3.82±2.87

-9.08±0.96

-

-

((CH3)2CH)2Se

-

-25.81±0.96

-

-21.82

101

Table 4.2 Continued.
(CH3(CH2)3)2Se

-

-31.50±1.20

-

-28.20

(CH3(CH2)4)2Se

-

-41.28±1.20

-

-37.08

(CH3(CH2)3)2Se2

-21.03±5.02

-

-

-

(CH3(CH2)2)2Se

-

-

-21.75±0.96

-

a

SBC stands for static bomb calorimetry, RBS stands for rotating bomb calorimetry, estimated values are
obtained based on the Rossini linear relationship, QSPR stands for the quantitative structure-property
relationships.
b
Data shown in bold are considered to be the most reliable and are thus used as reference data in the
present work.
c
Reference. 23. dReference. 22. eReference. 22. fReference. 74.

4.3 Results and Discussion
The ∆ °

,$¤¥ ′

of the constituent fragments shown in Figure 4.1 were calculated using

the atomization approach (RC0) via ccCA-P, ccCA-S3, ccCA-S4, ccCA-PS3, G3, G4, and
B3PW91/aug-cc-pVTZ and presented in Table 4.3. The calculated ∆ °

,$¤¥ ′

of the hydrocarbon

fragments are shown in Table 4.4, as they were calculated using ccCA, G3, and G4 in previous
studies.40,41

Table 4.3 Calculated enthalpies of formation (in kcal mol-1) for the elemental products and
reactants of organoselenium compounds via the atomization approach (RC0).

ccCA-P

ccCA-S3

ccCA-S4

ccCA-PS3

G3

G4

B3PW91/
aVTZa

Expt.

H2Se

7.19

6.85

7.16

7.02

7.91

8.12

6.75

7.03±0.190b

(CH3)2Se

0.93

-0.34

0.82

0.29

0.90

1.38

2.54

-2.39± 1.90c

(CH3)2Se2

7.19

5.65

7.12

6.42

7.04

8.02

5.28

6.22± 1.90c

a

aVTZ: aug-cc-pVTZ. bReference 79. cReference 21.

102

The calculated ∆ °

,$¤¥ ′

of selenide dihydride (H2Se) are in relatively good agreement

with the experimental value for all computational methods employed. All ccCA variants predict
a∆ °

,$¤¥

for H2Se that is within the experimental uncertainty. G3 and G4 both lead to an

underestimate of the ∆ °

,$¤¥

of H2Se by ~1.0 kcal mol-1 with respect to experiment, while

B3PW91 overestimates by 0.1 kcal mol-1. The ∆ °

,$¤¥ ′

of dimethyl selenide ((CH3)2Se)

calculated using the current composite methods are all off the reference value by 2.05 kcal mol-1
to 4.93 kcal mol-1, with ccCA-S3 being the closet to the reference value (0.15 kcal mol-1 off the
error bar). The ∆ °

,$¤¥ of

(CH3)2Se predicted using the QSPR approach (-1.77 kcal mol-1)74 is in

good agreement with the -2.39±1.90 kcal mol-1 suggested by Liebman. The calculated ∆ °

of dimethyl diselenide ((CH3)2Se2) all agree well with the value suggested by Liebman.

,$¤¥ ′

Table 4.4 Calculated enthalpies of formation (in kcal mol-1) for the hydrocarbon fragments via
the atomization approach (RC0).
ccCAP

ccCAS3

ccCAS4

ccCAPS3

G3

G4

B3PW91/
aVTZa

Expt.b

CH4

-17.93

-18.53

-18.00

-18.23

-18.02

-17.74

-16.92

-17.82±0.07

CH3CH3

-20.15

-21.21

-20.27

-20.68

-20.12

-19.71

-19.61

-20.03±0.05

CH2=CH2

12.82

11.93

12.78

12.37

12.61

12.68

12.56

12.6±0.1

CH3CH2CH3

-24.98

-26.50

-25.14

-25.74

-24.93

-24.45

-23.95

-25.0±0.1

CH3CH=CH3

5.33

4.24

5.24

4.65

5.13

5.21

4.33

4.8±0.2

(CH3)3CH

-31.70

-33.66

-31.90

-32.68

-31.78

-31.34

-29.11

-32.1±0.2

CH3(CH2)2CH3

-29.51

-31.48

-29.72

-30.50

-29.86

-29.35

-28.23

-30.0±0.2

CH3(CH2)3CH3

-34.28

-36.70

-34.53

-35.49

-34.79

-34.25

-32.45

-35.1±0.2

a

b

aVTZ= aug-cc-pVTZ. Reference 80.

103

4.3.1 Atomization Approach Using Composite Methods and B3PW91
The ∆ °

,$¤¥ ′

of the six target organoselenium molecules were calculated using the

atomization approach (RC0) via the ccCA-P, ccCA-S3, ccCA-S4, ccCA-PS3, G3, G4, and
B3PW91/aug-cc-pVTZ methods and are presented in Table 4.5 as well as the corresponding
experimental ∆ °

,$¤¥ ′

, MADs, and MSDs. The calculated ∆ °

,$¤¥ ′

of divinyl selenide for all

methods shown in Table 4.4 are closer to the static bomb measured23 value of 49.71±1.90 kcal
mol-1 than the rotating bomb measured22 value of 28.4±1.0 kcal mol-1. This comes as a support to
the evaluation of the static bomb measured value being more reliable based on its enthalpy of
hydrogenation. ccCA-S3 resulted in a ∆ °

,$¤¥

that is the closest to the experimental value with

a deviation of only 0.14 kcal mol-1. All other methods predicted a ∆ °

that is within 1.1 to 2.0 kcal mol-1 from experiment, yet the ∆ °

,$¤¥ ′

,$¤¥

of divinyl selenide

calculated using the G4

and B3PW91 methods are greater by 4.19 and 3.01 kcal mol-1, respectively, from the experiment.
The calculated ∆ °

,$¤¥

of diethyl selenide is best predicted by ccCA-S3 with only 0.36 kcal

mol-1 difference from the experimental value recommend by Liebman (-11.78±0.96 kcal mol-1).21

Jover et al.74 also predicted a ∆ °

,$¤¥ of

-10.68 kcal mol-1 for diethyl selenide using the QSPR

approach, which is in good agreement with Liebman’s recommended value. G3 and G4 deviate

by 2.48 and 3.17 kcal mol-1, respectively, from the experiment. The B3PW91 functional predicts
a∆ °

,$¤¥

that is 4.04 kcal mol-1 greater than the experimental value.

The computed ∆ °

experiment except the ∆ °

,$¤¥ ′

of diethyl diselenide all deviate less than 1.0 kcal mol-1 from

,$¤¥ predicted

by ccCA-S3 and ccCA-PS3 that deviates by 3.24 and

2.02 kcal mol-1 from experiment, which is close to the experimental uncertainty. The ∆ °

,$¤¥

of

diisopropyl selenide calculated using the ccCA-P is the closest to the experiment among the

104

other ccCA variants, followed by ccCA-S4. G3 predicts an ∆ °
from the experiment. B3PW91 results in an ∆ °

,$¤¥

,$¤¥ that

is 2.54 kcal mol-1 away

that is 9.28 kcal mol-1 lower than the

experiment. For dipropyl selenide, ccCA-P predicts the closest value to the Liebman’s
interpolated value21 (-21.75 ± 0.96 kcal mol-1). For dibutyl selenide, G3 predicts the closest
∆ °

,$¤¥

∆ °

,$¤¥ ′

to the experimental value, i.e. 1.78 kcal mol-1 lower than the experiment.

Overall, the ccCA-P, ccCA-S4, and G3 methods using the RC0 approach result in
with MADs of 1.68, 1.70, and 1.74 kcal mol-1, respectively, showing very good

agreement with the experiment with an average uncertainty of 1.53 kcal mol-1. ccCA-S3, in

contrast, results in a MAD of 3.10 kcal mol-1 and underestimates ∆ °

,$¤¥ ′

with a MSD of 2.93

kcal mol-1, as shown in Table 5.4. Previous ccCA studies38,40,41 found a similar underestimation

in the computed ∆ °

,$¤¥ ′

when using ccCA-S3, which utilizes the Schwartz-3 extrapolation

scheme.81 Due to this large underestimation of ccCA-S3, ccCA-PS3 results in a MAD of 2.53
kcal mol-1. The G4 method results in MAD of 2.85 kcal mol-1 and an overestimation of -2.85 kcal

mol-1 for the ∆ °

,$¤¥ ′

of organoselenium compounds, demonstrating a lower accuracy than

ccCA-P, ccCA-S4, and G3. B3PW91/aug-cc-pVTZ has the largest MAD with an overall
overestimation of the ∆ °

,$¤¥ ′

of organoselenium compounds. Overall, the ccCA-P variant

predicts the best agreement with the experiment using RC0 scheme for the ∆ °

,$¤¥ ′

of

organoselenium compounds. For organoselenium compounds containing more than six nonhydrogen atoms, the MP2-DK/aug-cc-pVTZ-DK calculation results in wrong electronic states;
hence this contribution was removed from the ccCA energy for these molecules. It is known that
this contribution becomes small with increasing the molecular size.

105

Table 4.5 Calculated enthalpies of formation (in kcal mol-1) for target organoselenium molecules via atomization approach (RC0).

(CH2=CH)2Se

ccCA-P

ccCA-S3

ccCA-S4

ccCA-PS3

G3

G4

B3PW91/augcc-pVTZ

Expt.

51.69

49.85

51.66

50.77

50.81

53.9

52.72

49.71±1.90a
28.44±0.96b

(CH3CH2)2Se

-9.25

-11.42

-10.34

-9.47

-9.3

-8.61

-7.74

-11.78±0.96b
-5.02±0.96a
-10.68c

(CH3CH2)2Se2

-4.62

-7.06

-4.8

-5.84

-4.22

-2.98

-4.12

-3.82±2.87a
-9.08±0.96b

((CH3)2CH)2Se

-26.59

-29.63

-26.9

-28.12

-23.27

-22.40

-16.53

-25.81±0.96 b
-21.82c

(CH3(CH2)2)2Se

-23.47

-26.54

-23.78

-25

-19.59

-18.84

-16.21

-21.75±0.96d

(CH3(CH2)3)2Se

-33.77

-37.73

-34.18

-35.75

-29.72

-28.94

-24.71

-31.50±1.20b
-28.20c

MAD

1.68

3.10

1.70

2.53

1.74

2.85

4.83

MSD

0.18

2.93

0.57

1.41

-1.61

-2.85

-4.73

a

Reference 23. bReference 22. cReference 74. dReference 21.

106

4.3.2 Homodesmotic Approach Using Composite Methods and B3PW91
The calculated ∆ °

,$¤¥ ′

of organoselenium compounds using the isodesmotic reaction

scheme (RC2) and the hypohomodesmotic reaction scheme (RC3) via composite methods (ccCA
variants, G3, and G4) and B3PW91/aug-cc-pVTZ are presented in Tables 4.6 and 4.7,
respectively. Overall, the MADs of all the composite methods were reduced when using the RC2
and RC3 schemes compared to the MADs obtained using the RC0 approach. The MADs of the
∆ °

,$¤¥ ′

calculated by B3PW91/aug-cc-pVTZ using the RC2 scheme was not significantly

reduced in comparison to the MAD using the RC0 approach, i.e. 4.83 vs. 4.23 kcal mol-1.
Nevertheless, the MAD obtained with B3PW91/aug-cc-pVTZ was decreased to 0.76 kcal mol-1
when using the RC3 reaction scheme compared with the RC0 scheme. The calculated ∆ °

,$¤¥ ′

of the principle organoselenium molecules using RC2 and RC3 via ccCA variants lie within the
experimental uncertainties of the corresponding experimental values. The most notable decrease
in the MADs of the ccCA variants occurs for the MAD of the ccCA-S3 ∆ °
(RC0) to 0.92 (RC2) and to 1.22 kcal mol-1 (RC3) as shown in Table 4.8.
The differences between the MAD and the MSD of the ∆ °

,$¤¥ ′

,$¤¥ ′

, i.e. from 3.10

calculated using all

four ccCA variants become negligible when using the RC2 and RC3 schemes, thus exhibiting
less dependency on the extrapolation schemes. The MAD of all four ccCA variants is reduced to
~0.93 kcal mol-1 when using the RC2 scheme and to ~1.24 kcal mol-1 using the RC3 scheme.

Compared to the RC0 approach, the MAD of the ∆ °

,$¤¥ ′

calculated using G3 was reduced by

0.17 kcal mol-1 when using the RC2 scheme and increased by 0.04 kcal mol-1 when using the

RC3 approach. On the other hand, G4 results in a larger decrease in the MAD of the ∆ °

,$¤¥ ′

of organoselenuim compounds when using RC2 and RC3 compared with G3, i.e. from 2.85

107

(RC0) to 1.47 (RC2) and 1.29 kcal mol-1 (RC3). The MSDs of the calculated ∆ °

,$¤¥ ′

were

reduced for all composite methods when using RC2 scheme compared to RC0, showing a
reduction of statistical bias, i.e. the method neither overestimates nor underestimates, which
increases the validity of the utilized method. Using the RC3 scheme, compared to RC0, the
reduction of the MSD for all the composite methods is inconsistent. The MSDs of ccCA-S3,
ccCA-SP3, and G4 were reduced when using RC3 compared to RC0, but they were increased for
ccCA-P, ccCA-S4 and G3. However, the MSD for the set of ∆ °

,$¤¥ ′

of all four ccCA variants

is ~0.1 kcal mol-1 when using the RC2 scheme and ~0.8 kcal mol-1 when using the RC3 scheme.
The MAD and the MSD of G3 for each scheme (RC2 and RC3) have the same value; in this
case, the MSD becomes insignificant. The MSD of the ∆ °

,$¤¥ ′

calculated using G4 was

reduced to 1.33 kcal mol-1 when using the RC2 and to 1.21 kcal mol-1 when using RC3 in
comparison to the RC0 approach. It is worth mentioning here that the average experimental
uncertainty in the target molecules is ±1.53 kcal mol-1 and the average experimental uncertainty
in the constituent molecules used for the RC2 scheme is ±1.41 kcal mol-1 and ±1.39 kcal mol-1
for the RC3 scheme. All composite methods have a MAD that is within these uncertainties when
using RC2 and RC3. However, B3PW91 has an MAD that is within the average experimental
uncertainties only when using the RC3 scheme.
Apart from that of G4, the largest deviation when using RC2 and RC3 schemes via

composite methods is found for the ∆ °

,$¤¥

of divinyl selenid, a conjugated system, with

deviations of -1.98 (-1.34), -2.00 (-1.36), -1.99 (-1.36), -1.99 (-1.35), and 2.13 (2.56) kcal mol-1

for ccCA-P, ccCA-S3, ccCA-S4, ccCA-PS3, and G3 when using RC2 (RC3), respectively.
Jorgensen40 found a similar large deviation in excess of 1.0 kcal mol-1 of the MADs of

∆ °

,$¤¥ ′

of organosulfur compounds containing π-bonds calculated using ccCA variants and

108

G3 methods using RC0 and RC3. Additionally, the same observation was found when
calculating the ∆ °

,$¤¥ ′

of hydrocarbons containing double bonds using ccCA variants and G3

via RC2 and RC3 schemes by Wilson.41 Compounds containing more than six non-hydrogen
atoms have also displayed large deviations in the MAD of their ∆ °

,$¤¥ ′

calculated using the

composite methods via RC2 and RC3 schemes with respect to experiments.40,41 A similar
statement can be true here for organoselenium compounds particularly when using RC3 scheme.

109

Table 4.6 Calculated enthalpies of formation (in kcal mol-1) for target molecules via the isodesmic approach (RC2).

(CH2=CH)2Se

a

ccCA-P

ccCA-S3

ccCA-S4

ccCA-PS3

G3

G4

B3PW91/augcc-pVTZ

Expt.

51.69

51.71

51.7

51.7

47.58

50.13

51.69

49.71±1.90a
28.44±0.96b

(CH3CH2)2Se

-12.31

-12.28

-12.32

-12.29

-12.8

-12.87

-9.68

-11.78±0.96b
-5.02±0.96a
-10.68c

(CH3CH2)2Se2

-5.39

-5.36

-5.4

-5.37

-5.25

-5.26

-2.2

-3.82±2.87a
-9.08±0.96b

((CH3)2CH)2Se

-25.35

-25.27

-25.36

-25.31

-26.99

-27.14

-17.5

-25.81±0.96b
-21.82c

(CH3(CH2)2)2Se

-22.23

-22.18

-22.24

-22.2

-23.31

-23.59

-17.17

-21.75±0.96d

(CH3(CH2)3)2Se

-32.10

-32.01

-32.11

-32.05

-33.65

-34.17

-24.7

-31.50±1.20b
-28.20c

MAD

0.94

0.92

0.94

0.93

1.58

1.47

4.23

MSD

0.12

0.07

0.13

0.10

1.58

1.33

-4.23

Reference 23. bReference 22. cReference 74. dReference 21.

110

Table 4.7 Calculated enthalpies of formation (in kcal mol-1) for target molecules via the hypohomodesmotic approach (RC3).

(CH2=CH)2Se

ccCA-P

ccCA-S3

ccCA-S4

ccCA-PS3

G3

G4

B3PW91/augcc-pVTZ

Expt.

51.05

51.07

51.07

51.06

47.15

49.95

51.59

49.71±1.90a
28.44±0.96b

(CH3CH2)2Se

-12.62

-12.61

-12.63

-12.61

-12.92

-12.84

-11.92

-11.78±0.96b
-5.02±0.96a
-10.68c

(CH3CH2)2Se2

-5.7

-5.68

-5.72

-5.69

-5.37

-5.23

-4.44

-3.82±2.87a
-9.08±0.96b

((CH3)2CH)2Se

-26.46

-26.42

-26.48

-26.44

-27.37

-27.04

-24.58

-25.81±0.96b
-21.82c

(CH3(CH2)2)2Se

-22.79

-22.78

-22.81

-22.79

-23.34

-23.28

-21.82

-21.75±0.96d

(CH3(CH2)3)2Se

-33.18

-33.15

-33.19

-33.16

-33.81

-33.77

-32.09

-31.50±1.20b
-28.20c

MAD

1.24

1.22

1.26

1.23

1.79

1.29

0.76

MSD

0.79

0.77

0.80

0.78

1.79

1.21

-0.28

a

Reference 23. bReference 22. cReference 74. dReference 21.

111

Table 4.8 Overall differences between RC0, RC2, and RC3 using composite methods and B3PW91.

ccCA-P

ccCA-S3

ccCA-S4

ccCA-PS3

G3

G4

B3PW91/augcc-pVTZ

MAD

1.68

3.10

1.70

2.53

1.74

2.85

4.83

MSD

0.18

2.93

0.57

1.41

-1.61

-2.85

-4.73

MAD

0.94

0.92

0.94

0.93

1.58

1.47

4.23

MSD

0.12

0.07

0.13

0.09

1.58

1.33

-4.23

MAD

1.24

1.22

1.26

1.23

1.79

1.29

0.76

MSD

0.79

0.77

0.80

0.78

1.79

1.21

-0.28

-0.74

-2.18

-0.75

-1.61

-0.17

-1.38

-0.60

-0.44

-1.87

-0.44

-1.30

0.04

-1.56

-4.07

0.30

0.30

0.31

0.31

0.21

-0.18

-3.48

RC0

RC2

RC3

RC2-RC0
Diff.
RC3-RC0
Diff.
RC2-RC3
Diff.

112

4.3.3 Atomization Approach Using Single Point Energies within the ccCA Method
The single point calculations involved within the ccCA methodology were utilized to

calculate the ∆ °

,$¤¥ ′

of the target molecules in order to assess the effect of the

thermochemical approaches on the level of theory utilized within the ccCA method. That is the
∆ °

,$¤¥ ′

of organoselenium compounds were calculated using the RC0 approach via

B3LYP/cc-pVTZ, MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, MP2/aug-cc-pVQZ, CCSD(T)/ccpVTZ, MP2(FC1)/aug-cc-pCVTZ, and MP2/cc-pVTZ using the B3LYP/cc-pVTZ geometries
and frequencies. The resulted ∆ °

,$¤¥ ′

are displayed in Table 4.9.

It is evident from the results shown in Table 4.9 that the size of the basis set employed

plays an important role in predicting accurate ∆ °
using RC0. The ∆ °

,$¤¥ ′

,$¤¥ ′

of organoselenium compounds when

calculated at the MP2/aug-cc-pVDZ level of theory, which involves

the smallest basis set utilized within ccCA methodology, have the largest MAD of 88.55 kcal
mol-1, whereas the ∆ °

,$¤¥ ′

calculated at the MP2/aug-cc-pVQZ level of theory, which is the

largest basis set utilized within ccCA methodology, are the closest to experiment with a MAD of
1.91 kcal mol-1. Thus, these calculations are very sensitive to the basis set size, which also was

seen when calculating the ∆ °

,$¤¥ ′

of organosulfur compounds using the same level of theories

via the RC0 approach.40 However, this trend was not obtained when utilizing the same methods

for a set of hydrocarbon compounds.41 The MAD of MP2/cc-pVTZ is lower than when using
CCSD(T) with the same basis set by 14.37 kcal mol-1, indicative of an outperforming of MP2
compared to CCSD(T) for this set of molecules. Moreover, the CCSD(T)/cc-pVTZ calculations
result in a large deviation from experiment, with a MAD of 40.82 kcal mol-1. Less than half the

113

Table 4.9 Calculated enthalpies of formation (in kcal mol-1) for the target molecules via the atomization approach (RC0) using the
specified level of theory at the B3LYP/cc-pVTZ geometry.a

(CH2=CH)2Se

B3LYP/
VTZ

MP2/
aVDZ

MP2/
aVTZ

MP2/
aVQZ

CCSD(T)/
VTZ

MP2(FC1)/
aCVTZ

MP2/
VTZ

Expt.

61.08

108.8

60.45

46.97

82.73

54.25

66.42

49.71±1.90b
28.44±0.96c

(CH3CH2)2Se

-0.11

61.15

4.72

-9.56

20.37

-1.57

11.77

-11.78±0.96c
-5.02±0.96b
-10.68d

(CH3CH2)2Se2

5.67

70.61

8.66

-7.79

28.64

-0.13

17.48

-3.82±2.87b
-9.08±0.96c

((CH3)2CH)2Se

-4.28

72.81

-5.14

-25.04

20.19

-13.57

4.8

-25.81±0.96c
-21.82d

(CH3(CH2)2)2Se

-4.08

77.97

-1.21

-21.36

22.76

-9.2

8.25

-21.75±0.96e

(CH3(CH2)3)2Se

-8.08

95.01

-6.89

-32.86

25.27

-16.53

5.01

-31.50±1.20c
-28.20d

MAD

15.86

88.55

17.59

1.91

40.82

9.70

26.45

MSD

-15.86

-88.55

-17.59

0.78

-40.82

-9.70

-26.45

a

VTZ: cc-pVTZ, aVDZ: aug-cc-pVDZ, aVTZ: aug-cc-pVTZ, aVQZ: aug-cc-pVQZ, aCVTZ: aug-cc-pCVTZ. bReference 23.
c
Reference 22. dReference 74. eReference 21.

114

deviation is found when using the MP2/aug-cc-pVTZ level of theory, emphasizing the
importance of using diffuse basis functions (aug-) for such systems. The calculations of
∆ °

,$¤¥ ′

using RC0 via these single point calculations not only are highly sensitive to the basis

set, but also to the method of choice. The second best performing method among the single point
calculations is the MP2(FC1)/aug-cc-pCVTZ method/basis set combination with a MAD of 9.70
kcal mol-1, which improves upon the MP2/aug-cc-pVTZ results by 7.89 kcal mol-1.
Due to the differential correlation effect that can affect the atomization approach, both the
inclusion of more functions and/or the inclusion of the core-core and core-valence correlation
functions can minimize the error associated with the differential correlation effect. All the results
shown in Table 4.9 indicate that MP2 is highly dependent on the basis set size and a large basis
set is crucial to obtain accurate ∆ °

,$¤¥ ′

of organoselenium species. The basis set effects can

be accounted for by extrapolating the energies to the complete basis set limit, as is done in the
ccCA method, e.g. MAD of ccCA-P is lower than the MAD of MP2/aug-cc-pVQZ level of
theory by 0.23 kcal mol-1. The MAD of the ∆ °

,$¤¥ ′

of organoselenium compounds calculated

using B3LYP/cc-pVTZ results in a MAD of 15.86 kcal mol-1 when using RC0. It is shown in

Table 4.9 that the deviation between theory and experiments increases with increasing molecular
size. All single point energy calculations, except MP2/aug-cc-pVQZ, tend to overestimate the
∆ °

,$¤¥ ′

of organoselenium compounds when using the RC0 approach compared to

experiment as seen from the MSDs shown in Table 4.9 The MP2/aug-cc-pVQZ method shows a
tendency for underestimation with a MSD of 0.78 kcal mol-1 which agrees with the findings from

Jorgensen’s study of organosulfur species.40

115

4.3.4 Homodesmotic Approach Using Single Point Energies within the ccCA Method
Shown in Table 4.10 and Table 4.11 are the ∆ °

,$¤¥ ′

calculated using the isodesmic

reaction scheme (RC2) and the hypohomodesmotic reaction scheme (RC3) via the single point
calculations involved within the ccCA methodology, respectively. The MADs of the ∆ °

,$¤¥ ′

calculated via the constituent energy calculations when using the thermochemical reaction
schemes (RC2 and RC3) compared to the RC0 approach were dramatically decreased, i.e. by
about 0.49-85.26 kcal mol-1 for RC2 and about 0.67-86.27 kcal mol-1 for RC3, as shown in
Tables 4.12. This reduction of the MADs for these levels of theory when using the RC2 and RC3
reaction schemes, shown in Table 4.12, is more significant than the impacts of the RC2 and RC3
schemes on the MADs of the composites methods when compared to RC0 as shown in Table 4.8.
This difference is justified because the composite methods tend to recover more correlation
energy than a single point energy calculation, reducing the differential correlation effect and
resulting in good agreement with experimental ∆ °

shown in Table 4.5.

The largest MAD of the calculated ∆ °

,$¤¥ ′

,$¤¥ ′

when using the RC0 approach as

when using RC0 is 88.55 kcal mol-1

obtained with the MP2/aug-cc-pVDZ level of theory. This MAD was lowered to 3.29 and 2.28
kcal mol-1 when using RC2 and RC3, respectively. The RC2 and RC3 strategies cancel most of
the errors originating from the differential correlation effect and size extensivity by constructing
error balanced reaction schemes. Thus, by using these reaction schemes as well as the
experimental ∆ °

,$¤¥ ′

of the constituent molecules to calculate ∆ °

,$¤¥ ′

, the deviation

between theory and experiment is reduced. RC2 and RC3 exhibit less dependency on the basis
set size, as largely is the case when using the RC0 approach. To illustrate, the MADs for the
∆ °

,$¤¥ ′

of MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, and MP2/aug-cc-pVQZ when using the

116

Table 4.10 Calculated enthalpies of formation (in kcal mol-1) for the target molecules via isodesmic reaction approach (RC2)
using the level of theories specified in the table, at the B3LYP/cc-pVTZ geometry.a

(CH2=CH)2Se

a
c

B3LYP/
VTZ

MP2/
aVDZ

MP2/
aVTZ

MP2/
aVQZ

CCSD(T)/
VTZ

MP2(FC1)/
aCVTZ

MP2/
VTZ

Expt.

52.17

49.95

49.91

49.87

51.94

49.52

49.71

49.71±1.90b
28.44±0.96c

(CH3CH2)2Se

-9.51

-13.87

-13

-12.73

-11.43

-13.58

-12.42

-11.78±0.96c
-5.02±0.96b
-10.68d

(CH3CH2)2Se2

-1.96

-7.69

-6.35

-5.98

-4.38

-7.09

-5.6

-3.82±2.87b
-9.08±0.96c

((CH3)2CH)2Se

-17.14

-30.54

-27.83

-27.1

-23.78

-29.04

-26.34

-25.81±0.96c
-21.82d

(CH3(CH2)2)2Se

-16.94

-25.38

-23.9

-23.41

-21.21

-24.68

-22.88

-21.75±0.96e

(CH3(CH2)3)2Se

-24.4

-36.66

-34.55

-33.8

-30.87

-35.47

-33.07

-31.50±1.20c
-28.20d

MAD

4.53

3.29

1.86

1.42

1.06

2.57

0.94

MSD

-4.53

3.21

1.80

1.37

-0.87

2.57

0.94

VTZ: cc-pVTZ, aVDZ: aug-cc-pVDZ, aVTZ: aug-cc-pVTZ, aVQZ: aug-cc-pVQZ, aCVTZ: aug-cc-pCVTZ. bReference 23.
Reference.22. dReference 74. eReference 21.

117

Table 4.11 Caculated enthalpies of formation (in kcal mol-1) for the target molecules via hypohomodesmotic reaction approach
(RC3) using the level of theories specified in the table, at the B3LYP/cc-pVTZ geometry.a

(CH2=CH)2Se

B3LYP/
VTZ

MP2/
aVDZ

MP2/
aVTZ

MP2/
aVQZ

CCSD(T)/
VTZ

MP2(FC1)/
aCVTZ

MP2/
VTZ

Expt.

51.65

49.84

50.49

50.39

51

50.22

50.03

49.71±1.90b
28.44±0.96c

(CH3CH2)2Se

-11.73

-13.37

-12.75

-12.56

-11.99

-13.25

-12.45

-11.78±0.96c
-5.02±0.96b
-10.68d

(CH3CH2)2Se2

-4.18

-7.18

-6.11

-5.82

-4.93

-6.76

-5.63

-3.82±2.87b
-9.08±0.96c

((CH3)2CH)2Se

-24.33

-28.72

-27.1

-26.62

-25.52

-28.1

-26.41

-25.81±0.96c
-21.82d

(CH3(CH2)2)2Se

-21.65

-24.14

-23.28

-23.01

-22.27

-23.87

-22.91

-21.75±0.96e

(CH3(CH2)3)2Se

-31.9

-34.82

-33.73

-33.39

-32.66

-34.37

-33.3

-31.50±1.20c
-28.20d

MAD

0.72

2.28

1.52

1.24

0.76

2.03

1.06

MSD

-0.47

2.24

1.26

1.01

0.24

1.86

0.95

a

VTZ: cc-pVTZ, aVDZ: aug-cc-pVDZ, aVTZ: aug-cc-pVTZ, aVQZ: aug-cc-pVQZ, aCVTZ: aug-cc-pCVTZ. bReference 23.
c
Reference 22. dReference 74. eReference 21.

118

Table 4.12 Overall differences between RC0, RC2, and RC3 using the level of theories specified in the table.a
B3LYP/
VTZ

MP2/
aVDZ

MP2/
aVTZ

MP2/
aVQZ

CCSD(T)/
VTZ

MP2(FC1)/
aCVTZ

MP2/
VTZ

MAD

15.86

88.55

17.59

1.91

40.82

9.70

26.45

MSD

-15.86

-88.55

-17.59

0.78

-40.82

-9.70

-26.45

MAD

4.53

3.29

1.86

1.42

1.06

2.57

0.94

MSD

-4.53

3.21

1.80

1.37

-0.87

2.57

0.94

MAD

0.72

2.28

1.52

1.24

0.76

2.03

1.06

MSD

-0.47

2.24

1.26

1.01

0.24

1.86

0.95

-11.33

-85.26

-15.73

-0.49

-39.76

-7.14

-25.51

-15.14

-86.27

-16.08

-0.67

-40.06

-7.67

-25.39

-3.81

-1.00

-0.35

-0.18

-0.29

-0.53

0.12

RC0

RC2

RC3

RC2-RC0
Diff.
RC3-RC0
Diff.
RC2-RC3
Diff.
a

VTZ: cc-pVTZ, aVDZ: aug-cc-pVDZ, aVTZ: aug-cc-pVTZ, aVQZ: aug-cc-pVQZ, aCVTZ: aug-cc-pCVTZ.

119

RC0 approach are 88.55, 17.59, and 1.91 kcal mol-1, which were reduced to 3.29, 1.86, and 1.42
kcal mol-1 when using the RC2 scheme and to 2.28, 1.52, and 1.24 kcal mol-1 when using the
RC3 scheme. The lowest MAD of the method/basis set combinations when using the RC2
approach is CCSD(T)/cc-pVTZ (MAD = 1.06 kcal mol-1), followed by MP2/cc-pVTZ rather than
MP2/aug-cc-pVQZ which is superior when using RC0. The RC3 approach allows for balancing
more errors of the reaction scheme than RC2 does, resulting in higher cancellation of errors
associated with the differential correlation effect. Thus, B3LYP/cc-pVTZ has the lowest MAD of
0.72 kcal mol-1 among all method/basis set combinations when using the RC3 approach, as
shown in Table 4.10, followed by CCSD(T)/cc-pVTZ with a MAD of 0.76 kcal mol-1 and
MP2/cc-pVTZ with a MAD of 1.06 kcal mol-1.
Method choice seems to be more important than basis set size when using RC2 and RC3
reaction schemes compared to RC0. These findings agree with results reported by Jorgensen.40

The MSD values show a tendency for underestimation of the ∆ °

,$¤¥ ′

by all the single point

energy calculations, except for the CCSD(T) and B3LYP methods, when using the RC2 and the
RC3 schemes, as shown in Table 4.10 and 4.11, instead of overestimation as it is using the RC0
scheme. The B3LYP/cc-pVTZ level of theory exhibits an overestimation in the calculated
∆ °

,$¤¥ ′

, on average, when using any of the utilized thermochemical approaches, while

CCSD(T) overestimates the ∆ °

,$¤¥ ′

calculated using the RC0 and RC2 approaches but

underestimate those calculated using the RC3 scheme, as shown in Table 4.12.

4.4 Conclusion
The thermochemical isodesmic (RC2) and hypohomodesmotic (RC3) reaction schemes

for hydrocarbon have been extended to include organoselenium compounds. The ∆ °
120

,$¤¥ ′

of

organoselenium species, including R2Se, where R is CH3-, C2H5-, C3H7-, C4H9-, iC3H7-, and
CH2=CH-, and (CH3CH2)2Se2, were predicted using the atomization approach (RC0) and the
isodesmic (RC2) and hypohomodesmotic (RC3) reaction schemes via several composite
methods, such as ccCA, G3 and G4, and the B3PW91 density functional. The quality of these
approaches has also been investigated. In addition, an assessment of the impact of RC0, RC2,
and RC3 on the single point energy calculations utilized within the ccCA has been examined.
The most important finding here is that while the RC2 and RC3 schemes allow for
cancellation of errors from differential correlation and size extensivity, the RC0 scheme via
ccCA-P (MAD=1.68 kcal mol-1), ccCA-S4 (MAD=1.70 kcal mol-1), and G3 (MAD=1.74 kcal

mol-1) is still an effective and simple approach for predicting ∆ °

,$¤¥ ′

of organoselenium

compounds that are within the experimental uncertainties (σ=1.53 kcal mol-1, on average). The
reduction in the MADs of the calculated ∆ °

,$¤¥ ′

using RC2 and RC3 was profound with the

ccCA-S3 method in which the MAD was reduced by -2.18 (RC2) and -1.87 (RC3) kcal mol-1

compared to RC0. Employing the RC2 and RC3 schemes, the MADs of all four ccCA variants
become nearly the same with ranges of 0.92 - 0.94 (RC2) and 1.22 - 1.26 (RC3) kcal mol-1,
showing less dependency on the extrapolation schemes. Thus, for high accuracy the use of the
RC2 reaction scheme with ccCA is recommended since is resulted in the reduction of the
maximum deviation of the ∆ °
experiment.

,$¤¥ ′

of the target organoselenium molecules with respect to

Trivial change in the MADs of the ∆ °

,$¤¥ ′

calculated using the RC2 and RC3 schemes

with the G3 method were observed compared to RC0 (from 1.74 to 1.58 (RC2) and to 1.79
(RC3) kcal mol-1), so G3 seems to be unbiased to any thermochemical schemes. The inclusion of
empirical parameters within Gn theory may be a reason for the low impact of these

121

thermochemical schemes on the G3 method. On the other hand, the G4 method results in a
systematic reduction in the MAD from 2.85 (RC0) to 1.47 (RC2) to 1.29 (RC3) kcal mol-1, while
B3PW91 only predicts accurate ∆ °

,$¤¥ ′

when used with the RC3 scheme.

The most significant reduction in MADs, as shown in Figure 4.4, is found when using

RC2 and RC3 via the method/basis set combinations involved within the ccCA methodology,
compared to RC0, emphasizing the importance of the use of these error balanced reaction
schemes (RC2 and RC3) with single point energy calculations. The MAD of the ∆ °

,$¤¥

of

organoselenium species calculated by the methods within ccCA is reduced by 0.49 - 85.26 kcal
mol-1 when using RC2 and by 0.67 - 86.27 kcal mol-1 when using RC3, in comparison to RC0.

122

MAD of the ∆H°f,298's of Organoselenium

MAD (kcal/mol)

Atomization (RC0)

Isodesmic (RC2)

Hypohomodesmotic (RC3)

85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0

Figure 4.4 The mean absolute deviations (MADs) of the calculated enthalpies of formation using three thermochemical
schemes, RC0, RC2, RC3, with composite methods and single point energy calculations utilized within ccCA methodology.

123

APPENDIX

124

APPENDIX
Figure 4.4 The optimized structures for organoselenium molecules at the B3LYP/cc-pVTZ level
of theory. a. Dimethyl selenide. b. Dimethyl diselenide. c. Divinyl selenide. d. Diethyl selenide.
e. Diethyl diselenide. f. Diisopropyl selenide. g. Dipropyl selenide. h. Dibutyl selenide

a. Dimethyl selenide

C,0.,1.4745463319,-0.5250668407
C,0.,-1.4745463319,-0.5250668407
H,0.,2.3979939937,0.0487822942
H,0.,-2.3979939937,0.0487822942
H,0.89334582,1.4319630523,-1.1430822182
H,-0.89334582,1.4319630523,-1.1430822182
H,-0.89334582,-1.4319630523,-1.1430822182
H,0.89334582,-1.4319630523,-1.1430822182
Se,0.,0.,0.7732299539

125

b. Dimethyl diselenide

C,-3.8566963534,0.4978802241,-0.1487157894
H,-2.9959769279,0.0321646867,0.3204593568
H,-3.5836945322,0.8699953899,-1.1352109631
H,-4.6807464241,-0.2032193801,-0.2310914273
C,-3.4519132533,1.0664446232,3.9259947929
H,-3.0519066265,2.0717550224,4.0080350634
H,-3.7179227193,0.6893268138,4.9125006592
H,-2.7344865202,0.3999894362,3.4580303513
Se,-4.431262183,2.0818797179,0.8836362695
Se,-5.1354589001,1.102407286,2.8919271468

126

c. Divinyl selenide

C,-1.6717478143,-1.1551364351,0.2263623732
C,-1.5145170703,0.0995145459,-0.1729240918
C,1.5145171709,0.0995150317,0.172924123
C,1.6717483174,-1.1551358988,-0.226362342
H,-2.6216442804,-1.651758326,0.0748045573
H,-0.8927855835,-1.7221448581,0.7137937834
H,-2.3281680491,0.6370998822,-0.6445860837
H,2.3281679773,0.6371006291,0.644586115
H,2.6216449427,-1.6517574851,-0.0748045261
H,0.8927862684,-1.7221445717,-0.7137937521
Se,-0.0000001354,1.2572272992,0.0000000156

127

d. Diethyl selenide

C,0.,1.4876577251,-0.6049163648
C,0.,-1.4876577251,-0.6049163648
C,0.,2.8300871235,0.1113327778
C,0.,-2.8300871235,0.1113327778
H,0.8844003853,1.3753237887,-1.2299306436
H,-0.8844003853,1.3753237887,-1.2299306436
H,0.8844003853,-1.3753237887,-1.2299306436
H,-0.8844003853,-1.3753237887,-1.2299306436
H,0.,3.6455581618,-0.6146868743
H,0.,-3.6455581618,-0.6146868743
H,-0.8822256968,2.9446536553,0.7418417228
H,0.8822256968,2.9446536553,0.7418417228
H,0.8822256968,-2.9446536553,0.7418417228
H,-0.8822256968,-2.9446536553,0.7418417228
Se,0.,0.,0.7009286041

128

e. Diethyl diselenide

C,-4.0040189665,0.6658354249,-0.2441569024
H,-4.54670732,-0.2719925307,-0.3255037137
H,-4.5834799815,1.3604152158,0.3584609682
C,-3.4105090249,0.8934826096,3.8815204752
H,-4.104934018,1.5576767945,3.3723835302
H,-3.9253549137,0.4675928726,4.7443516987
Se,-2.316788856,0.2763347679,0.7450209433
Se,-3.1438763359,-0.6945844731,2.7097772517
C,-2.128540207,1.6009534242,4.2796156284
H,-1.6020397625,1.9756550928,3.401878767
H,-2.3521537203,2.4540544872,4.925544467
H,-1.4577404208,0.9321636944,4.8184878256
C,-3.6682143629,1.2494055333,-1.6084883837
H,-4.5865424401,1.4656150546,-2.1583944699
H,-3.1074805542,2.1807438566,-1.5202773605
H,-3.0783422958,0.5545095955,-2.2071552451

129

f. Diisopropyl selenide

C,-0.0371068084,0.7260443361,-0.353968696
C,-1.0957241316,1.5967108623,0.3162987173
C,0.6902258789,-2.2470260565,-0.0867633906
H,-0.6902099186,2.5914756984,0.520535074
C,0.516936112,1.3710247215,-1.6201723962
H,0.9022900234,-1.9088823757,0.9278090291
H,-0.2746516616,1.5278835321,-2.3544088705
H,0.9551130577,2.3462888581,-1.386857929
H,1.2844510936,0.7572198116,-2.0882055811
H,-1.9668916712,1.7251414201,-0.3291530458
H,-1.4359482579,1.1631920134,1.2551462037
Se,-0.8105309195,-1.0859098533,-0.7140577528
C,1.9395793274,-2.1205034957,-0.9476863285
H,2.3298073342,-1.1035174715,-0.9563295404
H,2.7282478688,-2.7726868757,-0.5599633827
H,1.733559985,-2.4119594024,-1.9783350419
C,0.16310624,-3.6772808639,-0.0415738526
H,0.9409498616,-4.3493820403,0.328914838
H,-0.7032312878,-3.7672165665,0.6129666916
H,-0.1244239334,-4.0224540828,-1.03650531
H,0.7721469473,0.5345294808,0.3509850545

130

g. Dipropyl selenide

C,0.0000002585,1.4871445752,-0.7438891543
C,0.0000013975,-1.4871445747,-0.7438891556
H,0.8848261799,1.3772131001,-1.3704231853
H,-0.8848221014,1.3772124784,-1.3704281054
H,-0.8848210448,-1.377213153,-1.3704281086
H,0.8848272366,-1.3772124233,-1.3704231839
Se,-0.0000028472,0.0000000003,0.5621833724
C,-0.0000000222,-2.8354653726,-0.0335738398
H,-0.87509911,-2.9032470007,0.6170149326
H,0.8750954883,-2.9032462741,0.6170198199
C,0.0000032096,-4.0079414416,-1.0163934274
H,0.0000021249,-4.9618587066,-0.4873466401
H,-0.8814991074,-3.9850481132,-1.6600097778
H,0.881509101,-3.9850473815,-1.6600048562
C,-0.0000021874,2.8354653738,-0.0335738392
H,-0.8751013217,2.9032463328,0.6170149407
H,0.8750932767,2.9032469455,0.6170198128
C,0.0000001377,4.0079414418,-1.0163934279
H,-0.0000016676,4.9618587073,-0.4873466416
H,0.8815060387,3.9850480535,-1.6600048673
H,-0.8815021697,3.9850474403,-1.6600097678

131

h. Dibutyl selenide

C,-0.0000050541,1.4878682362,-0.7091398258
C,0.0000006042,-1.4878682366,-0.709139827
H,0.8848032967,1.3771797052,-1.3353544409
H,-0.8848059758,1.3771759473,-1.3353642749
H,-0.8848009689,-1.3771795899,-1.3353639854
H,0.8848083037,-1.3771760642,-1.3353547333
Se,-0.0000091736,-0.0000000002,0.596483834
C,-0.0000004214,-2.8349424563,0.0026831003
H,-0.8755992344,-2.9038466045,0.6542320099
H,0.8755919125,-2.9038431637,0.6542410734
C,0.0000069351,-4.0171651407,-0.9714082227
H,-0.8746248568,-3.9464770193,-1.624653031
H,0.8746451908,-3.946473573,-1.6246440039
C,-0.0000118779,2.8349424561,0.002683101
H,-0.8756112253,2.9038430175,0.6542316683
H,0.8755799216,2.9038467506,0.6542414164
C,-0.0000089751,4.0171651402,-0.9714082224
H,0.8746298497,3.9464771785,-1.6246436301
H,-0.8746401979,3.9464734124,-1.624653404
C,0.0000059521,-5.3715354958,-0.2640161782
H,-0.8808554474,-5.4849631396,0.3710055057
H,0.0000112789,-6.1937362553,-0.9808245605
H,0.8808612345,-5.4849596601,0.3710146126
C,-0.0000158487,5.3715354956,-0.2640161784
H,-0.0000136073,6.1937362548,-0.9808245609
H,-0.8808779874,5.4849595026,0.3710051296
H,0.8808386945,5.484963297,0.3710149883

132

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CHAPTER 5 TOWARDS A MORE RATIONAL DESIGN OF THE DIRECT
SYNTHESIS OF ANILINE: A DFT STUDY

5.1 Introduction
Green chemical synthesis has been of significant interest for the development of safe and
efficient reaction processes that reduce the generation of hazardous products and for economic
benefits in the chemical industry. One process that has widely attracted the attention is the direct
synthesis of aniline. Aniline (C6H5NH2) is an important building block in the chemical industry
as it can undergo numerous reactions either involving the amino group or the aromatic ring.
These reactions can be extended for various industrial applications including the production of
dyes, the production of polyurethane, use in the rubber industry, and in the manufacturing of
pharmaceuticals, to name a few.1,2 In 2013, global annual production of aniline was ~5 million
tons and was anticipated to reach 6.2 million tons by 2015.2 80% of aniline goes to the
production of methylene diphenylene isocyanate, which is used in polyurethane manufacture.1
The mass production of aniline demands an efficient, safe, and economical synthesis. While the
first reported production of aniline was in 1854 via the reduction of nitrobenzene, little
improvements in this process have been reported, and hence nitrobenzene remains the raw
material used by almost all commercial producers of aniline.1 Scheme 5.1 summarizes the
industrial synthesis of aniline, which is comprised of multiple steps. It begins with the nitration
of benzene using a mixture of nitric acid and sulfuric acid. The next step is the hydrogenation
(reduction) of the nitro group in the presence of a catalyst (Pt/Pd on carbon or Raney-Ni). Lastly,
separation and distillation are performed to purify aniline.1

141

NO 2

+

H2SO 4

+ HNO3

NH 2

NO 2

+

3 H2

Catalyst

+ 2 H2O

Scheme 5.1 Synthesis of aniline. Adapted from Reference 1.

The conventional route of the production of aniline, although it is practical and very
exothermic, has drawbacks. It is not economical with respect to the capital cost and to atom
economy. It also consumes a lot of energy, requires large amounts of corrosive acid catalysts and
produces acid sludges, and can be accompanied by a great amount of by-products.2 Thus, direct
chemical synthesis of aniline is of significant interest for the development of more economic and
environmentally friendly one-pot reaction process.
The direct route (Scheme 5.2) offers several advantages over the conventional process;
however, it has several challenges. The main challenge is the difficulty of activating the
benzene’s strong C-H bond (BDE = ~113 kcal mol-1) and ammonia’s strong N-H bond (~108
kcal mol-1) simultaneously.3 Utilizing ammonia (NH3) as an aminating agent is attractive due to
low cost and atom efficiency. Another issue associated with the direct process is that the
production of hydrogen can drive the reaction toward the formation of benzene, which reduces
the yield of aniline. Decomposition of ammonia to N2 and H2 at high temperature is also one of
the challenges that has to be inhibited to assure a high yield of aniline.

142

Scheme 5.2 The proposed direct route of the production of aniline.

Despite several experimental efforts,4–25 a one-pot process has not been adopted yet for
commercial applications, mostly due to low aniline yields. Most of the developments in this field
are targeted towards the determination of an effective aminating agent, either ammonia or an
ammonia derivative, in the presence of an effective catalyst. An oxidizing agent, such as oxygen
gas, metal oxide, or hydrogen peroxide is typically required. A significant advance includes the
use of the Ni/NiO/ZrO2 cataloreactant,19–22 to achieve direct amination of benzene to aniline. The
NiO is used as a reducible oxide that can oxidize the produced hydrogen as well as can be easily
reduced to metallic Ni0. Aniline’s yield from this reaction is about 13.6% at 623 K and 300 - 400
atm. Hagemeyer et al.5 conducted a large screening study and found that Rh/Ni-Mn/K-TiO2
cataloreactant produce the best benzene conversion and aniline selectivity. Both Hagemeyer’s
work5 and Hoffmann et al.7,8 emphasized the importance of metallic nickel as an active site for
the formation of aniline. Hoffmann further proved that elemental Ni is essential to activate
benzene’s C-H bond and ammonia’s N-H bond simultaneously by conducting a temperatureprogrammed reaction (TPR) experiment of the direct amination of benzene on the Ni/ZrO2
catalyst at temperature range 523 - 873 K and standard pressure.7 Although the DuPont’s
cataloreactant has shown to produce aniline from direct amination of benzene, no information

143

about the thermodynamics and the electronic properties of some intermediates involved in this
reaction are available.

Scheme 5.3 The overall modeled reaction for the direct production of aniline.

To explore possible reaction intermediates and to better understand the role of nickel in
direct aniline production, plane-wave DFT calculations were used to study the direct amination
of benzene by a Ni(111) surface (Scheme 5.3). DFT modeling of surface reactions has
demonstrated the potential for providing molecular-level understanding of heterogeneous
catalysts. Adsorption energies, structures, sites, and thermochemical analysis of proposed
reaction pathways relevant to the amination of benzene on the Ni(111) surface were investigated.
Ni(111) is chosen due to its stability and its efficacy toward the adsorption of aniline.26,27 It is
necessary to examine the adsorption behavior of aniline on the Ni(111) surface in detail,
including its adsorption geometry and energy, which has not been, to our knowledge, reported
prior, to get information that can facilitate further catalyst design. This study also aims to
compare and correlate a heterogeneous Ni(111)–imide model with the previous homogenous
nickel-imide model for the C-H amination reaction.28

144

5.2 Computational Details
5.2.1 Method
All calculations were carried out using plane wave density functional theory (PW-DFT)
as implemented in the Vienna Ab initio Simulation Package (VASP).29–32 The electron exchange
and correlation energies were addressed using the generalized gradient approximation as
proposed by Perdew-Burke-Ernzerhof (GGA-PBE).33,34 The electron ion interactions were
described using the projector augmented wave (PAW) method35,36 in which inner core electrons
are treated using pseudopotentials whereas valence electrons are described by a plane wave basis
set. In order to examine the effect of van der Waals (vdW) interactions on the adsorption energy
the dispersion corrected DFT-D337 approach was used in this study. To obtain accurate energies,
convergence tests were run to ensure optimal setting parameters to our calculations, shown in
Figures 5.7, 5.8, and 5.9 of the appendix. Plane wave basis sets were expanded within a 400 eV
energy cutoff, the Brillouin zone was integrated using 5x5x1 k-points mesh for adsorption
systems and only the gamma point was used for gas phase molecules. Since Ni has magnetic
properties, spin polarization was considered for open shell molecules and for all adsorption
systems to ensure accurate adsorption energies, as recommended by Kresse et al.38 The energy
criterion for electronic minimization was 10-6 eV and the ions were allowed to relax until all
atomic forces were less than 0.02 eV/Å. The Methfessel-Paxton smearing method39 was used
with σ = 0.2 eV. All calculations were performed at 0 K. Vibrational frequencies were calculated
using a 600 eV energy cutoff at the gamma k-point and the force convergence criterion was
tightened to be less than 10-5 eV/Å. For adsorbed systems, only the adsorbate and the topmost
layer were relaxed during the vibrational frequency calculations. The zero point energy (ZPE)
correction was added to all adsorption energies as follows:

145

<

3Å = !
#&'

ℎÆ#
2

(5.1)

where νi is the calculated real frequency of a system, 	n is the number of vibrations, and 	h is
Planck’s constant. For the electronic density of state (DOS) calculations, the k-point grid was
increased to 9x9x1.
5.2.2. Surface Model
The DFT-optimized lattice constant of Ni used to build the slab is 3.52 Å (see Figure
5.7), which agrees well with the experimental lattice constant of Ni, 3.524 Å.40 The Ni (111)
surface was modeled as a five-layer periodic slab in the (111) Miller plane as shown in Scheme
5.4. A vacuum thickness of 10 Å along the c axis was employed between repeated slabs. During
the geometry optimization, the top three layers were relaxed and the bottom two layers were kept
fixed. The total number of nickel atoms in a slab is 45 atoms per unit cell and the surface unit
cell is p(3x3). One molecule was adsorbed for each calculation.

Scheme 5.4 The Ni(111) surface model.

146

5.2.3 Thermochemistry
As mentioned in Hoffmann’s study,7 the reaction temperature plays a critical role for the
selectivity of aniline in the direct amination of benzene. DuPont’s direct synthesis reaction was
conducted at 623 K and 300 - 400 atm.21 In an attempt to reduce the pressure needed, Hoffman
carried out a TPR experiment of the direct amination of benzene with a prereduced Ni/ZrO2 as a
catalyst at ambient pressure and temperature range 523 - 873 K.7 The onset formation of aniline
was detected at temperatures lower than 600 K. Thus, in order to obtain realistic thermodynamics
of the direct amination of benzene on the Ni(111) surface, statistical thermodynamics using the
vibrational partition function were utilized to calculate the Gibbs free energies at 523 K as
follows:
Ç
where

− È

(5.2)

is the enthalpy of the system and is calculated as
=

where

=

FGF^C

FGF^C

+ 3Å +

DG\\

(5.3)

is the total energy of the system determined by DFT calculations, ZPE is the zero

point energy correction, calculated as shown in eqn (1), and
0 K to 523 K and is calculated as

where ž: is Boltzmann’s constant.

DG\\

<

= !
#&'

ℎÆ#

u ÉpÊ ⁄{Ë , − 1

DG\\

is the thermal correction from

(5.4)

Since all the molecules in this study are strongly bound to the Ni(111) surface, the

translational and rotational modes are frustrated and replaced by vibrational modes, as suggested

147

by Blaylock et al.41 The entropy correction to the energy of adsorbates È (shown in eqn (2)) only
includes the contribution from the vibrational modes, and it takes the form:
ℎÆ# ⁄ž:
È = ! Ì Ép ⁄{ ,
− ln·1 − u ”ÉpÊ ⁄{Ë , ¸Î
u Ê Ë −1
<

#&'

(5.5)

For gaseous molecules, the contributions from the transitional and rotational modes are included
within the thermal correction and entropy.

5.2.4 Method Calibration
To validate the utilized method for free molecules, the bond dissociation energy
(BDE) of the free molecules in the gas phase were calculated and compared with the available
experimental data as shown in Table 5.1. In addition to the calibration, these energies help to
correlate the dissociation of these molecules in the gas phase and on the Ni(111) surface. For a
molecule AB, the BDE is computed as: BDE = (EA + EB) - EAB where EA and EB are the
calculated total energies of molecule A and molecule B and EAB is the calculated total energy of
molecule AB. Homolytic BDE calculations often represent a challenge for DFT due to the
difference in electron correlation between a molecule and its fragments. Calculating reaction
energies is usually more accurate because of the cancellation of error. Nevertheless, the
calculated BDEs displayed in Table 5.1 generally show very good agreement with the
experimental bond energies especially when ZPE and thermal correction are added. PBE and
PBE-D3 BDEs are very similar. The largest difference between PBE and PBE-D3 is 1.1 kcal
mol-1 for aniline’s C-N BDE, but still within the experimental uncertainty. Therefore, as shown
in Table 5.1, no notable improvement in the results is found when including the dispersion
corrected functional. From the BDE results, breaking one C-H bond of benzene in the gas phase

148

is very endothermic, as expected, and requires a large amount of energy. We will show later how
the use of a catalyst can help reduce this energetic demand. The same observation is appropriate
for the first N-H dissociation energy of ammonia, as well as for NH2, NH, and aniline. The BDE
of aniline shows that breaking the C-N bond of aniline requires higher energy than N-H
dissociation.

Table 5.1 Bond dissociation energies (BDE) of gaseous molecules in kcal mol-1.

Bond Cleavage
(AB =A+B)

BDE
PBE

PBED3

PBE+ZPE+Hcorra

PBE-D3+ZPE+
Hcorra

Expt.b

C6H6 = C6H5 + H

113.5

113.9

110.1

110.4

112.9±0.6c

H2 = 2 H

104.6

104.6

105.1

105.1

104.2c

NH3= NH2 + H

112.6

112.6

107.7

107.7

107.6±0.1c

NH2 = NH + H

99.5

99.5

97.2

97.2

97.6d

C6H5NH2 = C6H5 + NH2

107.8

108.7

103.0

104.1

104.2±0.6c

Represent ¹

94.1

94.6

90.5

90.7

88.0±2.0e

C6H5NH2 = C6H5 NH + H
a

(298 K). bExperimental values are at 298 K. cReference 3. dReference 42. eReference 43.

As the adsorption of ammonia and benzene on the Ni(111) surface have been studied
before, their experimental adsorption energies were used to further validate the methods used in
this study. Table 5.2 shows calculated adsorption energies from this study using PBE, PBE-D3,
ZPE corrected adsorption energies, and the experimental adsorption energies for adsorbed
ammonia and adsorbed benzene on the Ni(111) surface. Low energy electron diffraction (LEED)
experiments44,45 and previous calculations46–48 confirmed that the nitrogen atom in ammonia is
bound directly to the Ni(111) surface, whereas hydrogen atoms point away from the surface, as
shown in Figure 5.1.a. The most stable adsorption site of NH3 is atop, where the nitrogen atom is

149

bound directly to a single Ni atom on the surface via the electron lone pair of the N atom of
ammonia. In addition, previous experiments49–51 and calculations52,53 show that the benzene ring
adsorbs parallel to the surface with all hydrogen atoms tilted away from the surface (Figure
5.1.b). Our results agree well with these previous findings. The PBE adsorption energies (shown
in Table 5.2) are in excellent agreement with experiments with ≤ 1.0 kcal mol-1 difference. When
adding the ZPE correction to the PBE adsorption energy of ammonia, the absorption energy is
equal to that from experiment, while the ZPE-corrected adsorption energy of benzene becomes
3.0 kcal mol-1 lower than the experimental value. This is still in reasonable agreement with
experiment, as the experimental error associated with the use of temperature-programmed
desorption (TPD) spectroscopy to approximate the adsorption energy of large systems, is
estimated to be within 3 kcal mol-1.54,55 This demonstrates the importance of including the ZPE
correction in the calculations of the adsorption energies, and thus the ZPE correction will be
included in all adsorption energies. To examine the effect of the vdW interactions on the binding
to the metal surface, the semi-empirical PBE-D3 functional was used. The computed adsorption
energies for ammonia and benzene using PBE-D3, shown in Table 5.2, shows an overbinding of
9 kcal mol-1 for ammonia and 38.4 kcal mol-1 for benzene that represent the dispersion energies
that contribute to the molecule-metal binding. A large dispersion energy of benzene on other
(111) surfaces, such as Pt(111), Pd(111), Ag(111), and Au(111), was also previously obtained
using different dispersion corrected methods.54,56 Grimme et al.37 pointed out that DFT-D3 is a
great tool to provide accurate adsorption energies for molecules and solids, in particular for
weakly bounded systems (physisorption interactions) where dispersive interactions are dominant.
For chemisorbed molecules, such as all the adsorbates in the present study, the interaction
between a molecule and a metal surface may not be captured in the DFT-D3 parameterization

150

and; therefore, leads to a large overbinding for the D3 corrections. DFT-D3 becomes more
important when more than one molecules adsorb on the surface. Tonigold et al.57 examined the
performance of DFT-D3 on several water-metal systems as compared to PBE, and found that
pure PBE adequately described the pure water-metal system adsorption behavior, but if
additional adsorbates were added to the surface, then DFT-D3 was more reliable. So, adding a
dispersion correction to the molecule-Ni(111) adsorption systems in the current study would not
be expected to improve the results relative to experiment, and this is demonstrated by the results
in Table 5.2. Since PBE adsorption energies are in excellent agreement with the experiment, the
PBE energies will be used later to calculate reaction thermodynamics.
Table 5.2 Adsorption energies (Ead) for ammonia and benzene adsorbed on a Ni(111) surface in
kcal mol-1.
Ead
Method

a

NH3/Ni(111) (atop)

C6H6/Ni(111) (bridge)

PBE

- 16.8

-19.1

PBE + ZPE

- 17.0

- 21.4

PBE-D3

- 25.8

-57.5

PBE-D3+ZPE

- 26.0

-59.8

Expt.

-17.0

a

-18.0

b

Reference 58. bReference 50.

a) NH3*

b) C6H6*

Figure 5.1 Adsorption structure of ammonia (a) and benzene (b) on the Ni(111) surface. (*)
Indicates an adsorbed molecule.

151

5.3 Results And Discussion
5.3.1 Adsorption Geometries and Energies
The first step in surface reactions is usually the adsorption of the species involved in the
reaction on the surface. Thus, it is of importance to study their adsorption behaviors. The
adsorption behavior of the NHx (x = 0 - 3) species and the aromatic species involved in the direct
amination of benzene on the Ni(111) surface are reported and discussed here. Geometry
optimizations were performed for all adsorption systems to find the most stable structure of the
molecule-surface interaction, i.e., the most favorable surface site for each adsorption process,
which has the lowest adsorption energy. The computed adsorption energy is defined as: Ead =
Eadsorbate+Ni(111) – Eadsorbate – ENi(111) where Ead is the binding energy of a molecule bound to the
surface, Eadsorbate+Ni(111) is the calculated total energy of the optimized adsorption system, and
Eadsorbate and ENi(111) are the calculated total energies of the isolated molecule and of the clean
surface, respectively. As mentioned above, a ZPE correction is added to all total energies. Only
the adsorption energies of the most stable structures on the Ni(111) are provided here.
5.3.1.1 NH3*, NH2*, NH*, N*, and H*
a. Adsorption sites and energies. Both NH2 and NH interact with the Ni(111) surface like
ammonia does (same orientation), that is via the nitrogen atom. However, each species interacts
with different active sites (see Figures 5.1.a, 5.2.a, and 5.2.b). Duan et al.46,59 studied the
adsorption sites and energies of NHx species on the Ni(111) surface and found that NH2 and NH
interact with the Ni(111) surface via bridge and fcc sites, respectively, which is consistent with
our findings. Duan reported the adsorption energies of NHx species in two publications.46,59 The
adsorption energies are different in the two papers. Their adsorption energies and the present
ones are listed in Table 5.3. Duan’s study used 3x3x1 k-points mesh whereas in this study a
152

higher k-point mesh (5x5x1) was used. Our results are in very good agreement with the data
provided by Duan.46 The calculated adsorption energy of ammonia from this work is identical to
the experimental value. It can be observed from Table 5.3 that the adsorption energy decreases
(increasing stability) with a decrease in the number of hydrogen atoms going from NH3 to N, as
expected, given an increase in unsaturation of the nitrogen in this order. This is evident giving
the different preferred interaction sites from the NH3/Ni(111) system to the NH/Ni(111) system.
Both NH2-Ni(111) and NH-Ni(111) bindings involve forward donation from the nitrogen’s lonepair electron and the back donation from the d-electrons of the Ni atom(s). More investigations
on the electronic properties of NH/Ni(111) and NH2/Ni(111) systems will be illustrated later.
Nitride and hydride both prefer to adsorb on the fcc site of the Ni(111) surface. Hydrogen
molecules tend to always adsorb dissociatively on the Ni(111) surface.38 Several studies on the
interaction of a hydrogen atom with different surfaces also demonstrated that the hydrogen atom
prefers to interact on the three-fold hollow site.38 PBE-D3 adsorption energies of NHx species
and H (see Table 5.3), although overestimated, reveal the same trend as PBE adsorption energies,
that is they are decreasing (relatively by the same magnitude as PBE) going from NH3 to N.
Table 5.3 Adsorption sites and adsorption energies (Ead) (in kcal mol-1) for NHx (x = 0 - 3)
species and H adsorbed on a Ni(111) surface.
Eada

Adsorbate

Adsorption
sites

PBE

PBE (Ref. b)

PBE (Ref. c)

PBE-D3

Expt.

NH3

atop

-17.0

-17.3

-15.0

-26.0

-17.0

NH2

bridge

-61.9

-63.0

-60.0

-69.7

-

NH

fcc

-103.8

-105.4

-101.0

-111.0

-

N

fcc

-121.0

-122.2

-119.7

-125.7

-

fcc
-64.5
-64.8
-64.6
-68.3
H
b
c
ZPE correction is included within the computed adsorption energy. Reference 46. Reference 59.
d
Reference 58.
a

153

a) NH2*

c) N*

b) NH*

d) H*

Figure 5.2 Adsorption sites of NH2 (a), NH (b), N (c), and H (d) on the Ni(111) surface.
(*) Indicates an adsorbed molecule.
b. Adsorption geometry. The predicted gas phase structural parameters of NH3, NH2, and NH
from this work (using PW-PBE) are in excellent agreement with experiments (see Table 5.4).
The predicted adsorbed structures of NHx species agree very well with previous calculations by
Duan et al.46 The N-Ni bond distance in the NH3/Ni(111) system is only 0.06 Å off from the
experimental measured distance.48 The N-H bond length in NH3 elongates by 0.004 Å when
adsorbed on the Ni(111) surface, but the N-H bond shortens by 0.01 Å and 0.03 Å in adsorbed
NH2 and NH, respectively. Differences in the N-H bond length can be attributed to the different
molecule-surface electronic interaction for each system. Furthermore, the HNH bond angles
open by 2.0° and 2.2° in NH3 when adsorbed on the Ni(111), whereas it opens by 5.1° in
adsorbed NH2. This expansion is due to the shape of the NH3 and NH2 becoming more
tetrahedral via adsorption. The distance between N and Ni decreases in the direction NH3 (2.03
Å), NH2 (1.93 Å), and NH (1.84 Å) highlight the strong binding of NH. In the N/Ni(111) system,
the N-Ni bonds are the shortest among other N-Ni bonds, see Table 5.4, so when nitrogen gets

154

more unsaturated it binds very tightly to the surface. Hydride, on the other hand, greatly overlaps
with the Ni atoms resulting in shorter H-Ni bonds compared to the N-Ni bond lengths, but the
NiHNi angles are larger than the NiNNi (in adsorbed nitride) by 2.4°.
Table 5.4 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed NHx
(x = 1 - 3) species, adsorbed N, and adsorbed H.
System
r(N-H)
a(HNH)
r(N-Ni)
[r(H-Ni)]
NH3
NH3 (expt.)
NH3/Ni(111)
NH3/Ni(111)(expt.)
NH2
NH2 (expt.)
NH2/Ni(111)
NH
NH (expt.)
NH/Ni(111)
N/Ni(111)d
H/Ni(111)e

1.021
1.021a, 1.023b
1.025
1.037
1.024a, 1.038b
1.025
1.051
1.036a, 1.051b
1.025
-

106.5
106.7
108.5, 108.7
102.5
103.4, 102.4c
107.6
-

2.031
1.97c
1.932, 1.931
-

-

1.835
1.759
[1.702]

a

Experimental bond lengths from Reference 60 (for NH3 and NH2) and Reference 61 (for NH).
Calculated bond lengths (using periodic PW91 functional) from Reference 62. cReference 63.
d
a(NiNNi) = 93.0°. ea(NiHNi) = 95.4°.
b

c. Vibrational Frequencies. In order to obtain a more complete picture of bond strengths and the
structural change via adsorption, the vibrational frequencies of gaseous and adsorbed NHx
species were calculated and are organized in Table 5.5. Experimental vibrational frequencies of
gas phase NH3, NH2, and NH and of adsorbed NH3 on Ni(111) are also given in Table 5.5. The
predicted vibrational frequencies from this work (not corrected for anharmonicity) are in
reasonable agreement with available experimental frequencies. When comparing the calculated
frequencies in gas phase and in adsorption, the decrease in the vibrational modes of NH3 via
adsorption is plausible owing to introducing the N-Ni binding that slightly weakens the N-H

155

bonds. This decrease ranges between 45 to 30 cm-1 in the frequencies; however, only the HNH
wagging mode increased by 112 cm-1 via adsorption consistent with enlarging of this angle, as
discussed earlier. On the other hand, the frequencies of NH2 and NH has increased upon
adsorption confirming the finding that the N-H bonds in these molecules become stronger when
interacting with Ni(111) surface.
Table 5.5 Vibrational frequencies (in cm-1) of free and adsorbed NH3, NH2, and NH.

Gas phasea

Adsorbed on a
Ni(111) surfacea

Gas phase (expt.)b

3505
3504
3380
1623
1623
1025

3465
3459
3341
1593
1590
1137

3444
3444
3337
1627
1627
950

N-H stretch (a1)
N-H stretch (a1)

3349
3254

3438
3358

3301
3219

HNH Bend (b2)

1497

1514

1497

NH3
N-H stretch (e)
N-H stretch (a1)
HNH Bend (e)
HNH Bend (a1)d

Adsorbed on a
Ni(111) surface
(expt.)c
3360
3270
1580
1140

NH2

NH
3169
3397
3283
N-H stretch
b
This work. Reference 64 (for NH3), reference 65 (for NH2), and reference 66 (for NH). cReference 67.
d
HNH wagging mode.
a

5.3.1.2 C6H6*, C6H5*, C6H5NH2*, and C6H5NH*
a. Adsorption sites and energies. As mentioned above, benzene adsorbs parallel to the surface
with all hydrogen atoms tilted away with respect to the surface (Figure 5.1.b). The calculated
adsorption energy of benzene including the ZPE correction is -21.4 kcal mol-1 (see Table 5.6)
coming mostly from π-interactions. The adsorption energy of phenyl on the Ni (111) surface is

156

more stable than that of adsorbed benzene by ~30 kcal mol-1, see Table 5.6. The strong binding
of phenyl compared to benzene is due to the strong σ-interaction introduced in the
phenyl/Ni(111) system that is not present in the benzene/Ni(111) system (only π-interactions)
resulting in different adsorption structures between these two systems. Phenyl adsorbs tilted with
respect to the surface on the fcc site Figure 5.3.a, which is a stronger binding site than the bridge
site (benzene’s most stable site). This adsorption orientation of phenyl was also found by Feng et
al.,68 but their adsorption energy of phenyl using the PBE method and slab model (using
different parameters compared to our study) is lower than ours by 92.8 kcal mol-1. Feng et al.68
also predicted an adsorption energy of benzene adsorbed on the bridge site that is 22.8 kcal mol-1
lower than the experimental adsorption energy of benzene. The adsorption energy of phenyl
when adsorbed nearly vertical to the Ni(111) surface on the hcp site is found to be less stable
than the tilted phenyl by approximately 3 kcal mol-1, as the former loses some of the πinteractions (see Figure 5.11.a in the appendix). Higher adsorption energy of phenyl is predicted
when adsorbed vertically on the bridge site, in which the π-electron interactions decrease the
most (Figure 5.11.b). The vertical orientation of phenyl may be likely when few binding sites are
available on the Ni(111) surface.
Table 5.6 Adsorption sites and adsorption energies (Ead) (in kcal mol-1) of the aromatic species
adsorbed on a Ni(111) surface.
Eada
Adsorbate

a

Adsorption sites
PBE

PBE-D3

Expt.b

C6H6 (parallel)

bridge

-21.4

-59.8

-18.0

C6H5 (tilted)

fcc

-51.1

-88.1

-

C6H5NH2(parallel)

bridge, and atop

-20.4

-63.6

-

C6H5NH (vertical)

bridge

-38.7

-56.9

-

b

ZPE correction is included within the computed adsorption energy. Reference 50.

157

Previous studies of the adsorption of aniline on nickel surfaces showed slightly different
adsorption behavior of aniline. On evaporated Ni films, aniline was found using X-ray
photoelectron spectroscopy (XPS) to adsorb molecularly by π-electrons and dissociatively as an
anion formed from losing a proton from the amino group.69 Studies by Huang and coworkers26,27 on the adsorption of aniline on Ni(100) and Ni(111) using fluorescence yield nearedge spectroscopy (FYNES) and (TPR) techniques revealed that adsorption of aniline is a
structure sensitive reaction and that the Ni(111) surface is considered the most stable for the
adsorption of aniline, where aniline does not easily undergo hydrogenolysis and hydrogenation
until temperatures of ~ 800 K and higher. Huang et al.26 concluded that aniline adsorbs on the
Ni(111) surface at a small angle via π-interactions only, whereas Myers et al.70 suggested that
aniline form an unreactive surface polymer (polyaniline) when adsorbed on the Ni(111) surface
that is stable to above 600 K. Same polyaniline was found on Ni(100) surface.71 In Hoffmann’s
TPR experiment,7,8 aniline was the only aromatic molecule detected below 610 K. When
relaxing the aniline/Ni(111) system starting from various initial structures, in the current study,
we found that aniline always interacts with the Ni(111) surface not only on the bridge site via the
aromatic ring π-interactions but also on the atop site via the amino group σ-interaction, see
Figures 5.3.b and 5.4.a. The adsorption energy of aniline is higher (less stable) than that for
benzene by 0.9 kcal mol

-1

indicating a slightly weaker π-interaction between aniline and the

Ni(111) surface compared to benzene. In addition, the N atom in aniline interacts slightly less
strongly with the Ni(111) surface than the N atom in ammonia. To confirm the adsorption
structure of aniline, a large slab model (5x5x4) of Ni(111) surface was constructed to study the
adsorption of aniline (Figures 5.4.b and 5.4.c). The adsorption energy of aniline on the larger
supercell p(5x5) is -26.3 kcal mol-1, lower (more stable) by ~6 kcal mol-1 than the adsorption

158

energy of aniline on the smaller supercell p(3x3). Aniline rotates on the large surface and adsorbs
on different kind of the bridge site (Figure 5.4.b), bridge site B (also known as bridge 0°),
compared to the adsorption on bridge site A (bridge 30o) on the p(3x3)-Ni(111) surface unit cell
(Figure 5.4.a). Aniline is found to be unstable on the hollow sites. Thus, the most stable
adsorption orientation of aniline is predicted to be via bridge site B and atop site. For consistency
the total energy of aniline adsorbed on the p(3x3) is used in calculating reaction
thermodynamics. Anilide, N(H)C6H5, observed on evaporated nickel films,69 prefers to adsorb
vertically on the Ni(111) surface on a bridge site (see Figure 5.3.c) with an adsorption energy
that is higher than vertical phenyl by 2.1 kcal mol-1 (Figure 5.11.b), which can be attributed to
the C-Ni bond being stronger, in which the aromatic ring directly interacts with the surface, than
N-Ni bond (the aromatic ring is away from the surface and causing a steric effect). The shortest
C-Ni bond length in vertically adsorbed phenyl is 1.953 Å versus 1.974 Å for the N-Ni bond
length in adsorbed anilide.
Similar to benzene, the PBE-D3 predicts lower adsorption energies for phenyl, aniline,
and anilide in comparison to the PBE adsorption energies. This overestimation may involve the
contribution of the vdW interactions to the molecule-metal binding, which is known to be
significant for aromatic systems (see Table 5.6). The dispersion energy of phenyl is very close to
benzene, whereas aniline has about 5 kcal mol-1 larger dispersion energy than benzene according
to the PBE-D3 results. As anticipated, anilide has the lowest dispersion energy among the
adsorbed aromatic species because the ring is not very close to the surface. The difference in
adsorption energy between parallel-adsorbed benzene and tilted-adsorbed phenyl is 30.0 kcal
mol-1 when using PBE and PBE-D3. Thus, PBE-D3 still provides correct qualitative trends of the
adsorption energies.

159

a) C6H5*

b) C6H5NH2*

c) C6H5NH*

Figure 5.3 Adsorption sites of phenyl (a), aniline (b), and anilide (c) on the Ni(111) surface.
(*) Indicates an adsorbed molecule.

b. Adsorption geometry. Important structural parameters of the free and adsorbed aromatic
species are shown in Table 5.7 and Table 5.8. A full list can be found in Table 5.14 and Table
5.15 of the Appendix. The C-C bonds in phenyl elongate, similar to benzene, when adsorbed on
the Ni(111) surface by 0.02 - 0.08 Å (see Table 5.7) resulting in a decrease in the bond order and
a degree of molecular distortion that can also be seen from the changes in the CCH bond angles
(Table 5.14). The C-H bond lengths of phenyl do not exhibit major changes via adsorption
except that they become titled out of the plane of the aromatic ring, as shown in Figure 5.3.a. The
C-Ni bonds in adsorbed phenyl vary in length, ranging from 1.905 to ~2.5 Å. The gradual
160

increase in the C-Ni bond lengths confirms that phenyl tilts from the surface, suggesting that it
interacts with Ni(111) in both a σ fashion (through the shortest 1.905 Å bond) as well as πinteractions with the remainder of the ring. This is in contrast to the C-Ni distances in adsorbed
benzene, which are all similar, ~ 2.1 Å.
a)

c)

b)

Figure 5.4 A top view of aniline adsorbed on the p(3x3) surface unit cell of Ni(111) on bridge
site A (a), on the p(5x5) surface unit cell on bridge site B (b), and a side view of aniline adsorbed
on the large 5x5x4 Ni(111) slab model.

Likewise in aniline, the C-C bonds get longer upon adsorption and the ring loses some
degree of unsaturation. The C-Ni bond lengths in aniline range from 2.04 to 2.09 Å, almost
similar to adsorbed benzene, except the two Cipso-Ni bond distances (Table 5.8). The carbon
atom connected to the amino group (Cipso) in adsorbed aniline interacts with two Ni atoms
(bridge sites) making the two Cipso-Ni bond distances longer (2.585 Å and 2.133 Å). The
perpendicular distance between the Cipso and the surface, though, is still ~2.1 Å, as shown in
Figure 5.3.b. Thus, the aromatic ring in aniline adsorbs parallel to the Ni(111) surface. The N-Ni
distance in adsorbed aniline is also 2.1 Å, which is similar to the C-Ni bond lengths but longer by
0.07 Å than the N-Ni bond length in adsorbed ammonia. This is consistent with ammonia being a
better σ donor than aniline. A steric effect may also play a role here in hindering the N atom
from binding strongly to the Ni(111) surface. In addition, the HNH bond angle of the amino

161

group in adsorbed aniline also opens as in adsorbed ammonia to accommodate a more tetrahedral
configuration about nitrogen.
Table 5.7 Bond lengths (r) in Å of free and adsorbed benzene and phenyl.
System

r(C-H)

r(C-C)

r(C-Ni)

C6H6

1.091

1.397

-

C6H6 (expt.)a

1.084

1.397

-

C6H6/Ni(111)

1.093, 1.095

1.434, 1.450

2.060, 2.085

C6H5

1.091, 1.092

1.405, 1.376, 1.398

C6H5(tilted)/Ni(111)

1.092, 1.095

1.438, 1.459, 1.433

2.237, 2.002, 2.411, 2.076,
2.487, 2.305, 1.905

a

Reference 60.

In adsorbed anilide, four of the C-C bonds of the aromatic ring (two Cipso-C bonds and the
other two C-C bonds that are parallel to them) become shorter instead of becoming longer via
adsorption as it is the case in aniline, benzene, and phenyl. The C-C bonds in adsorbed anilide
are all longer than the ones in adsorbed aniline. The C-N bond in anilide elongates by 0.076 Å
via adsorption, while it is still shorter than the C-N bond in adsorbed aniline. The nitrogen atom
in adsorbed anilide interacts with the Ni(111) via bridge sites as the same fashion as it is in
adsorbed amide (see Figure 5.1.a and Figure 5.3.c). Because of the steric effect resulting from
the aromatic ring in anilide, the N-Ni bonds in adsorbed anilide are longer by 0.065 and 0.044 Å
and the NiNCipso angle opens about 10° larger than the NiNH angle of adsorbed amide. That can
explain why the adsorption energy of anilide is predicted to be higher than amide’s adsorption
energy by 24 kcal mol-1.

162

Table 5.8 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed aniline and
anilide.
System
C6H5NH2 a

r(C-H)
1.091

C6H5NH2 (expt.)b,c
C6H5NH2/Ni(111)d

1.084
1.090,
1.096

1.021

C6H5NH

1.091

C6H5NH/Ni(111)e

1.103,
1.091

a

r(N-H)
1.014

r(C-C)
1.407, 1.393,
1.398

r(C-N)
1.394

r(C-Ni)
-

r(N-Ni)
-

1.397, 1.394
1.433, 1.448,
1.456, 1.452

1.402
1.435

2.056, 2.094,
2.040, 2.585,
2.133

2.084

1.032

1.407, 1.383,
1.437

1.340

-

1.030

1.392, 1.398,
1.410

1.416

1.995,
1.974

a(HNH) = 112.7°. bReference 72. ca(HNH) = 113.1°. da(HNH) = 110.0°. ea(NiNCipso)= 127.4°.

c. Vibrational Frequencies. The calculated vibrational frequencies of C-H, C-C, N-H, and C-N
bonds of free and adsorbed benzene, phenyl, aniline, and anilide are given in Table 5.9, as well
as their experimental frequencies in the gas phase and the experimental frequencies of benzene
adsorbed on the Ni(111) surface. A full list of the calculated frequencies can be found in Table
5.16 of the Appendix. Calculated gas phase frequencies are in good agreement with experiments
although not corrected for anharmonicity. From the lower C-C bond frequencies of adsorbed
benzene, phenyl, and aniline compared to the C-C in the gas phase, it is reasonable to conclude
that the adsorbed C-C bonds are not as strong as they are in the gas phase, mostly because of
their contribution to the π-interactions with the Ni (111) surface. The frequency of the C-C bond
of aniline only decreases by 59 cm-1 when adsorbed on the Ni(111) compared to a 147 cm-1
decrease in the same frequency for benzene, which supports our proposal that aniline has higher
adsorption energy than benzene because it involves weaker π-interactions, which also can be
seen from the slight differences in the C-Ni bond lengths in aniline compared to benzene, as
163

mentioned in the former section. On the other hand, the C-C stretch frequencies of adsorbed
anilide become higher by 27 cm-1 versus the gas phase indicating a stable aromatic ring. No large
differences in the C-H stretch modes are seen between the gas phase and the adsorbed molecules,
although they become slightly lower with adsorption. The C-H bond lengths do not change much
via adsorption since hydrogen atoms tilt away from the surface. Like the C-H stretching modes,
the N-H stretching modes display no significant differences in the frequencies between gas phase
and adsorbed molecules. The C-N stretching modes of aniline and anilide exhibit a high decrease
in the frequencies between free and adsorbed molecules. Although the C-N bond becomes longer
via adsorption, aniline was found to be stable against hydrogenolysis when adsorbed on the
Ni(111) surface in the presence of hydrogen but at very high temperature (more than 800 K).26
Table 5.9 C-H, C-C, C-N, and N-H vibrational frequencies (in cm-1) of gas phase and adsorbed C6H6,
C6H5, C6H5NH2, and C6H5NH.

Gas phasea

Adsorbed on a
Ni(111) surfacea

Gas phase
(expt.)b

3122
3121
3106
3105
1586
1586

3086
3084
3074
3065
1439
1422

3062
3068
3063
3047
1596
1596

3108
3105
3093
3088

3089
3084
3071
3061

3086
3072
3037
3060

1590

1426

1593

1527

1421

1497

N-H stretch (b2)

3580

3486

3500

(a1)

3479

3394

3418

C-H stretch (b2)

3125

3096

3053

C6H6
C-H stretch (e1u)

C-C stretch (e2g)
C6H5
C-H stretch (a1)

C-C stretch (b2)
C6H5NH2

Table 5.9 Continued.

164

Adsorbed on a
Ni(111) surface
(expt.)c
3025

1425

(a1)

3108

3087

3041

C-C stretch (a1)

1612

1553

1619

(b2)

1599

1446

1590

C-N stretch (a1)

1280

1137

1279

C-H bending (a1)

1168

1114

1173

N-H stretch

3313

3291

C-H stretch

3129

3129

3122

3113

1551

1578

1522

1566

1303

1237

C6H5NH

C-C stretch
C-N stretch

1155
1196
This work. Reference 64 (for C6H6), reference 73 (for C6H5), and reference 74 (for C6H5NH2).
c
Reference 75.
a

b

5.3.2 Decomposition Reactions
Reaction energies (ΔE), reaction enthalpies (ΔH) at 523 K, and reaction free energies
(ΔG) at 523 K were calculated for several decomposition reactions and are listed in Table 5.10
and 5.11.

5.3.2.1 Decomposition of Ammonia
Ammonia decomposition on close-packed surfaces of reactive transition metals requires
high pressure and temperature to overcome the decomposition barrier.76 The use of NiO in
DuPont’s cataloreactant may have favored the decomposition of ammonia into the NHx species,
as Hoffman et al.7 found that no NH3 was detected above 523 K, meaning that the Ni surface
were covered with NHx species. Adsorption of ammonia on the Ni(111) surface is an exergonic
reaction but can decompose by increasing the heat.7 The reaction energy, enthalpies and free
energies are shown in Table 5.10. Breaking two N-H bonds of ammonia to produce imide (NH3*
165

NH* + 2 H*) shows the lowest reaction enthalpy (-20.1 kcal mol-1), followed by breaking the
N-H bond of amide (NH2*

NH* + H*) (-13.7 kcal mol-1), and (NH3*

NH2* + H*) (-6.4 kcal

mol-1). Finally, the decomposition of NH* to H* and N* displays the highest reaction enthalpy.
According to the present results, the decomposition of ammonia on the Ni(111) surface to imide
is the most favorable, thus, imide is predicted to be the most prevalent species on the Ni(111)
surface among NHx species, although amide cannot be ruled out, while nitride seems less likely
as does undissociated ammonia, which is consistent with Daun’s calculations of the activation
energies.46 Daun’s found that the lowest energy barrier corresponds to the dehydrogenation of
the NH2* to give NH* and H*, in which NH2* diffuses on the surface from the moderate binding
bridge site to the strong binding fcc site. The adsorption energy of NH2 on the fcc site is higher
than the bridge site by 7 kcal mol-1 (see Figures 5.10.a in the Appendix and 5.2.a), but the imide
species binds more strongly and are more stable than amide on the fcc site (Table 5.3). A recent
experimental study of the decomposition of ammonia on the closed-packed surface Co(0001),
which is anticipated to carry similar reactivity of the Ni (111) surface, found that imide is the
most stable species among the NHx species and can be selectively produced using the electroninduced dissociation technique at low temperature.76 Gibbs free energies of the decomposition
reactions of ammonia on the Ni(111) surface at 523 K predicted that these reaction are exergonic
(except the dehydrogenation of imide), see Table 5.10, with the imide-Ni(111) being the most
favorable decomposition reaction of ammonia at this temperature. The differences between ΔH
and ΔG are small as shown from the results in Table 5.10 indicating small contributions from the
entropies.

Table 5.10 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the adsorption and
decomposition reactions of ammonia on the Ni(111) surface, all in kcal mol-1.a

166

Reaction pathways
Ò

ÏÐÑ + ∗ → ÏÐÑ∗
Ò

ÏÐÑ∗ + ∗ → ÏÐÁ∗ + Ð ∗
Ò

ÏÐÑ∗ + Á ∗ → ÏÐ ∗ + Á Ð ∗
Ò

ÏÐÁ∗ + ∗ → ÏÐ ∗ + Ð ∗
Ò

ÏÐ ∗ + ∗ → Ï ∗ + Ð ∗
a
(*) Indicates an adsorbed molecule.

ΔE

ΔH (523 K )

ΔG (523 K )

-17.0

-22.0

-19.0

-4.1

-6.4

-3.5

-15.6

-20.1

-14.4

-11.5

-13.7

-10.9

5.1

3.3

5.4

5.3.2.2 Decomposition of Benzene
As shown in Table 5.11, the decomposition of benzene to phenyl and hydrogen on the

Ni(111) surface is thermodynamically less favorable than the adsorption of benzene on the
Ni(111) surface. This result is expected given the difficulty to activate the C-H bond and the high
stability of the benzene ring. However, compared to the energy required to break the benzene’s
C-H bond in the gas phase (113 kcal mol-1), Table 5.1, the use of the Ni(111) surface does reduce
the endothermicity of breaking the C-H bond by ~99 kcal mol-1. These results lead to the
conclusion that benzene is more stable on the Ni(111) surface than phenyl and the C-H bond can
be possibly activated at high temperature.
Table 5.11 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the adsorption and
decomposition reactions of benzene on the Ni(111) surface, all in kcal mol-1.a
Reaction pathways
Ò

ÔÕ ÐÕ + ∗ → ÔÕ ÐÕ∗
Ò

ÔÕ ÐÕ∗ + ∗ → ÔÕ ÐÖ∗ + Ð ∗
a
(*) Indicates an adsorbed molecule.

ΔE

ΔH (523 K)

ΔG (523 K)

-21.4

-25.1

-22.1

5.3

1.8

6.8

5.3.3 Production of Aniline
Hoffman et al.7 represented a kinetic study of the semi-batch oxidative synthesis of
aniline catalyzed by NiO/ZrO2 and found that temperature is a critical parameter to move the
167

reaction forward. Full coverage of NHx species on the Ni surface is also required for the
formation of aniline so that it can control the adsorption geometry of benzene on the nickel
surface.7,8 Hoffman suggested that an adsorbed phenyl-type intermediate would be possible for
this process, yet no confirmation of this proposal has been provided. In this section, possible
reaction pathways between imide and benzene, since they are likely the most prevalent (stable)
species on the surface, are proposed and investigated based on their reaction enthalpies and
reaction free energies at 523 K. Surface reactions generally go through a catalytic cycle
comprised of elementary steps, beginning with adsorption, then reaction, and finally desorption.
Two mechanisms common in surface reactions are the Langmuir-Hinshelwood and Rideal-Eley
mechanisms.
5.3.3.1 Langmuir-Hinshelwood Mechanism
In this mechanism, all reactants involved in the reaction are adsorbed on the surface
before reacting. Under this scheme, two reaction processes for the production of aniline were
proposed: insertion and stepwise, see Table 5.12 and Scheme 5.5. The first reaction pathway
entails direct insertion of the imide into a C-H bond of adsorbed benzene generating new C-N
and N-H bonds and thus coordinated aniline. Then, aniline is desorbed. The overall reaction is
endergonic and must be aided with heating and/or pressure, as it is also endothermic by 21.5 kcal
mol-1 at 523 K.
The second reaction pathway modeled is a stepwise formation of the C-N and N-H
bonds. The first step proceeds by a C-H bond activation in which a benzene’s C-H bond breaks
and a Ni-C bond forms, resulting in C6H5/Ni(111) and NH2/Ni(111). These two species react in
the second exothermic step akin to a C-N formation process to produce aniline, which would
then be desorbed from the Ni(111) surface. The overall process is, of course, also endothermic

168

by ~21.4 kcal mol-1 at 523 K, but the calculations are interesting in that they suggest that the
initial C-H activation step is disfavored (ΔH = 24.5 kcal mol-1) relative to the second C-N
formation step (ΔH = -3.1 kcal mol-1). The uphill nature of the first step is consistent with the
dehydrogenation of benzene on the Ni(111) being unfeasible, as shown earlier. In part, this
disfavorability of the first step can be attributed to the loss of some of the π-interactions between
the aromatic ring and the surface in phenyl as compared to the adsorbed benzene, Figures 5.1.b
and 5.3.a. The ΔG of this reaction also favors the second step over the benzene’s C-H bond
activation indicating that formation of aniline is more entropically favored than the formation of
phenyl.
Table 5.12 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the proposed reaction
processes of the production of aniline on the Ni(111) surface, all in kcal mol-1.a
Reaction processes of the production
ΔE
ΔH (523 K)
ΔG (523 K)
of aniline
Langmuir-Hinshelwood mechanism
I. Insertion
∆

ÏÐ ∗ + ÔÕ ÐÕ∗ → ÔÕ ÐÖ ÏÐÁ∗ + ∗
II. C-H activation/C-N formation
∆

ÏÐ ∗ + ÔÕ ÐÕ∗ → ÏÐÁ∗ + ÔÕ ÐÖ∗
∆

ÏÐÁ∗ + ÔÕ ÐÖ∗ → ÔÕ ÐÖ ÏÐÁ∗ + ∗
Rideal-Eley mechanism
I. Coupling
∆

ÏÐ ∗ + ÔÕ ÐÕ + ∗ → ÔÕ ÐÖ ÏÐ∗ + Ð ∗

a

∆

ÔÕ ÐÖ ÏÐ∗ + Ð ∗ → ÔÕ ÐÖ ÏÐÁ∗ + ∗
(*) Indicates an adsorbed molecule.

17.0

21.5

14.8

24.9

24.5

25.2

-8.0

-3.1

-10.4

0.9

-2.6

-2.0

-5.3

-1.8

-6.8

5.3.3.2 Rideal-Eley Mechanism
In this reaction, not all of the reactants needed to be adsorbed prior to reacting. It is
possible that a gas phase reactant collides with a preadsorbed molecule on the surface. In the
third modeled reaction pathway, benzene is introduced to a preadsorbed imide on the Ni(111)
surface to produce H/Ni(111) and the N(H)C6H5/Ni(111), bound anilide, in which the aromatic
ring is nearly perpendicular to the surface and bound to the Ni(111) surface via N atom. A

169

coupling between NHC6H5 and H is followed to produce aniline. The first step in this reaction
pathway is more thermodynamically favorable (slightly exothermic) than the first step in the
second reaction pathway (C-H activation/C-N formation reaction), see Scheme 5.5. The
computed difference between these steps is 27.1 kcal mol-1 favoring the production of anilide.
Another reason for the production of surface-bound anilide/hydride being more favored than the
amide/phenyl is the existence of the hydrogen, which adsorbs strongly to the Ni(111) surface (64.5 kcal mol-1, Table 5.3). Both steps in this reaction are exergonic processes indicating that
binding via nitrogen is entropically favored. This reaction pathway is highly likely to achieve the
direct production of aniline. Although high temperatures are needed for the desorption reaction.
Table 5.13 Reaction energies ΔE, enthalpies ΔH, and free energies ΔG of the desorption reaction
of aniline on the Ni (111) surface, all in kcal mol-1.a
Reaction process

ΔE

ΔH (523 K)

ΔG (523 K)

20.3

25.1

22.1

Desorption of aniline
∆

ÔÕ ÐÖ ÏÐÁ∗ → ÔÕ ÐÖ ÏÐÁ + ∗
a
(*) Indicates an adsorbed molecule.

5.3.4 Desorption of Aniline
Desorption of aniline is calculated to cost 25.1 kcal mol-1 thermal energy at 523 K, as
shown in Table 5.13. Thus, heat is needed to overcome this barrier. Because the desorption
reaction involves increasing in entropy, owing to conversion from being surface-bound to gas
phase, the enthalpy barrier has to be overcome for this reaction to proceed.

170

Scheme 5.5 Possible reactions pathways for the production of aniline and the change in the
reaction free energies for each process.

5.3.5 Density of States
In order to interpret the electronic structure of the NH/Ni(111) and NH2/Ni(111) systems,
the density of states of these systems and of the clean Ni(111) surface were calculated.

171

Furthermore, the local density of state (LDOS) was also calculated for the N atom in the isolated
molecules as well as in the adsorption systems. The LDOS for the Ni atom interacting with the N
atom in the adsorption system was also calculated. Since the findings of the DOS and LDOS for
the NH2/Ni(111) system and the NH/Ni(111) system are similar, only the results of the later will
be discussed. The results of the DOS and the LDOS of the NH2/Ni(111) system are displayed in
Figure 5.12 of the Appendix.
Figures 5.5.a and 5.5.b show the LDOS of the N atom in the isolated NH and in the
NH/Ni(111) system, respectively. Each LDOS shows the contributions from s, p, and d bands in
the electronic structure. Figures 5.5.c and 5.5.d show the DOS of the clean Ni(111) surface and
the LDOS of one of the Ni atoms that interact with the NH, respectively. The Fermi level is set
to 0 eV, hence all energies are relative to the Fermi energy, Ef, which represents the energy of
the highest occupied electronic state.
By comparing between Figures 5.5.a and 5.5.b, it can clearly be seen that the two bands
at -13 and -10.5 eV in the isolated molecule have shifted via adsorption. The band at -13 eV
corresponds to the 2σ states (bonding) from the N atom in the NH whereas the band at -10.5 eV
corresponds to the 3σ state (lone pair) from the N atom in the NH. When the NH adsorbs on the
Ni(111) surface the bonding band shifts away from the Fermi level (-16 eV) while the lone pair
band shifts toward the Fermi level (-8 eV). So, the N bonding state does not contribute to the
NH-surface bonding whereas the N lone pair state contributes to the bonding with the surface. In
addition, the valence bands between -2 eV and the Fermi level in the isolated NH lose their
density and smear out via adsorption. These bands represent the N atom 1π states (2 unpaired
electrons) and the 3σ state of the NH (in the triplet state). These states involve most of the NHsurface bonding character.

172

On the other hand, Figure 5.5.d shows that the adsorption induces short and narrow bands
at about -16 and -8 eV in the LDOS of the Ni atom in the adsorption system as compared to
Figure 5.5.c (free Ni(111) surface). These bands correspond to the N atom in the adsorbed NH
(bonding states (-16 eV) and lone pair states (-8 eV)). The N atom 1π states are also shown at -5
eV, indicating that they are populated when interacting with the nickel surface. Figure 5.5.d
shows that the valence band is dominated by d states from Ni atoms. Therefore, the NH-surface
bonding (the valence band) is a mixture of Ni atom d states and N atom lone pair state and 1π
states to which the d-states contribute the most.
From the spin density plot, shown in Figure 5.6, spin up and spin down densities of N
atom are very similar. Which leads to the conclusion that the NH interacts with the surface more
as an imide (singlet NH2-) rather than as an imidyl (doublet NH•-) radical anion or as a nitrene
(triplet NH••) radical. The NH2 also interacts with the surface as an amide (NH2-) rather than as
an aminyl (NH2•) radical via analysis of its up and down spin densities, see Figure 5.13 of
Appendix. Furthermore, from our calculations, anilide is found to adsorb in similar way as amide
based on its adsorption structure and vibration, thus one may surmise that anilide interacts with
the surface as an anion (C6H5(H) N-) rather than anilinyl (C6H5(H) N•).
Electronic properties of imide on the heterogeneous Ni(111) surface are thus quite different from
the electronic states of a homogeneous imide-nickel model,28 where imide interacts as an imidyl
(NR•-) radical anion, R = hydrocarbyl substituent. These electronic states may allow
homogeneous imide systems to undergo hydrogen atom abstraction (HAA) reactions, which are
disfavored in heterogeneous models.

173

a) LDOS of N in a free NH

b) LDOS of N in the NH/Ni(111)
3
DOS

4σ* states

3σ states

DOS

2σ states
3σ states

1π states

4

4
3.5
3
2.5
2
1.5
1
0.5
0

2
1
0

-20

-10

0
E-Ef (eV)

10

20

-20

c) DOS of clean Ni(111) surface

-10

-5
0
E-Ef (eV)

5

10

15

d) LDOS of a Ni in the NH/Ni(111)
3.5
3
2.5
2
1.5
1
0.5
0

200

DOS

150
DOS

-15

100
50
0
-20

-10

0

10

-20

20

-15

E-Ef (eV)

-10

-5
0
E-Ef (eV)

5

10

15

Figure 5.5 The local density (LDOS) of N in NH (a), N (b), and Ni (d) in NH/Ni(111) system and
the density of states (DOS) of clean Ni(111) surface (c).

DOS

spin up
150

spin down

100

50

0
-20

-15

E-Ef (eV)

-10

-5

0

5

10

-50

-100

Figure 5.6 Spin density of the NH/Ni(111) system.

174

15

5.4. Conclusions
This study presents an initial step toward understanding and identifying relevant species
involved in the direct amination of benzene using first principles density functional calculations.
Calculations predict aniline adsorbs parallel to the surface via the aromatic ring and the nitrogen
atom. The adsorption energy of aniline is higher (less stable) than benzene indicating weaker π
interaction with the surface. Among all the species, imide (NH) and benzene are predicted to be
the most stable on the Ni(111) surface. The DOS calculations predict that NH interacts with the
surface as an imide (NH2-) and NH2 as amide (NH2-), and hence quite different from molecular
analogues, which have more radical character in the ligands. Three reaction pathways were
proposed relevant to the direct amination of benzene on the Ni(111) surface, and based on the
thermodynamics, the reaction involves producing a surface-bound anilide and then coupling
between NHC6H5 and H on the Ni(111) surface seems most likely to produce aniline than the
other reaction pathways. Anilide adsorbs vertically on the Ni(111) surface on similar way as an
amide, thus one may surmise that anilide interacts with the surface as an anion (C6H5(H) N-).
More detailed conclusions about the catalytic potential of Ni(111) surface for the direct
amination of benzene cannot be drawn at this stage until the kinetic study of the transition states,
coverage, and activation energies is completed.

175

APPENDIX

176

APPENDIX
-19.5

Total energy (eV)

-20.0
-20.5
-21.0
-21.5
-22.0
-22.5
3.35

3.40

3.45

3.50

3.55

3.60

3.65

Lattice parameter (Å)
200/999

250/999

300/999

400/999

450/999

500/999

350/999

Figure 5.7 Lattice constant convergence test for bulk fcc Ni using variable Ecutoff and fixed kpoints (9x9x9). The DFT-optimized lattice constant is 3.52 Å

Total energy (eV)

-238

-239

Ecutoff=500 eV
Ecutoff=400 eV

-240
1

2

3

4

5

6

7

8

KPOINTS (nxnx1)

Figure 5.8 K-points convergence test for the Ni(111) surface using two values of Ecutoff (400 and
500 eV). The optimal set of k-points for our systems is 5x5x1.

177

Total energy (eV)

-215
-220
-225
-230
-235
-240
-245
0

100

200

300

400

500

600

Ecutoff (eV)
Figure 5.9 Energy cut off convergence test for the Ni(111) surface using 5x5x1 k-points. The
optimal energy cut off for our systems is 400 eV.

178

a) NH2*(fcc site)

Ead = -54.9 kcal mol-1

b) NH2*(atop site)

Ead = -24.1 kcal mol-1

Figure 5.10 Adsorption sites and adsorption energies (Ead) of NH2 adsorbed on an fcc site (a),
and NH2 adsorbed on an atop site (b) of the Ni(111) surface. (*) Indicates an adsorbed molecule.
a) C6H5*(nearly vertical)
(hcp site)

Ead = - 48.4 kcal mol-1

b) C6H5* (vertical) (bridge site)

Ead = - 40.8 kcal mol-1

Figure 5.11 Adsorption sites and adsorption energies (Ead) of C6H5 adsorbed on an hcp site (a),
and C6H5 adsorbed on an bridge site (b) of the Ni(111) surface. (*) Indicates an adsorbed
molecule.

179

a) LDOS of N in NH2

DOS

4
3
2
1
0
-20

-15

-10

-5

0

5

10

15

E-Ef (eV)

b) LDOS of N in NH2/Ni(111)

DOS

4
3
2
1
0
-20

-15

-10

-5

0

5

10

15

E-Ef (eV)

Figure 5.12 The local density of states (LDOS) of N in NH2 (doublet) (a), N (b), in NH2/Ni(111)
system.

180

DOS

a) DOS of clean Ni(111) surface
180
160
140
120
100
80
60
40
20
0
-15

-10

-5

0

5

10

15

E-Ef (eV)

b) LDOS of a Ni the NH2/Ni(111)
4

DOS

3

2

1

0
-20

-15

-10

-5

0

5

10

15

E-Ef (eV)

Figure 5.13 The density of states (DOS) of clean Ni(111) surface (a) and the local density of
states (LDOS) of Ni in NH2/Ni(111) system (b).

181

spin up

DOS

150

spin down

100

50

0
-25

-20

-15

-10

-5

0

E-Ef (eV)

5

10

-50

-100

Figure 5.14 Spin density of the NH2/Ni(111) system.

182

15

Table 5.14 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed benzene and
phenyl.

Compound

r(C-H)

r(C-C)

a(CCH)

r(C-Ni)

a(CCC)

C6H6

1.091

1.397, 1.398

120.0

-

120.0

C6H6 (expt.)a

1.084

1.397

120.0

-

120.0

C6H6/Ni(111)*

1.093,
1.095

1.433, 1.449, 118.5, 118.0, 2.060, 2.081, 121.8, 121.1,
1.434, 1.450
117.9, 117.8
2.085, 2.079
117.7

C6H5

1.091,
1.092

1.405, 1.376, 122.6, 119.6, 1.398
120.3, 121.0

C6H5/Ni(111)**

1.092,
1.095,
1.094,
1.093

1.438, 1.429, 119.4, 120.3, 2.237,
1.458, 1.459, 119.3, 119.1, 2.411,
1.433, 1.432
118.4
2.475,
2.000,
1.905

a

126.2, 116.4,
120.1, 120.7
2.002,
2.076,
2.487,
2.305,

116.0,
119.8,119.6,
120.5, 118.7,
120.8

Reference 60. *CCCH = 161.9°, 161.3°, 151.8°, and 150.7°. ** CradiclCCH= 176.7° and 176.5°,
HCCradiclC= 144.7° and 148.3°, and CCCH= 164.2°, 161.5°, and 159.5°.

183

Table 5.15 Bond lengths (r) in Å and bond angles (a) in degree of free and adsorbed aniline and
anilide.

Compound

r(C-H)
[r(N-H)]

r(C-C)
[r(C-N)]

a(CCH)

r(C-Ni)
[r(N-Ni)]

a(CCN)
[a(HNH)]

a(CCC)

C6H5NH2

1.090,
1.092,
1.091
[1.014]

1.407,
1.393,
1.398
[1.394]

-

120.7
[112.7]

118.5,
120.5,
118.9,
120.8

C6H5NH2 (expt.)a

1.084

1.397,
1.394,
1.396
[1.402]

119.1,
120.6,
120.4,
120.1,
120.0
-

-

[113.1]

119.4,
120.1,
120.7,
118.9

C6H5NH2/Ni(111)

1.090,
1.093,
1.096,
1.094
[1.021,
1.022]

1.433,
1.448,
1.456,
1.430,
1.452,
1.451
[1.435]

117.6,
118.8,
118.3,
116.2,
118.9

2.056,
2.064,
2.094,
2.057,
2.040,
2.585, 2.133
[2.084]

116.0,
120.6
[110.0]

116.4,
121.7,
117.5,
120.4,
122.6

C6H5NH

1.090,
1.092,
1.091
[1.032]

1.407,
1.383,
1.437
[1.340]

118.3,
120.2,
119.8,
119.6,
121.8

-

124.6,
118.09

117.3,
120.9,
120.4,
120.1,
120.2,
121.1

1.403,
119.4,
119.2,
118.2,
120.2,
[1.995,
122.6
121.0,
1.392,
1.398,
120.4,
1.974]
120.4,
1.399,
119.5,
119.2,
1.393,
119.3
120.5,
1.410
120.8
[1.416]
a
Reference 72. *a(HNNi)= 108.2° and 104.3°, a(NiNNi)= 76.5°, a(NiNC)= 127.4° and 130.0°, and r(NiNi) = 2.458 Å.
C6H5NH/Ni(111) *

1.103,
1.092,
1.091,
1.094
[1.030]

184

Table 5.16 Calculated vibrational frequencies of gas phase and adsorbed aromatic species,
in cm-1.
Compound
Benzene

ZPE
Phenyl

Calculated vibrational frequencies (cm-1)
Gas phase
Adsorbed
3131
3122
3121
3106
3105
3096
1586
1586
1465
1465
1337
1336
1166
1165
1142
1036
1035
993
991
987
959
958
838
837
704
666
600
599
397
397
2.66
3120
3108
3105
3093
3088
1590
1527
1425
1425
1328
1268
1145
1145

3095
3086
3084
3074
3065
3059
1439
1422
1384
1376
1353
1291
1126
1120
1097
985
945
941
884
880
869
826
806
750
741
599
551
540
450
437
2.56
3112
3089
3085
3072
3061
1426
1422
1350
1347
1306
1194
1121
1106

185

Table 5.16 Continued.

ZPE
Aniline

1050
1029
998
969
957
939
869
792
701
655
597
576
412
383
2.31
3580
3479
3125
3108
3102
3087
3087
1612
1599
1582
1489
1457
1356
1324
1281
1168
1147
1109
1039
1026
983
958
941
859
814
802
740
685
614
549
519
489
404

981
951
947
915
862
850
790
754
735
628
584
550
516
445
2.24
3487
3395
3096
3088
3076
3063
3048
1553
1447
1419
1384
1372
1343
1272
1174
1115
1094
1070
971
950
907
865
840
793
763
741
707
706
573
548
498
485
463

186

Table 5.16 Continued.

ZPE
Anilide

ZPE

377
348
211
3.11
3313
3130
3123
3111
3102
3091
1552
1522
1450
1433
1347
1319
1303
1156
1143
1142
1062
1006
973
966
960
892
812
806
764
679
653
597
518
467
407
374
186
2.75

440
375
350
3.01
3292
3130
3114
3105
3084
2915
1578
1567
1472
1445
1371
1332
1237
1196
1167
1155
1084
1027
980
975
946
876
821
794
752
709
670
616
568
508
497
404
329
2.78

187

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195

CHAPTER 6 CONCLUDING REMARKS
In this dissertation, several computational approaches and thermochemical schemes have
been utilized to establish effective routes for the determination of accurate structural and
thermochemical properties of various sets of molecular systems. To assess the reliability of these
approaches, enthalpies of formation were calculated and compared to experimental data. Another
aspect of this work includes the application of periodic density functionals on a heterogeneous
catalytic process for the identification of possible reaction intermediates and the prediction of
thermodynamically preferred reaction pathways. A brief summary of these projects and possible
future directions is provided below.

6.1 DFT and Composite Methods Investigations
6.1.1 Enthalpies of Formation for Oxygen Fluoride Species via Atomization Approach
In Chapter 3, the reliability of the ccCA, G3, and G3B3 composite methods for the

prediction of the enthalpies (∆ °

,$¤¥ ′

of formation of oxygen fluoride species was assessed.

In addition to these methods, the study employed the M06 and M06-2X functionals with various

basis set sizes to examine their performance for the prediction of structures and ∆ °

,$¤¥ ′

same set of oxygen fluoride species. Only seven of these molecules have known ∆ °

of the

,$¤¥ ′

,

hence determining an accurate theoretical approach would help to enable reliable predictions in
the absence of experimental data. The ccCA-S3 method results in the lowest MAD among the
methods tested. The MAD for ccCA-S3 was 1.4 kcal mol-1 with respect to the reference data
(note, this includes data from experiments as well as high-level ab initio calculations). However,
the MAD of ccCA-S3 was reduced to 0.6 kcal mol-1 when compared to the enthalpies of
formation from the Active Thermochemical Tables (ATcT). The ATcT uses artificial intelligence
196

algorithms to reduce experimental uncertainties associated with the measured ∆ °

,$¤¥ ′

by

integrating experimental data with highly accurate theoretical thermochemical properties. G3 and
G3B3 achieved MAD of 1.5 kcal mol-1 with respect to the reference data for the ∆ °

,$¤¥ ′

of

oxygen fluoride species while incorporating an empirical parameter that is intended to reduce the
overall MAD. The MADs of G3 and G3B3 also were reduced when comparing to the ATcT
values (0.8 kcal mol-1 for G3 and 0.7 kcal mol-1 for G3B3). To come to a conclusion about the

performance of composite methods on halogen oxide species, ∆ °

,$¤¥ ′

of chlorine oxides

species are also calculated. The results show that ccCA-S3 still produces the lowest MAD of 1.1
kcal mol-1 for the chlorine oxides species, while G3 and G3B3 result in MADs of 2.3 and 3.5
kcal mol-1, respectively. Thus, ccCA-S3 is recommended for halogen oxide systems and is

promising for other halogen systems and peroxides. Another important finding from this study is
that although the M06 and M06-2X density functionals are considered useful methods for main
group species, they are not recommended for predicting structures and ∆ °

fluoride species.

,$¤¥ ′

for oxygen

6.1.2 Enthalpies of Formation for Organoselenium Compounds via Reactions Schemes
In Chapter 4, several thermochemical reaction schemes including isodesmic (RC2) and

hypohomodesmotic (RC3) reaction schemes were employed to predict ∆ °

,$¤¥ ′

of

organoselenium compounds via composite methods and density functionals and the results were
compared to the traditional atomization approach. The impact of the RC2 and RC3 schemes on
the accuracy of the predicted ∆ °

,$¤¥ ′

also was evaluated. Although RC2 and RC3 are both

known to cancel most of the errors that arise from the differential correlation effects and size

197

extensivity, their impact on the accuracy of the ∆ °

,$¤¥ ′

predicted using composite methods is

not significant except for ccCA-S3 with respect to the RC0 approach. The reduction in the MAD
of ccCA-S3 is -2.18 kcal mol-1 (RC2) and -1.87 (RC3) kcal mol-1 compared to RC0, showing

higher accuracy when using RC2 and RC3 reaction schemes. The MADs of all four ccCA
variants become nearly the same when using RC2 and RC3, which reduces the dependency on
the various extrapolation schemes. G3 was found to be independent on the choice of
thermochemical schemes, yet G4 shows a systematic reduction in the MAD going from RC0 to
RC3. In contrast to the composite methods, a large decrease in MADs was seen when using the
RC2 and RC3 schemes with the single point energy calculations utilized within the ccCA
methodology. It is then extremely important to use these reaction schemes instead of the RC0
approach to predict accurate ∆ °

,$¤¥ ′

for organoseleinum species. The accuracy of DFT

increases when using the RC3 reaction scheme with an MAD of 0.76 kcal mol-1 for the

calculated ∆ °

,$¤¥ ′

of organoselenium compounds, with respect to experiments.

6.1.3 Future Interest
Although ccCA performed reasonably well when applied to oxygen fluoride species and
chlorine oxides, it is of interest to examine the performance of more sophisticated methods such
as multireference-ccCA (MR-ccCA) on these highly correlated set of molecules. In addition,
because M06 and M06-2X perform less successfully with respect to experiment when applied to
systems such as oxygen fluorides using the atomization approach, the use of isodesmic reaction
schemes with these functionals would likely be more accurate based on results presented in these
studies.

198

Organoselenium species are very important molecules in various fields of chemistry,
materials science, and biochemistry. However, experimental thermochemical data, such as
enthalpies of formation, are either very limited or associated with high uncertainties. Therefore,
establishing reliable data experimentally and theoretically would be of great help for future work
with these types of molecules. Particularly, an expanded database of enthalpies of formation of
the elemental products and reactants of organoselenium species, which are very scarce, can
improve the accuracy of the thermochemical reaction schemes, such as RC3. These reaction
schemes then can be extended to define organoselenium compounds containing other
heteroatoms, such as selenone, selenoxide, and selenocysteine, etc.

6.2 Periodic DFT for the Direct Amination of Benzene on the Ni(111)
The direct amination of benzene to produce aniline was listed by Haggin1 as one of the
top ten most challenging reaction for catalysis. As an effort to study this reaction theoretically on
the Ni(111) surface, Chapter 5 presents an initial step of investigating various aspects such as
identifying the adsorption behaviors and energetics of all intermediates involved in this reaction.
First principle calculations predict that aniline adsorbs parallel to surface but the adsorption of
aniline is less stable than benzene adsorption. Imide and benzene are found to be the most
prevalent species among NHx and aromatic adsorbed species, respectively. Information from the
density of states shows that NH and NH2 species interact with the Ni(111) as imide (NH2-) and
amide (NH2-) rather than radicals as is the case in the molecular analogues resulting in different
C-H amination mechanisms. Three reaction pathways relevant to the direct amination of benzene
on the Ni(111) were proposed and the reaction involves producing a surface-bound anilide and

199

then coupling between NHC6H5 and H on the Ni(111) surface seems the most
thermodynamically favorable and, in turn, the most likely to produce aniline than other proposed
mechanisms.

6.2.1 Future Interest
In order to use our results to design heterogeneous catalysts for the direct synthetic of
aniline, a kinetic study is warranted. This includes the prediction of transition states and
activation barriers. Another aspect that would contribute to this work is a study of the coverage
effect of adsorbates on the Ni(111) surface, i.e. to calculate the adsorption of benzene on preadsorbed NHx at different coverages and to investigate the adsorbate-adsorbate interactions.
These calculations require the use of dispersion corrected density functional and a large surface
unit (not less than 6x6) to accommodate the large aromatic species. Since PBE-D3 was not
capable of capturing the molecule-surface interaction accurately, it would be of interest to use
other dispersion corrected functionals such as optB88-vdW as it has shown utility for several
adsorption systems.

200

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