simulation of spectroscopic properties of atoms and molecules · “effects of bound electronic...

Simulation of spectroscopic properties of

atoms and molecules

Lalitha Selvam

Dissertation submitted in fulfilment of requirements for the degree of

Doctor of Philosophy

Faculty of Information & Communication Technologies

Swinburne University of Technology

Australia

2012

@

Copyright 2012

By

Lalitha Selvam

I

Abstract

Abstract

Chemical phenomena are largely determined by the behaviour of

electrons in atoms or molecules. Knowledge on electronic properties is of key

importance to understand chemical reactions. In this study, electronic structures

of molecules are studied from the perspectives of both coordinate space and

momentum space. The latter enables us to further simulate positron annihilation

spectra of noble gas atoms and small molecules under appropriate conditions.

The responses of perfluoro effects in benzene and structural

modifications in cytidine nucleoside analogues are revealed through

spectroscopic information, in addition to properties such as geometries, intra-

molecular interactions, vibrational spectra and atomic site dependent properties

such as, charges and Fukui functions. Simulated spectra and orbital momentum

distributions (MDs) are validated with the available experimental results. It is

observed that density functional theory (DFT) models, in combination with

adequate basis sets, are able to produce optimal results for various properties.

The orbital based signatures which are associated with the uniqueness of the

chemical bonding of the molecules are revealed. From electron momentum

distributions, we have calculated gamma-ray spectra for positron annihilation of

noble gas atoms and small molecules based on an innovative “low energy plane

wave positron” (LEPWP) approximation. We found that the annihilation line

shapes, ε, depend significantly on their principal quantum number n and orbital

angular momentum quantum number l of the noble gases, whereas in small

molecules, the innermost valence orbital was found to produce reasonable

agreement with the experiment.

II

Dedicated to my beloved parents

III

Acknowledgments

Acknowledgments

I am elated to record my deep sense of gratitude to Professor Feng Wang, who supervised my Ph.D., for her encouragement, generous support and valuable guidance, and for the suggestions she made throughout the course of my research. The skill and ease with which she guided me through my research ensured that I would become a confident researcher. I also feel honoured to express my gratitude to Professor Elena Ivanova for her continuous support. I would like to thank Dr. Patrick Duffy for reading my thesis and for improving my English. I also wish to give many thanks to Swinburne University for the financial support they provided in the form of a Postgraduate Research Award (SUPRA)

that made it possible for me to come from India to engage in research at the university.

I also wish to express my sincere thanks to Professors Richard Sadus and Billy

Todd for their continuous encouragement rendered throughout the duration of my study. I would like to thank Dr. Quan Zhu for our stimulating discussions. I am deeply indebted, and immensely grateful, to Dr. Vladislav Vasilyev of the Australian National University (ANU) for his collaboration on the 3D-pdf generation. I would like to acknowledge Dr. Scott Lee for providing me with the digital traces of experimental spectra. I would like to place on record my sincere thanks to all my colleagues and seniors for their useful discussions at the Centre for Molecular Simulation. Special thanks are due to Ms. Fangfang, Ms. Anoja and Mr. Aravind, who were always supportive throughout my candidature, for their company, moral support and friendship. My friends are also my real supporters. I would like to place on record my sincere thanks to them – Hema, Asha, Senthil, Kasthuri, Vani, Thillai, Srini, Hari,

Payel, Subha, Raji, Swarna, Laxman, Ram, Vinoth for their constant care and persuasive support.

I am without words to express my heart-felt thanks to my parents who

encouraged me to travel abroad and to be away from them for more than three years, in order to pursue (successfully!) my interest in my career. With tears, I thank my dad and mother who does not physically exist now, but their blessings will be there to give me strength to proceed further positively in life. Bounteous thanks to my sister Sangeetha, my uncle, our sweet princess Vaishalini@angel, nephew Ruban Bala and my brother, Vengadesh, for their mellifluous love and splendid understanding which gave me the zeal to complete my study in Australia. I would like to thank all the members of my family, uncles, aunties , kutties who encouraged me at each and every moment of my life.

IV

Declaration

Declaration

I hereby declare that the thesis entitled “Simulation of spectroscopic properties

of atoms and molecules”, which is submitted in fulfilment of the requirements

for the Degree of Doctor of Philosophy in the Faculty of Information &

Communication Technologies of Swinburne University of Technology, is my

own work and that it contains no material which has been accepted for the award

to the candidate of any other degree of diploma, except where due reference is

made in text of the thesis. To the best of my knowledge and belief, it contains no

material previously published or written by another person except where due

reference is made in the text of the thesis.

Lalitha Selvam

2012

V

List of Publications

List of Publications

1. Lalitha Selvam, Vladislav Vasilyev and Feng Wang “Methylation of

zebularine: a quantum mechanical study incorporating with interactive

3D PDF graphs” J. Phys. Chem. B. 2009, 113, 11496.

2. Fangfang Chen, Lalitha Selvam and Feng Wang, “Blue shifted

intramolecular C-H...O improper hydrogen bonds in conformers of

zidovudine” Chem. Phys. Lett. 2010, 493, 358.

3. Feng Wang, Lalitha Selvam, Gleb Gribakin and Clifford C. Surko “Shell

electron contributions to gamma-ray spectra of electron-positron

annihilation in rare gases under plane wave approximation” J. Phys. B:

At. Mol. Opt. Phys. 2010, 43, 165207.

4. Lalitha Selvam and Feng Wang “Solvent effects on blue shifted improper

hydrogen bond of C-HO in deoxycytidine isomers” Chem. Phys. Lett.

2010, 500, 327.

5. Lalitha Selvam, Fangfang Chen and Feng Wang “Methylation of

zebularine investigated using density functional theory”, J. Comp. Chem.

2011, 32, 2077.

6. Feng Wang, Lalitha Selvam, Gleb Gribakin and Clifford C. Surko,

“Effects of bound electronic wavefunctions to gamma ray spectra of

positron annihilation in atoms and molecules.” in 19th Australian

Institute of Physics Congress. 2010: Melbourne.

7. Feng Wang, Xiaoguang Ma, Lalitha Selvam, Gleb Gribakin and Clifford

C. Surko, “Chemical structural effects on γ-ray spectra of positron

annihilation of fluorobenzenes.” (Submitted)

VI

Contents

Contents

ABSTRACT .......................................................................................................... I

ACKNOWLEDGMENTS ................................................................................. III

DECLARATION ................................................................................................ IV

LIST OF PUBLICATIONS ................................................................................V

CONTENTS ....................................................................................................... VI

LIST OF FIGURES .......................................................................................... IX

LIST OF TABLES ...........................................................................................XII

LIST OF ABBREVIATIONS........................................................................ XIV

INTRODUCTION ................................................................................................1

1.1 Overview of the dissertation .....................................................................5

THEORY AND METHODS ...............................................................................7

2. Introduction ....................................................................................................7

2.1 Electronic structure theory ...........................................................................8

2.1.1 The Schrödinger equation ......................................................................8

2.1.2 Born-Oppenheimer approximation ........................................................9

2.1.3 Hartree-Fock and post Hartree-Fock methods .....................................10

2.1.4 Density functional theory.....................................................................11

2.1.4.1 LDA and GGA ..............................................................................12

2.1.5 Basis sets ..............................................................................................14

2.1.6 Basis set superposition error ................................................................17

2.2 Electron (Photoelectron) spectroscopy (PES) ............................................17

2.3 Electron momentum spectroscopy .............................................................20

VII

Contents

2.4 From electron to positron ...........................................................................21

2.5 Solvent effects ............................................................................................23

2.6 Computational details .................................................................................24

PES AND EMS OF PERFLUORINATED BENZENES................................25

3. Introduction ..................................................................................................25

3.1 Benzene and its chemistry ..........................................................................26

3.2 Validation of models employed..................................................................27

3.2.1 Orbital momentum distributions of benzene........................................29

3.3 Position space properties of fluorinated benzenes......................................31

3.3.1 Energies and geometries ......................................................................31

3.3.2 Aromaticity ..........................................................................................34

3.3.3 Dipole moment and Hirshfeld charges ................................................37

3.4 Ionization energies......................................................................................40

3.4.1 Valence ionization energy spectra .......................................................42

3. 5 Momentum space properties......................................................................48

3.5.1 Orbital momentum distributions ..........................................................48

3.6 Summary.....................................................................................................56

INTRAMOLECULAR INTERACTIONS OF CYTIDINE NUCLEOSIDE ANALOGUES.....................................................................................................58

4. Introduction ..................................................................................................58

4.1 Sugar modified nucleosides........................................................................59

4.1.1 Geometries in vacuum and solvent phase ............................................61

4.1.2 Hydrogen bond networks .....................................................................63

4.1.3 Infrared spectroscopy ...........................................................................65

4.1.3.1 Solvent effects on IR spectra.........................................................68

4.2 Interactions in base modified nucleosides ..................................................72

4.2.1 Property changes in d5 with respect to zeb..........................................73

4.2.2 Valence space responses to methylation ..............................................76

4.2.3 Methyl affected orbitals in momentum space ......................................80

VIII

Contents

4.3 Summary.....................................................................................................83

FROM ELECTRON MOMENTUM SPECTROSCOPY TO GAMMA-RAY SPECTROSCOPY .............................................................................................85

5. Introduction ..................................................................................................85

5.1 The LEPWA development and validation..................................................87

5.2 FWHM assessment for noble gases............................................................89

5.2.1 Bound electron shell contributions ......................................................91

5.2.2 Gamma-ray spectrum trends in noble gases ........................................98

5.3 Gamma-ray spectra of small molecules ...................................................101

5.4 Summary...................................................................................................105

SUMMARY AND OUTLOOK .......................................................................107

APPENDIX .......................................................................................................109

REFERENCES .................................................................................................116

IX

List of Figures

List of Figures Figure 3. 1 Comparison of orbital momentum distributions of the outer valence

orbitals of benzene based on B3LYP/TZVP wavefunctions with the EMS

momentum distributions.......................................................................................30

Figure 3. 2 Chemical structures of fluorinated benzenes and their relative

energies based on the B3LYP/TZVP model. .......................................................32

Figure 3. 3 NICS-rate as a function of distance for the fluorinated benzenes. ...35

Figure 3. 4 First ionization energies (eV) of fluorinated benzenes based on the 42

Figure 3. 5 Valence ionization energy spectra of C6F6. The simulated spectra

using OVGF/TZVP (middle panel) and SAOP/et-pVQZ (top panel) are

compared with experimental photoelectron spectrum [118] (bottom panel). ......43

Figure 3. 6 Simulated valence ionization energy spectra of perfluorinated

benzenes using SAOP/et-pVQZ calculation. The “spectral peak” of the LUMO is

also presented for the comparison of the HOMO-LUMO gap.............................45

Figure 3. 7 Orbital energy (- i) correlation diagram of perfluorinated benzenes

with respect to benzene based on SAOP/et-pVQZ model. ..................................47

Figure 3. 8 Comparison of momentum distributions of the highest occupied

molecular orbital (HOMO) of benzene and its fluorinated species. ....................49

Figure 3. 9 HOMO orbital density distributions of fluorinated benzenes. ..........50

Figure 3. 10 The third highest occupied orbital (1a2u-THOMO) of the

perfluorinated benzenes MDs and its orbital density distributions. .....................51

Figure 3. 11 The innermost valence orbital of benzene (2a1g) with the correlated

orbitals of the perfluorinated benzenes, as an MDs and as an orbital density

distributions. .........................................................................................................52

Figure 3. 12 Comparison of theoretical momentum distributions of orb itals in

the outer valence space of difluorinated benzene isomers, 1,2-C6H4F2 (solid line),

1,3-C6H4F2 (dashed line), 1,4-C6H4F2 (dotted line). ............................................54

X

List of Figures

Figure 3. 13 Comparison of theoretical momentum distributions of orbitals in

the inner valence space of difluorinated benzene isomers, 1,2-C6H4F2 (solid line),

1,3-C6H4F2 (dash line), 1,4-C6H4F2 (dot line). .....................................................55

Figure 4. 1 Chemical structures and nomenclature of the nucleoside isomers 2 ′-

dC and 3′-dC.........................................................................................................60

Figure 4. 2 Comparison of simulated IR spectra of 2 ′-dC and 3′-dC in vacuum.

..............................................................................................................................67

Figure 4. 3 Comparison of simulated IR spectra of isomers (a) 2′-dC and (b) 3′-

dC in various solvents with respect to vacuum. ...................................................71

Figure 4. 4 Chemical structures and atom numbering of zebularine (zeb) (left)

and 1-(β-D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5) (right). ......................72

Figure 4. 5 Comparison of Hirshfeld charges of zeb and d5 based on the

LB94/et-pVQZ model. .........................................................................................74

Figure 4. 6 Fukui function of zeb and d5 pair. ....................................................75

Figure 4. 7 Valence photoelectron spectra of zeb and d5 simulated using the

SAOP/et-pVQZ model. ........................................................................................77

Figure 4. 8 Energy correlation diagram of valence orbital energies of zeb and d5

based on SAOP/et-pVQZ. ....................................................................................80

Figure 4. 9 Methyl dominated orbitals of d5 with its electron density and

momentum distribution. .......................................................................................81

Figure 4. 10 Secondary methyl orbitals identified in d5 compared with their

analogues in zeb. The electron density and momentum distributions are shown

for all orbitals. ......................................................................................................82

Figure 5. 1 Comparison of the annihilation γ-ray spectra in the outermost shell

of He and Ar calculated based on the PW approximation using the standard

Hartree–Fock method [101, 215] (solid lines) with the present study: He (circles)

and Ar (triangles). All spectra are normalized to unity at ε = 0. ..........................88

Figure 5. 2 Comparison of the annihilation –ray spectra of the outermost shells

of noble gases calculated using the HF/TZVP model for atomic electron

XI

List of Figures

wavefunctions: He (), Ne (), Ar (), Kr () and Xe (). All spectra are

normalized to unity at ε=0 [22]. ...........................................................................91

Figure 5. 3 Comparison of atomic electronic shell contributions to the

annihilation –ray spectra of Ne, calculated using the HF/TZVP model for the

atomic wavefunctions and the plane-wave approximation for the positron: (a)

summed by orbital type, and (b) specific orbitals. ...............................................95


annihilation –ray spectra of Kr, calculated using the HF/TZVP model for the




annihilation –ray spectra of Ar, calculated using the HF/TZVP model for the



Figure 5. 6 Comparison of outer shell (ns, np and ns+np) electron contributions

with the experimental spectra (solid circles) for Ar. ............................................99


with the experimental spectra (solid circles) for Kr. ............................................99

Figure 5. 8 The ns electron contributions to the annihilation –ray spectra of He,

Ne, Ar, Kr and Xe, calculated using the HF/TZVP model. ...............................100

Figure 5. 9 Orbital contributions to the positron annihilation spectra of (a)

nitrogen (N2) and (b) ammonia (NH3) using the HF/TZVP model. ...................103

Figure A- 1. Core ionization energy spectra of the perfluorinated benzenes based

on LB94/et-pVQZ model. ..................................................................................111

Figure A- 2. Total momentum distributions of the perfluorinated benzenes. ...112

Figure A- 3. Orbital density distributions of cytidine nucleoside analogues zeb

and d5. ................................................................................................................114

XII

List of Tables

List of Tables Table 3. 1 Comparison of valence vertical ionization energies (eV) of benzene

calculated using various theoretical models and compared with experiment [91].

..............................................................................................................................28

Table 3. 2 Geometric properties of the perfluorinated benzenes based on the

B3LYP/TZVP model............................................................................................33

Table 3.3 The calculated NICS(0), NICSmax and rmax values for the fluorine

benzenes. ..............................................................................................................37

Table 3.4 Electric dipole moments (µ in Debye) of perfluorinated benzene

calculated using the B3LYP/TZVP model...........................................................38

Table 3. 5 Hirshfeld charges (QH) of the benzene derivatives based on LB94/et-

pVQZ (a.u.). .........................................................................................................39

Table 3. 6 Calculated first ionization energies (eV) of perfluorinated benzenes

with the experimental results. ...............................................................................41

Table 4. 1 Geometric parameters of 2′-dC and 3′-dC in vacuum and in different

solvents with varied dielectric constants ()*. .....................................................62

Table 4. 2 Distances of C− H∙∙∙O, C− H∙∙∙ N and O− H∙∙∙O networks of 2 ′-dC

and 3′-dC in various solvents (Å).........................................................................64

Table 4. 3 Comparison of experiment with simulated vibrational frequencies of

2′-dC. ....................................................................................................................66

Table 4. 4. Infrared frequencies (v, cm-1) and assignment of nucleosides 2′-dC

and 3′-dC in vacuum and various solvents. ..........................................................69

Table 4. 5 Comparison of valence orbital ionization energies (eV) of zeb and d5

calculated using different models*. Methyl affected orbitals are underlined. .....78

Table 5. 1 Comparison of the FWHM of annihilation –ray spectra, ε (keV),

for noble gases based on the HF/TZVP model for the atomic electrons [22]. .....90

XIII

List of Tables

Table 5. 2 Bound electron shell contributions to the positron annihilation -ray

spectra (ε in keV) of the noble gases based on the HF/TZVP model for atomic

electron wavefunctions.........................................................................................92

Table 5. 3 Bound electron shell contribution and total FWHM of annihilation γ-

ray spectra, ε (in keV) for noble gases based on different methods. .................94

Table 5.4 FWHM of annihilation -ray spectra, (keV), for inorganic

molecules (valence space). The symbol * indicates degenerate orbitals. ..........102

Table 5. 5 FWHM of annihilation -ray spectra, (keV), for partially and fully

fluorinated hydrocarbons. *The orbitals are in the order of their energies. .......104

Table A- 1. Optimized geometric and electronic properties of the fluorinated

benzenes* ...........................................................................................................109

Table A- 2. C1s ionization energies of perfluorinated benzenes based on

LB94/TZVP model. Experimental IPs are in parenthesis [113]. Carbons

connected to fluorine atoms are underlined. ......................................................110

Table A- 3. Vibrational frequency shift of 2′-dC (3′-dC) nucleosides in solvents

with respect to vacuum (cm-1). ...........................................................................113

Table A- 4. Symmetry and electronic configuration of inorganic molecules and

fluorinated hydrocarbons....................................................................................115

XIV

List of Abbreviations

List of Abbreviations 6-31G* Triple split valence basis set with six Gaussian functions for

core and three primitives, containing three, one contractions respectively, for valence shell

6-311G** 6-311G with doubly added polarised functions 2’-dC 2’-deoxycytidine 3’-dC 3’-deoxycytidine ADC Algebraic-diagrammatic construction ADF Amsterdam density functional aug-cc-pVQZ

augmented basis set of correlation consistent polarised valence with quadruple zeta

B3LYP BO

Becke, three-parameter, Lee-Yang-Parr hybrid functional Born-Oppenheimer approximation

CC Coupled cluster CCSD(T) Coupled-cluster single and double excitation with triples CEBE Core-electron binding energies CI Configuration interaction DFT Density functional theory DNA Deoxyribonucleic acid DSA Dual space analysis EMS Electron momentum spectroscopy et-pVQZ Even tempered valence quadruple zeta with polarization

function FWHM Full width at half maximum GGA Generalized gradient approximation GTO Gaussian type orbital HOMO Highest occupied molecular orbital HF Hartree-Fock IP Ionization potential IR Infra red LB94 Exchange correlation functional of Van Leeuwen and

Baerends LDA Local density approximation LEPWA Low-energy plane wave approximation LUMO Lowest unoccupied molecular orbital MBPT Many body perturbation theory MD Momentum distribution MEP Molecular electrostatic potentials MO Molecular orbital MP Møller-Plesset NEXAFS Near-edge X-ray absorption fine structure

XV

List of Abbreviations

NHOMO Next HOMO OVGF Outer valence green function PCM Polarizable continuum model PES Photoelectron spectroscopy PWIA Plane wave impulse approximation RNA Ribonucleic acid SAOP Statistical average of orbital potentials STO Slater type orbital THFA Target Hartree-Fock approximation TKSA Target Kohn-Sham approximation TZVP Triplet zeta valence polarized UPS Ultraviolet photoelectron spectroscopy VIEs Vertical ionization energies VWN Vosko, Wilk and Nusair XC Exchange correlation XPS X-ray photoelectron spectroscopy

1

Introduction

CChhaapptteerr 11

Introduction

1. Introduction

Electronic structures are crucial for the behaviour of molecules such as

drugs and proteins. The accurate knowledge on electronic properties is of central

importance in understanding the reactivity and functionalities of molecules.

Structure dictates function. Structural properties provide information about the

complex biological processes. From a chemical point of view, a molecule is an

aggregation of nuclei and electrons linked through chemical bonds. Nuclei and

electrons are the fundamental particles that determine the nature of matter.

In 1900, Max Planck [1] postulated that energy could be emitted only in

quantized states, which basically triggered the development of quantum theory.

This breakthrough assisted in understanding the experimental data, such as the

position and source of spectroscopic peaks. Spectroscopy is concerned with the

absorption and emission of light by matter. Since the observation of spectra of

molecules is a very important method of measuring the properties of a quantum

system, spectroscopy was of extreme importance in the development of quantum

theory and with it, of the whole of science. But the usefulness of spectroscopy

lies not only in the power to verify quantum theory. Once the spectra of the

molecules of interest are known, it also allows the identification of the

composition of a substance, an ability which is of importance in almost all the

natural sciences. Chief among them is astronomy, which completely lacks the

2

Introduction

possibility of experiments and has to rely, for a large part, on spectroscopy to

verify its theories. It is no wonder that many scientific fields evolved together

with the understanding of spectroscopy.

Computational chemistry is a cornerstone application of modern

theoretical chemistry and has the potential to study various properties of

molecules that are difficult to determine experimentally. It covers various

theoretical methods which often can be defined as modelling chemistry based on

the atomic or molecular descriptions. Quantum mechanics is the theory from

which computational chemisty has been developed to study matters at the atomic

and molecular levels. After decades of success in the study of the structural

properties of various molecules using quantum mechanical methods, the

challenges in the application of such techniques to larger molecules are largely

due to algorithm and computational resources. However, significant advances in

computational power, combined with developments in algorithms promise to

tackle the structural problems of larger bio-molecules such as nucleic acid bases

and nucleosides in detail with spectroscopic accuracy [2].

In quantum mechanics, the static and dynamic behaviours of molecules

are described by the distribution of electrons. The shell-related electron

distribution gives a picture of a molecular orbital, which directly connects to the

chemical behaviour of a molecule. Molecular orbital theory is fundamental in

chemistry for understanding the molecules and their interactions [3]. Coulson [4]

stated that “the energy is not the only goodness of a wave function and in the

past we have been preoccupied with energy”. Molecular orbitals (and

wavefunctions) have been recognised as shelled electron density qualitatively. It

took decades for electron momentum spectroscopy (EMS) to make it possible to

quantitatively measure the wavefunctions (orbitals) of a molecule as cross

sections in momentum space [5, 6]. EMS is still the only technique available for

making quantitative measurements of molecular orbitals (orbital cross sections)

and binding energies in momentum space, and it has also been proven to be an

3

Introduction

excellent method by which to assess the quality of wavefunctions and, therefore,

the accuracy of quantum mechanical models [7].

Theoretically, EMS is also a powerful and comprehensive orbital and

energy based tool. Through dual space analysis (DSA) as developed by Wang [7],

EMS links with molecular orbital theory. The anisotropic nature of orbital- based

properties provides very useful information for the differentiation of isomers and

conformations which largely exist in organic and biomolecular systems [8].

Recently, EMS was applied to study valence electronic structures of pyrimidine,

a DNA base analogue [9]. The results which are obtained through EMS, when

combined with other information such as photoelectron spectra (PES), provide

powerful experimental support for the development and validation of higher

level theoretical models to study biomolecules such as the building blocks of life.

In return, such high level theoretical models can be further applied to study other

properties of molecules. For example, a number of biologically important

building blocks of life, such as uracil and methyluracils [10], cytosine, thymine

and adenine [11], purine and pyrimidine [12-18] have been studied recently

using this processes. Cutting-edge instrumental development, such as

synchrotron-sourced spectroscopy, pushes experimental front into higher and

higher resolution, leading to more detailed information which requires

significant theoretical knowledge and understanding at the molecular level. As a

result, the importance of experimental and theoretical collaboration has reached a

new level.

Electronic properties of molecules can be described by position space (r-

space) and momentum space (k-space). Orbital momentum distributions (MD)

can be calculated quantitatively, either in momentum space by solving the

Schrödinger equation in momentum space, or, more commonly, by Fourier

transforming the wavefunction obtained from position space by solving the

Schrödinger equation in position space. The orbitals as electron density in

position space exhibit different aspects when compared with the same orbitals as

momentum distributions, similar to different sides of a coin. The dual space

4

Introduction

analysis (DSA) [7], therefore, is able to provide additional dimensions of the

structure and chemical bonding information of molecules to enhance

understanding thereof [19]. As a result, the DSA has been applied to study

various biomolecular conformers and isomers [8, 20, 21].

A natural extension of EMS is gamma-ray spectroscopy. We recently

developed a low-energy plane wave approximation [22, 23] (LEPWA) to study

gamma-ray spectroscopy in the positron-electron annihilation in molecules.

Measurements of the annihilation gamma-rays and their spectra are used in a

variety of fields, including medicine and drug design, where positron emission

tomography (PET) is used to monitor metabolic and other biological processes

[24], and in materials science, where positron annihilation is used to characterise

materials and material surfaces. Positron-electron annihilation in molecules may

provide an innovative avenue to study electron-electron interactions and

ionization processes of molecules. Positrons are used for various purposes such

as studying the surfaces of materials and measuring both defect fraction and the

porosity of manufactured materials in material science. One exciting sc ientific

pursuit is the production, trapping and eventual spectroscopy of cold ant-

hydrogen [25-27]. Recently, gamma-ray emission has been measured to observe

the chances of thunderstorms occurring [28].

In this thesis, diverse spectroscopic properties have been studied for a

number of atoms and molecules using theoretical means, in collaboration with

experiments. Observation of spectra of molecules is very important for the

identification of the new species, and the acquisition of an understanding of the

properties and structures of the species. Accurate prediction of electron spectra

of molecules is essential for the comprehension of the information of their

structures and, therefore, properties. However, theoretical interpretation of the

spectra of many larger molecules remains as a series of challenges. For example,

quantitative treatment of the near-edge X-ray absorption fine structure

(NEXAFS) spectra for even small bio-molecules such as amino acids [29] and

DNA bases [30-32] is not yet fully understood. Therefore, theoretical studies are

5

Introduction

important and necessary for the simulation of spectroscopic properties to achieve

insight into a number of molecules.

1.1 Overview of the dissertation

This thesis focuses on detailed molecular level understanding of atoms

and molecules through various spectroscopic techniques such as photoelectron

spectroscopy, electron momentum spectroscopy and gamma-ray spectroscopy.

The present study will focus on:

Investigating the effect of fluorination in benzene by dual space

analysis.

Exploring the structure-property relationships of cytidine

nucleoside antibiotics.

Theoretical calculation of positron annihilation of atoms and

molecules from electron momentum spectroscopic information.

Chapter 2 outlines the theoretical aspects of quantum chemistry related to

electronic structural calculation of molecules. It gives the details of theories and

methods used in the calculations of electron and positron wavefunction of atoms

and molecules in this thesis.

Chapter 3 reports the substitution effects of fluorine at various positions

(ortho, meta and para) in the benzene, a model molecule. Fluorine is an

electronegative atom with a high number of medicinal applications against a

number of diseases [33, 34]. Various electronic structural properties and trends

of perfluorinated benzenes are investigated in both position and momentum

space representation. The impact of fluorine substituent in benzene is explained

through valence orbital momentum spectroscopy. We report the trends and

properties of series of fluorobenzenes (C6H6-nFn, n=1-6), besides aromaticity of

the species. The positional isomer dependence of di-, tri- and tetra- fluorinated

benzene are revealed through ionization energy spectra and orbital momentum

distributions.

6

Introduction

Chapter 4 concentrates on larger biomolecules such as cytidine

nucleoside analogues. The analogues are basically modified in base or sugar

moieties to achieve certain properties such as higher potency and lower toxicity.

Intramolecular interactions between the base and the sugar moieties in

nucleosides are very important interactions for the functionalities of drugs as

well as functional groups of DNA and RNA. Such interactions are studied in

both gas and solvent phases to mimic biological environments. Orbital-based

analysis has been carried out in the gas phase to identify the effects of functional

groups in the base of the nucleosides.

Chapter 5 presents the theoretical calculation of positron annihilation

with gas phase atoms and molecules, under low-energy plane wave

approximation. The development of the relationship between the gamma-ray

spectra and the EMS spectra under this approximation is given in the cases of

rare gases. In this chapter, we further applied this approximation to study small

molecules with available experimental measurement, in order to assess

theoretical models, such as exchange-correlation, as well as basis sets. Study of

positron opens an innovative opportunity to study electrons and their correlation

interactions in molecules.

7

Theory and methods

CChhaapptteerr 22

Theory and methods

2. Introduction

This chapter provides basics on theory of the various methods and

models in the present study. It will emphasise their strengths, applications,

weaknesses and limitations. However, this chapter will not cover the underlying

theory in detail.

In the beginning of 1900s, development of quantum mechanics (QM)

made it possible to calculate the properties of atoms and molecules. Paul Dirac

[35] stated that,

“The fundamental laws necessary for the mathematical treatment of a

large part of physics and the whole of chemistry are thus completely known, and

the difficulty lies only in the fact that application of these laws leads to equations

that are too complex to be solved”.

As modern computers were not available to solve the complex equations,

the application of quantum chemistry was limited in those early days. However,

the advent of sophisticated development in algorithm and computers such as

supercomputers has made computational chemistry more accessible to deal with

the complex systems. Computational chemistry comprises wide range of theories

and methods. In the present study, choices have been made on methods

according to best suit our problems.

8

Theory and methods

2.1 Electronic structure theory

Electronic structure methods are mainly based on the laws of quantum

mechanics rather than classical mechanics. Electrons are small particles, which

follow quantum mechanical laws. QM derives properties based on the

distribution of electrons. Thus the electron distribution in an orbital is directly

connected to chemical nature and interactions which provide information to

understand the molecules [3]. The elucidation of electronic structure is primarily

solved by the Schrödinger equation and a set of development of other theories.

2.1.1 The Schrödinger equation

Schrödinger equation was formulated by Erwin Schrödinger in 1926 [36],

and plays the key role in quantum mechanics. It describes how the quantum state

of a system changes with time. The Schrödinger equation (eigenvalue problem)

of a steady atomic or molecular system can be written as:

2. 1

where H is the Hamiltonian operator that represents the total energy operator and

E symbolizes the energy associated with the wavefunction. Here ψ is the solution

of the Schrödinger equation, that is, the wavefunction, which describes the

positions of electrons and nuclei within a molecule. The Hamiltonian in equation

(2.1) differs according to the specific physical situation.

The Hamiltonian operator is composed of two parts that reflects the

contribution of kinetic (T) and potential (V) energy terms:

2. 2

The kinetic energy operator is given by:

2. 3

9

Theory and methods

Here ħ is the Planck constant, m is the mass of the particle and is the

Laplace operator. The kinetic energy basically deals with the motion of the

electron of the molecular system.

Here the potential energy term of the coulombic interaction are

represented as:

2. 4

In the above equation, uppercase letters (I and J) denote nuclei whereas

lowercase (i and j) are used for electrons. Z is an atomic number and e is the

charges on the electron, where r and R is the distance between the two

particles. As the Schrödinger equation does not possess exact solutions,

approximations at different levels of theory are made to solve the equation.

Therefore, QM required the development of many approximations.

2.1.2 Born-Oppenheimer approximation

The first approximation derived to simplify the Schrödinger equation is

the Born-Oppenheimer (BO) approximation [37], which serves as a vehicle to

separate the motions of larger nuclei and smaller electrons. In a system, it is

assumed that electrons move much faster than nuclei due to the smaller mass of

electrons. Thus, at each movement of the nuclei, the fast moving electrons are

able to instantly adjust themselves so that one can consider that the electrons

move in a field of the nucleus in a fixed position. Under this approximation, the

kinetic energy term for the nuclei in the Schrödinger Hamiltonian equation can

be separated out so that one can write the electronic Schrödinger equation as,

2. 5

This approximation makes it computationally feasible to solve the electronic

Schrödinger equations. Subsequently, various theories have been developed to

calculate the electronic structures of systems.

10

Theory and methods

However, when dealing with heavy elements, the BO approximation may

break down at the time of computation exceeds its limit while calculating

molecular wavefunctions of larger molecules. As in this thesis, the elements

include hydrogen, carbon, nitrogen, oxygen and fluorine without heavy elements,

BO approximation will be applied.

2.1.3 Hartree-Fock and post Hartree-Fock methods

Hartree-Fock (HF) and post Hartree-Fock methods, which are also called

ab-initio methods as they do not involve empirically or semi-empirically

determined parameters, are widely used QM methods. The electronic

Schrödinger equation calculates the energy of an electron in the presence of all

other electrons, based on the independent particle approximation, also known as

molecular orbital theory. That is, in the HF theory, the electrons in a molecule

are assumed to be independent of one another by a series of one-electron

function called orbitals. Therefore, the total n-electron HF wavefunction is

expressed as a single anti-symmetric Slater determinant composed of one-

electron functions called spin orbitals, a product of spatial orbital and a spin

function (α or β).

The HF method is one of the approximations in QM, which solves the

electronic Schrödinger equation. The disadvantage of this method is that it

neglects the electron-electron correlation, , term in the potential energy

function and therefore, the HF method over estimates the total energy of the

system. The energy difference between the Hartree-Fock energy and the energy

calculated by the full electronic Schrödinger equation is called the correlation

energy ( which is defined as,

2.6

Here is the exact non-relativistic energy of the system and

is the Hartree-Fock energy. In practice, is not known and must be

approximated. As the correlation energy is of great significance in the

determination of accurate wavefunctions and therefore the properties of system,

11

Theory and methods

improvement of the Hartree-Fock energy through the inclusion of various

degrees of electron correlation energy dominates the development of quantum

mechanics in the past decades and still continues.

Post HF methods have been developed to improve the correlation energy

issues. Different approaches which are classified in the post HF methods include

configuration interaction (CI), many body perturbation theories (MBPT) and the

coupled cluster methods (CC). In this study, we applied MBPT (or MP) and CC

methods when applicable; hence the primary concerns about these methods will

be discussed.

The basic principle underlying in the MBPT is perturbation theory that

was developed by Moller and Plesset [38]. It is based upon the assumption that

the effects of correlation can be regarded as perturbation to the all-electron Fock

operator. The most accessible one is the Moller-Plesset method, which is the

second order MBPT and commonly known as MP2. Another robust method is

the CC with single and double excitation models with a perturbation correction

for triples, known as CCSD(T). Both the methods are able to produce results of

high accuracy. The major limitations of these methods are computationally

demanding and time consuming, which restrict their applications to larger

molecules such as nucleosides. As a result, MP2 [39, 40] and CCSD(T) [41]

methods are applied in this work for atoms and small molecules, which will be

discussed in Chapter 5.

2.1.4 Density functional theory

Density functional theory (DFT) offers alternative and a different

approach to the HF and post-HF methods. It is based on the electron density,

rather than the many-electron wavefunction [42]. Unlike wavefunction,

electron density is an observable physical quantity. DFT methods often produce

results of comparable accuracy at reasonable computational cost than much more

expensive post HF methods. The advent of modern computational method DFT

has offered great opportunities for the electronic structural studies [43].

12

Theory and methods

In 1964, Hohenberg and Kohn [44] introduced and proved two theorems.

One such theorem is the total energy of a system with n electrons can be

expressed as a functional of the electron density. The second one further proved

that the ground-sate density is the one that yields the lowest energy minimum.

Although Hohenberg and Kohn proved that it is possible to calculate the energy

from the density, it does not provide explaination how such calculations could be

done. Kohn and Sham (KS) in 1965 [45], showed the first step to make DFT

computationally viable by assuming a fictitious system of n non- interacting

electrons have a total density equal to the system of interest. The Kohn-Sham

equation of electron probability density is given by:

d 2. 7

where is the kinetic energy, is the classical coulomb repulsion energy

and d is the potential energy from any external fields .

is the exchange-correlation functional (XC), which includes exchange energy

and correlation energy due to the correlated electronic motion.

In the KS formulation, the exchange-correlation functional (XC), cannot

be calculated exactly so that how to fomulate the Exc term becomes challenging.

As a result, a number of approximations/formulations are introduced at various

levels and applications. The efficient development of the XC functionals is the

key for the success of DFT. In the next sections, we will discuss some selected

but milestone functionals in the development of DFT.

2.1.4.1 LDA and GGA

The DFT methods are generally categorised as local and gradient-

corrected/non- local functionals. The former depends only on the local

density.The simplest and widely used local exchange functionals is the local

density approximation (LDA). It assumes in LDA that exchange-correlation

energy per elecron in a homogeneous electron gas treats the electron density

locally. Later, local spin density approximation (LSDA) replaced LDA, since

13

Theory and methods

LSDA considers both the total density and a spin polarization function. An

another functional in this category for a uniform electron gas has been developed

by Vosko, Wilk and Nusair (VWN) [46].

As the local functionals uses only density, it underestimates the

interactions due to other atoms. For this reason, the generalized gradient

approximations (GGA) which go beyond the LDA approach were introduced. in

GGA, both the density and gradient of the density are considered. One of the

earliest and most popular GGA exchange functionals was first proposed by A. D.

Becke (B or B88) as a correction to the LSDA exchange energy [47]. Another

popular GGA method is Becke-Perdew (BP86), comprises the Becke exchange

[47] and Perdew86 [48] correlation potentials.

As the Exc in DFT methods are not know exactly, DFT methods improve

the performance from the HF methods due to the inclusion of the electron

correlation energy. However, the exchange energy in the HF method becomes

partially included in the DFT methods. As a result, one deveoped a class of

functionals as hybrid non-local functionals, in which the exchange energy is

given exactly, according to the HF treatment. It is considered to be robust,

perhaps it balances some of the weaknesses of DFT and HF methods. One of

most important hybrid DFT mdethod is called the Becke’s three parameter

hybrid functional known as B3LYP [47]. It is defined as:

a

a

a

2. 8

where a0 = 0.20, ax = 0.72 and ac = 0.81 are the three empirical paramaters;

and are the generalized gradient approximation formulated with the Becke

88 exchange functional [47] and the correlation functional of Lee, Yang and Parr

[49] and is the VWN correlation functional [46]. As many of the DFT

methods include functional which contain emprically determined parameters

such as the B3LYP, some prefer not to call DFT methods as ab initio methods.

Nevertheless, the success of the B3LYP method in a variety of predictions and

14

Theory and methods

systems, has made it the most commonly used hybrid functional in the DFT

literature. As predicted by Prof. W. T. Yang in 2009 in a private conversation

with Prof. Wang, that the position of B3LYP method in DFT would be hardly

replaced by other methods in the forseeing next few years.

In this thesis, the DFT based B3LYP method has been employed as the

major DFT method in the optimization and frequency calculations. Other

properties such as ionization spectra are simulated using the other improved XC

potentials with correct asymptotic behaviour such as orbital-dependent SAOP

(statistical average of orbital potentials) [50-52] and the LB94 (Van Leeuwen-

Baerends potentials) [53, 54] have been used in this work.

2.1.5 Basis sets

In any of the above mentioned methods, the first step is to solve the

electronic Schrödinger equation for the atomic or molecular wavefunctions. As

the wavefunction, ψ, is in the both sides of the eigenvalue equation (2.5), which

can only be resolved iteratively, starting from an initial guess. One of the most

useful methods is to expand the unknown wavefunction as a linear combination

of a set of known functions, called basis functions or basis sets,

2. 9

Here i=1,2,3,…n for the basis set which is a set of known functions such as

atomic hydrogen functions (Slater basis set) [55] or Gaussian basis set [56].

Mathematically, the solution of equation (2.5) becomes to diagonalize the

matrix for a set of coefficients, {Ci}. Appropriate basis set { } will be selected

based on the properties to be studied, the size of the system and the

computational resources available. Besides, the type of basis set used will largely

influence the accuracy of results. There are two types of basis sets such as Slater

type orbitals (STO’s) and Gaussian type orbitals (GTO’s). STO’s was first

developed by J. C. Slater [55]. They are exponentially dependent on the distance

between the nucleus and electron. They were primarily used for atomic and

15

Theory and methods

diatomic systems and not suited for three or four centred atoms for mathematical

reasons. An alternative approach to solve these three or four centred systems is

the use of Gaussian functions which was introduced by S. F. Boys [56]. It uses

the properties of Gaussian functions such as a product of two Gaussians

functions on different centres that gives a new Gaussian centred at a new

position in space; thereby the three and four centre integrals are reduced to two

centre integrals.

The advantage of GTOs is that the evaluation of the necessary integrals is

so much simpler mathematically than the STOs. However, this situation is

changed recently, due to the mathematical breakthrough in STO algorithm. As a

result, a number of STO basis sets are available - for example even-tempered

(ET) basis sets such as DZP, QZ3P, QZ+5P and pVQZ -- have been developed

and implemented in the Amsterdam Density Functional (ADF) computational

chemistry package [57], which speeds up the computation significantly. Even-

tempered basis sets have the advantage of relatively fewer optimization

parameters; therefore its development becomes more easy and systematic than

conventional basis sets. The other advantage is that STOs are relatively more

convenient to study the basis set limit due to the minimum risk of over

completeness problems [58]. The quality of basis sets should be considered

essentially for the properties to be compared and the molecules studied.

A range of basis sets are applied in this thesis in consideration with the

size of the system and the properties accounted for the study. It is necessary for a

basis set to both describe the changes in electron density and to resolve the

effects of dynamical electron correlation. A minimal basis set, in principle, gives

a good description of the atom (or a more complex system). However, neither it

can adequately describe the changes in the orbitals due to bonding (such as

contraction and polarisation), nor account for electron corre lation. As a result,

split GTOs are employed, using two or more contracted GTO’s (rather than just

one) to describe each atomic orbital; this leads to double-(DZ), triple-(TZ), etc.

basis sets. In order to obtain an appropriate description of a system ideally an

16

Theory and methods

infinite- basis set would be needed, however in reality; a compromise must be

made between the required accuracy, the time consumption and the availability

of computational resources. The triple zeta valence polarization basis set (TZVP)

[59] is used for atoms and small molecules in this study. This basis set has been

reported to produce the molecular orbital momentum distributions of molecules

and found to agree with the experimental measurements [60].

Other GTO basis sets used in this thesis are split valence basis sets: (1)

the Gaussian type basis functions of Pople and co-workers [61-63] and (2) the

correlation basis sets developed by Dunning et al. [64-67]. The Pople’s Gaussian

basis sets have their unique names such as 6-31G* and 6-311+G**. The former

basis set (6-31G*) is a valence double-zeta polarized basis set consisting of 6

primitive Gaussian functions for core electrons and 3 separate functions for

valence electrons, one for contraction, and ‘*’ indicates polarization (d) function.

The latter, valence triple-zeta basis set (6-311+G**), includes ‘**’ polarization

(d,p) function and ‘+’ refers to the diffuse functions. Both 6-31G* and 6-

311+G** basis sets are used in this work.

Dunning’s correlated consistent (CC) basis sets have different names,

such as cc-pVTZ and its augmented basis set aug-cc-pVTZ has been used in the

present study. The 'cc-p', denotes correlation-consistent polarized’, the ‘V’

indicates valence-only and TZ means triple-quality have the composition [5s,

4p, 2d, 1f]. The inclusion of diffuse functions in correlation consistent basis sets

is indicated by the prefix “aug-”. For a number of molecular properties, the cc-

pVTZ basis set is believed to be superior than the 6-311+G(**) basis set due to

the significant improvements in the description of the electron correlation

energy.

In the present study, we also employ STO based basis set such as et-

pVQZ, which is an improved even tempered (ET) slater type basis set developed

by Chong [58]. This basis set yields good results due to reduced basis set

17

Theory and methods

superposition errors. It is also computationally efficient as it contains fewer

functions than the GTOs to achieve the equivalent accuracy.

2.1.6 Basis set superposition error

If the basis set used is finite (hence incomplete), when the atoms interact

with the basis set allocated to each of them will overlap. This overlapping gives

the electrons a greater freedom to localize and consequently results in lowering

its energy. This lowering energy is therefore an artefact of working with limited

basis sets. This is called the basis set superposition error (BSSE) [68]. To correct

the BSSE, the most common approximation used is counterpoise (CP)

correction. These corrections are larger and more sensitive in case of electron

correlation methods. However, BSSE is expected to become smaller with

increasing basis set size and hence larger the basis, the results will be more

reliable.

If the properties to be studied are transitions such as spectral line energies,

the BSSE introduced can be cancelled to a large extent so that the BSSE caused

errors are small.

2.2 Electron (Photoelectron) spectroscopy (PES)

Spectroscopy can be defined as the study of interaction of atoms or

molecules with radiation. Spectroscopic studies were fundamental to the

development of quantum mechanics to explain several properties such as the

electronic structure, bonding nature and chemical composition of molecules.

Photoelectron spectroscopy is an important spectroscopic technique to study the

electronic structure of molecules, which is based on the photoelectric effect and

given as [69]:

2. 10

Where I is the vertical ionization energy (VIE) or the binding energy of an

electron used to attach to an atom or a molecule. When a photon source hv, is

18

Theory and methods

monoenergetic with the known wavelength and a small natural width, the kinetic

energy of the ejected electron Ee is measured with precision. Therefore the

binding energy can be determined.

Other spectroscopies are classified based on their radiation sources such

as X-ray (XPS) or Ultraviolet (UPS) or by the category of electrons ionized i.e

core or valence [70]. The rapid development in the field of spectroscopy ensures

us to measure spectroscopy of larger biological molecules from valence space to

core space, which brings challenges to spectral analysis such as assignment and

interpretation. Due to the fact that the signals of larger biomolecules are very

complex and therefore, theoretical support in this area has never been so

demanding. The major challenge in the experimental technique is the energy

source or resolution, which results in the congested spectra, limits capability for

detailed understanding. Therefore, the significant contribution from theoretical

calculations helps us to assign the spectra of molecules for comparable accuracy.

Energy required to remove an electron from the molecule is termed as

ionization energy. Strictly speaking, the Dyson orbitals (also known as ionized

orbitals) are the solution of the Dyson equation [71, 72], rather than the solutions

of the HF equations or the KS equations. The algebraic-diagrammatic

construction (ADC) [73-75] methods have been a powerful tool to study the

excitation and ionization spectra of molecules [76]. However, significantly the

computational costs for even medium sized molecules have unfortunately

restricted the applications of the ADC models to larger molecules such as

nucleosides. The outer valence Green’s function (OVGF) [77, 78] model is

therefore, an alternative development for the calculation of outer valence

ionization potentials for small to medium molecules [79, 80]. However, the

OVGF model does not have the capability for the ionization energies for inner

valence space and core space. In addition, the OVGF is derived for the ionization

energies; the corresponding Dyson orbitals are not available in this model.

A number of approximations are therefore, applied in order to estimate

the ionization energies for larger molecules to assist experimental analysis and

19

Theory and methods

interpretation. The most popular approximation is the Koopman’s theorem [81],

which is based on the HF theory. According to Koopman’s theorem, ionization

energies are approximately equal to the positive eigenvalue of an electron in an

occupied molecular orbital obtained from the Hartree-Fock theory.

The physical significance of KS orbitals and orbital energies has been a

long debate, which the present work will not detail here. Although many

researchers do not consider that KS orbitals even should be called orbitals in the

sense of molecular orbitals, the KS orbitals are constantly considered by many

other researchers as molecular orbitals with physical significance. For example,

the HF and KS orbitals of n-butane [60, 82] have been proven to be similar in

momentum space quantitatively. However, the orbitals energies of the KS

orbitals are not the negative of ionization energies, except for the highest

occupied molecular orbital (HOMO), for which the Janak theorem applies [83].

The HF orbital energies overestimate the ionization energies whereas the

KS orbital energies underestimate the VIEs. Due to the lack of accurate

theoretical models for larges molecules, some researchers [60, 84-86] used the

simply mean of the HF orbital energies and the corresponding KS orbital

energies to estimate the ionization energies for comparison with experimental

measurements.

The Nakai group at Wesada University has developed a model called

CV-B3LYP to calculate ionization energies of molecules accurately [87], which

recently applied to calculate the ionization energies of nucleoside, cytidine [88]

with a success. On the other hand, the development of DFT functionals such as

SAOP [89] and LB94 [54] which are both available in the ADF computational

package [57], employing the “meta-Koopman” theorem [52]. The DFT based

models have been applied promisingly to a number of biomolecules from

medium to larger sizes [20, 71, 79, 80, 90, 91], in addition to the OVGF model,

the DFT based models covers core and inner valence space of the ionization

energies with their orbital information available to further understand their

chemical bonding.

20

Theory and methods

2.3 Electron momentum spectroscopy

Electron momentum spectroscopy (EMS) is unique, since it measures

binding energies as well as orbital electron density distributions [92, 93]. EMS is

a binary (e, 2e) experiment in which an incident electron with high energy (E0)

induces ionization of molecular target. The scattered and ionized electrons are

subsequently detected in coincidence at equal kinetic energies and equal polar

angles, that is, E1 ≈ E2 and θ1=θ2 = 45° and therefore equal momentum p1 ≈ p2.

The initial momentum p of the ionized electron obeys, therefore,

n n

1/2 2. 11

where p0 is the momentum of the incident electron and φ is the azimuthal angle

between the two outgoing electrons. θ is the pseudorotational angle that is

different the azimuthal angle. Considering the BO approximation for the target

and ion wavefunction, the triple differential EMS cross-section for randomly

oriented molecules is given by,

d

2. 12

where K is a kinematical factor which is constant in the experiment, p is the

momentum of the target electron at the instant of ionization. and

are

the final ion f and the target molecular ion i of the ground electronic states. The

overlap between the initial and final electronic functions is termed as the one

electron Dyson orbital. The Dyson orbital can be approximated to HF orbitals

using target HF approximation (THFA) or Kohn Sham orbitals using target Kohn

Sham approximation (TKSA) at the level of Koopman’s theorem. Therefore, the

eq. 2.12 is further simplified as,

d

2. 13

, represents the Kohn Sham orbital in momentum space by fourier

transforming the wavefunctions from position space and

is the spectroscopic

21

Theory and methods

factor, denotes the probability of the one electron configuration in the final ion

wavefunction.

Theoretically, in DFT , the orbital in momentum space is

approximated by the Kohn-Sham (KS) orbitals of the ground electronic state

[94]. The advancement in the calculation of theoretical momentum profiles using

DFT has allowed high level of accuracy. As DFT calculations include a certain

degree of the electron correlation effects, the DFT models, with the required

accuracy and computational advantages, can be particularly applied to larger

molecules where post HF methods are not feasible. Wavefunctions are obtained

from position space using computational chemistry packages such as Gaussian03

and ADF in position space, which are Fourier transformed into orbital

momentum distributions in momentum space by using a package called NEMS

program [95].

2.4 From electron to positron

In momentum space, the probability of electron density distributions is

presented using momentum distribution of electrons. A natural development in

this direction is the Compton profile and gamma-ray spectroscopy [93]. A

positron is the anti-particle of an electron with positive charge and exactly the

same mass. Positrons and electrons have similarities and differences when

interacting with atoms and molecules. Positrons can undergo elastic collisions,

electronic and vibrational excitation collisions, ionization processes, etc., similar

to the electron. A detailed review of these processes can be found in Refs. [96-

98]. Beyond these interactions, annihilation is another type of interaction exists

between positron and electron.

Under the approximation of low energy, a positron with momentum k

annihilates with an electron in an orbital i, which produces two photons with a

total momentum P. The photon spectrum is determined by the annihilation

amplitude [22, 99, 100],

22

Theory and methods

d 2. 14

where is the wavefunction of the electron in the hole state and is the

positron wavefunction. If the positron is considered as a plane wave,

then is applied. For low positron momenta, k << 1 a.u., and

are appliedfor the range of positron coordinates where annihilation

occurs. This is equivalent to disregarding the positron wavefunction in Eq.

(2.14), so that the -ray spectrum is given by [22, 99, 100],

d

2. 15

Here is the gamma-ray energy spectrum relative to mc2 = 511 keV [101],

and is the total electron momentum density obtained by summation of

the orbital momentum distributions for the occupied orbitals in the system [92].

The is related to the cross section measured using the electron-

momentum spectroscopy (EMS) technique [93]. The conservation of momentum

during the annihilation process is the reason that annihilation radiation contains

information on the electron momentum distribution at the annihilation site.

Experimentally, the rate of direct annihilation of positrons is expressed in

terms of dimensionless parameter, Zeff, corresponding to effective number of

electrons. It can be defined as the time annihilation rate normalized to the rate for

a free electron gas. The total annihilation rate of the -ray spectrum is

conventionally expressed in terms of the parameter [99],

d

2. 16

In particular, Zeff = /(r02cnm), where , r0 , c, and nm, are the measured

annihilation rate, the classical electron radius, the speed of light, and the density

of the molecular gas, respectively. Theoretically, in the approximation of Eq.

(2.11), Zeff in Eq. (2.16) satisfies [102],

2. 17

23

Theory and methods

where Ne is the total number of electrons in the shell or in the atom (depending

on the orbitals involved in the sum over i in Eq. (2.16)).

2.5 Solvent effects

The objective of studying the solvation effects in chapter 4 is to observe

the cytidine nucleoside analogues in various solvated environments for its

electronic properties with respect to gas phase. A solvent environment modifies

the properties of the solvated molecules. Therefore, the response properties may

be different in the solvated environment. Thus, the study of solvent effects is

important to identify the chemical behaviour of the nucleosides in solvents. The

interaction between solute and solvent may influence the chemical and structural

behaviour of the molecules such as energy, geometry, vibration and

intermolecular interaction. Since no solvation studies have been reported

elsewhere in the literatures on these species, a study has been done to investigate

its properties in various solvents in the range of non-polar to polar solvents.

There are fundamentally two different ways of representing the solvent

environment – the discrete and the dielectric continuum approaches. Discrete

models are computationally expensive as it treats large part of molecules in a

more classical way. In the dielectric continuum models, the solvent molecules

are approximated by a homogeneous dielectric continuum characterized by its

dielectric constant ε. The solute is embedded in a cavity of certain shape and

size, where it interacts with the solvent. Based on this approach, different models

are developed depending on the cavity and the treatment of electrostatic

interaction between the solute and the continuum. The polarizable continuum

model (PCM) is one among the dielectric continuum models which is used to

model the solvation effects in this work. The solute molecule is treated quantum

mechanically in a cavity around it that assumes a molecular shape. The default

cavity in Gaussian G03 - United Atom model (UA0) and the other parameters

are set default in this work. Because of its conceptual and computational

simplicity, this theoretical method is chosen for the present study. Various

solvents with a range of dielectric constants () in an increase order of polarity

24

Theory and methods

from non-polar to polar, i.e., toluene (Tol = 2.37), dimethyl sulfoxide (DMSO

= 46.83), water ( = 78.36) and n-methyl formamide mixture (n-MF = 181.56),

are applied to study the spectra and properties of the nucleosides. As the very

strong polar n-MF solvent is available only in G09, the default parameters of

G03 were implemented in G09 for consistency. In addition, solvents such as

toluene and DMSO are chosen due to their applications in the experimental

studies of nucleosides. The solvent water is a universal solvent whereas, n-MF is

chosen for its high polarity nature.

2.6 Computational details

The computational packages such as Gaussian03 and 09 [103],

Amsterdam Density Functional (ADF) [57], together with other computer codes

developed within the group, have been used throughout this study for calculating

various molecular properties. The properties include geometries (bond length,

bond angle, torsion angle etc.), molecular energies, other electronic properties

such as dipole moment, atomic charges, electrostatic potentials and ionization

potentials; spectroscopic properties such as vibrational modes and frequency

shifts and molecular orbitals. All the calculations were carried out in the

supercomputers such as computing resources at National Computational

Infrastructure (NCI) (http://nf.nci.org.au/) and Green machine at Swinburne

University of Technology.

25

PES and EMS of perfluorinated benzenes

CChhaapptteerr 33


3. Introduction

A substitution reaction is a reaction in which an atom or group of atoms

(also called a functional group) replaces a hydrogen atom or another atom or

functional group in an organic molecule. In chemistry, substituent effects are of

central importance in understanding the chemical environment and for

understanding the influence that they have on the electronic, physico-chemical

and bio-chemical properties of a molecule. A substituent may cause effects such

as (i) redistributing the electron density within the molecule, (ii) exchanging the

electron denisty between the molecule and the substituent, and (iii) affecting

steric interactions in space [104]. The study of physical processes on a series of

substituted molecules is in general a very powerful tool for understanding their

electronic structure, because one can often gain significant insight when

examining effects and trends as a function of the chemical environment. Various

methods, such as X-ray charge studies and Bader atoms in molecules (AIM)

[105], have been developed to probe the substituent influences on the electronic

structures of the molecules.

26


3.1 Benzene and its chemistry

Benzene is a fundamental molecule in science, with a planar structure

containing a ring of six carbon atoms each with a hydrogen atom attached. This

chemical formula for benzene was proposed by Kekule in his Treatise of Organic

Chemistry [106, 107], a hundred and fifty years ago. Since then, benzene has

served as an important benchmark for both experimental and theoretical studies,

and should continue to be of great interest for many decades to come. One of the

most useful chemical properties of benzene is its ability to undergo substitution

reactions. For example, the first substituent impact on the benzene ring in

phenylsilane was reported in 1956 in an electron diffraction study [108]. The

first photoelectron spectroscopic (PES) study of benzene was reported by

Akopian et al. in 1961, using a variable wavelength light source [109]. The most

recent PES studies of benzene were carreid out using both synchrotron and HeI

radiation by Baltzer et al. in 1997 [110].

The many experimental and theoretical studies of benzene enable

validation of existing methods and models so that other molecules may be

studied with confidence. A number of spectroscopic studies have been carried

out to reveal the substituent effect of fluorine in benzene [111-128]. These

studies have documented various structural and chemical properties such as

relative stabilities, aromaticity, acidity, protonation, ionization energies, etc. as

well as symmetry based energy correlation and positron annihilation of

fluorinated benzene derivatives. A recent photophysical study reported that

increasing the number of fluorine substituents alters the nature of the excited

electronic states. The so-called perfluoro effect was observed for penta- and

hexa-fluorobenzene [129].

A number of fluorine substituted aromatic derivatives are commercially

well known ligands [33, 130, 131]. Fluorine is referred to as a "superhalogen"

atom due to the extent to which fluorine serves to polarize covalent bonds to

electropositive atoms. The σ electron-withdrawing and π electron-donating

nature are exhibited in fluorine substituted benzenes. The selective introduction

27


of a fluoro group into biologically active molecules has gained much attention by

medicinal chemists [33, 34], due to the following characteristics (1) fluorines

mimics hydrogens without much distortion in the geometry of the molecule; (2)

it is the most electronegative atom and (3) the strength of the C-F bond exceeds

that of the C-H bond, which induces biological activity and chemical stability of

the compounds [132]. Fluorobenzenes (FB) and fluorobenzimidazoles (FBZ)

have been proposed as novel nucleic acid base analogues to replace nucleobases

[133-135].

Benzene is a single ring molecule, which makes it attractive as a model

system for researchers. Therefore, in this chapter, we systematically explore the

trends and properties of a series of perfluorinated benzenes (C6H6-nFn, n=1-6) in

both position and momentum spaces. Unsubstituted benzene serves as a

reference system for fluorinated benzene derivatives and for the similarities and

differences of molecules in momentum space. As of this study, experimental

electron momentum spectroscopy (EMS) with limited resolution is available for

benzene [136-138] only. The lack of electron momentum space information for

the fluorinated benzene derivatives has motivated us to pursue this direction.

3.2 Validation of models employed

Although the models have been applied to a number of molecules,

benzene has been presented in this section to validate our methods/models used

for dual space analysis [60]. In addition, benzene has been explored in various

aspects for a number of decades both experimentally and theoretically. The

ground electronic state (X1A1g) of benzene possesses a closed shell with 15

doubly occupied orbitals including 5 degenerate orbitals. According to the

B3LYP/TZVP model, the highly symmetric benzene (with point group

symmetry of D6h) possesses the electronic configuration

(1a1g)2(1e1u)4(1e2g)4(1b1u)2(2a1g)2(e1u)4(e2g)4(3a1g)2(2b1u)2(1b2u)2(3e1u)4(1a2u)2(3e2g)4(1e1g)4

Table 3.1 reports the valence vertical ionization (binding) energies of benzene

using various models such as B3LYP/TZVP, SAOP/et-pVQZ and OVGF/TZVP,

28


along with the experimental data [139, 140] and other theoretical calculations

[139, 141]. From Table 3.1, it is found that the VIEs generated by SAOP/et-

pVQZ and OVGF/TZVP models produce comparable accuracy relative to the

experiment than the more sophisticated but significantly more expensive ADC(3)

calculations. The outer valence Green function (OVGF) approach produces

ionization energies closely matched to the experimental results in the outer

valence region. However, the success of the OVGF model is limited beyond the

outer valence region.

From Table 3.1, we observe that although the SAOP model overestimates

the VIEs of a couple of the outermost orbitals, such as the highest occupied

molecular orbital (HOMO), it provides accurate VIEs for the rest of the valence

shell of the system. Furthermore, the SAOP model is computationally less

expensive and so may be applied to the prediction of IPs of larger molecules

where the OVGF model is unwieldy. The discrepancies among theoretical

models may be attributed to a number of reasons such as orbital relaxation, self

interaction energy and configurational effects. Previous studies have realized that

B3LYP is good in reproducing the orbital diagrams and hence, we used SAOP to

analyze the VIEs and B3LYP to analyse the momentum distributions of the

orbitals.

Table 3. 1 Comparison of valence vertical ionization energies (eV) of benzene

calculated using various theoretical models and compared with experiment [91].

MO Theory Experiment

B-spline LCAOa ADC(3)b SAOPc OVGFd B3LYPe Expt.f Expt.g

1e1g 11.59 9.13(0.89) 10.58 9.09 7.06 9.2 9.24 3e2g 13.09 12.14(0.90) 12.44 12.06 9.53 11.5 11.49 1a2u 14.19 12.31(0.75) 13.32 12.28 10.15 12.3 13.02 3e1u 15.13 14.41(0.87) 14.46 14.39 11.63 13.9 13.94 1b1u 15.56 15.02(0.86) 15.07 14.78 12.33 15.5 15.44 2b2u 16.11 15.70(0.80) 15.47 15.76 12.66 14.8 14.79 3a1g 17.85 17.27(0.80) 17.12 - 14.41 16.9 16.85 2e2g 19.59 19.76(0.29) 19.11 - 16.53 19.2 18.72 2e1u 23.10 22.82(0.40) 22.77 - 20.43 22.5 22.49 2a1g 25.86 26.72(0.34) 25.55 - 23.40 25.9 -

29


aB-Spline LCAO method (ADF), Ref. [139]. bADC(3)/cc-pVDZ, Ref. [141]. cPresent study, SAOP/et-pVQZ [142, 143] functional embedded in ADF. dPresent study, OVGF/TZVP [77, 78] model. The spectroscopic pole strengths are above 0.80. ePresent study, B3LYP/TZVP//B3LYP/TZVP model. fRef. [139]. gRef. [140] (ionic state).

3.2.1 Orbital momentum distributions of benzene

Orbital momentum distributions (MDs) provide additional information

about the chemical bonding in a molecule. As a result, the valence orbital MDs

of benzene are calculated from the position space wavefunctions. Because

experimental orbital MDs of benzene are available, a comparison will serve as a

validation of our theoretical model. Figure 3.1 presents the simulated orbital

MDs of the HOMO (1e1g) and other outer valence orbitals (1a2u and 3a1g) along

with their electron densities of benzene [138]. The orbital energies are nearly

identical in the larger momentum region but the orbital MDs split as the

momentum decreases in 1e1g and 1a2u. The simulated HOMO (1e1g) MDs of

benzene agree well with the experimental orbital cross sections measured by

EMS, except at the lower momentum region of P < 0.25 a.u. The HOMO orbital

momentum profiles show a bell shaped p-electron domination, suggesting the π

bonding mechanism.

Note that the orbital MDs are very sensitive to the low momentum

region, which corresponds to larger r-region in coordinate space [93]. The

discrepancies between the experiment and the simulated in Figure 3.1,

particularly in orbitals 1e1g and 1a2u , indicate that the quantum mechanical

model needs improvement in its long range in some orbitals [7], which

represents one of the quantum mechanical bottlenecks in its development. The

discrepancies also caused by the experimental kinematic conditions [7] which

can be improved if the experimental conditions were folded into the simulation.

The consistent agreement of theory with the experiment in the present study

helped to proceed further to explore the effects of fluorination in benzene from

30


Figure 3. 1 Comparison of orbital momentum distributions of the outer valence

orbitals of benzene based on B3LYP/TZVP wavefunctions with the EMS

momentum distributions.

31


both traditional and non-traditional point of view from both position and

momentum spaces --- dual space analysis [60].

3.3 Position space properties of fluorinated benzenes

3.3.1 Energies and geometries

There are total of 12 fluorinated benzenes with two, three, and four

fluorines on the benzene ring. These isomers are shown in Figure 3.2. The

fluorine substituted benzenes possess five point group symmetries, depending on

the number of fluorine atoms present and their positions on the ring: D6h; D3h;

D2h; C2v; and Cs. The substituted benzenes undergo distortions to stabilize the

structures of the derivatives, in which the lower symmetry structures exhibit the

Jahn-Teller effect [144]. The unsubstituted benzene (C6H6) and fully substituted

benzene (C6F6) both possess D6h point group symmetry. All the carbon atoms are

equivalent in C6F6 and C6H6, as are the six fluorine (hydrogen) atoms.

Figure 3.2 shows the fluorinated benzenes and their associated total

electronic energies. As seen in this figure, the total energies do not seem to be

correlated with the symmetry of the structures in the case where more than one

isomer is present. For example, of the three difluorinated species, 1,3-

difluorobenzene (meta-, IIb), yields the lowest energy and has a C2v point group

symmetry. However, in the trifluorinated benzenes, 1,3,5-trifluorobenzene (IIIc)

is the lowest energy structure and has D3h symmetry. The lowest energy

structures among the isomers are underlined in the figure.

32


Figure 3. 2 Chemical structures of fluorinated benzenes and their relative

energies based on the B3LYP/TZVP model.

The geometries of the carbon skeleton of fluorine substituted benzenes

are tabulated in Table 3.2 based on B3LYP/TZVP calculations.

33


Table 3. 2 Geometric properties of the perfluorinated benzenes based on the B3LYP/TZVP model.

Properties C6H6 I IIa IIb IIc IIIa IIIb IIIc IVa IVb IVc V VI Bond Lengths(Å)

C1-C2 1.392 (1.392)a 1.384 1.389 1.385 1.385 1.390 1.389 1.386

(1.384)b 1.390 1.385 1.389 1.389 1.389

C2-C3 - 1.392 1.383 1.395 1.391 1.384 1.384 - 1.389 1.389 1.385 1.390 - C3-C4 - - 1.393 1.392 - 1.386 1.391 - 1.383 - - 1.384 - C4-C5 - - 1.391 - - 1.392 - - 1.392 - - - - C5-C6 - - - - - 1.383 - - - - - - -

C-H 1.083 1.083 1.082 1.081 1.082 1.081 1.081 1.080 (1.079) 1.081 1.080 1.081 1.081 -

- - - - 1.082 1.082 - - - - - -

C-F - 1.355 1.345 1.351 1.354 1.345 1.338 1.347 (1.343) 1.342 1.347 1.342 1.339 1.333

- - - - 1.342 1.343 - 1.335 1.339 - 1.335 - - - - 1.350 - - - 1.337 - 1.333 - R6 8.35 8.34 8.33 8.32 8.32 8.32 8.33 8.32 8.33 8.32 8.32 8.33 8 .33

Angle (deg) C1-C2-C3 120.000 118.385 120.509 116.991 118.865 120.812 121.182 116.855 119.479 117.646 120.544 119.235 120.000 C2-C3-C4 - 120.444 119.261 122.762 118.865 117.865 119.035 123.145 119.479 121.605 118.911 120.278 - C3-C4-C5 - 119.857 120.230 118.224 122.269 122.516 120.793 116.855 120.933 118.597 120.544 119.235 - C4-C5-C6 - - 120.230 121.036 - 118.648 121.182 123.145 119.588 121.605 120.544 121.341 - C5-C6-C1 - - 119.261 118.224 - 119.853 118.775 116.855 - 117.646 118.911 118.570 - C6-C1-C2 - 122.486 120.509 122.762 - 120.307 119.035 123.145 - 122.901 120.544 121.341 - F1-C1-C2 - 118.757 119.207 118.270 118.865 119.293 120.613 118.428 118.536 118.550 119.539 118.704 120.000 F2-C2-C3 - - 120.285 - - 119.823 120.379 - 119.850 - 119.917 119.937 - F3-C3-C4 - - - 118.968 - - - 118.428 120.671 118.543 - - - F4-C4-C5 - - - - 118.865 119.093 - - 120.530 120.701 119.539 120.828 - F5-C5-C6 - - - - - - - 118.428 - 119.852 119.917 119.955 - F6-C6-C1 - - - - - - 118.439 - - - - - -

aRef. [145] bRef. [146]

34


From the data in the table, it is apparent that fluorine substitution in benzene

affects the bond lengths within the ring. Fluorine substitution slightly reduces the

ring perimeter, R6 [21] (0.01 to 0.03 Å), with the ring perimeter of the unsubstituted

benzene being the largest (R6 = 8.35 Å). The C-C bond length shortens with the

increase of fluorine atoms in derivatives: this C-C bond length is 1.392 Å in

unsubstituted benzene but 1.384 Å in single fluorine benzene (I). With respect to

the C-F bonds, the bond lengths shrink gradually from 1.355 Å (I) to 1.333 Å (VI).

Bond angles do not show such trend but in general they decrease significantly with

respect to the fluorine attachment in benzene.

3.3.2 Aromaticity

Aromaticity is a fundamental concept in organic chemistry. It accounts for

the additional structural stability and chemical reactivity of compounds. Schleyer

and Jiao [147] stated that anisotropy of magnetic susceptibility and 1H NMR

chemical shifts are useful criterion for characterizing the aromaticity of a molecule.

However, the best criterion for assessing aromaticity is still in debate. One of the

most widely used indices is the nucleus independent chemical shift (NICS) [148].

Various comparative studies on the aromaticities of perfluorinated benzene have

been reported [113, 149, 150]. The present study employed the recently introduced

aromaticity indicator called the NICS-rate index [151], to assess the aromatic nature

of the fluorinated benzenes.

NICS-rates (NRR) are computed using the gauge- including atomic orbital

(GIAO) method at the B3LYP/6-311+G**//B3LYP/TZVP level. The probe (ghost

atom, Bq) is placed at the ring center of the molecule (0.0 Å) and its distance is

varied (up to 4.0 Å) perpendicular to the molecular plane at an interval of 0.2 Å.

NICS-rates are calculated from the two successive NICS values at a distance (r) of

0.2Å. The obtained NICS-rates are then plotted against distance (r) for NICS-rate

curve. The NICS-rate curve of perfluorinated benzenes are given in Figure 3.3. The

presence of the maximum/minimum in the NICS-rate curve of a molecule indicates

aromaticity/antiaromaticity of the molecules.

35


Figure 3. 3 NICS-rate as a function of distance for the fluorinated benzenes.

The NICS-rate curves in Figure 3.3 show that the curves shift upward as the

number of fluorine atoms increases. For example, the unsubstituted benzene, C6H6,

possesses a negative minimum and a large maximum, whereas the fully substituted

benzene, C6F6, exhibits no minimum but a significantly larger maximum. The

NICS-rate curves indicate that the aromaticity increases with the number of fluorine

atoms in the derivatives. However, this conclusion does not agree with a recent

study using the localized molecular orbital (LMO)-NICS chemical shifts analysis

[150], which indicates that the fluorinated benzenes have very similar ring LMO-

NICS(0)πzz values and therefore, C6F6 is as aromatic as benzene.

In contrast, Okazaki et al. [149] evaluated the aromaticity based on the

NICS(1)zz index and found diminished ring currents of the fluorobenzenes but the

observation was not substantiated clearly. Nevertheless, the present NICS-rate

index anticipates that benzene may be less aromatic than hexafluorobenzene (C6F6).

In other words, the effect of σ-electrons in NICS-rate curve is diminishing in

36


benzene and the π-electrons contribution is increased to reach its maximum at

nearly 1.5 Å, whereas in hexafluorobenzene, only π-electrons contribution is

predominated and it reaches maximum determining that it is highly aromatic than

benzene.

The NICS(0) values calculated for the fluorinated benzenes taken from a

comprehensive review of aromaticity [114] have been included in Table 3.3 with

the present NICSmax and rmax values. Three derivatives, that is, 1,3-C6H4F2, 1,2,6-

C6H3F3 and 1,2,3,4-C6H2F4 are predicted to be slightly more aromatic than their

isomers based on their NICSmax values given in Table 3.3. Interestingly, NICS (0)

gives the aromaticities of the rings in the same order as predicted by NICS-rate for

the fluorinated benzenes.

The LMO-NICSπzz method [150] predicted that the fluorine benzene

derivatives possess similar aromaticity. Due to various results by different methods,

a new NICS-rate method is used in this work for assessing the aromaticities of the

perfluorinated benzenes. It is noted in Figure 3.3 that while the maximum NICS-

rate for a derivative becomes larger as the number of fluorine atoms increases, the

position of the peak moves to smaller r values. This indicates that the aromaticity of

a derivative may be also associated with the distance from the ring centre.

In this thesis, based on the NICS index, we have developed a different

indicator for the aromaticity of the fluorobenzenes, that is, the NICS cross section

NICS [152]. The NICS [152] is the product of NICSmax and rmax. Here NICSmax is the

highest point in the NICS-rate curve and rmax is the corresponding distance. Table

3.3 lists the NICS cross sections for the fluorobenzenes. The NICS cross sections of

the fluorobenzenes are all similar, in particular, for benzene (C6H6) and

hexafluorobenzene (C6F6), the NICS cross sections are 9.65 and 9.70, respectively,

which indicates that the aromaticity of benzene and hexafluorobenzene are indeed

similar with benzene being slightly smaller.

37


Table 3.3 The calculated NICS(0), NICSmax and rmax values for the fluorine

benzenes.

Molecule NICS(0) (this work) NICS(0)a NICSmax rmax σNICS

C6H6 -8.01 -8.03 6.029 1.6 9.65 C6H5F -10.04 -9.98 6.257 1.6 10.01

1,2-C6H4F2 -11.94 -11.76 6.795 1.4 9.51 1,3-C6H4F2 -11.74 -11.70 6.646 1.4 9.30 1,4-C6H4F2 -11.60 -11.60 6.618 1.4 9.27

1,2,4-C6H3F3 -13.48 -13.43 7.141 1.4 10.00 1,2,6-C6H3F3 -13.62 -13.39 7.274 1.4 10.18 1,3,5-C6H3F3 -13.11 -13.16 6.888 1.4 9.64

1,2,3,4-C6H2F4 -15.33 -15.19 8.008 1.2 9.61 1,3,4,5-C6H2F4 -14.94 -14.94 7.769 1.2 9.32 1,2,4,5-C6H2F4 -15.20 -15.22 7.920 1.2 9.50

C6HF5 -16.76 -16.74 8.779 1.2 10.53 C6F6 -18.26 -18.23 9.704 1.0 9.70

aRef. [114] bRef. [151]

3.3.3 Dipole moment and Hirshfeld charges

The dipole moment of the perfluorinated benzenes in their ground electronic

states are reported in Table 3.4 in which calculations using different theoretical

models are compared with experiment. The Dipole moment obtained by the B3LYP

method compare well with the available experimental results, except for 1,2,6-

trifluorobenzene (IIIb), where the calculated dipole moment is almost twice as large

as the experimental value. The dipole moment may be categorized into three groups

based on the symmetry of the species, i.e., zero (µ=0.0), small (µ<2.0) and large

(µ>2.0). For example, all species belonging to the D2h, D3h and D6h point group

symmetry possess a symmetry centre and therefore, a zero dipole moment.

Benzene, hexafluorobenzene (VI), 1,4-difluorobenzene (IIc), 1,3,5-trifluorobenzene

(IIIc) and 1,2,4,5-tetrafluorobenzene (IVc) are in the zero dipole moment group.

The large dipole moment group includes 1,2-difluorobenzene (IIa), 1,2,6-

trifluorobenzene (IIIb) and 1,2,3,4-tetraflurobenzene (IVa) in which the fluorine

atoms are concentrated on one side of the ring so that the charge distributions are

38


not well balanced. The species in the small dipole moment group have one or more

fluorine atom(s) on the other side of the ring to balance some of the charge. The

only exception to this is fluorobenzene (I), which has only one fluorine atom.

Table 3.4 Electric dipole moments (µ in Debye) of perfluorinated benzene

calculated using the B3LYP/TZVP model.

Molecule B3LYP/TZVP Expt. [120] µx µy µz µtot C6H6 C6H6 0.00 0.00 0.00 0.00 0.00 C6H5F I 0.00 0.00 -1.69 1.69 1.60

1,2-C6H4F2 IIa 0.00 0.00 2.79 2.79 2.46 1,3-C6H4F2 IIb 0.00 0.00 1.66 1.66 1.51 1,4-C6H4F2 IIc 0.00 0.00 0.00 0.00 0.00

1,2,4-C6H3F3 IIIa -0.02 -1.57 0.00 1.57 - 1,2,6-C6H3F3 IIIb 0.00 0.00 -3.15 3.15 1.39 1,3,5-C6H3F3 IIIc 0.00 0.00 0.00 0.00 0.00

1,2,3,4-C6H2F4 IVa 0.00 0.00 -2.66 2.66 - 1,3,4,5-C6H2F4 IVb 0.00 0.00 1.49 1.49 - 1,2,4,5-C6H2F4 IVc 0.00 0.00 0.00 0.00 0.00

C6HF5 V 0.00 0.00 -1.49 1.49 1.44 C6F6 VI 0.00 0.00 0.00 0.00 0.00

Table 3.5 provides the Hirshfeld charge (QH) distributions generated using

the LB94/et-pVQZ [54] model. In Table 3.5, the Hirshfeld charges on the carbon

atoms are presented in a heatmap with a color bar, blue for positive and red for

negative charges as shown in the side bar. From the color changes on some of the

carbon atoms, the interesting dual role of carbon is revealed. In general, carbon is

negatively charged (red) when bonded to hydrogen. However, the charge on carbon

becomes positive (blue) when bonded to fluorine. Moreover, the greater the number

of fluorine atoms substituted, the more positively charged the carbons become.

Hydrogen atoms are more electropositive and fluorine atoms are more

electronegative than carbon. As a result, fluorine is always negatively charged,

whereas hydrogen is always positively charged in the

39


Table 3. 5 Hirshfeld charges (QH) of the benzene derivatives based on LB94/et-pVQZ (a.u.).

Site C6H6 I IIa IIb IIc IIIa IIIb IIIc IVa IVb IVc V VI C(1) -0.044 0.103 0.100 0.110 0.103 0.1 0.098 0.117 0.104 0.116 0.107 0.111 0.107 C(2) -0.044 -0.047 0.100 -0.051 -0.039 0.108 0.106 -0.052 0.103 -0.046 0.107 0.101 0.107 C(3) -0.044 -0.036 -0.041 0.110 -0.039 -0.044 -0.042 0.117 0.103 0.113 -0.038 0.109 0.107 C(4) -0.044 -0.045 -0.037 -0.048 0.103 0.110 -0.029 -0.052 0.104 0.096 0.107 0.101 0.107 C(5) -0.044 -0.036 -0.037 -0.028 -0.039 -0.04 -0.042 0.117 -0.035 0.113 0.107 0.111 0.107 C(6) -0.044 -0.047 -0.041 -0.048 -0.039 -0.033 0.106 -0.052 -0.035 -0.046 -0.038 -0.04 0.107

F(1) - -0.157 -0.140 -0.148 -0.153 -0.137 -0.123 -0.139 -0.129 -0.137 -0.129 -0.122 -0.107 F(2) - - -0.140 - - -0.132 -0.132 - -0.116 - -0.129 -0.114 -0.107 F(3) - - - -0.148 - - - -0.139 -0.116 -0.124 - -0.109 -0.107 F(4) - - - - -0.153 -0.145 - - -0.129 -0.121 -0.129 -0.114 -0.107 F(5) - - - - - - - -0.139 - -0.124 -0.129 -0.122 -0.107 F(6) - - - - - - -0.132 - - - - - -0.107

H(1) 0.044 - - - - - - - - - - - - H(2) 0.044 0.058 - 0.072 0.064 - - 0.075 - 0.080 - - - H(3) 0.044 0.050 0.064 - 0.064 0.077 0.066 - - - 0.083 - - H(4) 0.044 0.047 0.053 0.061 - - 0.059 0.075 - - - - - H(5) 0.044 0.050 0.053 0.056 0.064 0.066 0.066 - 0.072 - - - H(6) 0.044 0.058 0.064 0.061 0.064 0.069 - 0.075 0.072 0.080 0.083 0.085 -

40


derivatives. For the unsubstituted C6H6 or fully substituted C6F6, all the carbon

atoms exhibit opposite charges to either hydrogens or fluorines. However, the C-F

bonds in C6F6 are more polarized than the C-H bonds in C6H6, as shown by their

QH.

The electronegative fluorine atom induces charges on the atoms in a

derivative and so further induces polarization of the bonds around it. The QH on the

hydrogen atoms are also dependent on the distance from where the fluorine is: the

further the hydrogen positions, the less positive QH is on the hydrogen. For

example, the hydrogen atoms connecting to the ortho-, meta- and para-carbons are

considerably farther away from the fluorine atom, so that the positive charges on

these hydrogen atoms at the other end of the C-H bonds are rather small, as 0.058

(ortho-), 0.050 (meta-) and 0.047 a.u. (para-), accordingly. The hydrogen atoms do

not change their signs as they are always positively charged in the species,

regardless of how many fluorine atoms are involved. In fact, fluorine substitution

also enhances the positive charges of the remaining hydrogen atoms. For example,

in benzene, QH of the hydrogen atoms are +0.044 a.u., whereas in C6F5H, the QH of

the hydrogen is nearly doubled and gives +0.085 a.u.

3.4 Ionization energies

Table 3.6 details the orbital energies of the HOMO and lowest unoccupied

molecular orbital (LUMO), the HOMO-LUMO energy gap, and the experimental

first VIEs of the perfluorinated benzenes. Estimates of the first VIEs of fluorinated

benzenes are in the range of 10.50 to 11.50 eV by SAOP/et-pVQZ (meta Koopmans

theorem) [153] and 9.00 to 9.90 eV by OVGF/TZVP [77] calculations. The OVGF

model shows good agreement with the experimental data for the fluorinated species.

After a global energy shift, the SAOP and OVGF model agree well, indicating that

the orbital relaxation may play an important role in prediction of the VIEs.

41


Table 3. 6 Calculated first ionization energies (eV) of perfluorinated benzenes with

the experimental results.

Molecule SAOP OVGF Expt. HOMO LUMO GAP HOMO LUMO GAP First IPs

C6H6 10.58 5.45 5.14 9.09 2.37 6.72 9.30a, 9.25b C6H5F 10.59 5.77 4.82 9.14 2.01 7.13 9.20c,d

1,2-C6H4F2 10.75 5.95 4.80 9.30 1.89 7.41 9.30e, 9.60f 1,3-C6H4F2 10.79 5.98 4.81 9.35 1.86 7.49 9.20g, 9.32e 1,4-C6H4F2 10.61 6.11 4.50 9.19 1.67 7.52 9.16b, 9.40h

1,2,4-C6H3F3 10.82 6.25 4.57 9.23 1.59 7.64 9.30i 1,2,6-C6H3F3 11.08 6.03 5.05 9.63 1.92 7.71 9.70g, 9.40b 1,3,5-C6H3F3 11.16 6.04 5.12 9.71 1.93 7.78 9.50g,9.64j

1,2,3,4-C6H2F4 11.10 6.32 4.78 9.48 1.61 7.87 9.60j, 9.55 e 1,3,4,5-C6H2F4 11.10 6.31 4.79 9.49 1.63 7.86 9.56e 1,2,4,5-C6H2F4 10.94 6.47 4.47 9.33 1.42 7.91 9.20g, 9.36e

C6HF5 11.25 6.48 4.77 9.62 1.51 8.11 9.73k, 9.70j C6F6 11.54 6.80 4.74 9.90 1.62 8.28 9.80g, 9.90b

aRef. [154] bRef. [155] c,dRef. [156, 157] eRef. [158] fRef. [159] gRef. [160] hRef. [161] iRef. [116] jRef. [162] kRef. [163]

Figure 3.4 reports the trends of the first ionization energies of the fluorinated

benzenes based on the OVGF/TZVP model. It shows that the number of fluorine

atoms indeed contributes to the observed increases in the first IEs. It is noted that of

the isomers, i.e., di-, tri- and tetra-fluorinated benzenes, the most stable species

possesses the highest first IEs, i.e. 1,3-C6H4F2 (IIb), 1,3,5-C6H3F3 (IIIc) and

1,3,4,5-C6H2F4 (IVb) with an energy of 9.35, 9.71, 9.49, respectively. This is

consistent with their stability: the more stable the molecule, the more difficulty it

will be to ionize. The same trend can also be seen in the HOMO-LUMO gaps in

Table 3.6. A larger HOMO-LUMO energy gap is predicted when the number of

fluorine atoms increase and the most stable energy structure has the highest energy

42


gap among the isomers. The OVGF/TZVP calculations yield larger energy gaps

than the SAOP/et-pVQZ model.

It is interesting to note that the first IP of the C6H3F3 isomer is very

dependent on the symmetry of the isomers. In Figure 3.4, the first IPs of 1,3,5-

C6H3F3 (IIIc) and 1,2,6-C6H3F3 (IIIb) are larger than for 1,2,4-C6H3F3 (IIIa). This

may be because higher symmetry stabilizes the system by allowing the HOMO

electrons to delocalize to a greater extent.

Figure 3. 4 First ionization energies (eV) of fluorinated benzenes based on the

OVGF/TZVP calculations.

3.4.1 Valence ionization energy spectra

Photoelectron spectroscopy (PES) is an extremely useful technique for

studying the electronic structures of molecules. Theoretical spectral simulations

have been an integral avenue part of the interpretation of experimental results and

the determination of information such as orbital symmetry and chemical bonding.

43


Figure 3.5 compares a recent experimental PES [118] and the simulated PES

of hexafluorobenzene (VI). The PES was recorded at photon energy of 30eV in

2007 [118]. The simulated valence ionization energy spectra of hexafluorobenzene,

using the OVGF/TZVP (middle panel) and the SAOP/et-pVQZ (top panel) models

with a full width at half maximum (FWHM) of 0.50eV, are also shown in this

figure. The PES simulated using the SAOP/et-pVQZ model has been subjected to a

global red shift (all peaks are lowered in energy) of 1.2eV to best align the

theoretical peaks with the experimental spectrum [118]. Both the simulated spectra

(the SAOP model after the shift) exhibit a good agreement with the experimental

binding energy spectra.

Figure 3. 5 Valence ionization energy spectra of C6F6. The simulated spectra using

OVGF/TZVP (middle panel) and SAOP/et-pVQZ (top panel) are compared with

experimental photoelectron spectrum [118] (bottom panel).

44


The OVGF model reproduces the outer valence region of the spectrum (upto

18eV) well but is unable to do so in the inner valence region (beyond 18eV) of the

PES because of model limitations. The SAOP/et-pVQZ model (after the energy

shift) is able to reproduce the peaks for the entire valence space. It is noted that the

orbital symmetry assignment such as b1u and b2u are swapped between experiment

and SAOP/et-pVQZ in the spectra.

The good agreement between the VIEs produced using the SAOP/et-pVQZ

model and the experimental PES of hexafluorobenzene indicates that the SAOP

model is able to produce the VIEs for other derivatives for a systematic comparison.

We, therefore, simulated the PES for all the perfluorinated benzene species which

are presented in Figure 3.6. In this figure, the valence ionization energy spectra are

produced using a Gaussian shape function with a FWHM of 0.40eV. In general, the

ionization spectra show a global blue shift with increase of number of fluorine

atoms. The spectra exhibit apparent similarities with certain differences in the

middle valence region (approximately 12-20eV) in benzene indicating that the

fluorinated benzenes are structurally correlated but not the same. This has also been

observed in the PES of aliphatic amino acids [164].

Valence orbitals can reveal fundamental structural information. For

example, they are responsible for forming and breaking chemical bonds in

molecules and chemical reactions. The ground electronic state of benzene (X1A1g)

has 15 occupied valence orbitals including 5 degenerate orbita ls. The substitution of

a fluorine atom (in place of a hydrogen atom) contributes an extra three valence

orbitals to that derivative. For example, the 15 valence energy levels (degenerate

orbitals are counted as one energy level) in benzene with n=0 (n is the number of

substituted fluorine atoms) will become 18, 21, 24, 27, 30 and 33 levels for n=1, 2,

3, 4, 5 and 6 respectively. The interactions among the valence electrons and spectra

will therefore be different for each of the species.

45


Figure 3.6 compares the valence ionization spectra of all benzene

derivatives. Relative to benzene, the spectral peaks can be categorised into three

groups: benzene-related spectral peaks (in the outer and inner valence region),

fluorine-dominated peaks (innermost valence region, IP > 35eV) and molecular

specific (signature) orbitals (in the middle region).

Figure 3. 6 Simulated valence ionization energy spectra of perfluorinated benzenes

using SAOP/et-pVQZ calculation. The “spectral peak” of the LUMO is also

presented for the comparison of the HOMO-LUMO gap.

46


Philis et al. [125] attempted to correlate the higher energy spectral peaks

(orbitals) of fluorinated benzene species with reference to benzene. However, the

correlation has been made for only the three outer valence orbitals of benzene (i.e.

1e1g, 3e2g, 1a2u) and perfluorinated benzene. In the present study, the correlation of

orbitals has been extended to the inner valence region, where the inner valence

orbitals for benzene and the fluorinated species are very similar, as can be noted

from the spectra in the Figure 3.6.

Figure 3.7 displays the orbital based valence ionization energy correlation

diagram. The correlation of valence orbitals of perfluorinated benzene with respect

to benzene can be seen. On fluorination, the point group symmetry (D6h) of benzene

is reduced to lower point group symmetry. As a result, certain symmetric operations

no longer exist and therefore, remove some orbital degeneracy. Degenerate orbitals

in benzene are thus split into two individual orbitals in the fluorinated species, as

dictated by the Jahn-Teller theorem [144]. For example, the degenerate HOMO

orbital (1e1g) in benzene and 2e1g of hexafluorobenzene become non-degenerate

once the symmetry is reduced from D6h to D2h, C2v and Cs in the other fluorinated

benzene species. However, 1,3,5-C6H3F3, which is highly symmetric (D3h) shows

orbital degeneracy. The benzene related orbitals in the outer (1e1g, 3e2g, 1a2u and

3e1u) and inner valence region (2a1g, 2e1u, 2e2g and 3a1g) of benzene are correlated to

the corresponding orbitals in the perfluorinated benzene species based on their

orbital symmetry and their energies. The innermost orbitals in the spectra (IP

>35eV) are categorised into either fluorine-specific orbitals (functional group

region of the perfluorinated benzene). The number of fluorine-dominated orbitals in

the innermost valence region increases as the number of fluorine atoms increases

i.e. in I (C6H5F) there is only one fluorine atom and therefore one fluorine-

dominated orbital. The number of fluorine-dominated orbitals peaks at six for C6F6.

This is reflected by the intensity of the spectral peak related to fluorine-dominated

orbitals (i.e. IP >35eV) in Figure 3.6; it rises with the number of fluorine atoms.

However, this fluorine spectral peak does not exist in benzene as it lacks a fluorine

atom.

47


Figure 3. 7 Orbital energy (- i) correlation diagram of perfluorinated benzenes with respect to benzene based

on SAOP/et-pVQZ model.

48


The effect of fluorine substitution in benzene can be clearly observed in

the middle band of the valence region (in the box of 13.0-19.50eV as marked in

the figure), which serves as signature orbitals or the “finger print” region that is

unique to a specific fluorinated species. For example, the “parent”orbitals (1b2u

and 2b1u) in the middle valence space of benzene split into 4, 6, 8, 10, 12 and 14

orbitals, respectively, from I-C6H5F to VI-C6F6 as the number of fluorine atoms

increases in the molecules. The similarities of fluorinated benzenes shown in the

spectra will be analysed using orbital momentum distributions in the next

section.

3. 5 Momentum space properties

Momentum space information provides additional information to that

provided by coordinate space in the study of structural similarities of molecules.

Properties such as orbital density distributions obtained in coordinate space are

only qualitative. Therefore, we have applied DSA [60] to extract a more

comprehensive picture. In DSA, momentum space information is obtained to

reveal additional orbital information quantitatively together with photoelectron

spectroscopy.

3.5.1 Orbital momentum distributions

The photoelectron spectra discussed in the previous section have

demonstrated that certain groups of orbitals, i.e. outer and inner valence

molecular orbitals, are similar among the fluorinated benzenes. Substitution of

hydrogen atoms by fluorine atoms in benzene causes significant changes in the

middle band (as marked by the box in Figure 3.6) of the valence region. Orbital

MDs of the selected benzene-related orbitals of the perfluorinated benzenes are

given in Figures 3.8 - 3.11 along with their density distributions in coordinate

space. Figure 3.8 presents the HOMO orbital MDs of benzene and the

fluorinated derivatives. Only the doubly degenerated benzene orbital, 1eg, is

shown in Figure 3.8.

49


Figure 3. 8 Comparison of momentum distributions of the highest occupied

molecular orbital (HOMO) of benzene and its fluorinated species.

The orbital density distributions of fluorinated benzenes given in Figure

3.9 are more or less similar to the HOMOs of benzene (1e1g) qualitatively in

coordinate space. Their orbital MDs in Figure 3.8 more clearly show the

similarities and differences of the orbitals (in momentum space). In both

coordinate space and momentum space, the HOMOs are p-type. However, it is

difficult to differentiate the orbitals as they exhibit very similar distributions in

their electron densities in coordinate space. In momentum space, apart from

some minor contributions from fluorine atoms in the small momentum region of

p <1.0 a.u, the orbital MDs exhibits a bell shape (Gaussian- like distribution) in

their MDs. The major differences among the HOMOs of the benzene derivatives

are the maximum intensities and their full width at half maximum (FWHM). The

more fluorine atoms in the derivatives, the small cross sections in their orbital

MDs and the smaller their FWHMs. For example, benzene, which has n=0

fluorine atoms, possesses the highest HOMO cross section in Figure 3.8. In

50


addition, the maximum relative intensity of the HOMO of C6H5F, which has

only n=1 fluorine atom, is approximately twice as much as the maximum relative

intensity of C6F6 which possesses six fluorine atoms. Although subtle, it is

evident that the orbital MDs can be seen as approximately six bands. Each band

represents the number of fluorine atoms, n(F), in the derivatives. Among isomers

with the same number of fluorine atoms, certain intensity differences among the

orbital MDs indeed shows a positional dependency of the fluorine atoms found

in their orbital charge distributions.

Figure 3. 9 HOMO orbital density distributions of fluorinated benzenes.

51


Figure 3.10 presents the third HOMO (THOMO - 1a2u) of benzene with

the correlated orbitals in the perfluorinated species. Similar trends found in the

orbital MDs of the HOMO are maintained in the orbital MDs of the THOMO of

benzene and its derivative orbital MDs. Again, the THOMOs are also

dominantly p-type orbitals and exhibit bell shaped orbital MDs. The similar

behaviour of HOMOs and THOMOs is consistent with our earlier observations

in previous sections.

Figure 3. 10 The third highest occupied orbital (1a2u-THOMO) of the

perfluorinated benzenes MDs and its orbital density distributions.

52


Figure 3.11 depicts the innermost valence orbital of the species. The

innermost valence orbitals show similarities among one another, as they are all

half-bell shaped orbital MDs, therefore illustrating a dominantly s-type character.

Figure 3. 11 The innermost valence orbital of benzene (2a1g) with the correlated

orbitals of the perfluorinated benzenes, as an MDs and as an orbital density

distributions.

53


The relative intensities of the orbital MDs in Figure 3.11 differ with

different numbers of fluorine atoms in the molecule. The intensity differences are

readily apparent in the region of P < 0.50 a.u, which corresponds to larger

distances in coordinate space. Otherwise, the general trends in orbital MDs are

very similar to those exhibited by the outermost valence orbitals, discussed

previously.

Perhaps the most notable difference between the innermost and outermost

valence orbitals of the derivatives is that the innermost valence orbitals of the

isomers of the same n(F) are almost identical in their innermost valence orbital

MDs. This may be due to the fact that the momentum distributions have been

spherically averaged, which would eliminate angular differences in the orbitals.

The similarities among the fluorinated benzenes have been established

using momentum space information. To demonstrate the positional isomeric

effect caused by fluorine substituents, orbital MDs of difluorinated benzene

(C6H4F2) isomers are discussed here. The MOs in the outer and inner valence

space of the difluorinated isomers are presented in momentum space in Figure

3.12 and Figure 3.13 respectively.

From Figures 3.12, and 3.13, it is seen that some of the orbitals of the

isomers are related in some way, reflecting the positions of the two fluorine

atoms on the benzene ring. Some orbitals, for example, orbitals, MO1 (HOMO)

– MO4, MO9 – MO11 and MO18 – MO21, show similarities in shape, but differ

in intensity. In addition, all of these orbitals are p-type with the exception of

MO19 and MO21, which are inner valence shell orbitals and s-type. In particular,

orbital MO19 is almost identical for all difluorinated benzenes, indicating that

this orbital is not affected by position of the fluorine atoms in the three isomers.

54


Figure 3. 12 Comparison of theoretical momentum distributions of orbitals in the

outer valence space of difluorinated benzene isomers, 1,2-C6H4F2 (solid line),

1,3-C6H4F2 (dashed line), 1,4-C6H4F2 (dotted line).

55


Figure 3. 13 Comparison of theoretical momentum distributions of orbitals in the

inner valence space of difluorinated benzene isomers, 1,2-C6H4F2 (solid line), 1,3-

C6H4F2 (dash line), 1,4-C6H4F2 (dot line).

56


Some orbitals in the outer valence space, such as MO5 – MO7, look quite

different. However, a closer examination of these orbitals indicates that they are

consistent with their molecular point group symmetries. Orbitals MO5 – MO7

exhibit a hybrid character for C6H4F2 but a bell-shaped -orbital for the 1,3–

C6H4F2 isomer. For example, MO5-MO7 have two “humps” for both the 1,2–

and 1,3–C6H4F2 orbitals. However, the relative intensities of the “humps” are

reversed for the two isomers; the 1,2- isomer has the higher intensity at higher

momentum, and the 1,3- isomer has it at lower momentum. Symmetry related

orbital MD changes do not seem to have as much of an impact on their inner

valence shell orbitals, likely because they are more localized.

3.6 Summary

Electronic structural changes with respect to fluorine substitution in

benzene have been studied in this chapter. Properties reflecting the impact of

fluorine substitution on benzene (aromaticity, dipole moment, Hirshfeld charges,

valence ionization energies and theoretical orbital momentum distributions) have

been presented and discussed. Dual space analysis has been employed to reveal

additional information that is not readily apparent from position space alone.

Anisotropic properties such as dipole moment evidently vary according to the

point group symmetry of the species. Hirshfeld charges on carbon atoms switch

between either positive (when forming C-F bonds) or negative (when forming C-

H bonds) in order to balance the electronegative nature of the fluorine atom.

An increase in the number of fluorine atoms increases the valence

ionization energies linearly in fluorinated benzene species. Substitution of

fluorine for hydrogen atoms in benzene has a significant effect in the middle

valence region (14-17eV) of the binding energy spectra, regarded as the “finger

print” region. Similarities in the outer and inner valence region with respect to

unsubstituted benzene have also been presented. Orbitals identified as “benzene-

like” are demonstrated in momentum space by showing that the related

fluorinated benzene orbitals appear similar. Difluorinated benzene isomers are

also differentiated using orbital momentum distributions. The present study

57


indicates that dual space analysis is a useful technique for revealing subtle

differences among the isomers. The agreement of MDs between the theory and

experiment is good, in an overall, except at the points P < 0.25 and 0.5 a.u, and

this may be attributed to the B3LYP/TZVP model used in this study. The orbital

energies are nearly identical in the larger momentum region but the orbital MDs

split as the momentum decreases in general. Small deviations found in orbital

MDs of benzene with respect to experiment may be due to the orbital anisotropy

and exchange energies of the B3LYP method. However use of certain DFT

methods with a basis set requires more research effort in order to ensure that the

models employed are proper to a particular species.

58

Intramolecular interactions of cytidine nucleoside analogues

CChhaapptteerr 44


4. Introduction

Deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) are nucleic

acid polymers composed of monomeric nucleosides covalently linked through

3′→5′ phosphodiester linkages. Nucleosides consist of a nucleic acid base and a

deoxyribose (sugar) moiety bonded through a β−N1-glycosidic C-N linkage

[165]. Structures of nucleosides and their inter and intramolecular interactions

are fundamental in the study of the double helix and conductivity of DNA/RNA

fibres [30]; in addition, they determine the functionalities of a class of ligands.

The interactions can be very different when nucleosides undergo structural

modifications. The structurally modified nucleosides are termed as “nucleoside

analogues”.

Nucleobase and nucleoside analogues are widely used as

chemotherapeutic agents in the treatment of cancer and viral diseases [166].

Derivatives of the same nucleoside may show different docking pattern in

ligand-protein interactions. For example, relocation or attachment of a hydroxyl

group, forming the structural analogues of uridine, determines the

transportability of nucleoside analogues, including anticancer or antiviral

nucleoside drugs, such as human concentrative nucleoside transporters hCNT1

and hCNT3 [167]. Many base modified nucleoside analogues are successful

therapeutic candidates for the treatment of tumours and cancers. Cytidine

derivatives are also good antimetabolites with respect to the uridine derivatives.

59


For example, ara-cytidine is one of the most effective drugs used in the

treatment of acute leukaemia as well as other hematopoietic malignancies [166,

168].

The theoretical calculations on perfluorinated benzene studied in the

previous chapter provided confidence in the quantum mechanical models used to

apply further to study this class of larger molecules. In this chapter, we will

focus on the cytidine derivatives -- that is, the effects of structural changes in

sugar and in base moieties of cytidine nucleoside analogues, in order to reveal

the structure-property relationships through electronic structure and

spectroscopy.

4.1 Sugar modified nucleosides

Conformation of nucleosides plays a major role in determining biological

activity. Intramolecular interactions between sugar and the base of a nucleoside

influence the puckering preferences of the sugar ring, and ultimately, the drug

potency. The positions of hydroxyl group in a sugar determine the hydrogen

bond network of the nucleoside, and are responsible for the site selectivity of

protein- ligand interaction. The canonical structure of the 2′deoxyribonucleosides

[169, 170] and ribonucleosides [170] has been investigated theoretically for its

energetic and conformational properties.

The molecule 2′-deoxycytidine (2′-dC) is a derivative of cytidine with

one hydroxyl group (OH) removed at the C(2′) position in the ribose sugar ring. It

behaves energetically different to other 2′deoxyribonucleosides. The X-ray

crystal structure of 2′-deoxycytidine has been studied by Young et al. [171].

Theoretical investigations have established that the most energetically favourable

conformer of 2′-dC adopts C3′endo/anti north in contrast to other nucleosides

associated with a C2′endo/anti south conformation [170]. Such unique behaviour

of 2′-deoxycytidine is supported by intramolecular hydrogen bonding

interactions using AIM topological analysis [172].

60


Deoxycytidines such as 2′-dC may exist in different isomeric forms

depending on the positions of the hydroxyl (OH) group in the furanose ring. For

example, when the C(3′) position lacks a hydroxyl group then chemically it is

known as 3′-deoxycytidine (3′-dC). The molecule 3′-dC was found to be a

selective inhibitor of pre-ribosomal RNA in HeLa cells and a reversible inhibitor

of DNA replication in RNA accumulation [173]. It showed an inhibitory effect

on RNA polymerase I and III synthesized in cotton cotyledons in in vivo

condition [174]. There is no theoretical data available yet for 3′-dC. The present

study differentiates the intramolecular interactions pattern involved in nucleoside

isomers 2′-dC and 3′-dC due to the relocation of the hydroxyl group in the sugar

moiety, in vacuum and various solvents. Figure 4.1 gives the chemical structures

and nomenclature of 2′-dC and 3′-dC. In three dimensional (3D) space, the

structures of 3′-dC have been reported in the forms of two independent structures

such as the C3′-endo/anti conformations in the gauche-gauche form and gauche-

trans orientation [175].

Figure 4. 1 Chemical structures and nomenclature of the nucleoside isomers 2′-

dC and 3′-dC.

2′-dC: R1=H, R2=OH 3′-dC: R1=OH, R2=H

61


4.1.1 Geometries in vacuum and solvent phase

Optimized geometries for 2′-dC and 3′-dC in vacuum (gas phase) and in

various solutions, namely, toluene, DMSO, water and n-methyl formamide have

been tabulated in Table 4.1 with the available experimental and other theoretical

results. The PCM model has been employed and the solvents are selected in the

order of increasing polarity from non-polar to polar, i.e., toluene (Tol, =2.37),

dimethyl sulfoxide (DMSO, =46.83), water (=78.36) and n-methyl formamide

mixture (n-MF, =181.56).

Although the present theoretical calculations agree well with the

experiment [171] and other theory for 2′-dC [169], but they do not for 3′-dC. For

example, the type of sugar orientation of 3′-dC differs between theory and

experiment, with theory predicting C3′-endo while experiment predicts C3′-

endo-C2′-exo [171]. The variation is probably due to the constraints imposed by

the crystal phase in the experiment, whereas in vacuum or solution (the

theoretical calculations), there is more freedom of motion. Nevertheless, the

sugar type in 3′-dC reported in experiment [175] is significantly different from

that predicted by both vacuum and solutions.

Solvation has influenced the electronic structural properties of both the

isomers in a different way. The effect of solvents is generally negligible on the

isotropic geometric properties such as bond lengths. For example, the ring

perimeters of sugar and the base are not significantly affected by the solvents or

the orientation of the sugar. Anisotropic properties do tend to change in solution,

however. For example, the dipole moment gradually increases as the polarity of

the solvent changes from non-polar to more polar. The dipole moment of 2′-dC

changes from 6.25 Debye in vacuum to 9.13 Debye in n-MF solution, whereas

from 4.89 Debye in vacuum to 8.55 Debye in n-MF solution in 3′-dC. It is noted

that some properties of the 2′-dC and 3′-dC may behave in opposite ways in

vacuum and in solutions.

62


Table 4. 1 Geometric parameters of 2′-dC and 3′-dC in vacuum and in different solvents with varied dielectric constants ()*.

Parameters

2'-dC 3'-dC

Vacuum Toluene

(=2.37)

DMSO

(=46.83)

Water

(=78.36)

n-MF

(=181.56) Expt.

a

Other

workb

Vacuum Toluene

(=2.37)

DMSO

(=46.83)

Water

(=78.36)

n-MF

(=181.56) Expt.

c

R5(Å) 7.48 7.47 7.48 7.48 7.47 7.46 7.46 7.49 7.49 7.49 7.49 7.49 7.43

R6(Å) 8.28 8.28 8.27 8.27 8.27 8.23 - 8.26 8.26 8.26 8.26 8.26 8.20

(◦) 197.92 200.22 201.09 201.14 200.99 201.2 196 -168.79 -169.48 -171.55 -169.05 -172.12 172.10

(◦) 55.08 55.03 54.79 54.49 53.45 56.7 55 171.45 173.66 178.97 177.23 178.32 173.70

µ (D) 6.25 7.43 9.05 9.10 9.13 - - 4.89 6.03 7.77 8.06 8.55 -

<R2> (a.u.) 3884.53 3878.25 3869.76 3871.08 3873.10 - - 3780.81 3786.16 3799.29 3820.92 3829.06 -

∆E/Kcal.mol-1

0.00 11.43 27.20 28.01 29.33 - - 0 8.51 20.46 21.91 24.36 -

ZPE(Kcal.mol-1

) 146.84 146.15 144.96 144.87 144.60 - - 147.39 146.60 145.52 145.38 144.91 -

Type

C3'-

endo,

North

C3'-

endo,

North

C3'-endo,

North

C3'-endo,

North

C3'-endo,

North

C3'-

endo

-C2'-

exo

C3'-

endo,

North

C3'-exo

South

C3'-exo

South

C3'-exo

South

C3'-exo

South

C3'-exo

South

C3'-

endo

North

*Present work based on B3LYP/6-31G* model in vacuum and other solvents. a In crystal phase, See Ref.[171]. bBased on B3LYP/6-31G(d) in vacuum, See Ref. [169]. cSee Ref. [175].

63


For example, in 2′-dC, the angle, the pseudorotation amplitude vm and

the electronic spatial extent <R2> are largest in vacuum (when compared to the

solution results). The opposite is true for 3′-dC, where the vacuum results are

smaller than those for the solution. This indicates that the two nucleoside

isomers may engage in very different intramolecular interactions. They must

therefore, possess different shapes and interact with solvents in different

manners.

4.1.2 Hydrogen bond networks

Biomolecules such as nucleosides, nucleotides and their analogues

usually engage in various intermolecular and intramolecular interactions, each

of which affects the arrangements and shapes of the molecules. Hydrogen

bonding (HB) is one such interaction. Table 4.2 reports the distances between

the hydrogen atom and the oxygen or nitrogen atoms of 2′-dC and 3′-dC in

vacuum. In this table, H…O or H…N distances that are smaller than a cut-off

geometric criterion of 2.80 Å [176, 177] are underlined, these being indicative

of the presence of hydrogen bonding. Although other criteria like the Bader’s

bond critical point (BCP) [178], which by itself is not a sufficient condition

[179] for predicting HBs, are also available, a simple cut-off criterion of 2.80 Å

[176, 177] is employed in this study.

Hydrogen bonds may exist either between sugar-base (SB) or sugar-

sugar (SS) atoms in the nucleosides, as previously noted [180]. Sugar

conformations such as endo or exo, south or north, are associated with the

unique HBs in the nucleosides. For example, 2′-dC favours the C3′-endo north

conformation, whereas other nucleosides prefer the C2′-endo south

conformation [170]. The unique behaviour of the 2′-dC nucleoside is due to

significant C(6)-H∙∙∙O(5′) intramolecular HBs [172]. The C(6)−H bonded

hydrogen interactions with either the O(4′) or O(5′) atom are the common

hydrogen bonds in the anti conformation of pyrimidine nucleosides.

64


Table 4. 2 Distances of C− H∙∙∙O, C− H∙∙∙ N and O− H∙∙∙O networks of 2′-dC and 3′-dC in various solvents (Å).

The H-bonds in which the H…X distance is smaller than 2.80 Å are highlighted and underlined in the table.

2′-dC gas Toluene DMSO Water n-MF 3′-dC gas Toluene DMSO Water n-MF Sugar-Sugar (SS)

C(1)− H∙∙∙ O(3) 4.453 4.458 4.463 4.461 4.456 C(1)− H∙∙∙ O(2) 2.513 2.517 2.521 2.521 2.557 C(2)− H∙∙∙ O(3) 3.003 3.000 2.997 2.996 2.991 C(2)− H∙∙∙ O(2) 2.078 2.078 2.080 2.080 2.082 C(2)− H∙∙∙ O(3) 2.660 2.659 2.658 2.656 2.655 C(3)− H∙∙∙ O(2) 2.941 2.943 2.945 2.947 2.936 C(3)− H∙∙∙ O(3) 2.004 2.005 2.008 2.009 2.003 C(3)− H∙∙∙ O(2) 2.455 2.469 2.493 2.481 2.488 C(4)− H∙∙∙ O(3) 2.603 2.604 2.604 2.604 2.614 C(4)− H∙∙∙ O(2) 4.326 4.340 4.363 4.344 4.317 C(5)− H∙∙∙ O(3) 3.022 3.030 3.036 3.037 3.059 C(5)− H∙∙∙ O(2) 4.390 4.379 4.358 4.387 4.500 C(1)− H∙∙∙ O(4) 2.066 2.063 2.060 2.060 2.061 C(1)− H∙∙∙ O(4) 2.061 2.060 2.062 2.061 2.074 C(4)− H∙∙∙ O(4) 2.077 2.078 2.081 2.081 2.077 C(4)− H∙∙∙ O(4) 2.045 2.048 2.052 2.055 2.059 C(5)− H∙∙∙ O(4) 3.349 3.353 3.358 3.357 3.355 C(5)− H∙∙∙ O(4) 2.739 2.730 2.704 2.717 2.705 C(5)− H∙∙∙ O(4) 2.647 2.651 2.654 2.652 2.638 C(5)− H∙∙∙ O(4) 3.370 3.372 3.381 3.378 3.368 C(3)− H∙∙∙ O(5) 2.491 2.498 2.511 2.510 2.482 C(3)− H∙∙∙ O(5) 4.100 4.096 4.077 4.080 4.056 C(4)− H∙∙∙ O(5) 3.333 3.337 3.343 3.343 3.335 C(4)− H∙∙∙ O(5) 2.679 2.675 2.668 2.672 2.655 C(5)− H∙∙∙ O(5) 2.093 2.093 2.093 2.092 2.092 C(5)− H∙∙∙ O(5) 2.086 2.086 2.082 2.092 2.093

C(5)− H ∙∙∙ O(5) 2.090 2.090 2.089 2.090 2.090 C(5)− H ∙∙∙ O(5) 2.039 2.038 2.036 2.037 2.026 Sugar-Base (SB)

C(6) − H∙∙∙ O(4) 2.316 2.317 2.317 2.317 2.318 C(6) − H∙∙∙ O(4) 2.318 2.303 2.267 2.306 2.251 C(6) − H∙∙∙ O(5) 2.311 2.254 2.243 2.253 2.265 C(6) − H∙∙∙ O(5) 2.702 2.754 2.878 2.872 3.320 C(1)− H∙∙∙ O(2) 2.379 2.382 2.403 2.402 2.379 C(1)− H∙∙∙ O(2) 2.499 2.516 2.552 2.524 2.518 C(2)− H∙∙∙ O(2) 2.749 2.838 2.889 2.885 2.865 C(2)− H∙∙∙ O(2) 3.105 3.108 3.101 3.141 3.346 C(1)− H∙∙∙ N(1) 2.063 2.067 2.073 2.072 2.065 C(1)− H∙∙∙ N(1) 2.078 2.081 2.086 2.083 2.080 C(2)− H∙∙∙ N(1) 2.617 2.623 2.626 2.626 2.623 C(2)− H∙∙∙ N(1) 2.551 2.556 2.562 2.560 2.611 C(5) − H∙∙∙ N(3) 2.699 2.692 2.683 2.683 2.691 C(5) − H∙∙∙ N(3) 2.705 2.699 2.690 2.689 2.696 O(3)− H∙∙∙ O(2) 5.580 5.731 5.808 5.796 5.773 O(2)− H∙∙∙ O(2) 1.874 1.870 1.866 1.876 1.789 O(5)− H∙∙∙ O(4) 3.750 3.759 3.772 3.374 3.718 O(5)− H∙∙∙ O(4) 2.205 2.279 2.446 2.389 2.420

65


The 2′-dC and 3′-dC isomers display certain isomer-specific HBs, which

are highlighted in Table 4.2. For example, in the 2′-dC isomer, the C(2′)-H∙∙∙O(2)

(SB) bond is only presented in the gas phase based on the 2.80 Å criterion,

whereas the H∙∙∙O(2) distances are elongated in all the solvents in the table

beyond the cut-off. In addition, the SB intramolecular hydrogen bond C(6)-

H∙∙∙O(5′) in 3′-dC greatly influences the conformational behaviour in vacuum

and in toluene but it is found to be insignificant in other solvents with stronger

dielectric constants such as DMSO, water and n-MF.

Particular isomers also display unique SS hydrogen bonds in some cases.

For example, C(2′)-H′′∙∙∙O(3′), C(4′)-H∙∙∙O(3′), C(5′)-H′′∙∙∙O(4′) and C(3′)-H∙∙∙O(5′) is

only observed in 2′-dC, whereas its isomer 3′-dC forms its own unique

hydrogen bonds, such as C(1′)-H∙∙∙O(2′), C(2′)-H∙∙∙O(2′), C(5′)-H∙∙∙O(4′) and C(4′)-

H∙∙∙O(5′). Another interesting hydrogen bond interaction is the O-H∙∙∙O bond

network. For example, O(2′)-H∙∙∙O(2) and O(5′)-H∙∙∙O(4′) networks only appear in

the 3′-dC isomer. One of the reasons why 2′-dC is present in the DNA double

helix rather than its isomer 3′-dC might be steric hindrance caused by O(2′)-

H∙∙∙O(2) type of interactions involved with O(2′)-H hydroxyl group in 3′-dC.

Other reasons may attribute for a preference to 2′-dC in DNA is yet to be

discovered.

4.1.3 Infrared spectroscopy

Vibrational spectroscopy is an effective means of examining the

intramolecular interactions of conformers/isomers. Table 4.3 presents the IR

frequencies of 2′-dC and their assignments using the experimental data of Li et

al. [181]. Note that the scale factor 0.9613 has been applied to the calculated

frequencies, in order to approximately correct the anharmonicity error

introduced by the model (B3LYP/6-31G*), as recommended by previous

studies [182-185]. As seen from this table, the scaled frequencies agree

reasonably well with the experiment. Note that in the higher frequency region,

the experimental frequencies are Raman spectral lines rather than IR.

66


Table 4. 3 Comparison of experiment with simulated vibrational frequencies of

2′-dC.

Mode No.

Calculated wavenumbers

(Scaled by 0.94)

Expt.* IR (Raman) 300K Assignment#

81 3540.6 - vO(5′)-H 80 3497.1 (3397.3) vO(3′)-H 79 3483.8 (3369.2) vN-H-H Asym 78 3370.5 (3333.8) vN-H-H Sym 77 3053.0 (3117.1) vC(6)-H 76 3032.8 (3100.4) vC(5)-H 75 2977.9 (2892) vC(2′)-H 74 2942.0 - vC(1′)-H 73 2932.4 (2922.6) vC(3′)-H 72 2868.1 - vC(5′)-H-H Asym 71 2865.3 - vC(2′)-H-H Sym 70 2834.6 - vC(5′)-H-H Sym 69 2797.0 - vC(4′)-H 68 1666.4 1711.5 (1705.4) vC(2)=O

66 1595.7 1670.1(1668.5) vC(5)-C(6), N(4)-H(1)-H(2) scissors

65 1556.8 1590.2 N(4)-H(1)-H(2) scissors

64 1480.2 1574.6 vC(4)-C(5), bC(5)-H 63 1442.1 - C(5′)-H-H scissors

62 1436.3 - bC(6)-H, C(5)-H rocking

61 1425.3 - C(2′)-H-H scissors 60 1387.0 1539.9(1539.3) ωC(5′)-H-H, O(5′)-H 59 1373.2 1421.7(1426.3) ωC(3′)-H, O(3′)-H 58 1363.4 - ωC(1′)-H

57 1343.3 1371.1(1369.1) ωC(4′)-H, C(3′)-H, O(3’)-H

*Experiment, see Ref. [181].

#v stretch, asym – antisymmetric stretch, sym – symmetric stretch, ω wagging,

δ bending, def. – deformation.

67


Figure 4.2 presents a comparison of the simulated infrared spectra of the

2′-dC and 3′-dC isomers in vacuum, which shows the structural differences of

the molecular pair. The IR spectral peaks in the region between 2900 and 3900

cm-1 provide information pertaining to HBs present in the isomers. This region

illuminates the structural differences in the isomer pair, indicating that the

relocation of hydroxyl (OH) group from the C(3′) position in 2′-dC to the C(2′)

position in 3′-dC results in significant changes in intramolecular interactions.

Figure 4. 2 Comparison of simulated IR spectra of 2′-dC and 3′-dC in vacuum.

Usually, formation of any X−H∙∙∙Y hydrogen bonds causes a red shift of

the X−H stretching frequency in their IR spectra [186]. This would be the case

68


for the vibration associated with the O(2′)/O(3′)-H bonds of 3′-dC. The spectral

peak assigned to the O(2′)-H is intense and shows a red shift typical of the usual

hydrogen bonding pattern with O(2) in the base moiety. Blue shifted IR

frequencies are usually identified in intermolecular hydrogen bonds [187] rather

than intramolecular hydrogen bonds, since a reference conformation is required

to identify a shift. Recently, we proposed a novel method for the study of blue-

shifted IR spectral peaks of intramolecular hydrogen bonds for nucleosides

using their conformers as the reference [180, 188]. One example of this, the

O(3′)-H∙∙∙O(2) interactions, which thus far have been identified only in vacuum

and not in solvated environments, display a vibration with an improper blue

shift, due to an HB. Other improper blue shifted IR spectral peaks in 3′-dC

include the C(4′)-H stretch, which shifts blue due to an intramolecular HB

formation with O(4′), which is only present in this isomer. It exhibits an

improper blue shift of 103cm-1 relative to 2′-dC isomer (as marked by the dash

line in the Figure 4.2).

4.1.3.1 Solvent effects on IR spectra

Table 4.4 compares the stretching frequencies (above 2900 cm-1) of the

deoxycytidine nucleosides in vacuum and in solvents. In general, the IR

spectral peaks show a global red shift of about 100 to 150 cm-1 in the frequency

region below 2900 cm-1. The amount of red shift with respect to solvents varies

with their dielectric constants. That is, the more polar the solvent, the greater

the red shift in the vibrational frequencies. This effect is more pronounced in 2′-

dC than in 3′-dC. For example, one of the O(5′)-H stretch vibrations of 2′-dC is

3766.61 cm-1 in vacuum, but changes to 3649.52 cm-1 in toluene (=2.37),

3441.72 cm-1 in DMSO (=48.83), 3431.69 cm-1 in water (=78.36) and

3415.06 cm-1 in n-MF (=181.56). A similar trend of red shift for the O(5′)-H

peak is also observed in 3′-dC: 3724.53 cm-1 (vacuum), 3687.10 cm-1 (toluene),

3556.60 cm-1 (DMSO), 3529.37 cm-1 (water), 3503.18 cm-1 (n-MF). However,

some vibrational frequencies do not follow this trend.

69


Table 4. 4. Infrared frequencies (v, cm-1) and assignment of nucleosides 2′-dC and 3′-dC in vacuum and various solvents.

Gas Toluene DMSO Water n-MF v Assign. v Assign. v Assign. v Assign. v Assign.

2′-dC 3766.61 O(5’)-H 3657.22 N-H-H asym 3573.73 N-H-H Asym 3570.61 N-H-H Asym 3564.27 N-H-H Asym 3720.27 O(3’)-H 3649.52 O(5’)-H 3461.06 N-H-H Sym 3458.32 N-H-H Sym 3452.60 N-H-H Sym 3706.19 N-H-H asym 3612.11 O(3’)-H 3441.72 O(5’)-H 3431.69 O(5’)-H 3415.06 O(5’)-H 3585.65 N-H-H sym 3538.21 N-H-H sym 3399.68 O(3’)-H 3387.53 O(3’)-H 3370.56 O(3’)-H 3247.85 C(6)-H 3240.73 C(6)-H 3227.78 C(6)-H 3227.84 C(6)-H 3224.90 C(6)-H 3226.34 C(5)-H 3211.61 C(5)-H 3184.89 C(5)-H 3184.48 C(5)-H 3182.51 C(5)-H 3167.95 C(2’)-H-H asym 3156.51 C(2’)-H-H asym 3143.05 C(2’)-H-H asym 3142.54 C(2’)-H-H asym 3140.46 C(2’)-H-H asym 3129.74 C(1’)-H 3117.22 C(1’)-H 3098.77 C(1’)-H 3096.96 C(1’)-H 3092.70 C(1’)-H 3119.61 C(3’)-H 3106.08 C(3’)-H 3083.54 C(3’)-H 3079.88 C(3’)-H 3072.43 C(3’)-H 3051.18 C(5’)-H-H asym 3050.86 C(2’)-H-H sym 3052.31 C(2’)-H-H sym 3052.33 C(2’)-H-H sym 3050.96 C(2’)-H-H sym 3048.19 C(2’)-H-H sym 3046.75 C(5’)-H-H asym 3042.95 C(5’)-H-H asym 3043.22 C(5’)-H-H asym 3040.82 C(5’)-H-H asym 3015.48 C(5’)-H-H sym 3011.00 C(5’)-H-H sym 3004.69 C(5’)-H-H sym 3004.48 C(5’)-H-H sym 3003.61 C(5’)-H-H sym 2975.56 C(4’)-H 2974.90 C(4’)-H 2972.19 C(4’)-H 2973.15 C(4’)-H 2971.30 C(4’)-H

3′-dC 3724.53 O(5’)-H 3687.10 O(5’)-H 3566.21 N-H-H asym 3566.96 N-H-H sym 3563.62 N-H-H asym 3721.43 N-H-H asym 3668.71 N-H-H asym 3556.60 O(5’)-H 3529.37 O(5’)-H 3503.18 O(2’)-H 3598.06 N-H-H sym 3548.18 O(2’)-H 3527.34 O(2’)-H 3462.13 O(2’)-H 3450.88 N-H-H sym 3563.49 O(2’)-H 3545.91 N-H-H sym 3454.68 N-H-H sym 3455.10 N-H-H sym 3419.75 O(5’)-H 3272.53 C(6)-H 3273.96 C(6)-H 3271.25 C(6)-H 3257.35 C(6)-H 3208.78 C(6)-H 3233.03 C(5)-H 3216.51 C(5)-H 3187.42 C(5)-H 3187.04 C(5)-H 3183.18 C(5)-H 3133.00 C(3’)-H-H asym 3128.63 C(3’)-H-H asym 3123.23 C(3’)-H-H asym 3123.21 C(3’)-H-H asym 3118.86 C(3’)-H-H asym 3096.18 C(5’)-H-H asym 3089.34 C(5’)-H-H asym 3077.39 C(5’)-H-H asym 3081.17 C(5’)-H-H asym 3086.78 C(5’)-H-H asym 3090.52 C(1’)-H 3079.75 C(3’)-H-H sym 3070.35 C(3’)-H-H sym 3071.02 C(3’)-H-H sym 3069.03 C(3’)-H-H sym 3084.23 C(3’)-H-H sym 3071.84 C(1’)-H 3054.30 C(1’)-H 3054.81 C(1’)-H 3053.43 C(1’)-H 3078.71 C(4’)-H 3069.54 C(4’)-H 3042.50 C(4’)-H 3041.48 C(4’)-H 3030.20 C(4’)-H 2994.59 C(5’)-H-H sym 2995.99 C(5’)-H-H sym 2992.60 C(5’)-H-H sym 2989.58 C(5’)-H-H sym 2993.68 C(5’)-H-H sym 2982.32 C(2’)-H 2982.59 C(2’)-H 2978.18 C(2’)-H 2979.00 C(2’)-H 2977.43 C(2’)-H

70


For example, the C(2′)-H-H symmetric stretch vibrations of 2′-dC is

3048.19 cm-1 in vacuum, and becomes 3050.86 cm-1 in toluene (=2.37), 3052.31

cm-1 in DMSO (=48.83), 3052.33 cm-1 in water (=78.36) and 3050.96 cm-1 in

n-MF (=181.56). The red shift found in the nucleosides does not linearly

depend on the dielectric constants of the solvents. For example, the red shift of

C(6)–H in 3′-dC is smaller in the non-polar solvent toluene (3273.96cm-1) than in

polar solvents (e.g., n-MF) (3208.78cm-1) with respect to vacuum (3272.53cm-

1). In the case of 2′-dC, the C(6)-H peak position follows the red shift pattern.

These shifts are mainly caused by solute-solvent interactions, and the resulting

structural rearrangements may result in either a small or large red/blue shift.

Figure 4.3 presents the simulated IR spectra of (a) 2′-dC and (b) 3′-dC in

both vacuum and in the solvents. In the functional group frequency region

between 3300cm-1 and 2900cm-1, the basic spectrum pattern observed in vacuum

persists in the solvents for both the nucleosides. Solvents do cause some changes

-- for example the blue or red shift observed in the nucleosides is found to

diminish in the various non-ploar and polar solvents. The most pronounced

example is the improper blue-shifted peak of the C(4′)–H stretch mode and is

marked by an asterisk (*) in the spectra. It is apparent that the trend of the

improper hydrogen bond blue shift of the C(4′)-H stretch vibration mode in 3′-dC

decreases with increasing polarity of the solvents. For example, the blue shift of

C(4′)-H is approximately 103, 94, 82, 81, 72 cm-1, in the solvents with increasing

polarity, i.e. vacuum, toluene, DMSO, water and n-MF, respectively. Solvents

red shift the IR spectra of the deoxyribonucleosides with respect to vacuum and

reduce the improper blue shift, but do not change the nature of the shift (red or

blue). As can be seen from the spectra, solvent effects on the C(4′)–H vibration in

3′-dC are more apparent than these in 2′-dC, particularly in strong polar solvents.

Recent studies have exhibited [180] reduction in blue shifted frequencies of AZT

in aqueous solvents compared to its gas phase counterpart. The present study

suggests that the relationship between the blue shift and the polarity of the

solvents is non- linear [188].

71


Figure 4. 3 Comparison of simulated IR spectra of isomers (a) 2′-dC and (b) 3′-

dC in various solvents with respect to vacuum.

(a)

(b)

72


4.2 Interactions in base modified nucleosides

Some cytosine analogues such as 2-H pyrimidinone have been reported

as mechanism-based inhibitor of DNA methyltransferases enzyme [189]. These

2-pyrimidinone nucleosides have been reported as inhibitors of the enzyme

cytidine deaminases (CDA) [190, 191]. A cytidine derivative, 1-(β-D-

ribofuranosyl)-2-pyrimidinone (zebularine or zeb) inhibits the CDA [190] and

methyltransferase [192] enzymes, thereby acting as an antitumor and anticancer

drug. It was primarily synthesized as a bacteriostatic agent [193] nearly three

decades ago; recent biochemical investigations indicated that zeb is a potent

enzyme inhibitor [190]. Compared to other antitumor drugs such as 5-

azacytidine, zeb has a considerably lower toxicity. The favourable chemical

stability of zeb facilitates oral administration and makes it a promising candidate

for reversing DNA methylation [97].

Figure 4.4 gives the chemical structures of two zebularine analogs, i.e.,

1-(β-D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5) and 1-(β-D-ribofuranosyl)-

4-methyl-2-pyrimidinone (4M2P). These two compounds were evaluated for

their inhibitory actions against the CDA of Escherichia coli [190], where they

showed less activity than zeb.

OH

OH

O

OH

N

N

O

1'2'

3' 4'

2'

3'

123

45

6

5'

4'

2

OH

OH

O

OH

N

N

O

H3C

1'2'3' 4'

2'

3'

123

45

6

7

5'

4'

2

Figure 4. 4 Chemical structures and atom numbering of zebularine (zeb) (left)

and 1-(β-D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5) (right).

1-(β-D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5)

1-(β-D-ribofuranosyl)-2-pyrimidinone (zeb)

73


d5 is considered as modified thymine derivative, however, it does not

base pair with the adenine nucleoside [194, 195]. In the DNA decamer, d5 was

substituted for thymine, which affected the overall behaviour of DNA strand due

to local perturbation [196]. Recently, a theoretical investigation of the

fluorescence behaviour of 5-methyl-2-pyrimidinone (base alone) was reported

[197].

Methylation of zeb at the C(5) position produces d5. Structurally, d5 and

zeb are similar except at the base. d5 has a methyl fragment at the C(5) position of

the pyrimidine ring where zeb does not. Because the methyl group is an alkyl

one, it can produce an inductive effect. There have been efforts to study methyl

effects on the external chemical effects of nucleosides. It was found that the

methyl group is not a highly reactive one but has a pronounced inhibitive

influence on the methylation of DNA [198]. In addition, studies on thymine

revealed that the methyl group within its structure is important for the stability of

DNA and has a considerable effect on the helical structure of the DNA [199]. In

the present work, we are studying the effect of the methyl group on the zeb

structure using spectroscopic methods and DSA.

4.2.1 Property changes in d5 with respect to zeb

Hirshfeld charges are important anisotropic properties when exploring

the behaviour of atoms in molecules. Figure 4.5 provides the comparison of the

atomic Hirshfeld charges (QH) based on the LB94/et-pVQZ model. The results

show that the N and O sites possess negative charges, which can be used as

electron donors to accept protons. In a compound, the oxygens and nitrogens are

negative, although the oxygen sites have a greater negative charge than the

nitrogen sites. The C atoms balance the negative charges and are positive except

at the C(5) site, which has a negative charge in both d5 and zeb [90].

74


Figure 4. 5 Comparison of Hirshfeld charges of zeb and d5 based on the

LB94/et-pVQZ model.

Most of the non-hydrogen atomic sites in zeb and d5 have similar QH

values, with the exception of C(5) and the methyl carbon atom, C(7), which both

have negative charges. The electron distributions on the sugar moiety do not

change apparently, presumably because the methyl substitution happens on the

base moiety. With the exception of the C(5) and C(7) sites, there are insignificant

changes on most of the non-hydrogen atomic sites in the base moiety of the

compound pair. The C(5) site exhibits a significant negative charge in d5 with

respect to that of zeb. The charge on C(7) of d5 appears to originate from the C(5)

position, where it is attached. Because of this, the methyl fragment appears to be

electron-rich, which leads to the inductive effect observed in d5.

The condensed Fukui function [200] based on the Hirshfeld partitioning

scheme was also calculated from the LB94/et-pVQZ model. It is a useful

descriptor in the identification of the nucleophilic/electrophilic behaviour of a

specific site within a molecule. The Condensed Fukui function, f-- indicates the

75


capacity of an electrophilic attack, and is presented in Figure 4.6. The condensed

Fukui function shows that the reactive sites are the oxygens and nitrogens. For

the carbons, the sugar carbons are less reactive than the base carbons. The sugar

carbons are engaged with saturated C–C and C–H bonds. Atoms in the base are

predicted to be more reactive than those on the sugar atoms.

Figure 4. 6 Fukui function of zeb and d5 pair.

The Fukui functions of the molecular pair allow their reactivities to be

divided into three regions: inactive regions with f- < 0.03; medium activity

regions with 0.03 f- < 0.06; and active regions with f - > 0.06. These regions

are demarcated by the dashed lines in the figure. In general, the sugar sites are

predicted to be less active than the base sites, whereas the base sites are

dominated by either active or medium f - regions in this figure. For example, all

the sugar carbons are in the inactive region with f -< 0.03, whereas all the base

carbons are located in the medium active region with 0.03 f- < 0.06, except for

76


the C(5) site which is in the active region with f - > 0.06. This may account for the

fact that the methyl group in d5 is attached at C(5) site.

The oxygen sites on the sugar cover the widest range of Fukui function

values in this figure, appearing in all three regions. The activities of the oxygen

and nitrogen sites in the nucleosides vary widely, ranging over all three zones.

For example, the sugar O(2’) and the base keto O(2) and N(3) sites are very active

sites; all are in the active zone with O(2) and N(3) being significantly more active

than the sugar C(2’) site. On the other hand, they can be quite inactive such as the

sugar O(3’) site. The very different Fukui functions regarding each atomic site in

the nucleosides suggest that the chemical reactivity of these oxygen atoms is

quite different.

The variation of the Fukui function for the atoms of the base also reflects

the conjugation system C(5)-C(4)=N(3)-C(2)=O(2) of the pyrimidine base of the

nucleosides. As shown in Figure 4.6, the Fukui functions of sites C(5), N(3) and

O(2) change significantly from zeb to d5, whereas C(4) and C(2), which are located

between the three sites showing a large change, do not exhibit such changes. The

other side on the pyrimidine ring, that is, C(5)=C(6)-N(1)-C(2), does not take part in

such conjugation and, as a result, the Fukui functions of the C(6) and N(1) sites do

not change significantly. These properties demonstrate that methylation

influences specific sites at the d5 nucleoside.

4.2.2 Valence space responses to methylation

X-ray photoelectron spectra of molecules depend not only on their

binding energies but also on the distribution or intensities of the ionized states in

the region. Valence ionization potentials (IPs) of zeb and d5 have been

calculated quantum mechanically using SAOP/et-pVQZ [143] and OVGF/TZVP

[77, 78]. Figure 4.7 compares the simulated X-ray photoelectron spectra (XPS)

of zeb and d5, based on the SAOP/et-pVQZ model (and resolution-folded with a

FWHM of 0.40eV) [90].

77


Figure 4. 7 Valence photoelectron spectra of zeb and d5 simulated using the

SAOP/et-pVQZ model.

From a spectral point of view, the valence shell of the nucleoside pair

shows apparent species dependent changes, but after an energy shift, the spectral

patterns in figure. 4.7 exhibit certain similarities, such as the spectral peaks in the

regions above 19eV. The outer valence region of the spectra, however, seems

quite different. This is because the distribution and density of the orbitals in the

outer-valence shell are more congested in comparison to the inner-valence shells.

The greater density of ionization peaks accounts for the apparent difference in

the XPS in the energy region less than 19eV. In addition, a methyl effect is

apparent in the outer valence space, because the energy gaps (ΔEHOMO-LUMO)

between the HOMO and LUMO of the molecule pair differ by 0.25eV. The

78


ΔEHOMO-LUMO is given by 3.35eV for zeb but reduces to 3.10eV for d5 in the

present calculation [90]. The decrease of the HOMO-LUMO gap in d5 indicates

that it can be more reactive than zeb.

Table 4.5 compares the IPs of zeb with those of d5, calculated using the

SAOP/et-pVQZ and OVGF/TZVP models. The negative orbital energies (-εi)

produced by the B3LYP/aug-cc-pVTZ model are also given in the table for

comparison. It is seen that valence ionization potentials produced by the

OVGF/TZVP model agree with the SAOP/et-pVQZ model in the inner valence

region.

Table 4. 5 Comparison of valence orbital ionization energies (eV) of zeb and d5

calculated using different models*. Methyl affected orbitals are underlined.

zeb d5 MO Orbital OVGF SAOP B3LYP Orbital OVGF SAOP B3LYP

1(HOMO) 60a 08.41 10.35 06.69 64a 08.12 10.11 06.37 2 59a 09.67 10.60 07.30 63a 09.56 10.50 07.12 3 58a 10.04 10.80 07.48 62a 09.97 10.71 07.32 4 57a 10.56 11.21 07.90 61a 10.47 11.12 07.73 5 56a 10.79 11.46 08.19 60a 10.85 11.40 08.06 6 55a 11.27 11.95 08.67 59a 11.06 11.86 08.51 7 54a 11.67 12.29 09.02 58a 11.52 12.22 08.88 8 57a 11.84 12.57 09.14 9 53a 12.10 12.75 09.40 56a 12.00 12.73 09.45 10 52a 12.08 12.79 09.60 55a 12.37 12.88 09.54 11 51a 12.42 13.15 09.89 54a 13.11 13.25 10.02 12 50a 13.20 13.36 10.18 53a 13.30 13.46 10.25 13 49a 13.37 13.56 10.41 52a 13.49 13.75 10.60 14 48a 13.75 13.93 10.78 51a 13.88 13.95 10.82 15 47a 13.97 14.16 11.17 50a 13.95 14.23 11.19 16 46a 14.50 14.58 11.53 49a 14.43 14.48 11.35 17 45a 14.55 14.78 11.80 48a 14.49 14.66 11.56 18 47a 14.67 14.70 11.63 19 44a 14.81 14.86 11.92 46a 14.86 14.76 11.73 20 43a 14.86 15.14 12.10 45a 14.81 15.04 12.04 21 42a 15.17 15.41 12.48 44a 14.83 15.18 12.10 22 41a 15.65 15.70 12.77 43a 15.32 15.55 12.53 23 40a 15.68 15.95 12.98 42a 15.67 15.88 12.84 24 39a 16.23 16.20 13.27 41a 16.16 16.12 13.12 25 38a 16.28 16.29 13.42 40a 16.28 16.26 13.32 26 37a 16.58 16.64 13.75 39a 16.50 16.58 13.62 27 36a 17.66 17.29 14.46 38a 17.21 17.03 14.11 28 35a 17.73 17.68 14.82 37a 17.79 17.58 14.65 29 34a 18.03 17.77 15.04 36a - 17.74 14.90 30 33a 18.09 18.11 15.31 35a - 18.02 15.18 31 32a 18.91 18.53 15.78 34a - 18.35 15.51 32 31a - 19.66 17.00 33a - 19.58 16.85

79


Table 4.5 continued 33 30a - 19.91 17.23 32a - 19.76 17.02 34 29a - 20.48 17.90 31a - 20.19 17.48 35 28a - 21.12 18.58 30a - 20.96 18.34 36 27a - 21.87 19.37 29a - 21.61 19.03 37 - 28a - 22.15 19.61 38 26a - 23.54 21.13 27a - 23.61 21.12 39 25a - 24.18 21.77 26a - 24.09 21.61 40 24a - 24.36 22.03 25a - 24.72 22.34 41 23a - 27.40 25.22 24a - 27.31 25.05 42 22a - 28.91 26.76 23a - 28.78 26.55 43 21a - 30.51 28.33 22a - 30.44 28.18 44 20a - 30.79 28.67 21a - 30.70 28.50 45 19a - 30.89 28.79 20a - 30.81 28.63 46 18a - 31.11 29.02 19a - 31.04 28.86

Figure 4.8 presents the valence ionization energy correlation of zeb and

d5 based on the SAOP/et-pVQZ model. In addition to the “insertion” of binding

energies arising because of the insertion of the CH3 group, the methyl group

causes perturbations in the binding energy spectrum of the outer valence shell of

zeb, as shown in Figure 4.8. In d5, the molecular orbitals of the methyl moiety

affect all energies throughout the valence shell to some degree. Unlike small

molecules such as L-Alanine [201], the methyl group MOs are delocalized over

the entire valence space of the d5 molecule. The binding energy levels of the

corresponding zeb thus generally tend to shift to lower binding energies in d5,

with the exception of a few energy levels in the vicinity of the “inserted” energy

levels in d5, i.e., MO8, MO18 and MO37 in d5. The extra orbitals contributed by

the CH3 fragment causes the shift, though.

Based on the contributions of the methyl electrons in the valence shell, d5

MO’s can be classified as follows: group I orbitals (MO8, 18 and 37) which are

predominantly methyl orbitals (only in d5) and group II orbitals (MO1 (HOMO),

13, 21, 27, 34, 36 and 40), which are affected by the presence of the methyl

group, but which are themselves not primarily methyl group orbitals [90]. The

methyl-affected orbitals are underlined in Table 4.5. The frontier orbitals

(HOMO and LUMO) are primarily localized in the base ring, which agrees with

the results of the condensed Fukui function. In fact, the HOMO and LUMO

80


orbitals are quite similar in both nucleosides, except for a small downwards

energy shift in d5.

Figure 4. 8 Energy correlation diagram of valence orbital energies of zeb and d5

based on SAOP/et-pVQZ.

4.2.3 Methyl affected orbitals in momentum space

The methyl fragment in d5 is the major source of variation in the valence

region, as the methyl affected MOs are delocalized over the entire valence region

in d5 [90]. In order to further understand how the methyl group affects the

character of the valence orbitals, the theoretical momentum profiles of primary

methyl MOs (that is, group I) along with its electron density distributions are

81


calculated and presented in Figure 4.9. Even though the methyl signature MOs 8,

18 and 37 are grouped based on the methyl charge concentration, they exhibit

different types of bonding in all the three orbitals and their momentum

distributions indicate that the MOs are not related to one another. For example,

MO8 displays π type of bonding whereas MO18 shows a hybrid (s and p)

contribution, mostly dominated by p electrons and MO37 is predominantly a

sigma bonding orbital. However, charge density distributions are localizing on

the methyl group is increasing (MO8 < MO18 < MO37) when hole move

towards the inner valence for the inner valence orbitals more than the outer

valence orbitals. This can be clearly visualised from the orbital contour map in

Figure 4.9 [202].

Figure 4. 9 Methyl dominated orbitals of d5 with its electron density and

momentum distribution.

82


Secondary methyl related orbitals identified are HOMO, MOs 13, 21, 27,

34, 36 and 40 of d5 are correlated with zeb based on their binding energy shift.

Figure 4.10 provides details of these methyl related orbitals of zeb and d5 in

pairs, in both position and momentum space. As can be seen in this figure, it can

be difficult to pair the zeb and d5 orbitals based on their information in position

space, as the orbitals are quite different in zeb and in d5. However, the orbital

momentum profiles clearly show a certain association between the pairs in the

momentum region of p >1.0 a.u.

Figure 4. 10 Secondary methyl orbitals identified in d5 compared with their

analogues in zeb. The electron density and momentum distributions are shown

for all orbitals.

83


Nevertheless, differences in the methyl affected orbitals are also clearly

reflected by their distinctive orbital momentum profiles in the region of p <1.0

a.u. For example, the MO13 pair, i.e., orbitals 49a (zeb) and 52a (d5), which are

associated with binding energies of 13.56 eV and 13.75 eV, respectively,

possesses quite dissimilar electron densities. The electron density concentration

of this orbital in zeb is predominantly on sugar. However, for d5, the electron

density is spread out over both the sugar and base moieties. This is also

demonstrated by their orbital momentum profiles, which exhibit large variations

in small momentum region. The shape of the orbital momentum profiles signify

the sp-hybridcharacters with s-electron dominance in zeb, whereas in d5 p-

electrons seems to dominate in this orbital [202].

In another example, orbital charge densities of the MO34 pair, i.e., 29a

(zeb) and 31a (d5), are found to be similar in position space with the exception

of the methyl group in d5, their orbital momentum profiles in the small

momentum region of p < 0.50 a.u. amplify the differences in the base moiety

caused by the methyl group. Similarly, orbital pair MO40, 24a (zeb) and 25a

(d5), look alike in their electron density, but the electron charge distribution in

the sugar segment of d5 causes the orbital momentum profiles to be significantly

changed. In summary, these secondary methyl related orbitals of zeb and d5

show that, despite their association, the structures of their associated molecules

cause a variation in their character. The orbital profiles provide useful bonding

mechanism information in zeb and d5.

4.3 Summary

In summary, the effects of modifications in the sugar and base moieties

of the nucleoside cytidine derivatives have been studied quantum mechanically,

using spectroscopic and orbital based information. Relocation of the OH group at

C(2’)/C(3’) positions in the sugar moiety of the deoxycytidine isomers in vacuum

and in various solvents has been studied and compared with the available

experiments. It is found that the vacuum, solvent and crystal phase resulted in

different sugar puckering due to varied constraints in the three dimensional space.

84


This may be more significant in 3′-dC, as the experimental pseudorotational

phase angle is significantly different from the predicted/calculated from vacuum

and in solutions. The 2′-dC and 3′-dC isomers present peculiar sugar-sugar and

sugar-base intramolecular hydrogen bonds, in which the 3′-dC nucleoside

interacts with solvents causing certain C–H stretch IR frequencies to be blue-

shifted. In general, solvents lead to a global red shift with respect to vacuum in

both the isomers.

The electronic structures of the cytidine analogues, zebularine and d5

have been investigated with a focus on the methylation at the C(5) site in the base

of zeb to give d5. Site-dependent properties such as Hirshfeld charges and

condensed Fukui functions change more apparently at this site of methylation. In

particular, the Fukui function shows the conjugation of the C(5)-C(4)=N(3)-

C(2)=O(2) with an alternative strong-weak pattern in the pyrimidine base ring.

Detailed orbital based analysis is able to reveal the complex structures of the

nucleoside pair, as properties and behaviour of the methylation have a significant

impact on the electronic structures of the two analogues. In valence space, the

extra methyl group in the base moiety affects binding energy spectra more

significantly in outer valence region than the inner valence region. The methyl

affected orbitals are identified and the difference between the analogues are

revealed through momentum space information.

85

From electron momentum spectroscopy to gamma-ray spectroscopy

CChhaapptteerr 55


5. Introduction

The chemical phenomena of atoms and molecules are largely determined

by the behaviour of their electrons. The electronic structures of molecules are

more commonly studied and most widely understood in terms of position space

representation. In the 1940s, Coulson and Duncanson investigated the electronic

structures of molecules and bonding concepts in momentum space [203, 204].

Subsequently, electron momentum spectroscopy (EMS) was developed. EMS

offers a unique insight into valence individual orbital electron momentum

densities (momentum distributions - MD) [93]. Because EMS experiments reveal

their information in momentum space, it is said to provide a complementary

picture of chemical phenomena. As indicated by Weigold and McCarthy [93],

two natural outgrowths of the EMS technique are Compton profiles and gamma-

ray spectroscopy.

A positron (e+) is an antielectron (e-). The existence of antimatter was

first proposed by Paul Dirac in 1930 [205] and latter observed by C. D Anderson

in 1932 [206, 207], who gave the positron its name. Positron interactions can

cause electronic, vibrational or rotational excitations of the target or collide

elastically leaving the target in its original state, as in electron scattering. When a

positron collides with an atomic or molecular target electron, either two or three

86


-ray photons are produced, changing the charge of the target. This process is

called direct annihilation. The other process is the formation of a positron-

electron bound state called positronium (Ps), which is unique to positron

scattering. This bound state can be either ortho- or para-positronium, which

exhibit different properties based on the spin states (symmetric or anti-

symmetric, respectively).

In an atom or a molecule, positron annihilation leads to the removal of

one electron from the system. Thus positron annihilation is an ionization process,

but it is qualitatively different from conventional ionization processes [101, 208]

such as those involved in conventional mass spectroscopy and in (e, 2e)

scattering. A positron can interact with atoms and molecules in several ways in

the gas phase. The interactions of positrons with various targets have been

studied for many decades [209-211] and many fundamental questions are still

remain unanswered [212]. From an experimental outlook, positrons are much

less common than electrons, and as a consequence, techniques to study positron

scattering are more difficult and less well developed. Since the positron is

distinguishable from the electrons in the interactions, the full wavefunction is not

required to be anti-symmetric with respect to exchange of the positron and the

target electrons. Thus in the theoretical approach, this eliminates the exchange

interaction between the positron and the target [100]. Positron studies, therefore,

provide challenges with respect to electrons, and as a result much investigation is

warranted in this direction to understand the interaction of positrons with

electrons in atoms and molecules.

In the previous chapters, electronic structures of molecules were studied

for electron-electron interactions. This chapter focuses on the positron-electron

interaction that produces γ-ray annihilation spectra through the low-energy plane

wave approximation (LEPWA) [22]. This method was developed in Wang

group to estimate total atomic and molecular electronic contributions to gamma-

ray spectroscopy. This chapter will show the applications of the ir model to noble

gases and small molecules.

87


5.1 The LEPWA development and validation

It has been demonstrated by Iwata et al. [101] and Van Reeth et al. [213]

that in the case of bound electrons, the -ray spectrum is dominated by the

electron contribution. However, the degree to which the bound electrons

dominate the gamma-ray spectrum of molecules remains undetermined.

Extensive measurements of momentum distributions of electron-positron pairs

have been performed in solids, liquids and gas targets [101, 214]. For recent

development of this area, refer to the recent review of Gribakin, Young and

Surko [100].

In this chapter, the LEPWA [22] is applied to study positron annihilation

on atoms and small molecules. We further extend the power of theoretical

studies to explore the profile of individual orbitals of atoms or small molecules.

In this approximation, the atomic or molecular electron shell contributions to the

positron annihilation -ray spectra can be estimated. Modern computational

models, such as HF, post-HF models (i.e., MP2 and CCSD(T)) and DFT based

models, can be used for this purpose. These models include varied levels of

electron correlation to produce the electronic wavefunctions. As quantum

mechanical models consist of theory and basis set, we can assess their

contributions to the gamma-ray spectra separately, when either theory or basis

set stays the same. For example, if the basis set stays the same, then the major

differences between the simulated gamma-ray spectra will be from the levels of

electron correlation in the theory, which enables an estimation of the effects of

electron correlation on the gamma-ray spectrum. On the other hand, if the theory

stays the same, we will be able to assess the completeness of the basis set.

In the present thesis, the basis set employed is fixed as the Godbout

density functional triple zeta with valence polarised orbitals (TZVP) [59], which

is found to produce good agreement with the experimental MDs of benzene in

the previous chapter as well as in the literature [60]. In addition, it is also a basis

set which is small enough to apply to larger molecules.

88


The LEPWA [22] has been applied to the noble gases such as He and Ar

to validate our method. Figure 5.1 presents the annihilation –ray spectra for He

(1s orbital) and Ar (3s and 3p orbitals) as a function of photon energy shift ε.

Here a momentum cut-off is 10 a.u.

Figure 5. 1 Comparison of the annihilation γ-ray spectra in the outermost shell

of He and Ar calculated based on the PW approximation using the standard

Hartree–Fock method [101, 215] (solid lines) with the present study: He (circles)

and Ar (triangles). All spectra are normalized to unity at ε = 0.

In Figure 5.1, the solid lines are calculations using the unit positron

wavefunction (which corresponds to the plane-wave (PW) approximation at low

positron momenta) [101, 215], and the symbols () and () show the present

calculations [22] for Ar and He, respectively. The annihilation –ray spectra are

symmetric, w(–) = w(), hence only positive photon energies ( > 0 keV) are

shown in Figure 5.1. All spectra are normalized to unity at = 0. It is found from

Figure 5.1 that in the LEPW approximation, the momentum distributions of the

atomic electrons in the outermost shells of He and Ar are reproduced well. This

89


is a significant result of the present approach to produce the shapes of the –ray

spectra in noble gases. As a result, the method is applied to more complex

systems such as small molecules here using modern computational chemistry

techniques.

5.2 FWHM assessment for noble gases

Experimental gamma-ray spectra for positron annihilation in noble gases

have been reported [101]. The annihilation line shape parameter, namely, the full

width at half maximum (FWHM), ε, of the –ray annihilation spectra for noble

gases with available atomic HF calculations (where the positron orbital is treated

by both HF and PW models) and the results from experiment are compared in

Table 5.1 [22]. The atomic electron wavefunctions are calculated using the

HF/TZVP model. The electronic spatial extent R2 and the mean-squared radii

of the valence orbitals, np, Rnp of the noble gases are also tabulated as an

indicator of atomic size. Here R2, which is a single number that attempts to

describe the size of an atom or a molecule, is computed as the expectation value

of electron density times the square of the distance from the centre of mass of the

molecule (or atom) [103], and Rnp is taken from Radtsig and Smirnov [216].

The annihilation spectral width ε of the noble gases exhibits an opposite

trend with respect to size; that is, ε decreases as R2 increases (except for He)

or Rnp increases [22]. The calculated ε values reveal that the apparent

discrepancies between the FWHM from the calculated total electron

contributions [22] and the measurement [215]. Namely, the FWHM are 5.1 keV

(Ne) > 3.85 keV (Ar) < 4.07 keV (Kr), whereas the measured values are 3.36

keV (Ne) > 2.30 keV (Ar) > 2.09 keV (Kr). However, as shown in the same

table, the ε values for the outer valence electron shell agree well with the

measurements and also follow the same trend. Note that the properties in this

table for Xe are only listed as references for completeness as the basis set for Xe

is the DZVP (i.e., the TZVP basis set is not available for Xe) [22].

90


Table 5. 1 Comparison of the FWHM of annihilation –ray spectra, ε (keV),

for noble gases based on the HF/TZVP model for the atomic electrons [22].

Noble Gases

ε(PW) Total

ε(PW) Valence

Expt. [101]

(ε)a

ε(HF) [99, 215]

ε(PW)d

R2 (a.u)

Rnpe

(a.u)

He 2.99 (2.99) 2.50 0.16 2.53 2.95 2.35 0.927 Ne 5.14 4.94 3.36 0.32 3.82 9.33 0.965 Ar 3.85 3.31 2.30 0.31 2.65 3.30 25.94 1.663 Kr 4.07 2.93 2.09 0.29 2.38 39.45 1.952 Xeb -c 2.48 1.92 0.22 2.06 62.83 2.338

a(ε) = (ε (PW, Val) - ε (Expt.))/ε (PW, Val). bFor Xe the basis set is DGDZVP as TZVP is not available for Xe. cThe current program is unable to access inner shells of Xe due to the large number of shells. dProduced by one of the authors, Gribakin, using a different algorithm. eSee ref [216].

Figure 5.2 compares the calculated –ray spectra of the outer valence electrons

(ns + np) of the noble gases as a function of photon energy. From this figure, it is

noted that He and Ne exhibit certain similarities in their –ray spectra, in which

they can be fitted better using a single Gaussian function. On the other hand, the

–ray spectra of heavier noble gas atoms, such as Ar, Kr and Xe, have a

“shoulder” (inflection point) and may be fitted better as the sum of two-Gaussian

distributions (this approximation was used for determining ε in Ref. [215]). The

present spectra in Figure 5.2 show contributions from the outer valence shell

only, i.e., ns and np electrons, without convolution of the experimental

conditions (i.e., not including the detector resolution function) whereas in Ref.

[99], it is identified that the contributions are from the two outermost shells of

(n1)s, (n1)p, (and (n1)d, for Kr and Xe), ns and np electrons, fitted using

two-Gaussian functions.

91


Figure 5. 2 Comparison of the annihilation –ray spectra of the outermost shells

of noble gases calculated using the HF/TZVP model for atomic electron

wavefunctions: He (), Ne (), Ar (), Kr () and Xe (). All spectra are

normalized to unity at ε=0 [22].

5.2.1 Bound electron shell contributions

The positron-electron annihilation spectra of the noble gases are very

sensitive to the atomic electron shells where the bound electrons reside (i.e., to

the principle quantum number, n and the orbital angular quantum number, l).

Table 5.2 reports the bound electron contributions to and Zeff for the spectra of

the noble gases [22].

92


Table 5. 2 Bound electron shell contributions to the positron annihilation -ray

spectra (ε in keV) of the noble gases based on the HF/TZVP model for atomic

electron wavefunctions.

He Ne Ar Kr Xea

Shell ε Zeff ε Zeff ε Zeff ε Zeff ε Zeff

1s 2.99 2.00 16.27 1.48 22.23 0.67 25.31 0.13 - -

2s - - 3.52 1.95 7.90 1.79 16.90 1.54 21.84 0.91

3s - - - - 2.39 1.98 6.43 1.80 10.67 1.44

4s - - - - - - 2.15 1.98 4.89 1.87

5s 1.80 1.98

2p - - 5.86 5.98 15.77 5.39 26.86 1.80 29.42 0.44

3p - - - - 3.77 5.94 11.86 5.34 20.68 4.73

4p - - - - - - 3.30 5.95 8.68 5.56

5p - - - - - - - - 2.80 5.95

3d - - - - - - 16.25 8.97 27.09 4.25

4d - - - - - - - - 10.89 9.14

S(l=0) - - 3.98 3.43 2.94 4.43 2.77 5.44 - -

P(l=1) - - 5.86 5.98 4.29 11.33 3.90 13.09 3.53 16.68

Core - - 16.27 1.48 12.62 7.84 13.08 19.57 - -

Valence - - 4.94 7.93 3.31 7.92 2.93 7.93 2.48 7.93

Total 2.99 2.00 5.14 9.41 3.85 15.76 4.07 27.50 - -

Exptb 2.50 3.36 2.30 2.09 1.92

aThe basis set for Xe is DZVP whereas the other noble gases use the TZVP basis.

As a result, the last two columns (italic) for Xe are only provided for reference. bSee Ref. [101].

Generally, Zeff is the time annihilation rate normalized to the rate for a

free electron gas. Theoretically, Zeff is equal to Z, the actual number of electrons

(Zeff ≈ Z). However, the experimental Zeff of rare gases and small molecules

indicate that the Zeff can be significantly different from the number of electrons

in the atoms or molecules, which also depends on the chemical environment. The

causes of such phenomena are still unclear [100], and are outside of the scope of

this thesis.

93


The innermost shells of the noble gases, either 1s or 2p, exhibit the

largest shift (ε), which are significantly larger than the measured ε values.

Thus these contributions are less likely to dominate the –ray spectra. This is in

agreement with previous findings that the contributions from the inner shells are

very small, never exceeding a few percent [101]. In addition, the wavefunctions

(orbitals) of the innermost s and p electrons in heavier noble gas atoms (i.e., Ar

and beyond) extend to significantly larger momentum regions, namely, possibly

greater than the 10 a.u. cut-off momentum in the present study. As a result, it is

the innermost electrons that are associated with a most significant “electron

density loss” at this cut-off momentum [22]. For example, for the 1s orbital of

Ar, ε = 22.03 keV from the HF/TZVP model, but the theoretically calculated

Zeff (with an upper limit of 2.0) is only 0.67, which accounts for only 33.5% of

the total 1s electron density in the Ar 1s shell. The ε for the 2p orbital of Ar is

15.77 keV using the same model, while the theoretical Zeff value (upper limit of

6.0) is 5.39, thus including almost 90% of the 2p electron density in these

orbitals.

For other atomic electrons, the ε values vary considerably from shell to

shell, that is, with the quantum numbers n and l, which is in agreement with

previous studies [99, 215]. For example, for the same orbital angular momentum,

e.g., l = 0, ε decreases as the principal quantum number, n, is increased,

whereas for the same n, e.g., n = 3, the trend is the opposite: ε increases as the

orbital angular quantum number l is increased. However, it is found that the

outermost ns electrons of the noble gases have –ray annihilation line shape

parameters ε closest to the measured Es, which are highlighted in this table.

That is, the 1s orbital for He, 2s for Ne, 3s for Ar, 4s for Kr and 5s for Xe.

Table 5.3 compares the previously available theoretical and experimental

total and bound electron shell contributions of noble gas atoms with those from

different levels of theory which include varied levels of electron correlation

energies such as HF, B3LYP, MP2 and CCSD(T). The TZVP (DZVP for Xe)

basis set was used for the calculations carried out for the current study [22].

94


Table 5. 3 Bound electron shell contribution and total FWHM of annihilation γ-

ray spectra, ε (in keV) for noble gases based on different methods.

Shell HF/ TZVP

B3LYP/ TZVP

MP2/ TZVP

CCSD(T) /TZVP

Theory[215]

Expt.[101]

ε Zeff ε Zeff ε Zeff ε Zeff ε He

1s 2.99 2.00 2.95 2.00 2.99 2.00 2.98 2.00 - 2.50 Ne

1s 16.27 1.48 16.23 1.48 16.27 1.48 16.27 1.48 - - 2s 3.52 1.95 3.47 1.95 3.49 1.95 3.52 1.95 - - 2p 5.86 5.98 5.73 5.98 5.78 5.98 5.86 5.98 - -

Total 5.14 9.41 5.04 9.41 5.08 9.41 5.14 9.41 - 3.36 Ar

1s 22.23 0.67 22.26 0.67 22.23 0.67 22.23 0.67 - - 2s 7.90 1.79 7.82 1.79 7.90 1.79 7.90 1.79 5.18 - 3s 2.39 1.98 2.39 1.98 2.39 1.98 2.39 1.98 1.86 - 2p 15.77 5.39 15.65 5.39 15.77 5.39 15.77 5.39 9.41 - 3p 3.77 5.94 3.75 5.94 3.77 5.94 3.77 5.94 2.89 -

Total 3.85 15.76 3.84 15.76 3.85 15.76 3.85 15.76 2.65 2.30 Kr

1s 25.31 0.13 25.31 0.13 25.31 0.13 25.31 0.13 - - 2s 16.90 1.54 16.91 1.54 16.90 1.54 16.90 1.54 - - 3s 6.43 1.80 6.38 1.80 6.43 1.80 6.43 1.80 4.35 - 4s 2.15 1.98 2.17 1.97 2.15 1.97 2.15 1.98 1.66 - 2p 26.86 1.80 26.89 1.79 26.86 1.80 26.86 1.80 - - 3p 11.86 5.34 11.78 5.35 11.86 5.34 11.86 5.34 7.65 - 4p 3.30 5.95 3.27 5.95 3.30 5.95 3.30 5.95 2.56 - 3d 16.25 8.97 16.14 8.97 16.18 8.97 16.25 8.97 8.85 -

Total 4.07 27.50 4.08 27.51 4.08 27.50 4.07 27.50 2.38 2.09 Xe

1s - - - - - - - - - - 2s 21.84 0.91 21.79 0.91 21.77 0.91 21.77 0.91 - - 3s 10.67 1.44 10.65 1.44 10.67 1.44 10.67 1.44 - - 4s 4.89 1.87 4.88 1.87 4.89 1.87 4.89 1.87 3.34 - 5s 1.80 1.98 1.83 1.99 1.80 1.99 1.80 1.99 1.41 - 2p 29.42 0.44 29.32 0.43 29.29 0.43 29.29 0.43 - - 3p 2.68 4.73 20.60 4.73 20.66 4.73 20.66 4.73 - - 4p 8.68 5.56 8.66 5.56 8.68 5.56 8.68 5.56 5.80 - 5p 2.80 5.95 2.81 5.96 2.80 5.96 2.80 5.96 2.22 - 3d 27.09 4.25 26.96 4.23 27.02 4.21 27.02 4.21 - - 4d 10.88 9.14 10.86 9.14 10.88 9.16 10.88 9.16 6.73 -

Total - - - - - - - - 2.06 1.92

It is observed that the FWHM values of noble gas atoms are not affected

significantly by the models. Therefore, for atoms, the level of theory employed

(and the inclusion or not of correlation in it) does not have a significant impact

on the calculation of annihilation –ray spectra [22].

95


Figure 5.3 compares the atomic electron contributions to the annihilation

–ray spectra of Ne with (a) collective contributions from s electrons, p

electrons, core electrons, valence electrons and total electrons; and (b) the orbital

(subshell, n and l) based contributions [22].


annihilation –ray spectra of Ne, calculated using the HF/TZVP model for the


summed by orbital type, and (b) specific orbitals.

96


From Figure 5.3(a), it is apparent that the contributions from the p

electrons (dot-dash line) indeed exhibit very similar shapes to the contributions

from all the electrons (solid line), whereas the contributions from the s-electrons

(long dash line) are much smaller, and have a lesser effect on the shape of the

total spectrum. Valence spectra (short dash line) are almost similar to those of

the p electrons, which are also similar to the total –ray spectra of Ne. Figure

5.3(b) shows the individual shell contributions to the spectra. The dominant 2p

electrons are similar to the total spectra of Ne, whereas 1s or 2s electrons exhibit

very different shapes to the total spectra shown in the figure. As a result, their

contributions to the total spectra of Ne are small.

Figures 5.4 and 5.5 show the bound electron contributions to the –ray

spectra of Ar and Kr, respectively. Figure 5.4(a) reports the collective

contributions from the s electrons, p electrons, core electrons, valence electrons

and all electrons. As is the case for Ne, the contributions from the p electrons

(dot-dash line) indeed exhibit very similar shapes to the contributions from all

the electrons (solid line), whereas the contributions from the s-electrons (long

dashed line) are much smaller, and have a weaker effect on the shape of the total

spectrum [22]. Similar observations hold for Kr as shown in Figure 5.5(a), where

the sum of the p electrons has a similar shape to the total spectra, as given in

Figure 5.5(a). The –ray spectra of the s and p electrons of Ar and Kr are almost

“parallel” except in the larger photon energy region above 5 keV. However, the

outer valence electrons, 3s and 3p (Ar) or 4s and 4p (Kr) (short dash line),

exhibit apparent differences in shape to the contribution of the other orbitals of

Ar or Kr.

97


Figure 5. 5 Comparison of atomic electronic shell

contributions to the annihilation –ray spectra of Ar, calculated

using the HF/TZVP model for the atomic wavefunctions and

the plane-wave approximation for the positron: (a) summed by

orbital type, and (b) specific orbitals.

Figure 5. 4 Comparison of atomic electronic shell

contributions to the annihilation –ray spectra of Kr, calculated

using the HF/TZVP model for the atomic wavefunctions and

the plane-wave approximation for the positron: (a) summed by

orbital type, and (b) specific orbitals.

98


Figure 5.4(b) shows the individual orbital (subshell, n and l)

contributions to the –ray spectrum of Ar. The outer valence shell indeed

behaves very differently from the shells with smaller quantum numbers, such as

the 1s, 2s and 2p shells. The ε values of the atomic electrons in other than the

outermost shell are very different from the experimental ε values, indicating

their relatively small contributions to the –ray spectrum of Ar. The fact that the

ε of the calculated total contribution from all atomic electrons of Ar exhibits

less similarity to the experiment than do either the 3s or 3p orbitals indicates that

the measured spectra are not the result of a simple direct sum over the

contributions of all atomic electrons. Rather, the annihilation measurements

reflect contributions from particular orbitals in the outer valence shell, such as ns

electrons. This is in considerable part due to the positron repulsion from the

nucleus which further suppresses their effect on ε. Individual orbital

contributions to the total spectra of Kr in Figure 5.5(b) behave in a similar

fashion to Ar.

5.2.2 Gamma-ray spectrum trends in noble gases

The dominant bound electron contributions to the –ray spectra of the

noble gas Ar have been compared with experiment [215]. Figure 5.6 gives the

contributions of the outer valence electrons of Ar (3s, 3p and 3s+3p) compared

with experiment, which has been least-squares fitted to two Gaussian functions.

Figure 5.7 compares the outer valence shell contributions of Kr (4s, 4p and

4s+4p) to the gamma-ray spectra with the experimental data that has also been

fitted to two Gaussian functions. The spectra are simulated at the HF level of

theory and normalized to unity at ε =0. In the region of small photon energies,

namely ε < 3 keV, the agreement between the 3s electrons of Ar and the

measurements is excellent (in fact, the two curves are in parallel), whereas the 3p

electrons exhibit slightly better agreement in the region of photon energies from

4 to 8 keV. Note, that the theoretical spectrum does not consider the broadening

by the energy resolution function of the detector.

99



with the experimental spectra (solid circles) for Ar.


with the experimental spectra (solid circles) for Kr.

100


It is seen from the Figure 5.7 that the 4s (red dashed line) and 4p (blue

short-dashed line) electron contributions to the –ray spectrum of Kr indicate

similar features as those in the Ar case. Furthermore, the 4s electron spectra

agree well with the experiment (through two Gaussian fit).

Figure 5.8 reports the simulated –ray spectra of the outer valence ns

electrons of the noble gases, together with their ε values. Although the spectral

shapes and the FWHM ε of the noble gases are quite different, certain trends

are observed. Starting at Ne, inflection points are observed in the spectra, at

approximately 6 keV for Ne, 3 keV for Ar and 2.5 keV for Kr. These features are

related to the nodes in the spatial wavefunctions of the ns orbitals with n> 1.

Such changes in the shapes of the spectra suggest that more than one Gauss ian

function is needed to appropriately fit the spectra. For Xe, two such inflection

points are visible, at approximately 2 keV and 6.5 keV, indicating that even more

Gaussian fitting functions are needed in this case to represent the spectrum over

a wider range of energies. Compared with Kr, the position of the first minimum

in Xe has moved to smaller energy, leading to a decrease in the corresponding ε

[22].

Figure 5. 8 The ns electron contributions to the annihilation –ray spectra of He,

Ne, Ar, Kr and Xe, calculated using the HF/TZVP model.

101


5.3 Gamma-ray spectra of small molecules

Even small molecules are significantly more complicated than atoms, as

molecules possess multiple centres and have interactions among the component

atoms. In addition, larger molecules have a significantly different chemical

environment, which contributes to the gamma-ray spectra, as observed by the

Surko group [98].

In this thesis, we present our recent work on the gamma-ray spectra

arising from positron annihilation for small molecules [217]. Table 5.4 reports

contributions from orbitals and quantum mechanical models to the –ray spectra

’s for small molecules. Apart from H2, larger diatomic molecules, such as N2

and O2, show the dominance of their 2g orbitals to the –ray spectra linewidths.

Note that in some triatomic molecules such as H2O and NH3, their ’s are very

close to the innermost valence orbital 2a1. Similar to the noble gases, the

innermost outer valence orbitals of these molecules show a close agreement with

the experimental results except for CO. In the case of CO, two orbitals (3σ and

5σ) are found to make the dominant contributions whereas the outermost orbital

(5σ) has a Δ that is reasonably close to the experiment.

It is apparent that the degree of inclusion of electron correlation in the

molecular wavefunction affects the electron-positron annihilation spectra of the

molecules [217]. This is a very different character, comparing to atomic studies.

This is particularly so in O2 as the agreement with the experimental linewidth

() of the –ray spectra with the dominant orbital contribution (2g) improves

as the amount of electron correlation included in the calculation increases. For

example, the 2g contribution of O2 =2.82 keV in the HF model but =2.74

keV in the CCSD(T) model (exp=2.74 keV). It is further noted that in N2, the

inclusion of electron correlation in the quantum mechanical model changes the

choice of orbital that makes the dominant contribution to the –ray spectra

linewidth (), from the 3g orbital in the HF model to the 2g orbital when

electron correlation is included in the calculation.

102


Table 5.4 FWHM of annihilation -ray spectra, (keV), for inorganic

molecules (valence space). The symbol * indicates degenerate orbitals.

Orbital Sym.

HF/TZVP(6-311++G**)

B3LYP /TZVP

MP2(full) /TZVP

CCSD(T)/TZVP

Expt. [101]

H2 1σg 2.02 2.01 2.04 2.02 1.71

N2 2σg 2.82(2.82) 2.80 2.24 2.08 - 2σu 3.46(3.46) 3.42 3.31 3.21 - 3σg 2.30(2.25) 3.98 4.29 4.30 -

1πu* 3.99(3.97) 3.22 3.66 3.32 - Valence 3.35(3.35) 3.31 3.21 3.08 -

Total 3.59(3.50) 3.56 3.42 3.27 2.32 O2

2σg 2.82(2.82) 2.82 2.71 2.74 - 2σu 3.90(3.90) 3.81 3.86 3.87 - 1πu 4.45(4.43) 4.08 4.26 4.37 - 3σg 4.23(4.09) 4.25 4.65 4.71 - 2πu 4.22(4.22) 4.27 4.27 4.10 - 1πg 5.76(5.71) 5.64 5.66 5.75 -

Valence 4.01(4.00) 3.94 3.95 3.96 - Total 4.24(4.22) 4.16 4.17 4.19 2.73

CO 3σ 2.89 2.88 2.83 2.85 - 4σ 4.05 3.93 4.04 3.99 - 1π* 4.16 4.12 4.12 4.12 - 5σ 2.07 1.99 2.05 2.08 -

Valence 3.30 3.25 3.27 3.30 - Total 3.56 3.51 3.53 3.55 2.23

CO2 3σg 2.32 2.31 2.27 2.30 - 2σu 3.86 3.86 3.72 3.77 - 4 σg 4.26 4.19 4.22 4.24 -

3σu 4.88 4.55 5.06 5.05 - 1πu* 3.92 3.83 3.85 3.88 - 1πg* 4.85 4.83 4.82 4.80 -

Valence 3.88 3.83 3.83 3.85 - Total 4.13 4.07 4.07 4.10 2.63

H2O 2a1 2.66 2.64 2.64 2.65 - 1b2 4.20 4.10 4.14 4.15 - 3a1 4.17 4.05 4.11 4.15 - 1b1 4.27 4.19 4.21 4.27 -

Valence 3.66 3.60 3.75 3.64 - Total 3.80 3.73 3.61 3.78 2.59

NH3 2a1 2.31 2.29 2.29 2.30 - 1e1* 3.77 3.70 3.74 3.74 - 3a1 3.58 3.50 3.54 3.57 -

Valence 3.21 3.17 3.18 3.20 - Total 3.33 3.28 3.30 3.32 2.27

103


The choice of basis set also affects the molecular electronic

wavefunctions and therefore the –ray spectral linewidths. In Table 5.3,

calculations using a different basis set (6-311++G**) and the HF model are also

given in brackets. Nearly half of the valence orbital Δ values are affected by the

basis set. One example is the 3g in N2 and another are the 2g, 3g and 1u

orbitals in O2. However, how the basis set affects the spectra is unclear and

warrants further investigation, outside the scope of this thesis. Orbital

contributions to the gamma-ray spectra of the positron annihilation of N2 and

NH3 are illustrated in Figure 5.9, which agree with the data given in Table 5.4.

Figure 5. 9 Orbital contributions to the positron annihilation spectra of (a)

nitrogen (N2) and (b) ammonia (NH3) using the HF/TZVP model.

(a)

(b)

104


Table 5.5 compares the various quantum mechanical models with respect

to their shell electron contributions to the –ray spectras of a series of

polyatomic molecules, namely methane (CH4) and its fluorinated derivatives

(CH3F, CH2F2, CHF3 and CF4). Methane, CH4, and carbon tetrafluoride, CF4,

both possesses Td point group symmetry, which may provide certain grounds for

the comparison of the chemical environment to the spectra. In contrast to what

has been observed for the diatomic molecules studied previously, the –ray

spectra ’s of the methane derivatives are dominated by different orbitals for

each molecule, rather than the corresponding orbitals; the dominant orbitals are

2a1 for methane, but 3a1 and 4a1 for fluoromethane as well as difluoromethane,

the 3a1 and 2e orbitals for trifluoromethane, and the 3a1 and 2t2 for (larger)

carbon tetrafluoride. As a result, when the molecule contains more electrons than

CH4, there appears to be more than one orbital that contributes significantly to

the values and gamma-ray spectra.

Table 5. 5 FWHM of annihilation -ray spectra, (keV), for partially and fully

fluorinated hydrocarbons. *The orbitals are in the order of their energies.

Orbital Sym. HF/TZVP B3LYP/

TZVP MP2(full)/

TZVP CCSD(T)/

TZVP Expt. [101]

FWHM FWHM FWHM FWHM CH4

2a1 1.97 1.96 1.96 1.97 1t2* 3.34 3.30 3.34 3.34

Valence 2.84 2.81 2.83 2.84 Total 2.95 2.92 2.94 2.95 2.09

CH3F 3a1 2.90 2.85 2.88 2.90 4a1 2.51 2.51 2.53 2.51 1e1* 3.78 3.84 3.85 3.78 5a1 4.56 3.48 4.43 4.56

2e1* 4.29 4.69 4.16 4.29 Valence 3.51 3.47 3.49 3.51

Total 3.68 3.64 3.66 3.68 2.77 CH2F2

3a1 2.39 2.36 2.37 2.39 2b2 3.70 3.71 3.68 3.70 4a1 3.25 3.26 3.30 3.25 1b1 3.63 3.49 3.64 3.63 5a1 4.03 3.86 3.96 4.03 3b2 5.43 5.41 5.40 5.43 1a2 5.36 5.28 5.29 5.36 4b2 5.90 4.60 5.82 5.90

105


6a1 4.57 5.70 4.38 4.57 Table 5.5 continued

2b2 4.68 4.86 4.56 4.68 Valence 4.00 3.92 3.94 3.98

Total 4.21 4.12 4.14 4.18 2.86 CHF3

3a1 2.14 2.13 2.12 2.14 2e* 3.74 3.75 3.72 3.74 4a1 3.96 3.96 4.01 3.96 5a1 3.78 3.67 3.72 3.78 3e* 5.09 5.17 5.05 5.09 4e* 5.21 4.99 5.14 5.21 5e* 5.90 5.62 5.81 5.90 1a2 6.10 6.08 6.07 6.10 6a1 4.61 4.56 4.42 4.61

Valence 4.29 4.22 4.25 4.29 Total 4.51 4.44 4.46 4.50 2.85

CF4 3a1 2.00 2.01 1.98 2.00 2t2* 3.76 3.77 3.74 3.76 4a1 4.62 4.62 4.61 4.63 3t2* 4.95 5.03 4.92 4.95 1e1* 4.88 4.80 4.82 4.88 4t2* 5.85 5.37 5.75 5.85 1t1* 6.14 6.12 6.11 6.14

Valence 4.52 4.45 4.47 4.52 Total 4.47 4.68 4.70 4.75 3.04

5.4 Summary

The present chapter applies the low-energy plane wave approximation to

simulate the γ-ray spectra of positron-electron annihilation in noble gases and

small molecules using robust modern computational chemistry tools for the

bound electron wavefunctions. The following conclusions arise from this study:

The gamma-ray spectra of positron-electron annihilation of atoms and

small molecules are dominated by the atomic and molecular electrons.

The outermost s electrons of the noble gases exhibit spectral line shapes

in close agreement with experiment, indicating that the measured spectra

are not a simple sum over the momentum densities for all electrons.

Moderate agreement with the experimental spectral line shapes, e.g., the

full-width at half maximum parameter ε, is achieved. The theoretical

calculations predict the general trend of the experimental linewidths in

106


noble gases, though it differs by approximately 30% from the

measurements. One reason for the discrepancy may be due to the fact that

the low energy plane wave approximation neglects the positron

wavefunction.

In the case of small molecules, the innermost valence orbital is found to

produce Δ values that agree with the experiment, whereas larger

molecules show a significant contribution to Δ from two orbitals.

The inclusion of varying degrees of electron correlation in the quantum

mechanical models for the atomic or molecular electron wavefunction

has a greater effect for in the small molecules than it does in the noble

gases. Because molecules are complex than atoms, outer valence orbitals

are found to be affected to a much greater extent by electron correlation

than are the inner valence orbitals.

107

Summary and Outlook

CChhaapptteerr 66

Summary and Outlook

Theoretical developments in the study of interactions between electrons

and positrons in the annihilation processes have lagged far behind experimental

developments, and have been a subject of research for some time. The

interconnection existing between these two particles may be used to provide

significant information about the chemical systems being studied. Spectroscopy

is a powerful technique to probe the electronic structure of molecules and matter.

Various spectroscopic techniques have been used to study electronic structure

and other important properties of atoms and molecules in this thesis. The

calculated properties are validated with the available experimental measurements

from photoelectron spectroscopy, electron momentum spectroscopy, and

gamma-ray spectroscopy.

A variety of quantum mechanical models such as HF, DFT, OVGF, MP2,

and CCSD(T) in combination with Slater and Gaussian basis sets have been

employed to probe the electronic structural properties of the atoms and

molecules of interest. The OVGF model best describes the outer valence

ionization energies of perfluorinated benzenes, whereas the SAOP model was

found to give accurate VIEs for the complete valence shell of molecules. Orbital

based signatures in momentum space combined with the orbital diagram from

position space are used to demonstrate the similarities among the fluorinated

benzenes. The positional isomers of the difluorinated benzenes exhibited

significant differences in the mid-valence spectral region of 14-17eV, where the

orbital momentum distributions are also readily distinguishable.

The studies of the sugar or base modified nucleoside cytidine analogues

provided information on the changes occurring in the electronic structures due to

108

Summary and Outlook

modifications. The results of infrared and Raman spectroscopic calculations for

2’-dC and 3’-dC in the gas phase and various solvent phases reveal that these two

isomers differ in their spectra due to the unique hydrogen bonding networks they

each possess. Various solvents ranging from non-polar to polar were observed to

cause global red shifts in the IR spectra relative to gas phase for both the

isomers. Other base-modified analogues, such as zeb and d5 exhibit significant

valence orbital responses with respect to the additional methyl fragment in the

base. These findings are further supported by the orbital MDs.

Calculations of the spectra arising from positron and electron annihilation

in atoms and small molecules have also been attempted. This work indicated that

atomic or molecular electrons dominate the contributions to the gamma-ray

spectrum, contributing approximately 70% of the observed property to any given

measurement. Various levels of electron correlation (HF, B3LYP, MP2,

CCSD(T)) have been assessed against available experimental gamma-ray

spectra. Electron correlation effects in the gamma-ray spectra seem more

significant in smaller molecules rather than small atoms. The present work is

also extended to larger molecules to understand the positron annihilation spectra

for those systems.

The quantum mechanical models used in this study provide useful

information about the structure, energetics and interactions of the chemical

systems. Understanding the relationship between the structures and properties of

the biological compounds provides insights into their biomechanisms, which

makes them an attractive and powerful tool in drug development. Though the

drugs are also analysed using various modelling techniques such as docking,

simulation etc., the quantum mechanical methods provides insight into the

energy, geometry, and electronic features (e.g. dipole moment, HOMO, LUMO,

etc.,) and their correlation to the reactivity and behaviour of systems in an

isolated environment.

109

Appendix

Appendix Table A- 1. Optimized geometric and electronic properties of the fluorinated benzenes*

Molecule name and chemical formula Point group

State E (a.u) µ/Debye

Benzene C6H6 D6h X1A1g 0 0 Fluorobenzene C6H5F (I) C2v X1A1 -99.278 1.69 (1.60)

1,2-difluorobenzene C6H4F2 (IIa) C2v X1A1 -198.548 2.79 (2.46) 1,3-difluorobenzene C6H4F2 (IIb) C2v X1A1 -198.554 1.66 (1.51) 1,2-difluorobenzene C6H4F2 (IIc) C2v X1A1 -198.548 2.79 (2.46) 1,3-difluorobenzene C6H4F2 (IIIa) C2v X1A1 -198.554 1.66 (1.51)

1,2,6-trifluorobenzene C6H3F3 (IIIb) C2v X1A1 -297.817 3.15 (1.39) 1,3,5-trifluorobenzene C6H3F3 (IIIc) D3h X1A1 -297.829 0

1,2,3,4-tetrafluorobenzene C6H2F4 (IVa) C2v X1A1 -397.085 2.66 1,3,4,5-tetrafluorobenzene C6H2F4 (IVb) C2v X1A1 -397.091 1.49 1,2,4,5-tetrafluorobenzene C6H2F4 (IVc) D2h X1Ag -397.090 0

Pentafluorobenzene C6HF5 (V) C2v X1A1 -496.351 1.49 (1.44) Hexafluorobenzene C6F6 (VI) D6h X1A1g -595.611 0

E (a.u) = EC6H6-nFn - EC6H6

*Experimental dipole moments [120] are in parentheses.

Minimal structures among isomers are marked in bold.

110

Appendix

Table A- 2. C1s ionization energies of perfluorinated benzenes based on

LB94/TZVP model. Experimental IPs are in parenthesis [113]. Carbons

connected to fluorine atoms are underlined.

Molecule C(1) C(2) C(3) C(4) C(5) C(6) C6H6 289.510

(290.377) 289.506 289.506 289.498 289.498 289.494

I 292.005 (292.812)

289.925 (290.692)

289.961 (290.753)

289.808 (290.558)

289.960 (290.753)

289.924 (290.692)

IIa 292.458 (293.129)

292.450 (293.129)

290.328 (291.011)

290.242 (290.901

290.233 (290.901)

290.328 (291.011)

IIb 292.470 (293.181)

290.339 (291.007)

292.470 (293.181)

290.219 (290.843)

290.404 (291.096)

290.220 (290.843)

IIc 292.315 (292.989)

290.379 (291.039)

290.371 (291.039)

292.315 (292.989)

290.379 (291.039)

290.371 (291.039)

IIIa 292.753 292.918 290.743 292.754 290.647 290.773 IIIb 292.901

(293.480) 292.868

(293.402) 290.602

(293.480) 290.661

(291.150) 290.601

(291.251) 292.867

(291.150) IIIc 292.919

(293.554) 290.620

(291.155) 292.919

(293.554) 290.620

(291.155) 292.919

(293.554) 290.620

(291.155) IVa 293.138

(293.607) 293.311

(293.765) 293.303

(293.765) 293.138

(293.607) 291.030

(291.483) 291.022

(291.483) IVb 293.315 291.003 293.178 293.178 293.315 291.003 IVc 293.193

(293.625) 293.185

(293.625) 291.140

(291.620) 293.193

(293.625) 293.185

(293.625) 291.140

(291.620) V 293.568

(293.965) 293.568

(293.878) 293.706

(294.090) 293.560

(293.878) 293.560

(293.965) 291.383

(291.745) VI 293.938

(294.199) 293.934 293.934 293.926 293.926 293.922

111

Appendix

Figure A- 1. Core ionization energy spectra of the perfluorinated benzenes based

on LB94/et-pVQZ model.

112

Appendix

Figure A- 2. Total momentum distributions of the perfluorinated benzenes.

113

Appendix

Table A- 3. Vibrational frequency shift of 2′-dC (3′-dC) nucleosides in solvents

with respect to vacuum (cm-1).

Vib. Mode v(Tol) v(DMSO) v(water) v(n-MF) C(6)-H -7.12(1.43) -20.07(-1.28) -20.01(-15.18) -22.95(-63.75) C(5)-H -14.73(-16.52) -41.45(-45.61) -41.86(-45.99) -43.83(-50.03 C(1’ )-H -12.52(-18.68) -30.97(-48.02) -32.78(-49.04) -37.04(-60.32)

C(5’ )-H-H asym -4.43(-6.84) -8.23(-18.79) -7.96(-15.01) -10.36(-9.4) C(5’ )-H-H sym -4.48(1.40) -10.79(-1.99) -11.00(-5.01) -11.87(-0.91)

C(4’ )-H -0.66(-9.17) -3.37(-24.41) -2.41(-23.90) -4.26(-25.28) O(5’ )-H -117.09(-37.43) -324.89(-324.89) -334.92(-262.4) -351.55(304.78

N-H-H asym -48.97(-52.72) -132.46(-155.22) -135.58(-154.47) -141.92(-157.81) N-H-H sym -47.44(-52.15) -124.59(-143.38) -127.33(-142.96) -133.05(-147.18)

114

Appendix

Figure A- 3. Orbital density distributions of cytidine nucleoside analogues zeb and d5.

Molecule THOMO NHOMO HOMO LUMO

zeb

d5

115

Appendix

Table A- 4. Symmetry and electronic configuration of inorganic molecules and

fluorinated hydrocarbons.

Molecular name and its formula Sym. Core Valence

Inorganic molecules Hydrogen, H2 D∞h (1σg)2

Nitrogen, N2 D∞h (1σg)2

(2σu)2 (2σg)2(2σu)2(3σg)2(1πu)4

Oxygen, O2, D∞h (1σg)2

(2σu)2 (2σg)2(2σu)2(1πu)2(3σg)2(2πu)2(1πg)2

Carbonmonoxide, CO C∞v (1σ)2(2σ)2 (3σ)2(4σ)2(1π)4(5σ)2

Carbondioxide, CO2 D∞h (1σu)2(1σg)2

(2σg)2 (3σg)2(2σu)2(4σg)2(3σu)2(1πu)4(1πg)4

Water, H2O C2v (1a1)2 (2a1)2(1b2)2(3a1)2(1b1)2 Ammonia, NH3 C3v (1a1)2 (2a1)2(1e1)2(2e1)2(3a1)2

Partially and fully fluorinated hydrocarbons Methane, CH4 Td (1a1)2 (2a1)2(1t2)6

Trifluoromethane, CH3F C3v (1a1)2 (2a1)2 (3a1)2(1e1)4(5a1)2(2e1)4

Difluoromethane, CH2F2 C2v (1b2)2(1a1)2

(2a1)2 (3a1)2(2b2)2(4a1)2(1b1)2(5a1)2(3b2)2(1a2)2(4b2)2(6a1)2

(2b1)2 Methylfluoride,

CHF3 C3v (1e1)4(1a1)2

(2a1)2 (3a1)2(2e1)4(4a1)2(5a1)2(3e1)4(4e1)4(5e1)4(1a2)2(6a1)2

Carbontetrafluoride, CF4 Td

(1t2)6(1a1)2

(2a1)2 (3a1)2 (2t2)6(4a1)2(3t2)6(1e1)4(4t2)6(1t1)6

116

References

References 1. Planck, M., The theory of heat radiation. Second ed. 1914, Philadelphia:

Blakiston's Son & Co. 22. 2. Jensen, F., Introduction to computational chemistry. Second ed. 2007:

John Wiley & Sons, Ltd. 3. Fukui, K., The role of frontier orbitals in chemical reactions. Nobel

lecture, 1981. 4. Coulson, C. A., Present State of Molecular Structure Calculations.

Reviews of Modern Physics, 1960. 32(2): p. 170. 5. Erich, W. and McCarthy, I. E., Electron Momentum Spectroscopy. 1999,

New York: Kluwer Academic/Plenum Publishers. 6. Weigold, E., Dey, S., Dixon, A. J., and McCarthy, I. E., (e, 2e)

Spectroscopy of methane. Chemical Physics Letters, 1976. 41(1): p. 21. 7. Wang, F., Assessment of quantum mechanical models based on resolved

orbital momentum distributions of n-Butane in the outer valance shell. Journal of Physical Chemistry A, 2003. 107: p. 10199.

8. Wang, F. and Pang, W., Valence orbital response to conformers of n-butane. Molecular Simulation, 2007. 33: p. 1173.

9. Ning, C. G., Liu, K., Luo, Z. H., Zhang, S. F., and Deng, J. K., Electron momentum spectroscopy study on valence electronic structures of pyrimidine. Chemical Physics Letters, 2009. 476: p. 157.

10. Holland, D. M. P., Potts, A. W., Karlsson, L., Zaytseva, I. L., Trofimon, A. B., and Schirmer, J., A study of the valence shell electronic structure of uracil and the methyluracils. Chemical Physics, 2008. 353: p. 47.

11. Trofimov, A. B., Schirmer, J., Kobychev, V. B., Potts, A. W., Holland, D. M. P., and Karlsson, L., Photoelectron spectra of the nucleobases cytosine, thymine and adenine. Journal of Physics B: Atomic, Molecular and Optical Physics, 2006. 39: p. 305.

12. Dolgounitcheva, O., Zakrzewski, V. G., and Ortiz, J. V., Journal of Physical Chemistry A, 2003. 107: p. 822.

13. Fujii, K., Akamatsu, K., and Yokoya, A., Journal of Physical Chemistry B, 2004. 108: p. 8031.

14. Peeling, J. and Hruska, F. E., Canadian Journal of Chemistry, 1978. 56: p. 1555.

15. Potts, A. W., Holland, D. M. P., Trofimov, A. B., Schirmer, J., Karlsson, L., and Siegbahn, K., Journal of Physics B: Atomic and Molecular Physics, 2003. 36: p. 3129.

16. Slav ek, P., Winter, B., Faubel, M., Bradforth, S. E., and Jungwirth, P., Ionization Energies of Aqueous Nucleic Acids: Photoelectron Spectroscopy of Pyrimidine Nucleosides and ab Initio Calculations. Journal of the American Chemical Society, 2009. 131(18): p. 6460.

17. Vall- llosera, G., Gao, B., kivimaki, A., Coreno, M., Ruiz, J. A., Simone, M. d., Agren, H., and Rachlew, E., The Journal of Chemical Physics, 2008. 128: p. 044316.

117

References

18. Wang, F., Zhu, Q., and Ivanova, E., Inner-shell chemical shift of DNA/RNA bases and inheritance from their parent purine and pyrimidine. Journal of Synchrotron Radiation, 2008. 15: p. 624.

19. Wang, F., Electron Momentum Spectroscopy and Its Applications to Molecules of Biological Interest. Journal of Physics: Conference Series (JPCS), 2007. 963(1): p. 54.

20. Saha, S., Wang, F., Guerra, C. F., and Bickelhaupt, F. M., Outer valence orbital response to proton positions in prototropic tautomers of adenine. Journal of Computational Methods in Sciences and Engineering, 2006. 6(5): p. 251.

21. Wang, F., Downton, M. T., and Kidwani, N., Adenine tautomer electronic structural signatures studied using dual space analysis. Journal of Theoretical and Computational Chemistry, 2005. 4(1): p. 247.

22. Wang, F., Selvam, L., Gribakin, G. F., and Surko, C. M., Electron shell contributions to gamma-ray spectra of positron annihilation in noble gases. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010. 43(16): p. 165207.

23. Green, D. G., Saha, S., Wang, F., Gribakin, G. F., and Surko, C. M., Calculation of Gamma Spectra for Positron Annihilation on Molecules. Materials Science Forum, 2011. 666: p. 21.

24. Wahl, R. L., Principles and Practice of Positron Emission Tomography. 2002, Philadelphia, PA: Lippincott, Williams and Wilkins.

25. Amoretti, M., Amsler, C., Bonomi, G., Bouchta, A., Bowe, P., Carraro, C., Cesar, C. L., Charlton, M., Collier, M. J. T., Doser, M., Filippini, V., Fine, K. S., Fontana, A., Fujiwara, M. C., Funakoshi, R., Genova, P., Hangst, J. S., Hayano, R. S., Holzscheiter, M. H., Jorgensen, L. V., Lagomarsino, V., Landua, R., Lindelof, D., Rizzini, E. L., Macri, M., Madsen, N., Manuzio, G., Marchesotti, M., Montagna, P., Pruys, H., Regenfus, C., Riedler, P., Rochet, J., Rotondi, A., Rouleau, G., Testera, G., Variola, A., Watson, T. L., and van der Werf, D. P., Production and detection of cold antihydrogen atoms. Nature, 2002. 419(6906): p. 456.

26. Andresen, G., Bertsche, W., Boston, A., Bowe, P. D., Cesar, C. L., Chapman, S., Charlton, M., Chartier, M., Deutsch, A., Fajans, J., Fujiwara, M. C., Funakoshi, R., Gill, D. R., Gomberoff, K., Hangst, J. S., Hayano, R. S., Hydomako, R., Jenkins, M. J., oslash, rgensen, L. V., Kurchaninov, L., Madsen, N., Nolan, P., Olchanski, K., Olin, A., Povilus, A., Robicheaux, F., Sarid, E., Silveira, D. M., Storey, J. W., Telle, H. H., Thompson, R. I., van der Werf, D. P., Wurtele, J. S., and Yamazaki, Y., Antimatter Plasmas in a Multipole Trap for Antihydrogen. Physical Review Letters, 2007. 98(2): p. 023402.

27. Gabrielse, G., Bowden, N. S., Oxley, P., Speck, A., Storry, C. H., Tan, J. N., Wessels, M., Grzonka, D., Oelert, W., Schepers, G., Sefzick, T., Walz, J., Pittner, H., auml, nsch, T. W., and Hessels, E. A., Background-Free Observation of Cold Antihydrogen with Field-Ionization Analysis of Its States. Physical Review Letters, 2002. 89(21): p. 213401.

28. Team, A., Tavani, M., Marisaldi, M., Labanti, C., Fuschino, F., Argan, A., Trois, A., Giommi, P., Colafrancesco, S., Pittori, C., Palma, F.,

118

References

Trifoglio, M., Gianotti, F., Bulgarelli, A., Vittorini, V., Verrecchia, F., Salotti, L., Barbiellini, G., Caraveo, P., Cattaneo, P. W., Chen, A., Contessi, T., Costa, E., D'Ammando, F., Del Monte, E., De Paris, G., Di Cocco, G., Di Persio, G., Donnarumma, I., Evangelista, Y., Feroci, M., Ferrari, A., Galli, M., Giuliani, A., Giusti, M., Lapshov, I., Lazzarotto, F., Lipari, P., Longo, F., Mereghetti, S., Morelli, E., Moretti, E., Morselli, A., Pacciani, L., Pellizzoni, A., Perotti, F., Piano, G., Picozza, P., Pilia, M., Pucella, G., Prest, M., Rapisarda, M., Rappoldi, A., Rossi, E., Rubini, A., Sabatini, S., Scalise, E., Soffitta, P., Striani, E., Vallazza, E., Vercellone, S., Zambra, A., and Zanello, D., Terrestrial Gamma-Ray Flashes as Powerful Particle Accelerators. Physical Review Letters, 2011. 106(1): p. 018501.

29. Mochizuki, Y., Koide, H., Imamura, T., and Takemiya, H., HF-STEX and RASSCF calculations on nitrogen K-shell X-ray absorption of purine base and its derivative. Journal of Synchrotron Radiation, 2001. 8(2): p. 1003.

30. Harada, Y., Takeuchi, T., Kino, H., Fukushima, A., Takakura, K., Hieda, K., Nakao, A., Shin, S., and Fukuyama, H., Electronic Structure of DNA Nucleobases and Their Dinucleotides Explored by Soft X-ray Spectroscopy. The Journal of Physical Chemistry A, 2006. 110(49): p. 13227.

31. MacNaughton, J., Moewes, A., and Kurmaev, E. Z., Electronic Structure of the Nucleobases. The Journal of Physical Chemistry B, 2005. 109(16): p. 7749.

32. Magulick, J., Beerbom, M. M., Lägel, B., and Schlaf, R., Ionization Energy and Electronic Structure of Polycytidine. The Journal of Physical Chemistry B, 2006. 110(6): p. 2692.

33. Hagmann, W. K., The Many Roles for Fluorine in Medicinal Chemistry. Journal of Medicinal Chemistry, 2008. 51(15): p. 4359.

34. Ismail, F. M. D., Important fluorinated drugs in experimental and clinical use. Journal of Fluorine Chemistry, 2002. 118(1-2): p. 27.

35. Dirac, P. A. M., Quantum Mechanics of Many-Electron Systems. Proceedings of the Royal Society of London. Series A, 1929. 123(792): p. 714.

36. Schrodinger, E., An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review, 1926. 28(6): p. 1049.

37. Born, M. and Oppenheimer, R., Zur Quantentheorie der Molekeln. Annalen der Physik, 1927. 389(20): p. 457.

38. Moller, C. and Plesset, M. S., Note on an Approximation Treatment for Many-Electron Systems. Physical Review, 1934. 46(7): p. 618.

39. Frisch, M. J., Head-Gordon, M., and Pople, J. A., Semi-direct algorithms for the MP2 energy and gradient. Chemical Physics Letters, 1990. 166(3): p. 281.

40. Head-Gordon, M., Pople, J. A., and Frisch, M. J., MP2 energy evaluation by direct methods. Chemical Physics Letters, 1988. 153(6): p. 503.

41. Scuseria, G. E., Janssen, C. L., and Schaefer Iii, H. F., An efficient reformulation of the closed-shell coupled cluster single and double

119

References

excitation (CCSD) equations. The Journal of Chemical Physics, 1988. 89(12): p. 7382.

42. Parr, R. G. and Yang, W., Density-functional theory of atoms and molecules. 1989, New York: Oxford University Press.

43. Korth, M. and Grimme, S., "Mindless" DFT Benchmarking. Journal of Chemical Theory and Computation, 2009. 5(4): p. 993.

44. Hohenberg, P. and Kohn, W., Inhomogeneous Electron Gas. Physical Review, 1964. 136(3B): p. B864.

45. Kohn, W. and Sham, L. J., Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 1965. 140(4A): p. A1133.

46. Vosko, S. H., Wilk, L., and Nusair, M., Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis Canadian Journal of Physics, 1980. 58(8): p. 1200.

47. Becke, A. D., Density-functional exchange-energy approximation with correct asymptotic behavior. Physical Review A, 1988. 38(6): p. 3098.

48. Perdew, J. P., Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Physical Review B, 1986. 33(12): p. 8822.

49. Lee, C., Yang, W., and Parr, R. G., Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Physical Review B, 1988. 37(2): p. 785.

50. Gritsenko, O., van Leeuwen, R., and Baerends, E. J., Analysis of electron interaction and atomic shell structure in terms of local potentials. The Journal of Chemical Physics, 1994. 101(10): p. 8955.

51. Gritsenko, O. V., Schipper, P. R. T., and Baerends, E. J., Approximation of the exchange-correlation Kohn-Sham potential with a statistical average of different orbital model potentials. Chemical Physics Letters, 1999. 302(3-4): p. 199.

52. Gritsenko, O. V., van Leeuwen, R., and Baerends, E. J., Molecular Kohn-Sham exchange-correlation potential from the correlated ab initio electron density. Physical Review A, 1995. 52(3): p. 1870.

53. Stener, M., Furlan, S., and Decleva, P., Density functional calculations of photoionization with an exchange-correlation potential with the correct asymptotic behaviour. Journal of Physics B: Atomic, Molecular and Optical Physics, 2000. 33(5): p. 1081.

54. van Leeuwen, R. and Baerends, E. J., Exchange-correlation potential with correct asymptotic behavior. Physical Review A, 1994. 49(4): p. 2421.

55. Slater, J. C., Atomic Shielding Constants. Physical Review, 1930. 36(1): p. 57.

56. Boys, S. F. and Cook, G. B., Mathematical Problems in the Complete Quantum Predictions of Chemical Phenomena. Reviews of Modern Physics, 1960. 32(2): p. 285.

57. Baerends, E. J., Autschbach, J., Bérces, A., Bo, C., Boerrigter, P. M., Cavallo, L., Chong, D. P., Deng, L., Dickson, R. M., Ellis, D. E., van Faassen, M., Fan, L., Fischer, T. H., Guerra, C. F., van Gisbergen, S. J. A., Groeneveld, J. A., Gritsenko, O.V., Grüning, M., Harris, F. E., Van

120

References

den Hoek, P., Jacobsen, H., Jensen, L., van Kessel, G., Kootstra, F., Van Lenthe, E., McCormack, D., Michalak, A., Osinga, V. P., Patchkovskii, S., Philipsen, P. H. T., Post, D., Pye, C. C., Ravenek, W., Ros, P., Schipper, P. R. T., Schreckenbach, G., Snijders, J. G., Solà, M., Swart, M., Swerhone, D., te Velde, G., Vernooijs, P., Versluis, L., Visser, O., Wang, F., van Wezenbeek, E., Wiesenekker, G., Wolff, S. K., Woo, T. K., Yakovlev, A., Ziegler, T., ADF2004.01. 2004.

58. Chong, D. P., Van Lenthe, E., Van Gisbergen, S., and Baerends, E. J., Even-tempered slater-type orbitals revisited: From hydrogen to krypton. Journal of Computational Chemistry, 2004. 25(8): p. 1030.

59. Godbout, N., Salahub, D. R., Andzelm, J., and Wimmer, E., Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron though neon, optimization technique and validation. Canadian Journal of Chemistry, 1992. 70(2): p. 560.

60. Wang, F., Assessment of Quantum Mechanical Models Based on Resolved Orbital Momentum Distributions of n-Butane in the Outer Valence Shell. The Journal of Physical Chemistry A, 2003. 107(47): p. 10199.

61. Francl, M. M., Pietro, W. J., Hehre, W. J., Binkley, J. S., Gordon, M. S., DeFrees, D. J., and Pople, J. A., Self-consistent molecular orbital methods. XXIII. A polarization-type basis set for second-row elements. The Journal of Chemical Physics, 1982. 77(7): p. 3654.

62. Frisch, M. J., Pople, J. A., and Binkley, J. S., Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. The Journal of Chemical Physics, 1984. 80(7): p. 3265.

63. Rassolov, V. A., Pople, J. A., Ratner, M. A., and Windus, T. L., 6-31G* basis set for atoms K through Zn. The Journal of Chemical Physics, 1998. 109(4): p. 1223.

64. Dunning, J. T. H., Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. The Journal of Chemical Physics, 1989. 90(2): p. 1007.

65. Dunning, J. T. H., Peterson, K. A., and Wilson, A. K., Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited. The Journal of Chemical Physics, 2001. 114(21): p. 9244.

66. Kendall, R. A., Dunning, J. T. H., and Harrison, R. J., Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. The Journal of Chemical Physics, 1992. 96(9): p. 6796.

67. Woon, D. E. and Dunning, J. T. H., Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon. The Journal of Chemical Physics, 1993. 98(2): p. 1358.

68. Balabin, R. M., Enthalpy difference between conformations of normal alkanes: Intramolecular basis set superposition error (BSSE) in the case of n-butane and n-hexane. The Journal of Chemical Physics, 2008. 129(16): p. 164101.

69. Carlson, T. A., Photoelectron Spectroscopy. Annual Review of Physical Chemistry, 1975. 26(1): p. 211.

121

References

70. Green, J. C., Photoelectron Spectroscopy: Study of Valence Bands in Solids. Annual Review of Physical Chemistry, 1977. 28(1): p. 161.

71. Duffy, P., Sordo, J. A., and Feng, W., Valence orbital response to pseudorotation of tetrahydrofuran: A snapshot using dual space analysis. The Journal of Chemical Physics, 2008. 128(12): p. 125102.

72. Winkler, P., Yaris, R., and Lovett, R., Solution of Dyson's equation employing Siegert boundary conditions. Physical Review A, 1981. 23(4): p. 1787.

73. Schirmer, J., Beyond the random-phase approximation: A new approximation scheme for the polarization propagator. Physical Review A, 1982. 26(5): p. 2395.

74. Schirmer, J., Cederbaum, L. S., and Walter, O., New approach to the one-particle Green's function for finite Fermi systems. Physical Review A, 1983. 28(3): p. 1237.

75. Tarantelli, A. and Cederbaum, L. S., Particle-particle propagator in the algebraic diagrammatic construction scheme at third order. Physical Review A, 1989. 39(4): p. 1656.

76. Plekan, O., Feyer, V., Richter, R., Coreno, M., de Simone, M., Prince, K. C., Trofimov, A. B., Gromov, E. V., Zaytseva, I. L., and Schirmer, J., A theoretical and experimental study of the near edge X-ray absorption fine structure (NEXAFS) and X-ray photoelectron spectra (XPS) of nucleobases: Thymine and adenine. Chemical Physics, 2008. 347(1-3): p. 360.

77. Cederbaum, L. S., One-body Green's function for atoms and molecules: theory and application. Journal of Physics B: Atomic and Molecular Physics, 1975. 8(2): p. 290.

78. Ortiz, J. V., Electron binding energies of anionic alkali metal atoms from partial fourth order electron propagator theory calculations. The Journal of Chemical Physics, 1988. 89(10): p. 6348.

79. Arachchilage, A. P. W., Wang, F., Feyer, V., Plekan, O., and Prince, K. C., Correlation of electronic structures of three cyclic dipeptides with their photoemission spectra. The Journal of Chemical Physics, 2010. 133(17): p. 174319.

80. Wang, F., Applications of ionization spectroscopy to study small bio-molecules. Journal of Physics: Conference Series, 2008. 141(1): p. 012019.

81. Koopmans, T., Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms. Physica 1, 1933. 1(1-6): p. 104.

82. Wang, F. and Downton, M., Inner valence shell bonding mechanism of n-butane studied using orbital momentum distributions of its conformational isomers Journal of Physics B: Atomic, Molecular and Optical Physics, 2004. 37(3): p. 557.

83. Janak, J. F., Proof that ∂E/∂ni=ε in density-functional theory. Physical Review B, 1978. 18(12): p. 7165.

122

References

84. Saha, S., Wang, F., Falzon, C. T., and Brunger, M. J., Coexistence of 1,3-butadiene conformers in ionization energies and Dyson orbitals. Journal of Chemical Physics, 2005. 123(12): p. 124315.

85. Tixiera, S., Shapleya, W. A., Zhenga, Y., Chonga, D. P., Brion, C. E., Shib, Z., and Wolfe, S., Electron densities for the outer valence orbitals of pyridine: comparison of EMS measurements with near Hartree-Fock limit and density functional theory calculations. Chemical Physics, 2001. 270(2): p. 263.

86. Zhu, Q., Wang, F., and Ivanova, E., Impact of ketone and amino on the inner shell of guanine. Journal of Synchrotron Radiation, 2009. 16(4): p. 545.

87. Nakata, A., Imamura, Y., Otsuka, T., and Nakai, H., Time-dependent density functional theory calculations for core-excited states: Assessment of standard exchange-correlation functionals and development of a novel hybrid functional. The Journal of Chemical Physics, 2006. 124(9): p. 094105.

88. Thompson, A., Saha, S., Wang, F., Tsuchimochi, T., Nakata, A., Imamura, Y., and Nakai, H., Density Functional Study on Core Ionization Spectra of Cytidine and Its Fragments. Bulletin of Chemical society of Japan, 2009. 82(2): p. 187.

89. Schipper, P. R. T., Gritsenko, O. V., Gisbergen, S. J. A. v., and Baerends, E. J., Molecular Calculations of Excitation Energies and (Hyper)Polarizabilities with a Statistical Average of Orbital Model Exchange-Correlation Potentials. The Journal of Chemical Physics, 2000. 112(3): p. 1344.

90. Selvam, L., Vasilyev, V., and Wang, F., Methylation of Zebularine: A Quantum Mechanical Study Incorporating Interactive 3D pdf Graphs. The Journal of Physical Chemistry B, 2009. 113(33): p. 11496.

91. Ganesan, A., Wang, F., and Falzon, C., Intramolecular interactions of L-phenylalanine: Valence ionization spectra and orbital momentum distributions of its fragment molecules. Journal of Computational Chemistry, 2011. 32(3): p. 525.

92. McCarthy, I. E. and Weigold, E., Electron momentum spectroscopy of atoms and molecules. Reports on Progress in Physics, 1991. 54(6): p. 789.

93. Weigold, E. and McCathy, I. E., Electron Momentum Spectroscopy. 1999, New York: Kluwer Academic/Plenum Publishers.

94. Duffy, P., Clark, S. A. C., Brion, C. E., Casida, M. E., Chong, D. P., Davidson, E. R., and Maxwell, C., Electron momentum spectroscopy of the valence orbitals of acetylene: Quantitative comparisons using near Hartree-Fock limit and correlated wavefunctions. Chemical Physics, 1992. 165(2-3): p. 183.

95. Ning, C. G., Hajgató, B., Huang, Y. R., Zhang, S. F., Liu, K., Luo, Z. H., Knippenberg, S., Deng, J. K., and Deleuze, M. S., High resolution electron momentum spectroscopy of the valence orbitals of water. Chemical Physics, 2008. 343(1): p. 19.

123

References

96. Marler, J. P. and Surko, C. M., Positron-impact ionization, positronium formation, and electronic excitation cross sections for diatomic molecules. Physical Review A, 2005. 72(6): p. 062713.

97. Marquez, V. E., Kelley, J. A., Agbaria, R., Ben-Kasus, T., Cheng, J. C., Yoo, C. B., and Jones, P. A., Zebularine: A Unique Molecule for an Epigenetically Based Strategy in Cancer Chemotherapy. Nucleosides, Nucleotides, and Nucleic Acids, 2005. 1058(1): p. 246.

98. Surko, C. M., Gribakin, G. F., and Buckman, S. J., Low-energy positron interactions with atoms and molecules. Journal of Physics B: Atomic, Molecular and Optical Physics, 2005. 38(6): p. R57.

99. Dunlop, L. J. M. and Gribakin, G. F., Many-body theory of gamma spectra from positron-atom annihilation. Journal of Physics B: Atomic, Molecular and Optical Physics, 2006. 39(7): p. 1647.

100. Gribakin, G. F., Young, J. A., and Surko, C. M., Positron-molecule interactions: Resonant attachment, annihilation, and bound states. Reviews of Modern Physics, 2010. 82(3): p. 2557.

101. Iwata, K., Greaves, R. G., and Surko, C. M., -ray spectra from positron annihilation on atoms and molecules. Physical Review A, 1997. 55(5): p. 3586.

102. McCoy, E. F. and Sykes, M. J., Quantum-mechanical QSAR/QSPR descriptors from momentum-space wave functions. Journal of Chemical Information and Computer Sciences, 2003. 43(2): p. 545.

103. Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Montgomery, J. J. A., Vreven, T., Kudin, K. N., Burant, J. C., Millam, J. M., Iyengar, S. S., Tomasi, J., Barone, V., Mennucci, B., Cossi, M., Scalmani, G., Rega, N., Petersson, G. A., Nakatsuji, H., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Kelna, M., Li, X., Knox, J. E., Hratchian, H. P., Cross, J. B., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R. E., Yazyev, O., Austin, A. J., Cammi, R., Pomelli, C., Ochterski, J. W., Ayala, P. Y., Morokuma, K., Voth, G. A., Salvador, P., Dannenberg, J. J., Zakrzewski, V. G., Dapprich, A., Daniels, A. D., Strain, M. C., Farkas, O., Malick, D. K., Rabuck, A. D., Raghavachari, K., Foresman, J. B., Ortiz, J. V., Cui, Q., Baboul, A. G., Clifford, S., Cioslowski, J., Stefanov, B. B., Liu, G., Liashenko, A., Piskorz, P., Komaromi, I., Martin, R. L., Fox, D. J., Keith, T., Ak-Laham, M. A., Peng, C. Y., Nanayakkara, A., Challacombe, M., Gill, P. M. W., Johnson, B., Chen, W., Wong, M. W., Gonzalez, C., and Pople, J. A., GAUSSIAN 03, RevisionC.02, . Gaussian, Inc., Wallingford, CT,, 2004.

104. Campanelli, A. R., Domenicano, A., and Ramondo, F., Electronegativity, Resonance, and Steric Effects and the Structure of Monosubstituted Benzene Rings: An ab Initio MO Study. The Journal of Physical Chemistry A, 2003. 107(33): p. 6429.

105. Bader, R. F. W., Atoms in molecules. Accounts of Chemical Research, 1985. 18(1): p. 9.

106. Kekulé, F. A., Sur la constitution des substances aromatiques. Bulletin de la Societe Chimique de Paris, 1865. 3: p. 98.

124

References

107. Kekulé, F. A., Untersuchungen uber aromatische Verbindungen. Liebigs Annalen der Chemie, 1866. 137: p. 129.

108. Keidel, F. A. and Bauer, S. H., Structures of Toluene, Phenylsilane, and Diphenyldichlorosilane. The Journal of Chemical Physics, 1956. 25(6): p. 1218.

109. Akopian, M. E., Vilesov, F. I., and Terenin, A. N., Sov. Phys. Doklady (Engl. Transl.), 1961. 6: p. 490.

110. Baltzer, P., Karlsson, L., Wannberg, B., Öhrwall, G., Holland, D. M. P., MacDonald, M. A., Hayes, M. A., and von Niessen, W., An experimental and theoretical study of the valence shell photoelectron spectrum of the benzene molecule. Chemical Physics, 1997. 224(1): p. 95.

111. Banna, M. S. and Shirley, D. A., On the use of yttrium and sodium anodes in photoelectron spectroscopy. Journal of Electron Spectroscopy and Related Phenomena, 1976. 8(1): p. 23.

112. Brundle, C. R., Robin, M. B., and Kuebler, N. A., Perfluoro effect in photoelectron spectroscopy. II. Aromatic molecules. Journal of the American Chemical Society, 1972. 94(5): p. 1466.

113. Carroll, T. X., Thomas, T. D., Bergersen, H., and Borve, K. J., Fluorine as a π Donor. Carbon 1s Photoelectron Spectroscopy and Proton Affinities of Fluorobenzenes. Journal of Organic Chemistry, 2006. 71(5): p. 1961.

114. Chen, Z., Wannere, C. S., Corminboeuf, C., Puchta, R., and Schleyer, P. v. R., Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion. Chemical Reviews, 2005. 105(10): p. 3842.

115. Clark, D. T., Kilcast, D., Adams, D. B., and Musgrave, W. K. R., An ESCA study of the molecular core binding energies of the fluorobenzenes. Journal of Electron Spectroscopy and Related Phenomena, 1972. 1(3): p. 227.

116. Clark, I. D. and Frost, D. C., A Study of the Energy Levels in Benzene and Some Fluorobenzenes by Photoelectron Spectroscopy. Journal of the American Chemical Society, 1967. 89(2): p. 244.

117. Davis, D. W., Shirley, D. A., and Thomas, T. D., X-ray photoelectron spectroscopy of fluorinated benzenes. Journal of the American Chemical Society, 1972. 94(19): p. 6565.

118. Decleva, P., Stener, M., Holland, D. M. P., Potts, A. W., and Karllsson, L., Perfluoro effects in the occupied and virtual valence orbitals of hexafluorobenzene. Journal of Physics B: Atomic, Molecular and Optical Physics, 2007. 40(14): p. 2939.

119. Hasegawa, A., Itagaki, Y., and Shiotani, M., EPR spectra and structure of the radical cations of fluorinated benzenes Journal Chemical Society Perkin Transactions 2, 1997(9): p. 1625.

120. Hirata, K., Kobayashi, Y., and Wang, C.-L., Positronium Annihilation in Fluorinated Benzene Derivatives. Bulletin Chemical Society Japan, 1999. 72(11): p. 2379.

121. Karlsson, L., Mattsson, L., Jadrny, R., Bergmark, T., and Siegbahn, K., Valence Electron Spectra of Benzene and the Hexafluorides of Sulphur, Molybdenum, Tungsten and Uranium. An Application of Multichannel

125

References

Detector Technique to UV-Valence Electron Spectroscopy. Physica Scripta, 1976. 14(5): p. 230.

122. Maksic, Z. B., Kova evic, B., and Kova ek, D., Simple Ab Initio Model for Calculating the Absolute Proton Affinity of Aromatics. The Journal of Physical Chemistry A, 1997. 101(40): p. 7446.

123. Namazian, M. and Coote, M. L., Gas-phase acidity, bond dissociation energy and enthalpy of formation of fluorine-substituted benzenes: A theoretical study. Journal of Fluorine Chemistry, 2009. 130(7): p. 621.

124. Palmer, M. H., Moyes, W., Spiers, M., and Ridyard, J. N. A., The electronic structure of substituted benzenes; AB initio calculations and photoelectron spectra for the methyl- and fluoro-benzenes and fluorotoluenes. Journal of Molecular Structure, 1978. 49(1): p. 105.

125. Philis, J., Bolovinos, A., Andritsopoulos, G., Pantos, E., and Tsekeris, P., A comparison of the absorption spectra of the fluorobenzenes and benzene in the region 4.5-9.5 eV. Journal of Physics B: Atomic and Molecular Physics, 1981. 14(19): p. 3621.

126. Potts, A. W., Price, W. C., Streets, D. G., and Williams, T. A., Photoelectron spectra of benzene and some fluorobenzenes. Faraday Discussions of the Chemical Society, 1972. 54: p. 168.

127. Streets, D. G. and Potts, A. W., Photoelectron spectra of inner valence shells. Part 2.-Unsaturated hydrocarbons. Journal of the Chemical Society, Faraday Transactions 2: Molecular and Chemical Physics, 1974. 70: p. 1505.

128. Wang, J. T. and Williams, F., 13C Hyperfine interaction in the hexafluorobenzene radical anion. Chemical Physics Letters, 1980. 71(3): p. 471.

129. Mondal, T. and Mahapatra, S., Photophysics of fluorinated benzene I. Quantum chemistry. The Journal of Chemical Physics, 2010. 133(8): p. 084304.

130. Khetan, S. K. and Collins, T. J., Human Pharmaceuticals in the Aquatic Environment: A Challenge to Green Chemistry. Chemical Reviews, 2007. 107(6): p. 2319.

131. Patani, G. A. and LaVoie, E. J., Bioisosterism: A Rational Approach in Drug Design. Chemical Reviews, 1996. 96(8): p. 3147.

132. Liu, P., Sharon, A., and Chu, C. K., Fluorinated nucleosides: Synthesis and biological implication. Journal of Fluorine Chemistry, 2008. 129(9): p. 743.

133. Leist, R., Frey, J., Ottiger, P., Frey, H. M., Leutwyler, S., Bachorz, R., and Klopper, W., Nucleobase–Fluorobenzene Interactions: Hydrogen Bonding Wins over π Stacking. Angewandte Chemie International Edition, 2007. 46(39): p. 7449.

134. Parsch, J. and Engels, J. W., Stacking and Stability of RNA Duplexes Containing Fluorobenzene and Fluorobenzimidazole Nucleosides. Nucleosides, Nucleotides and Nucleic Acids, 2001. 20(4): p. 815.

135. Parsch, J. and Engels, J. W., C−F···H−C Hydrogen Bonds in Ribonucleic Acids. Journal of the American Chemical Society, 2002. 124(20): p. 5664.

126

References

136. Bharathi, S. M., Grisogono, A. M., Lahmam-Bennani, A., Pascual, R., and Weigold, E., Electron momentum spectroscopy of molecular core states. Journal of Electron Spectroscopy and Related Phenomena, 1991. 53(4): p. 271.

137. Fuss, I., McCarthy, I. E., Minchinton, A., Weigold, E., and Larkins, F. P., Momentum distributions and ionization potentials for the valence orbitals of benzene. Chemical Physics, 1981. 63(1-2): p. 19.

138. Samardzic, O., J, B. M., Grisogono, A.-M., and Weigold, E., Electron momentum spectroscopy studies on ring compounds. I. Benzene. Journal of Physics B: Atomic, Molecular and Optical Physics, 1993. 26(21): p. 3921.

139. Stener, M., Fronzoni, G., and Decleva, P., Time-dependent density-functional theory for molecular photoionization with noniterative algorithm and multicenter B-spline basis set: CS2 and C6H6 case studies. The Journal of Chemical Physics, 2005. 122(23): p. 234301.

140. Yencha, A. J., Hall, R. I., Avaldi, L., Dawber, G., McConkey, A. G., MacDonald, M. A., and King, G. C., Threshold photoelectron spectroscopy of benzene up to 26.5 eV. Canadian Journal of Chemistry, 2004. 82(6): p. 1061.

141. Deleuze, M. S., Trofimov, A. B., and Cederbaum, L. S., Valence one-electron and shake-up ionization bands of polycyclic aromatic hydrocarbons. I. Benzene, naphthalene, anthracene, naphthacene, and pentacene. The Journal of Chemical Physics, 2001. 115(13): p. 5859.

142. Chong, D. P., Augmenting basis set for time-dependent density functional theory calculation of excitation energies: Slater-type orbitals for hydrogen to krypton. Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, 2005. 103(6): p. 749.

143. Schipper, P. R. T., Gritsenko, O. V., van Gisbergen, S. J. A., and Baerends, E. J., Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials. The Journal of Chemical Physics, 2000. 112(3): p. 1344.

144. Jahn, H. A. and Teller, E., Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy. Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1937. 161(905): p. 220.

145. Duflot, D., Flament, J. P., Heinesch, J., and Hubin-Franskin, M. J., Re-analysis of the K-shell spectrum of benzene. Journal of Electron Spectroscopy and Related Phenomena, 2000. 113(1): p. 79.

146. Kwon, C. H. and Kim, M. S., One-photon mass-analyzed threshold ionization spectroscopy of 1,3,5-trifluorobenzene: The Jahn-Teller effect and vibrational analysis for the molecular cation in the ground electronic state. The Journal of Chemical Physics, 2004. 121(6): p. 2622.

147. Schleyer, P. v. R. and Jiao, H., What is aromaticity. Pure Applied Chemistry, 1996. 68(2): p. 209.

148. Schleyer, P. v. R., Maerker, C., Dransfeld, A., Jiao, H., and Hommes, N. J. R. v. E., Nucleus-Independent Chemical Shifts: A Simple and Efficient

127

References

Aromaticity Probe. Journal of the American Chemical Society, 1996. 118(26): p. 6317.

149. Okazaki, T. and Laali, K. K., Transannular π-π interactions in janusenes and in related rigid systems with cofacial aromatic rings; gauging aromaticity in the hydrocarbons and in model carbocations; a DFT study. Organic & Biomolecular Chemistry, 2006. 4(16): p. 3085.

150. Wu, J. I., P hl hofer, F. G., Schleyer, P. v. R., Puchta, R., Kiran, B., Mauksch, M., Hommes, N. J. R. v. E., Alkorta, I., and Elguero, J., The Effect of Perfluorination on the Aromaticity of Benzene and Heterocyclic Six-Membered Rings. The Journal of Physical Chemistry A, 2009. 113(24): p. 6789.

151. Noorizadeh, S. and Dardab, M., A new NICS-based aromaticity index; NICS-rate. Chemical Physics Letters, 2010. 493(4-6): p. 376.

152. Selvam, L. and Wang, F., Propeties of perfluorinated benzenes based on density functional theory. (To be submitted).

153. Chong, D. P., Interpretation of the Kohn-Sham orbital energies as approximate vertical ionization potentials. Journal of Chemical Physics, 2002. 116(5): p. 1760.

154. Klasinc, L., Kovac, B., and Gusten, H., Photoelectron spectra of acenes. Electronic structure and substituent effects. Pure Applied Chemistry, 1983. 55(2): p. 289.

155. Bieri, G. and Åsbrink, L., 30.4-nm He(II) photoelectron spectra of organic molecules : Part I. Hydrocarbons. Journal of Electron Spectroscopy and Related Phenomena, 1980. 20(1): p. 149.

156. Fujisawa, S., Ohno, K., Masuda, S., and Harada, Y., Penning ionization electron spectroscopy of monohalobenzenes: fluorobenzene, chlorobenzene, bromobenzene, and iodohenzene. Journal of the American Chemical Society, 1986. 108(21): p. 6505.

157. Kimura, K., Katsumata, S., Achiba, Y., Yamazaki, T., and Iwata, S., Ionization energies, Ab initio assignments, and valence electronic structure for 200 molecules in Handbook of HeI Photoelectron Spectra of Fundamental Organic Compounds. 1981, Tokyo: Japan Scientific Society Press.

158. Streets, D. G. and Ceasar, G. P., Inductive and mesomeric effects on the π orbitals of halobenzenes. Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, 1973. 26(4): p. 1037.

159. Kelessinger, M., Ionization potentials of substituted benzenes. Angewandte Chemie International Edition, 1972. 11: p. 525.

160. Maier, J. P. and Thommen, F., Fluorescence quantum yields and lifetimes of fluorobenzene cations in selected levels of their B[combining tilde] and C[combining tilde] states determined by photoelectron-photon coincidence spectroscopy. Chemical Physics, 1981. 57(3): p. 319.

161. Rieger, D., Reiser, G., Mueller-Dethlefs, K., and Schlag, E. W., Zero kinetic energy photoelectron spectroscopy of p-difluorobenzene. The Journal of Physical Chemistry, 1992. 96(1): p. 12.

162. Sell, J. A., Mintz, D. M., and Kuppermann, A., Photoelectron angular distributions of carbon--carbon PI electroncs in ethylene, benzene, and

128

References

their fluorinated derivatives. Chemical Physics Letters, 1978. 58(4): p. 601.

163. Trudell, B. C. and Price, S. J. W., The ultraviolet photoelectron spectra of C6F5X compounds, X = (F, Cl, Br, I, H, CH3). Canadian Journal of Chemistry, 1979. 57(17): p. 2256.

164. Ganesan, A., Wang, F., Brunger, M., and Prince, K. (2011) Effects of alkyl side chains on properties of aliphatic amino acids probed using quantum chemical calculations. Journal of Synchrotron Radiation 18, DOI: 10.1107/S0909049511029499.

165. Saenger, W., Principles of Nucleic Acid Structure. 1988, New York: Springer.

166. Peters, G. J., ed. Deoxynucleoside analogs in cancer therapy. 2006, Humana Press Inc.: New Jersey.

167. Zhang, J., Visser, F., Vickers, M. F., Lang, T., Robins, M. J., Nielsen, L. P. C., Nowak, I., Baldwin, S. A., Young, J. D., and Cass, C. E., Uridine Binding Motifs of Human Concentrative Nucleoside Transporters 1 and 3 Produced in Saccharomyces cerevisiae. Molecular Pharmacology, 2003. 64(6): p. 1512.

168. Galmarini, C. M., Jordheim, L., and Dumontet, C., Pyrimidine nucleoside analogs in cancer treatment. Expert Review of Anticancer Therapy, 2003. 3(5): p. 717.

169. Shishkin, O. V., Pelmenschikov, A., Hovorun, D. M., and Leszczynski, J., Molecular structure of free canonical 2'-deoxyribonucleosides: a density functional study. Journal of Molecular Structure, 2000. 526(1-3): p. 329.

170. Hocquet, A., Leulliot, N., and Ghomi, M., Ground-State Properties of Nucleic Acid Constituents Studied by Density Functional Calculations. 3. Role of Sugar Puckering and Base Orientation on the Energetics and Geometry of 2‘-Deoxyribonucleosides and Ribonucleosides. The Journal of Physical Chemistry B, 2000. 104(18): p. 4560.

171. Young, D. W. and Wilson, H. R., The crystal and molecular structure of 2'-deoxycytidine. Acta Crystallographica Section B, 1975. 31(4): p. 961.

172. Hocquet, A., Intramolecular hydrogen bonding in 2'-deoxyribonucleosides: an AIM topological study of the electronic density. Physical Chemistry Chemical Physics, 2001. 3(15): p. 3192.

173. Brooks, R. F., 3' Deoxycytidine, like hydroxyurea, inhibits DNA synthesis without preventing the initiation of the cell cycle. Cell Biology International Reports, 1978. 2(3): p. 279.

174. Harris, B. and Dure, L. S., Differential effects of 3'-deoxy nucleosides on RNA synthesis in cotton cotyledons. Biochemistry, 1974. 13(27): p. 5463.

175. Karthe, P., Gautham, N., Kumar, A., and Katti, S. B., The Three-Dimensional Structure of 3′-Deoxycytidine. Nucleosides and Nucleotides, 1997. 16(1): p. 1.

176. Ganesan, A. and Wang, F., Intramolecular interactions of L-phenylalanine revealed by inner shell chemical shift. The Journal of Chemical Physics, 2009. 131(4): p. 044321.

129

References

177. Huang, Z., Yu, W., and Lin, Z., Exploration of the full conformational landscapes of gaseous aromatic amino acid phenylalanine: An ab initio study. Journal of Molecular Structure: THEOCHEM, 2006. 758(2-3): p. 195.

178. Bader, R. F. W., A quantum theory of molecular structure and its applications. Chemical Reviews, 1991. 91(5): p. 893.

179. Shishkin, O. V., Palamarchuk, G. V., Gorb, L., and Leszczynski, J., Intramolecular Hydrogen Bonds in Canonical 2‘-Deoxyribonucleotides: An Atoms in Molecules Study. The Journal of Physical Chemistry B, 2006. 110(9): p. 4413.

180. Chen, F., Selvam, L., and Wang, F., Blue shifted intramolecular C-H···O improper hydrogen bonds in conformers of zidovudine. Chemical Physics Letters, 2010. 493(4-6): p. 358.

181. Li, J., Lee, S. A., Anderson, A., Lettress, L., Griffey, R. H., and Mohan, V., Temperature-dependent Raman and infrared spectra of nucleosides. III - deoxycytidine. Journal of Raman Spectroscopy, 2003. 34(3): p. 183.

182. Boese, A. D., Martin, J. M. L., and Handy, N. C., The role of the basis set: Assessing density functional theory. The Journal of Chemical Physics, 2003. 119(6): p. 3005.

183. Curtiss, L. A., Raghavachari, K., Redfern, P. C., and Pople, J. A., Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation. Chemical Physics Letters, 1997. 270(5-6): p. 419.

184. Lopez-Tocon, I., Pelaez, D., Soto, J., Rico, R., Cai, C., Lopez-Romero, J. M., and Otero, J. C., Raman Study of the Rigidity of Penta-p-phenylene Derivatives Used as Legs in Molecular Tripods. The Journal of Physical Chemistry B, 2008. 112(17): p. 5363.

185. Scott, A. P. and Radom, L., Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Moller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors. The Journal of Physical Chemistry, 1996. 100(41): p. 16502.

186. Li, A. Y., Chemical origin of blue- and redshifted hydrogen bonds: Intramolecular hyperconjugation and its coupling with intermolecular hyperconjugation. The Journal of Chemical Physics, 2007. 126(15): p. 154102.

187. Hobza, P. and Havlas, Z., Blue-Shifting Hydrogen Bonds. Chemical Reviews, 2000. 100(11): p. 4253.

188. Selvam, L., Chen, F., and Wang, F., Solvent effects on blue shifted improper hydrogen bond of C-H...O in deoxycytidine isomers. Chemical Physics Letters, 2010. 500(4-6): p. 327.

189. Hurd, P. J., Whitmarsh, A. J., Baldwin, G. S., Kelly, S. M., Waltho, J. P., Price, N. C., Connolly, B. A., and Hornby, D. P., Mechanism-based inhibition of C5-cytosine DNA methyltransferases by 2-H pyrimidinone. Journal of Molecular Biology, 1999. 286(2): p. 389.

190. Holy, A., Ludzisa, A., Votruba, I., Sediva, K., and Pischel, H., Preparation of Analogues of cytosine and 2-Pyrimidionone nucleosides and their effect on bacterial (Escherichia coli A19) Cytidine

130

References

Aminohydrolase. Collection of Czechoslovak Chemical Communications, 1985. 50(2): p. 393.

191. Kim, C. H., Marquez, V. E., Mao, D. T., Haines, D. R., and McCormack, J. J., Synthesis of pyrimidin-2-one nucleosides as acid-stable inhibitors of cytidine deaminase. Journal of Medicinal Chemistry, 1986. 29(8): p. 1374.

192. Zhou, L., Cheng, X., Connolly, B. A., Dickman, M. J., Hurd, P. J., and Hornby, D. P., Zebularine: A novel DNA methylation inhibitor that forms a covalent complex with DNA methyltransferases. Journal of Molecular Biology, 2002. 321(4): p. 591.

193. McCormack, J. J., Marquez, V. E., Liu, P. S., Vistica, D. T., and Driscoll, J. S., Inhibition of cytidine deaminase by 2-oxopyrimidine riboside and related compounds. Biochemical Pharmacology, 1980. 29(5): p. 830.

194. Connolly, B. A. and Newman, P. C., Synthesis and properties of oligonucleotides containing 4-thiothyniidine, 5-methyl-2-pyrunidinone-1-{beta}-D(2'-dexoyriboside) and 2-thiothvmidine. Nucleic Acids Research, 1989. 17(13): p. 4957.

195. Gildea, B. and McLaughlin, L. W., The synthesis of 2-pyrimidinone nucleosides and their incorporation into oligodeoxynucleotides. Nucleic Acids Research, 1989. 17(6): p. 2261.

196. Wu, P., Nordlund, T. M., Gildea, B., and McLaughlin, L. W., Base stacking and unstacking as determined from a DNA decamer containing a fluorescent base. Biochemistry, 1990. 29(27): p. 6508.

197. Kistler, K. A. and Matsika, S., The Fluorescence Mechanism of 5-Methyl-2-Pyrimidinone: An Ab Initio Study of a Fluorescent Pyrimidine Analog. Photochemistry & Photobiology, 2007. 83(3): p. 611.

198. Newell-Price, J., Clark, A. J. L., and King, P., DNA Methylation and Silencing of Gene Expression. Trends in Endocrinology and Metabolism, 2000. 11(4): p. 142.

199. Wärmländer, S., Sponer, J. E., Sponer, J., and Leijon, M., The Influence of the Thymine C5 Methyl Group on Spontaneous Base Pair Breathing in DNA. Journal of Biological Chemistry, 2002. 277(32): p. 28491.

200. Fukui, K., Role of Frontier Orbitals in Chemical Reactions. Science, 1982. 218(4574): p. 747.

201. Falzon, C. T., Wang, F., and Pang, W., Orbital signatures of methyl in l-alanine. The Journal of Physical Chemistry B, 2006. 110(19): p. 9713.

202. Selvam, L., Chen, F. F., and Wang, F., Methylation of zebularine investigated using density functional theory calculations. Journal of Computational Chemistry, 2011. 32(10): p. 2077.

203. Coulson, C. A. and Duncanson, W. E., Momentum Distribution in Molecular Systems. Mathematical Proceedings of the Cambridge Philosophical Society, 1941. 37(01): p. 67.

204. Coulson, C. A. and Duncanson, W. E., Momentum distribution in molecular systems. Part VI. Shape of the Compton line for methane CH4. Mathematical Proceedings of the Cambridge Philosophical Society, 1942. 38(01): p. 100.

131

References

205. Dirac, P. A. M., On the Annihilation of Electrons and Protons. Mathematical Proceedings of the Cambridge Philosophical Society, 1930. 26(03): p. 361.

206. Anderson, C. D., The apparent existence of easily deflectable positives. Science, 1932. 76: p. 238.

207. Anderson, C. D., The positive electron. Physical Review, 1933. 43: p. 491.

208. Glish, G. L., Greaves, R. G., McLuckey, S. A., Hulett, L. D., Surko, C. M., Xu, J., and Donohue, D. L., Ion production by positron-molecule resonances. Physical Review A, 1994. 49(4): p. 2389.

209. Charlton, M. and Humberston, J. W., Positron Physics. 2001, New York: Cambridge University Press.

210. Griffith, T. C. and Heyland, G. R., Experimental aspects of the study of the interaction of low-energy positrons with gases. Physics Reports, 1978. 39(3): p. 169.

211. Kauppila, W. E. and Stein, T. S., Comparisons of Positron And Electron Scattering By Gases, in Advances In Atomic, Molecular, and Optical Physics, B. Sir David and B. Benjamin, Editors. 1989, Academic Press. p. 1.

212. Surko, C. M. and Gianturco, F. A., New directions in antimatter chemistry and physics. 2001, Dordrecht: Kluwer Academic Publishers.

213. Van Reeth, P., Humberston, J. W., Iwata, K., Greaves, R. G., and Surko, C. M., Annihilation in low-energy positron-helium scattering. Journal of Physics B: Atomic, Molecular and Optical Physics, 1996. 29(12): p. L465.

214. Puska, M. J. and Nieminen, R. M., Theory of positrons in solids and on solid surfaces. Reviews of Modern Physics, 1994. 66(3): p. 841.

215. Iwata, K., Gribakin, G. F., Greaves, R. G., and Surko, C. M., Positron annihilation with inner-shell electrons in noble gas atoms. Physical Review Letters, 1997. 79(1): p. 39.

216. Radtsig, A. A. and Smirnov, B. M., Parameters of Atoms and Atomic Ions: Handbook. 1986, Moscow: Energoatomizdat.

217. Wang, F., Selvam, L., Gribakin, G., and Surko, C. M., Effects of bound electronic wavefunctions to gamma ray spectra of positron annihilation in atoms and small molecules in 19th Australian Institute of Physics Congress. 2010: Melbourne.

simulation of spectroscopic properties of atoms and molecules · “effects of bound electronic...

Documents