A density functional theory study on structure and mechanism of some isomerization and cycloaddition reactions

Vrije Universiteit Brussel
Faculteit Wetenschappen
Onderzoeksgroep Algemene Chemie

Vrije Universiteit Brussel
Faculteit Wetenschaid Alge

A Density Functional Theory
Study on Structure and
Mechanism of some Isomerization
and Cycloaddition Reactions

Loc Thanh Nguyen

Promotors:
Prof. Dr. Paul Geerlings,
Vrije Universiteit Brussel
Prof. Dr. Minh Tho Nguyen,
Katholieke Universiteit Leuven

Proefschrift voorgelegd tot het
behalen van de wettelijke graad
van Doctor in de Wetenschappen

October 2002


Acknowledgements
The story of this thesis started in September 1997 with the “Interuniversity Program for
Education in Computational Chemistry in Vietnam” supported by the Flemish
Government (project VIET/97-4). Professor Minh Tho Nguyen at the Katholieke

Universiteit Leuven (KULeuven), the main promoter of this project, together with
professor Paul Geerlings at the Vrije Universiteit Brussel (VUB) and professor Kris
Van Alsenoy of the Universiteit van Antwerpen (UIA), has opened a door for me to
enter the fascinating field of computational chemistry when providing me an
opportunity to join two of the research groups involved, first the KULeuven group, then
the VUB one.
At the beginning, every quantum theory was new for me. But, from that time, both
professors had tried hard not only to give me a sound background but also to look for
financial resources. Finally they used their own research funds, namely the
Geconcerteerde Onderzoeksacties (GOA) and the DFT Research community of the
Fund for Scientific Research (FWO-Vlaanderen), along with the kind support of their
colleagues (professor Luc Vanquickenborne, professor Arnout Ceulemans, professor
Kristine Pierloot, professor Marc Hendrickx (KULeuven) and professor Frank De Proft
(VUB)), to give me a unique chance to perform research at the doctoral level in the
department of chemistry, VUB, but on a joint research project between both VUB and
KULeuven quantum chemistry groups. The last doctoral year fellowship was granted by
the Vrije Universiteit Brussel. Therefore, I would first like to express my sincere thanks
to both universities, the research funds, professors Nguyen and Geerlings as well as
their colleagues for their kind support. I would like to express my deep gratitude to
professor Paul Geerlings and professor Minh Tho Nguyen for their constant
encouragement, scientific guidance and patient supervision of my research work.
This work would not have been achievable without the friendly support and efficient
help from many other people. In particular, I wish to acknowledge professor Frank De
Proft (VUB), Dr. Wilfried Langenaeker (VUB; now at Janssen Pharmaceutica) and Dr.
Asit Kumar Chandra (KULeuven, now in India) for patiently answering my technical
problems and valuable help. I would also like to thank professor Kalidas Sen (India) for
uncomplainingly explaining my theoretical questions during his short visiting day at
VUB. A special thank is also sent to professor Kris Van Alsenoy for helping me with
the Hirshfeld charge calculations. I am particularly grateful to Dr. Hans Vansweevelt
(KULeuven) for computational help and to the VUB Computer Center for support. Mrs.

Rita Jungbluth (KULeuven) and Mrs. Martine De Valck (VUB) are also acknowledged
for administrative help.
The days would have passed far more slowly without the support of my friends, both at
the KULeuven and VUB, providing me such a rich source of conversation, education
and entertainment. My warmest gratitude goes to my friends Trung Ngoc Le, Hung
Thanh Le, Hue Minh Thi Nguyen, Thanh Lam Nguyen, Nam Cam Pham, Nguyen


ii

Acknowledgement

Nguyen Pham-Tran, David Delaere, Dr. Annelies Delabie, Dr. Steven Creve, Dr.
Raman Sumathy (KULeuven), Ricardo Vivas-Reyes, Bennasser Safi, Dr. Gregory Van
Lier, Pierre Mignon, Dr. Frederik J. C. Tielens, Dr. Robert Balawender, Dr. Stefan
Loverix, Greet Boon, Goedele Roos, Jan Baert, Montserrat Cases Amat (VUB) … and
many more. I could not have asked for a better working environment and friendship.
Furthermore I also owe a debt of thanks to Mr. Diet Van Tran and his family, Mrs. Mai
Phuong Le and her two nice daughters, my friends (Nho Hao Dinh, Chau Ngan
Nguyen-Vo, Ngoc Lien Truong, Phuong Khuong Ong, Minh Tri Nhan, Chi Thanh
Truong, Thu Phong Phan-Vo, Lam Thanh Nguyen, Thai An Mai, Thi Xuan Tran … and
many more), who have no direct relation with my research, but they have given me
much concern and useful help during my stays in Belgium.
My thanks also extend to my home university in Vietnam, the Faculty of Chemical
Engineering, HoChiMinh City University of Technology (HUT), for administrative
support. I would like to acknowledge professor Van Luong Dao for scientific guidance
and valuable advice of my research work in Vietnam. I am indebted to professor Van
Bon Pham, professor Huu Nieu Nguyen, professor Van Lua Nguyen, professor Van
Hang Tong, professor Huu Khiem Mai, professor Thuong Truong Le, professor Khac
Chuong Tran, professor Viet Hoa Thi Tran, professor Minh Tan Phan, Msc. Dinh Pho

Nguyen, Mrs. Thi Dung Huynh, Msc. Ba Minh Vu, Mr. Hung Dung Tran, Msc. Minh
Nam Hoang, Msc. Thanh Son Thanh Do, Mr. Van Co Ngo, Msc. Thanh Trung Duong,
Msc. Huu Thao Vo, Dr. Dac Thanh Nguyen, Dr. Van Phuoc Nguyen, Dr. Ngoc Hanh
Nguyen, Mrs. Thi Thu Nguyen, Mrs. Kim Anh Thi Lam, Mrs. Ngoc Phu Thi Nguyen
(HUT) and Mr. Cat Si Thanh Le (HoChiMinh City) for their continuous support and
valuable help. Many thanks also go to my colleagues and my friends in HUT for their
cooperation, friendship and encouragement.
Especially, I would express heartfelt thanks to my parents, my parents-in-law, my
brothers, my sisters and their families, for their love, invaluable help and support
throughout my life.
Finally, I would like to give my special thanks to my wife, Dieu Chan Thi Truong, and
our two children, Huong Lan Ngoc Nguyen and Thanh Triet Nguyen, for their love,
patience and encouragement that enabled me to complete this work.


Table of Contents
Acknowledgments .............................................................................................................. i
Table of Contents ............................................................................................................... iii
Summary ............................................................................................................................ vii
Samenvatting ...................................................................................................................... ix
Chapter 1 Introduction ................................................................................................... 1
1.1
Computational Chemistry................................................................................... 1
1.1.1
Current Situation................................................................................................. 1
1.1.2
Methods .............................................................................................................. 2
1.2
Structures and reaction mechanism in organic chemistry .................................. 4
1.3

Scope of the Thesis............................................................................................. 10
1.4
References .......................................................................................................... 11
Chapter 2 Theoretical Background ................................................................................ 13
2.1
Wave function Ab Initio methods ...................................................................... 13
2.1.1
Schrödinger equation.......................................................................................... 13
2.1.2
The Hartree-Fock theory .................................................................................... 14
2.1.2.1 Restricted closed-shell Hartree-Fock: The Roothaan-Hall equations ................ 16
2.1.2.2 Unrestricted open-shell Hartree-Fock: The Pople-Nesbet equations ................. 17
2.1.3
Post Hartree-Fock methods ................................................................................ 18
2.1.3.1 The Configuration Interaction method ............................................................... 19
2.1.3.2 The Coupled Cluster method.............................................................................. 20
2.1.3.3 The Møller-Plesset Perturbation method............................................................ 20
2.1.4
Basis sets............................................................................................................. 22
2.1.4.1 Minimal basis sets .............................................................................................. 22
2.1.4.2 Scaling the orbital by splitting the minimal basis set ......................................... 23
2.1.4.2.1 Split valence basis sets ....................................................................................... 23
2.1.4.2.2 Double zeta basis sets ......................................................................................... 23
2.1.4.3 Extended basis sets ............................................................................................. 24
2.1.4.3.1 Polarization basis functions ................................................................................ 24
2.1.4.3.2 Diffuse basis functions ....................................................................................... 24
2.1.4.4 Dunning's correlation consistent basis sets......................................................... 24
2.1.5
Molecular quantities ........................................................................................... 25
2.1.5.1 The electron density function ............................................................................. 25

2.1.5.2 Atomic charges ................................................................................................... 25
2.1.5.2.1 The Mulliken population analysis method ......................................................... 25
2.1.5.2.2 The natural population analysis.......................................................................... 26
2.1.5.2.3 The electrostatic potential derived charges ........................................................ 27
2.2
Density Functional Theory ................................................................................. 27


iv

2.2.1
2.2.2
2.2.3
2.2.3.1
2.2.3.2
2.2.3.3
2.2.4
2.2.4.1
2.2.4.2
2.2.4.3
2.2.4.4
2.3
2.3.1
2.3.2
2.3.2.1
2.3.2.2
2.3.3
2.3.3.1
2.3.3.2
2.4

Table of Contents

The Thomas-Fermi-Dirac theory........................................................................ 28
The Kohn-Sham method..................................................................................... 28
The exchange-correlation energy functional ...................................................... 30
Local Density methods ....................................................................................... 30
Gradient Corrected methods............................................................................... 30
Hybrid methods .................................................................................................. 30
DFT-based chemical concepts............................................................................ 31
The chemical potential........................................................................................ 31
Hardness and Softness ........................................................................................ 32
The Fukui function and local softness................................................................ 33
The Local Hard and Soft Acids and Bases principle.......................................... 34
Solvent effect...................................................................................................... 34
Introduction ........................................................................................................ 34
Solvation models ................................................................................................ 35
Explicit solvation models ................................................................................... 35
Implicit solvation models ................................................................................... 36
The PCM model.................................................................................................. 37
Introduction ........................................................................................................ 37
Model Implementation ....................................................................................... 37
References .......................................................................................................... 39

Chapter 3 Computational Details................................................................................... 41
3.1
Software and Hardware ...................................................................................... 41
3.2
References .......................................................................................................... 43
Chapter 4 Application of Density Functional Theory (DFT) in constructing the

Potential Energy Surface for Simple Isomerization and Fragmentation
Reactions ............................................................................................................ 45
4.1
Introduction ...................................................................................................... 45
4.2
Theoretical study of the CH3 + NS and related reactions: mechanism
of HCN formation............................................................................................. 48
4.2.1
Introduction ........................................................................................................ 48
4.2.2
Methods of Calculations..................................................................................... 48
4.2.3
Results and Discussion ....................................................................................... 48
4.2.4
Conclusions ........................................................................................................ 55
4.3
Theoretical Study of the Potential Energy Surface Related to NH2 +
NS Reaction: N2 versus H2 Elimination.......................................................... 56
4.3.1
Introduction ........................................................................................................ 56
4.3.2
Methods of Calculations..................................................................................... 56
4.3.3
Results and Discussion ....................................................................................... 57
4.3.4
Conclusions ........................................................................................................ 65
4.4
General Conclusion .......................................................................................... 66
4.5
References.......................................................................................................... 67

Chapter 5 Application of Density Functional Theory (DFT) in studying
Cycloaddition Reactions..................................................................................... 71
5.1
Introduction ...................................................................................................... 71


Table of Contents

5.2

v

Mechanism of [2+1] Cycloadditions of Hydrogen Isocyanide to
Acetylenes .......................................................................................................... 76
5.2.1
Introduction ........................................................................................................ 76
5.2.2
Methods of Calculation ...................................................................................... 77
5.2.3
Results and Discussion ....................................................................................... 77
5.2.3.1 Preliminary analysis of frontier orbital interactions ........................................... 77
5.2.3.2 Addition of the unsubstituted system HN≡C + HC≡CH (Reaction H) .............. 78
5.2.3.3 Addition of HN≡C to HC≡C-CH3 (Reaction M)................................................ 82
5.2.3.4 Addition of HN≡C to HC≡C-NH2 (Reaction A) ................................................ 84
5.2.3.5 Addition of HN≡C to HC≡C-F (Reaction F)...................................................... 87
5.2.3.6 Asynchronism in Addition.................................................................................. 90
5.2.4
Conclusions ........................................................................................................ 98
5.3
[2+1] Cycloadditions of CO and CS to Acetylenes ........................................ 99

5.3.1
Cyclopropenones and cyclopropenethiones: decomposition via
intermediates..................................................................................................... 99
5.3.1.1 Introduction ........................................................................................................ 99
5.3.1.2 Methods of Calculation ...................................................................................... 100
5.3.1.3 Results and Discussion ....................................................................................... 100
5.3.1.3.1 Analysis of the nature of the reaction partners ................................................... 100
5.3.1.3.2 Reaction of H-C≡C-H with C=X (X = O, S)...................................................... 101
5.3.1.3.2.1 Potential energy surfaces .................................................................................. 101
5.3.1.3.2.2 Solvent effect.................................................................................................... 107
5.3.1.3.2.3 Estimation of the vertical first excitation energies ........................................... 107
5.3.1.3.3 Reaction of H-C≡C-F with C=X (X = O, S)....................................................... 108
5.3.1.3.4 Reaction of F-C≡C-F with C=X (X = O, S) ....................................................... 111
5.3.1.3.5 Profiles of hardness, polarizability and activation energy along an IRC
path ..................................................................................................................... 113
5.3.1.4 Conclusions ........................................................................................................ 115
5.3.2
[2 + 1] Cycloaddition of CO and CS to Acetylenes forming
Cyclopropenones and Cyclopropenethiones .................................................. 116
5.3.2.1 Introduction ........................................................................................................ 116
5.3.2.2 Methods of Calculation ...................................................................................... 117
5.3.2.3 Results and Discussion ....................................................................................... 118
5.3.2.3.1 Classification of the reactants as nucleophile or electrophile............................. 118
5.3.2.3.2 Potential Energy Surfaces................................................................................... 119
5.3.2.3.2.1 Reaction of H-C≡C-CH3 with CX (X = O, S) .................................................. 119
5.3.2.3.2.2 Reaction of H-C≡C-OH.................................................................................... 123
5.3.2.3.2.3 Reaction of H-C≡C-NH2 .................................................................................. 124
5.3.2.3.2.4 Reaction of H-C≡C-C6H5 ................................................................................. 125
5.3.2.3.2.5 Reaction of HO-C≡C-CH3 ................................................................................ 127
5.3.2.3.2.6 Reaction of HO-C≡C-C6H5 .............................................................................. 128

5.3.2.3.3 Effects of substituents on the aromaticity of cyclo-propenones and
cyclopropenethiones ........................................................................................... 132
5.3.2.3.4 Site selectivity in the initial attack of the addition ............................................. 133
5.3.2.4 Conclusions ........................................................................................................ 136
5.4
1,3-Dipolar cycloadditions of thionitroso compounds (R–N=S)................... 138
5.4.1
Introduction ........................................................................................................ 138


vi

Table of Contents

5.4.2
5.4.3
5.4.3.1
5.4.3.1.1
5.4.3.1.2
5.4.3.1.3
5.4.3.1.4
5.4.3.2
5.4.3.3
5.4.4
5.5

Details of calculations ........................................................................................ 138
Results and discussion ........................................................................................ 139
Structure and energetics...................................................................................... 139
The HC≡N+–O- + HN=S addition (A)................................................................ 139

The HC≡N+–O- + H2N–N=S addition (B).......................................................... 140
The HN=N+=N- + HN=S addition (C)................................................................ 141
Additions of substituted systems. ....................................................................... 143
Regiochemistry of the addition: testing the local HSAB principle .................... 144
Testing the maximum hardness principle........................................................... 147
Conclusions ........................................................................................................ 149
Nitrous Oxide as a 1,3-Dipole: A Study of Its Cycloaddition
Mechanism ........................................................................................................ 150
5.5.1
Introduction ........................................................................................................ 150
5.5.2
Details of Calculation ......................................................................................... 152
5.5.3
Results and Discussion ....................................................................................... 152
5.5.3.1 Frontier Molecular Orbital Analysis................................................................... 152
5.5.3.2 The 1,3-DC of N2O to acetylene ........................................................................ 154
5.5.3.3 The 1,3-DC of N2O to substituted alkynes ......................................................... 157
5.5.3.3.1 Geometries.......................................................................................................... 157
5.5.3.3.2 Energy barriers and solvent effect ...................................................................... 159
5.5.3.3.3 Regioselectivity .................................................................................................. 161
5.5.4
Conclusions ........................................................................................................ 166
5.6
1,3-Dipolar cycloadditions of diazoalkanes, hydrazoic acid and
nitrous oxide to acetylenes, phosphaalkynes and cyanides: a
regioselectivity study ........................................................................................ 168
5.6.1
Introduction ........................................................................................................ 168
5.6.2
Details of Calculation ......................................................................................... 171

5.6.3
Results and Discussion ....................................................................................... 171
5.6.3.1 The 1,3-DC of Diazoalkanes .............................................................................. 171
5.6.3.2 The 1,3-DC of Hydrazoic acid and Nitrous Oxide............................................. 178
5.6.4
Conclusions ........................................................................................................ 182
5.7
General Conclusion .......................................................................................... 184
5.8
References.......................................................................................................... 187
Chapter 6

General Conclusions .................................................................................. 197

Appendices ........................................................................................................................ 199
A1. List of Symbols and Abbreviations ............................................................................. 199
A2. List of supplementary Tables and Figures in §5.3.2 and §5.6..................................... 201
A3. List of Publications ...................................................................................................... 212


Summary
In this thesis we apply the Density Functional Theory (DFT) in its Kohn Sham
formulation using the B3LYP functional, for constructing of the potential energy
surface (PES) for some isomerization and fragmentation reactions and studying a
number of [2+1] and 1,3-dipolar cycloadditions.
The PES constructions for the isomerization and fragmentation reactions involving two
NS moieties, [CH3NS] and [NH2NS] show that, with respect to the CCSD(T) values, the
B3LYP method tends to overestimate the energy gaps between equilibrium structures
relative to the starting structures (CH3NS or NH2NS). The energy ordering however
remains almost unchanged. Moreover, the most significant chemical results of the

theoretical studies are a prediction on the preferential formation of HCN in the CH3 +
NS reaction and the fact that both radicals NH2 and NS can go through an initial barrierfree nitrogen-nitrogen association giving NH2NS, which in turn tends to follow a lowenergy two-step path leading to the stable products, N2 and H2S. A one-step elimination
of H2 seems to be a more energy-demanding process.
The theoretical studies of the [2+1] cycloaddition of hydrogen isocyanide (HN≡C), CX
(X = O, S) to acetylenes demonstrates that these reactions proceed in two steps: addition
of the carbon atom in HN≡C or CX to a carbon atom of the acetylenes giving rise to an
intermediate, followed by a ring closure step of the latter to form at last the
cycloadducts. The intermediate has the properties of a semi-carbene, semi-zwitterion
and its structure is best described as a resonance hybrid between a carbene and a
zwitterion. In all cases acetylenes behave as nucleophiles. The investigation of the
hardness and polarizability profiles along the IRC reaction paths shows that there is a
maximum in the polarizability profile besides an inverse relationship between hardness
and polarizability.
In the cycloadditions of CX to acetylenes, it is also shown that the promotion of an
electron from the ground state to an excited state for any reaction partner requires a
large amount of energy. As such, all investigated reactions are expected to take place in
the ground state rather than in an excited state. We also show that the solvent effect is
small on the reactions, and tends to stabilize all the isomers.
Different reactivity criteria such as Frontier Molecular Orbital (FMO) coefficients, local
softness, hardness, polarizability and nucleus-independent chemical shifts (NICS) are
used to predict the site selectivity in all studied cases, and the NICS, FMO coefficients,
local softness seem to yield the best results among them.
The 1,3-dipolar cycloadditions (1,3-DC) of fulminic acid (HCNO) and the simple
azides (XNNN, X=H, CH3, NH2) to thionitroso compounds (R-N=S, R = H, NH2) are
generally characterized by their rather low energy barriers. In the cases of azides, the
reaction is not stereospecific. In all cases, they show a certain regioselectivity favoring
the formation of a cycloadduct.
The 1,3-DC reactions of diazoalkanes, hydrazoic acid and nitrous oxide to the polar

viii

Summary

dipolarophiles considered are concerted but asynchronous processes. When approaching
a polar dipolarophile partner either the C-end of a diazo derivative, or the N(R) of an
azide or the O-atom of nitrous oxide, consistently acts as a new bond donor and the
other molecular terminus being the new bond acceptor. As a consequence, the lone pair
of the central nitrogen, formed upon bending of the dipole, originates from the triple
N≡N bond. Those cycloaddition reactions are essentially orbital-controlled, which is
supported by the successful prediction of the regioselectivity based on reactivity criteria
that are basically generalized forms of FMO theory. The local softness differences and
FMO coefficient products remain the criteria of choice in predicting the regioselectivity
of cycloaddition reactions. Among available population analysis methods to define the
atomic charges, the Natural Population Analysis (NPA) seems to give the best support
to the local Hard and Soft Acids and Bases (HSAB) principle.
In the cycloadditions of nitrous oxide to acetylenes, in general, the shape of the
potential energy surface appears not to be affected by the polarity of the solvent.
Although all Ts’s are aromatic, their aromaticity does not influence the regioselectivity
of the reactions. In this study the less aromatic, more polar and more asynchronous Ts is
the Ts-normal.


Samenvatting
In deze thesis wordt Density Functional Theory (DFT) toegepast in de Kohn Sham
formulering, met gebruik van de B3LYP functionaal, om het Potentiële Energie
Oppervlak (PES) van een aantal isomerisatie en fragmentatiereacties te bestuderen,
alsook een aantal [2+1] en 1,3-dipolaire cycloaddities.
De PES constructie voor de isomerisatie en fragmentatiereacties voor twee NS
entiteiten bevattende species, [CH3NS] en [NH2NS], toont aan dat, in vergelijking met

CCSD(T), de B3LYP methode de energieverschillen overschat tussen
evenwichtsstructuren, transitietoestanden en de startstructuren (CH3NS of NH2NS). De
ordening van de energieën daarentegen is bijna steeds onveranderd. De meest
significante chemische resultaten van de theoretische studie zijn enerzijds een
voorspelling van de voorkeur van vorming van HCN in de CH3 + NS reactie, anderzijds
het feit dat beide radicalen, NH2 en NS, een initiële barrièrevrije stikstof-stikstof
associatie vertonen, aanleiding gevend tot NH2NS. Op zijn beurt volgt NH2NS een laagenergetisch tweestapsmechanisme leidend tot de stabiele eindproducten N2 en H2S. Een
eenstapseliminatie van H2 blijkt een energetisch minder gunstig proces te zijn.
De theoretische studie van de [2+1] cycloadditie van waterstofisocyanide (HN≡C) en
CX (X = O, S) aan acetylenen toont aan dat deze reacties in twee stappen verlopen :
additie van het koolstofatoom in HN≡C of CX aan een koolstofatoom van de acetylenen
wat aanleiding geeft tot een intermediair, gevolgd door een ringsluiting met finaal
vorming van het cycloadduct. Het intermediair blijkt de eigenschappen van een semicarbeen, semi-zwitterion te hebben. Zijn structuur wordt het best beschreven als een
resonantiehybride tussen een carbeen en een zwitterion. In alle gevallen blijken
acetylenen zich als nucleofiel te gedragen. Het onderzoek van de hardheid en de
polariseerbaarheidsprofielen langsheen het IRC reactiepad toont aan dat er een
maximum in het polariseerbaarheidsprofiel is. Een inverse relatie tussen hardheid en
polarisabiliteit wordt vastgesteld.
Bij de cycloaddities van CX op acetylenen wordt ook aangetoond dat de overgang van
de electronische grondtoestand naar een aangeslagen toestand voor elk van de
reactiepartners veel energie vergt. Men kan daarom verwachten dat alle reacties
plaatsgrijpen vanuit de grondtoestand en niet vanuit een aangeslagen toestand. Ook
wordt aangetoond dat het solvent effect op deze reacties klein is en dat het alle isomeren
stabiliseert.
Verschillende reactiviteitscriteria zoals de "Frontier Molecular Orbital" (FMO)
coëfficiënten en de lokale zachtheid, hardheid, polariseerbaarheid en de "nucleusindependent chemical shifts" (NICS) worden gebruikt om de "site selectivity" te
voorspellen in alle beschouwde gevallen. De NICS, FMO coëfficiënten en de lokale
zachtheid blijken hierbij de beste resultaten op te leveren.
De 1,3-dipolaire cycloaddities (1,3-DC) van HCNO en eenvoudige azides (XNNN, X =
H, CH3, NH2) op thionitroso verbindingen (R-N=S, R = H, NH2) worden over het

x

Samenvatting

algemeen gekarakteriseerd door vrij lage energiebarrières. In het geval van azides is de
reactie niet stereospecifiek. In alle gevallen vertonen deze reacties een zekere
regioselectiviteit in de vorming van de cycloadducten.
De 1,3-DC reacties van diazoalkanen, waterstofazide en distikstofmonoxide aan de
beschouwde polaire dipolarofielen zijn geconcerteerde maar asynchrone processen. Bij
nadering van een polair dipolarofiel zal ofwel het terminale C-atoom van een
diazoderivaat, het N(R) atoom van een azide of het O-atoom van distikstofmonoxide,
onveranderlijk dienst doen als donorcentrum voor een nieuwe binding terwijl het andere
uiteinde van het molecule als bindingsacceptor zal fungeren. Bijgevolg vindt het Niet
Gebonden Elektronenpaar van het centrale stikstofatoom, dat ontstaat bij "bending" van
het dipool, zijn oorsprong in de drievoudige N≡N binding. Deze cycloadditiereacties
zijn essentieel orbitaal-gecontroleerd wat bevestigd wordt door de succesvolle
voorspelling van regioselectiviteit gebaseerd op reactiviteitscriteria die als
veralgemening van de FMO theorie kunnen beschouwd worden. Verschillen in lokale
zachtheid en producten van FMO coëfficiënten blijken de beste criteria te zijn om de
regioselectiviteit van cycloadditiereacties te voorspellen. Binnen de voorhanden zijnde
populatie analysemethodes die toelaten atomaire ladingen te genereren blijkt de
"Natural Population Analysis" (NPA) het sterkst het lokale "Hard and Soft Acids and
Bases" (HSAB) principe te ondersteunen.
In de cycloaddities van de distikstofmonoxide aan acetylenen blijkt over het algemeen
dat het potentiële energieoppervlak niet vervormd wordt door de polariteit van het
solvent. Hoewel alle transitietoestanden aromatisch zijn, blijkt aromaticiteit de
regioselectiviteit van de reacties niet te beïnvloeden. De meest voordelige ("normale")
transitietoestand (Ts-normal) blijkt in deze studie steeds de meest aromatische, meest

polaire en meest asynchrone transitietoestand te zijn.


1.

Introduction

1.1 Computational Chemistry
1.1.1 Current Situation
With the coming of the 21st century, chemical industry has to face considerable
challenges of increased globalization of markets; societal demands for improved
environmental performance; financial market needs for increased profitability and
capital productivity; higher customer expectations; and more highly skilled work force
requirements.1 To meet these challenges and take the opportunities for future growth,
the chemical industry must accomplish five broad goals over the next two decades.
Those include improvements of operations with a focus on better management of the
supply chain; efficient use of raw and recycled materials, better generation and use of
energy; continuation of playing a leadership role in balancing environmental and
economic demands; longer term investment in Research & Development (R&D); and
finally, balanced investments in technology by leveraging the capabilities of
government, academe, and the chemical industry as a whole through targeted
collaborative efforts in R&D.1
To meet industry goals for the 21st century, the R&D should be conducted in a number
of areas,1 consisting of new chemical science and engineering technology; supply chain
management; information systems; and manufacturing and operations. New chemical
science and engineering technology, that will promote more cost-efficient and higher
performance products and processes, comprises chemical science and enabling
technology. The latter identified as essential to the industry’s future includes process
science and engineering (e.g., engineering scale-up and design, thermodynamics and
kinetics, reaction engineering); chemical measurement; and computational technologies

(e.g., computational chemistry, simulation of processes and operations, smart systems,
computational fluid dynamics).1,2
Computational chemistry is usually referred to as a series of mathematical methods,
well enough developed so that they can be automatically implemented on a computer3
to solve chemical problems mostly at the molecular level. It initially began in chemistry
and physics with the development of quantum mechanics in the 1920s and considerable
efforts have been done in the development of methods and codes. Nobel Prize in
chemistry has been awarded to Linus Carl Pauling in 1954 for his research into the
nature of the chemical bond and its application to the elucidation of the structure of
complex substances. Robert Sanderson Mulliken received the Nobel Prize in 1966 for
his fundamental work concerning chemical bonds and the electronic structure of
molecules by the molecular orbital method. William N. Lipscomb won the prize in 1976
for his studies on the structure of boranes illuminating problems of chemical bonding.
In 1981 the prize was given jointly to Kenichi Fukui and Roald Hoffmann for the


2

Chapter 1

Frontier orbital theory of chemical reactivity, developed independently, concerning the
course of chemical reactions. The 1998 Nobel Prize in chemistry went to John A. Pople
and Walter Kohn for their respective work in developing computational chemistry
methods (Pople) and density functional theory (Kohn).4 In recent years, involvement in
computational chemistry activities by organizations over the world has also risen
dramatically.2
A variety of chemical systems with a wide range of complexity can be described by
computational chemistry. By predicting the characteristics and behavior of a system,
computational chemistry can powerfully be used to improve the efficiency of existing
operating systems or the design of new systems. It is being used to complete, guide and

sometimes replace experimental methods, reducing the amount of time and money spent
on research to bring ideas from the lab to practical application.2
In chemistry, computational chemistry can play an important role in the design of new
chemical products, materials, and catalysts. For example, by calculating the energy
associated with a chemical reaction, it is possible to study the reaction pathways to
determine whether a reaction is thermodynamically allowed. Computational chemistry
can also be used to reliably predict a wide range of spectroscopic properties from
Ultraviolet and Visible Spectroscopy (UV), Infrared and Fourier Transform Infrared
Spectroscopy (IR), Nuclear Magnetic Resonance Spectroscopy (NMR)…) to help in the
identification of chemical species such as reaction intermediates. Electronic structure
calculations are also able to provide useful understanding of bonding, orbital energies
and shapes, which can be used to design new molecules with selective reactivity.
Computational tools have also been applied with varying degrees of success in
adhesives, coatings, polymers, and surfactants and in the prediction of the toxicity of
chemicals.2

1.1.2 Methods
The goal of computational chemistry is to solve complex equations such as the
Schrödinger equation HΨ = EΨ (H is the Hamilton operator or Hamiltonian for a
system of electrons and nuclei, Ψ is the wave function and E is the energy) for
electronic and nuclear motion, which accurately describe phenomena at the atomic or
molecular level.
Computational chemistry includes calculations at the quantum, atomistic or molecular,
mesoscales, as well as methods that form bridges between scales. At the quantum scale,
computations try to solve the Schrödinger equation and obtain the ground state (or the
excited state) energies and other properties (such as molecular geometry, vibrational
and NMR spectroscopic data, multipolar moments…) of chemical species. The
atomistic or molecular scale involves a wide variety of computations, usually done by
molecular dynamics or Monte Carlo methods using classical force fields. At this scale,
thermodynamic properties (critical points, pressures), transport properties (mass and

heat transfer) and phase equilibria can be expressed. The aims of mesoscale calculations
are to identify the qualitative trends in a system given specific chemical structures,
compositions, and process conditions; to quantitatively predict the continuum properties
of the system on scales as large as 10 microns with accuracies similar to atomistic level
calculations; and to accurately model larger systems on the physical timescale much
greater than 100 nanoseconds. Finally, bridging techniques provide continuity and
interface between the various scales; so the results of calculations at one scale can be


Chapter 1

3

used as input parameters to calculations at another scale.2 In this thesis, we only focus
on the quantum scale computations.
A variety of methods, each having their own specific approximations and accuracies,
have been invented, developed and widely used at the quantum scale. Roughly, these
methods can be divided into two main categories: the semi-empirical methods, which
use simplified Hamiltonian together with sets of parameters directly taken from
experimental data and the ab initio methods which, in contrast, use the correct
molecular Hamiltonian and no experimental data, except for the values of the
fundamental physical constants.
In the semi-empirical calculations, certain pieces of information such as two electron
integrals are approximated or completely omitted. To compensate the errors introduced
by omitting part of the calculation and to give the best possible agreement with
experimental data, the method is parameterized by curve fitting in a few parameters or
numbers. A number of semi-empirical methods are available today such as Complete
Neglect of Differential Overlap (CNDO), Intermediate Neglect of Differential Overlap
(INDO), Neglect of Diatomic Differential Overlap (NDDO), Modified INDO
(MINDO/3), (Including parameters for transition metals (ZINDO)), Modified NDO

(MNDO), Austin Model 1 (AM1), Parametric Model 3 (PM3)… Semi-empirical
calculations have been very successful in the description of organic chemistry, where
there are only a few elements used extensively and the molecules are of moderate size.
However, semi-empirical methods have been devised specifically for the description of
inorganic chemistry as well.3
The good side of semi-empirical calculations is that they are much faster than the ab
initio approaches. The bad side of semi-empirical calculations is that the results can be
erratic. If the molecule being computed is similar to molecules in the database used to
parameterize the method, then the results may be very good. If the molecule being
computed is considerably different from anything in the parameterization set, the
answers may be very poor.3,5,7
The ab initio methods again can be divided into two separate categories: the wavefunctional ab initio methods,5-8 where the wave function Ψ is used as the basic source of
information for an atomic or molecular system and Density Functional Theory
(DFT),9,10 where the electron density is used for that purpose.
The most common wave-functional ab initio technique is the Hartree-Fock (HF) level
based on the use of one-electron functions (orbitals) to construct the many-electron
wave function, obeying the Pauli principle. A single determinantal wave function is
used for this purpose. The coulombic electron-electron repulsion is only accounted for
in an average fashion; therefore, the HF method is also referred to as mean field
approximation. The molecular orbitals are formed from linear combinations of atomic
orbitals or usually from linear combinations of basis functions. Due to these
approximations, HF calculations give a computed energy greater than the Hartree-Fock
limit (the best single determinantal wave function that can be obtained, which is
however not the exact solution to the Schrödinger equation due to the incomplete
treatment of electron correlation).3
Several types of correlated calculations beginning with a HF calculation then correcting
for the explicit electron-electron repulsion are available today. Some of these methods
are Møller-Plesset perturbation theory (MPn, where n is the order of correction), MultiConfiguration Self Consistent Field (MCSCF), Configuration Interaction (CI) and

4

Chapter 1

Coupled Cluster theory (CC).
The good side of ab initio methods is that they eventually converge to the exact solution
if all of the approximations are made sufficiently small in magnitude. The bad side of ab
initio methods is that they are expensive as considering enormous amounts of computer
CPU time, memory and disk space. The HF method originally scaled as about N4,
where N is the number of basis functions, so doubling the basis set will take a
calculation 16 times as long to complete. This situation is much worse in the correlated
calculation scales. In practice, extremely accurate solutions can only be obtained when
the molecule contains less than or equal to half a dozen electrons.3 In recent years, the
factor “4” has been dramatically reduced thanks to the progress in computer power and
algorithms.
An alternative ab initio method is the Density Functional Theory (DFT). This method is
based on the electron density, which for an N-electron system, only depends on three
coordinates, independently of the number of electrons as compared to 4N coordinates
(including spin coordinate) of the wave function in the wave-functional ab initio
approaches. The complexity of a wave function increases with the number of electrons,
whereas the electron density has the same number of variables, independently of the
system size; therefore, the significance of the DFT method is the reduction of
calculation cost. Moreover, for about the same cost of doing a HF calculation, DFT
includes a significant part of the electron correlation.10 The disadvantage of DFT is that
the explicit form of the Hamiltonian written in terms of the electron density is not
known.
At the present moment, there are three main lines of research in DFT:
1) Fundamental DFT: extends the objective of DFT to excited states, external fields,
time-dependent process… or finds new physical knowledge about atomic or molecular
systems.

2) Conceptual DFT: concentrates on the applications of chemical concepts derived from
DFT, particularly in explaining the reactivity of reactants. Those concepts include
electronegativity, global hardness, global and local softness, Fukui functions, …
3) Computational DFT: develops new generations of functionals to be able to compute
faster and more precisely various atomic, molecular or solid state properties.
In this thesis we concentrate on the Density Functional Theory method and, particularly,
on the application of DFT in studying product structures and mechanisms of some
organic chemical reactions. Its objectives belong to the Conceptual DFT field. The
Computations themselves are also done with DFT methods, the techniques not being the
focus of our research, standard as they are.

1.2 Structures and
organic chemistry

reaction

mechanism

in

The reaction mechanism is a microscopic description of the course of a reaction,
showing the transformation of starting material into products as a series of discreet
steps, each of which may produce a distinct intermediate. This description makes it
possible to understand why a reaction takes place, thus providing a procedure to predict
the influences of changing reaction conditions and enables us to estimate the results of


Chapter 1

5

related reactions. The insights into how and why a given reaction occurs often reveal
close relationships between reactions that originally might be thought to be unrelated.
Moreover, the study of reaction mechanisms can be used as a basis to develop new
transformations and improve existing procedures. However, explaining the ways by
which the reagents in a reaction mixture are converted to the observed products requires
careful interpretation of painstaking experiments.11
In traditional organic chemistry, the experimental types providing data and the methods
used to extract information about reaction mechanisms from the data can be
summarized as follows.11
1. Identification of starting material, intermediates and products
Starting materials are tested for purity, whereas reaction products are separated by
distillation, crystallization or chromatography, and then identified by using chemical
tests, infrared, mass (MS), and NMR spectroscopy. Additional starting materials are
often designed and synthesized to test various aspects of the mechanism. The proposed
mechanism should be able to explain all of the products, the dependence of the reaction
products on starting material structure (substrate, nucleophile or electrophile), and any
observed regioselectivity. Normally, little information is gained about how the reaction
occurred by looking at the products, so additional experiments are necessary.
On the other hand, in a multistep reaction, the identification of the intermediates is also
a main objective of studies of reaction mechanism. The intermediate may be isolated by
interrupting the reaction (lowering the temperature rapidly or adding a reagent that stops
the reaction) or trapped by adding a compound that is expected to react specifically with
the intermediate. Because of its low concentration, the intermediate is normally studied
by spectroscopic methods such as ultraviolet-visible (UV-VIS), infrared (IR), nuclear
magnetic resonance (NMR), and electron paramagnetic resonance (EPR) spectroscopy.
2. Thermodynamic data
Any reaction is always accompanied by a change in enthalpy (ΔH), entropy (ΔS), and
free energy (ΔG). The equilibrium constant K relates these changes by the fundamental
equation ΔG0 = - RTlnK, with ΔG = ΔH – TΔS and the superscript 0 referring to

standard state.
These quantities are characteristics of the reactants and products, but are independent of
the reaction path; hence they cannot provide insight into mechanisms. However,
information about ΔG, ΔH, and ΔS may indicate the feasibility of any specific reaction.
The enthalpies and free energies of formation for many compounds can be obtained
from tabulated thermodynamic data.
3. Kinetic data
Kinetic data can provide much detailed insight into reaction mechanisms. The rate of a
given reaction is determined by measuring the concentration of products or reactants as
a function of time (about 20 measurements) for 10-20 concentrations of each reagent.
The presence or absence of equilibria between reactants and products is also tested by
addition of products or product analogues. Generally, any method (such as
spectroscopic techniques, continuous pH measurement, acid-base titration, conductance
measurement, polarimetry…) based on the properties relating to the concentration of
reactants or products can be used to determine the reaction rate.
The purpose of a kinetic investigation is to set up quantitative relationships between the
concentration of reactants, catalysts and the rate of the reaction, which are summarized


6

Chapter 1

in the rate law. The relationship between a kinetic expression and a reaction mechanism
can be evaluated by considering the rates for the successive steps in a multistep
reaction. The overall rate of a reaction will depend on the rate of the step, which is slow
relative to other steps, and this step is called the rate-determining step. Normally,
kinetic data provide information only about the rate-determining step and steps
preceding it. The steps following the rate-determining step are bypassed since their rates
do not affect the overall rate.

A kinetic study normally starts from postulating possible mechanisms, then comparing
the observed rate law with the proposed mechanisms, and finally eliminating those
mechanisms that are incompatible with the observed kinetics. However, sometimes,
several mechanisms give rise to identical predicted rate expressions. In this case, the
mechanisms are called kinetically equivalent, and it is not possible to choose between
them on the basis of kinetic data.
4. Substituent effects and linear free-energy relationship
Between substituent groups and chemical properties, there are a number of important
relationships, which can be quantitatively expressed in some cases. The most widely
applied of these relationships is the Hammett equation, which relates rates and
equilibria for many reactions of compounds containing substituted phenyl groups.
It was noted in the 1930s that there is a linear correlation between the ratio of the rate
constant for hydrolysis of ethyl benzoate (k1) to the rate constant for the substituted
esters (k2) and the ratio of the corresponding acid dissociation constants (K1 and K2).12
Similar relationships are also observed for many other reactions of aromatic
compounds. Furthermore, from this linear correlation it can be shown that the change in
the free energy of activation for hydrolysis of substituted benzoates is directly
proportional to the change in the free energy of ionization caused by the same
substituents on benzoic acid. The correlations due to the directly proportional changes
in free energies are called linear free-energy relationships.
The Hammett free-energy relationship is expressed in the following equations:
log(K2/K1) = log(k2/k1) = σρ
The values of σ and ρ are empirically defined by the selection of the reference reaction,
in this case, the ionization of benzoic acids. The reaction constant ρ is arbitrarily
assigned the value 1 and the substituent constant σ is determined for a series of
substituent groups by measuring the corresponding acid dissociation constants. The σ
values are then used in the correlation of other reactions, and the ρ values of the
reactions are thus determined. While the value of ρ reflects the sensitivity of the
particular reaction to substituent effects, the value of σ indicates the effect of the
substituent group on the free-energy ionization of the substituted benzoic acid.

Beside the resonance and field (including inductive) effects, which are common in
reactions of aromatic compounds, electronegativity and polarizability are also included
in the substituent effect. The general form of the Hammett free-energy relationship can
be written as:
log(K2/K1) = log(k2/k1) = σFρF + σRρR + σχρχ+ σαρα
where σF, ρF are the field; σR, ρR the resonance; σχ, ρχ the electronegativity; and σα, ρα
the polarizability substituent constants and reaction constants, respectively.
The linear free-energy relationships can provide insight into reaction mechanisms and


Chapter 1

7

enable us to predict reaction rates and equilibria. When the ionization of benzoic acid is
chosen as a reference reaction for the Hammett equation, it leads to σ > 0 for electronwithdrawing groups and σ < 0 for electron-donating groups, since the former groups
favor the ionization of the acid and the latter groups have the opposite effect. Moreover,
further consideration of the Hammett equation shows that ρ will be positive for all
reactions favored by electron-withdrawing groups and negative for all reactions favored
by electron-donating groups. If the reaction rates for a series of substituents show a
suitable correlation, both the sign and the magnitude of ρ will give information (such as
the distribution of charge) about the transition state for the reaction.
It should be noted that not all reactions could be fitted by the Hammett equation or its
modified forms, which is commonly due to the change in mechanism as substituents
vary. For example, in a multistep reaction one step may be rate-determining in the
region of electron-withdrawing substituents, but a different step may become ratelimiting as the substituents become electron-donating.
5. Isotope effects
The replacement of an atom by one of its isotopes is a useful tool in the study of
reaction mechanisms. Isotopic substitution often involves replacing protium by
deuterium (or tritium) but the principle is applicable to nuclei other than hydrogen,

however, the quantitative differences are largest for hydrogen. Isotopic substitution does
not qualitatively affect the course of the reaction, but it has a measurable effect on the
reaction rates. If the bond to the isotopically substituted atom is broken in the ratedetermining step, the rate will be affected by isotopic substitution, which is called the
primary kinetic isotope effect. In this case, due to different masses, the contributions to
the zero-point energy of the vibrations associated with the bond are not the same
leading to different activation energies and reaction rates. Isotope effects may also be
observed even when the substituent hydrogen atom is not directly involved in the
reaction. Such effects are called secondary kinetic isotope effects, which result from a
tightening or loosening of the bond at the transition state. On the other hand, isotopes
are used as tracers to determine the route that a particular atom takes during the
reaction. Determination of the location of an isotope is usually done by NMR or MS,
and does not require techniques based on radioactivity. The proposed mechanism will
explain both the location and the effect of isotopes on the reaction rate.
6. Catalysis
Catalysts do not affect the reaction equilibrium but they increase the rate of one or more
steps in a reaction mechanism by lowering the corresponding activation energies.
Reaction rates and rate laws are determined to verify if the suspect catalyst affects the
rate. Moreover, the products are examined to ensure that catalysts do not incorporate
into the products. The proposed mechanism should include the role of the catalyst in a
chemically reasonable manner.
7. Stereochemistry
Stereochemistry is the study of the three dimensional arrangement in space of the atoms
in molecules and the way it changes upon reaction. Different compounds that have the
same molecular formula are called isomers, which can be classified as constitutional
isomers and stereoisomers. Constitutional isomers will have the same number and types
of atoms, but they are connected in a different order. In stereoisomers, the atoms are
connected sequentially in the same way, but the isomers differ in the way the atoms are


8

Chapter 1

arranged in space. There are two major sub-classes of stereoisomers; conformational
isomers, which interconvert through rotations around single bonds, and configurational
isomers, which differ in the arrangement of their atoms in space and therefore cannot
interconvert. Configurational isomers are divided into enantiomers and diastereomers.
Enantiomers are comprised of a chiral compound, which cannot superimpose on its
mirror image, and its mirror image. Stereoisomers, which are not enantiomers, are
called diastereomers. A process wherein enantiomers are separated is called a
resolution. A collection containing equal amounts of two enantiomers is called a
racemic mixture or racemate. A reaction that forms a racemate is called a racemization.
The study of the stereo-chemical course of organic reactions, which can be determined
by using instrumental techniques such as IR and NMR spectroscopy, optical rotatory
dispersion, and circular dichroism, often leads to detailed insight into reaction
mechanism. Normally, mechanistic postulates are made to predict the stereochemical
outcome of the reaction and then compared with the observed products.
8. Solvent effect
Solvents can affect the identity of the products, the course and the rate of reactions.
Solvents can be classified as protic solvents, which contain relatively mobile protons
such as those bonded to oxygen, nitrogen, or sulphur; and aprotic solvents, in which all
hydrogen is bonded to carbon. They are also classified as polar solvents, which have
high dielectric constants and do have effects on reaction rates, and non-polar solvents.
Furthermore, it is important to distinguish between the macroscopic effects related to
the properties of the bulk solvent and the effects based on the details of structure. For
example, the dielectric constant is a measure of the ability of the bulk material to
increase the capacity of a condenser. In terms of structure, the dielectric constant is
proportional to the dipole moment and the polarizability of the molecule. Polarizability,
in turn, refers to the ease of electron density distortion of the molecule. One important
property of solvent molecules is the response of a solvent to changes in charge

distribution as the reaction occurs. The dielectric constant indicates the ability of the
solvent to accommodate the separation of charge. However, being a macroscopic
property, it conveys little information about the ability of the solvent molecules to
interact with the solute molecules at close range. The direct solute – solvent interactions
will depend on the specific structures of the molecules. The mechanism must explain
the effect of different solvents on the reaction rate and any incorporation of solvent into
the reaction products.
9. Other reaction characteristics
Occasionally a reaction rate or outcome depends on the size or material of the container,
as it often does for free radical chain reactions. In this case the mechanism must take
into account the effect of hidden reagents or catalysts like water and oxygen, which
divert reactions, especially those involving organometallic compounds.
In summary, experimental methods give data, which allow only indirect conclusions to
the overall reaction pathway because they all are based on the studies of only the initial
and the final state of every elementary step of the reaction.


Chapter 1

9

Computational chemistry at quantum scale opens up new possibilities of studying
chemical reactions and enables the researchers to calculate all critical parameters of the
mechanism of a reaction.
In order to generally describe the structural changes in a reacting system, it is necessary
to solve the time-dependent Schrödinger equation. However, even approximate
solutions to this equation for a system only containing several atoms are extraordinarily
complicated. On the other hand, most chemical reactions do not significantly exhibit
quantum effects at room temperature. Hence, to describe the dynamics of a chemical
reaction, another approach is employed, namely, the calculation of the potential energy

surface (PES).13
The PES of a system is a geometric surface describing the variation of its potential
energy (the sum of electronic energy and nuclear repulsion energy) as a function of the
coordinates of all nuclei in the system. In case the system contains N nuclei, there are
3N coordinates defining the geometry. Of these coordinates, three describe the overall
translation of the molecule, and three describe the overall rotation of the molecule with
respect to the three principal axes of inertia. For a linear molecule, only two coordinates
are necessary for describing the rotation. Therefore, the number of the independent
coordinates (degrees of freedom) that fully determine the PES is 3N – 6 (or 3N – 5 in
the case of a linear molecule).13
The energetically easiest passage from reactant to products on the potential energy
contour map defines the potential energy profile on which the potential energy is plotted
as a function of one geometric coordinate. For an elementary reaction such as A-B + C
→ A-C + B, that geometric coordinate is the reaction coordinate, whereas for a stepwise
reaction it is the succession of reaction coordinates for the successive individual
reaction steps. The reaction coordinate is defined as the geometric parameter (bond
length, bond angle…) that changes smoothly from the configuration of the reactants
through that of the transition state to the configuration of the products. Typically, the
reaction coordinate is chosen to follow the path along the gradient (path of shallowest
ascent or deepest descent) of potential energy from reactants to products.13
In practice, to have enough information on the mechanism and the kinetics of a
chemical reaction, it is not necessary to know the full function but only some portions
of the PES, mainly those corresponding to the minima (reactants, intermediates,
products) and to the saddle points (transition structure).13
Studying the PES of a system, one can obtain various important characteristics of the
reaction: relative energies of the reactants and the products (energy of reaction); relative
energies of the reactants and the transition state (activation energy); the curvature of the
PES in the minima zone or the saddle point region, which can be used to determine the
vibration spectrum, the entropy and the kinetic isotopic effects (ratio between the
reaction rate constant of the compound with the light isotope and that of the compound

containing the heavy isotope); geometrical characteristics of the reactants, the products
and the transition state. Moreover, based on the activation energies from the PES
containing more than one reaction pathway, one can determine and then explain which
path is energetically favored. In mass spectrometry studies, using the calculated
energies of the isomers and the energy barriers between them, one can predict and
explain which isomer is more stable than the others. Furthermore, by verifying the
existence of the intermediates in the reaction pathway, one can determine whether the
reaction is concerted or stepwise.


10

Chapter 1

Besides the information from the PES, one tries to use the information on the starting
structures to explain and predict the first stages of the reaction, which can be done by
using a variety of reactivity indices. In the wave function ab intio approaches, the
Frontier Molecular Orbital (FMO) theory14 is widely applied. The coefficients and the
shapes5,15 of the Highest Occupied Molecular Orbital (HOMO) and of the Lowest
Unoccupied Molecular Orbital (LUMO) are used to explain why a reaction is favored
over another. In the DFT framework, the global and local softness in conjunction with
the hard and soft acids and bases (HSAB) principle16 become the useful tools10,17-21 to
predict the favored product on the basis of the electronic properties of the isolated
reactants. The idea of the aromaticity of the transition state22-23 is also applied for this
purpose.

1.3 Scope of the Thesis
“Structure and Mechanism in Organic Chemistry” has been the title of a very influential
book in physical organic chemistry, written by Ingold in the early fifties.24 It has been
used by several generations of organic chemists as a guide in the sometimes

bewildering forest of organic reactions.
Since then the field has known impressive developments and in recent years quantum
chemical/computational methods turned out to be an important tool to elucidate reaction
mechanisms as discussed in §1.2. It is in this direction that in our thesis we concentrate
on the “Structure and Mechanism” of some isomerization, [2+1] and 1,3-dipolar
cycloaddition reactions, using Density Functional Theory methods. In each kind of
reaction, the structures and relative energies of reactants, transition structures,
intermediates and final products will be determined to construct the potential energy
surface. Besides, the DFT-based reactivity descriptors such as hardness, global and
local softness, Fukui functions and indices of aromaticity (if possible) are also
calculated. From those parameters, we will analyze the reaction steps, the favored site in
the initial attack, the stability of intermediates and final products, the effect of
substituents and solvents on the reacting system.
Starting with a general overview of the current situation and the methods used in
computational chemistry, the first chapter discusses the ways to determine “Structure
and Mechanism” in traditional organic chemistry and in computational chemistry.
Chapter 2 presents a general introduction to the most currently used methods in
computational/theoretical chemistry and provides DFT-based reactivity criteria together
with others as tools for studying “Structure and Mechanism” of chemical reactions. The
computational details including software and hardware used in this thesis are discussed
in chapter 3. Chapter 4 uses Density Functional Theory methods to construct the
potential energy surface for simple isomerization and fragmentations reactions
involving two NS moieties, [CH3NS] and [NH2NS]. The [2+1] cycloaddition reactions
of hydrogen isocyanide (HN≡C), CX (X = O, S) to acetylenes are reported in chapter 5.
Besides, the 1,3-dipolar cycloaddition (1,3-DC) of fulminic acid (HCNO) and the
simple azides (XNNN, X=H, CH3, NH2) to thionitroso compounds (R-N=S, R = H,
NH2); the 1,3-DC of diazoalkanes, hydrazoic acid and nitrous oxide to polar
dipolarophiles are also included. Finally, chapter 6 gives the general conclusion of this
work and further development of Density Functional Theory methods.

Chapter 1

11

1.4 References
1.

Technology Vision 2020: The U.S. Chemical Industry,
The American Chemical Society, American Institute of Chemical Engineers,
The Chemical Manufacturers Association, The Council for Chemical
Research, and The Synthetic Organic Chemical Manufacturers Association,
December, 1996.
/>
2.

Technology Roadmap for Computational Chemistry
Dixon, D. A. et al., The Council for Chemical Research, 1999.
/>
3.
4.

Young, D. Computational Chemistry: A Practical Guide for Applying
Techniques to Real World Problems; John Wiley & Son: Chichester, 2001.
Nobel Prize in Chemistry Winners 2001-1901.
/>
5.
6.
7.
8.

9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.

Jensen, F. Introduction to Computational Chemistry; John Wiley & Son:
Chichester, 1999.
Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry; MacMillan: New
York, 1989.
Levine, I. N. Quantum Chemistry (Fourth Edition); Prentice Hall, Englewood
Cliffs: New Jersey, 1991.
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; Wiley: New York, 1986.
Hohenberg, P.; Kohn, W. Phys. Rev. B 1964, 136, 864.
Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules;
Oxford University Press: New York, 1989.
Carey, F. A.; Sundberg, R. J. Advanced Organic Chemistry, Part A:
Structure and Mechanisms; Plenum Press: New York, 1990.
Hammett, L. P. J. Am. Chem. Soc. 1937, 59, 96.
Minkin, V. I.; Simkin, B. Ya.; Minyaev, R. M. Quantum Chemistry of
Organic Compound, Mechanisms of Reaction; Springer-Verlag: Berlin, 1990.

Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry;
Verlag Chemie: Weinheim, 1970.
Fleming, I. Frontier Orbitals and Organic Chemical Reactions; Wiley:
Chichester, 1978.
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12

Chapter 1

22.
23.
24.

De Proft, F.; Geerlings, P. Chem. Rev. 2001, 101, 1451.
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121, 6737.
Ingold, C. K. Structure and Mechanism in Organic Chemistry; 2d ed.;
Cornell University Press: Ithaca, New York, 1969.


2.

Theoretical Background

2.1 Wave function Ab Initio methods
2.1.1 Schrödinger equation
Electrons are very light particles and display both particle and wave characteristics;
therefore, they can be described in terms of a wave function Ψ. The wave function
concept and the equation describing its change with time were put forward in 1926 by
Erwin Schrödinger. This equation, known as the non-relativistic time-dependent
Schrödinger equation, can be written as follows1,2
∂Ψ
(2.1.1)
HΨ = i η
∂t
where H is the Hamilton operator (Hamiltonian), and η is the Planck constant divided
by 2π.
If the Hamiltonian does not contain the time variable explicitly, the time dependence of
the wave function can be separated out as a simple phase factor. Denoting r as the
position vector, in the one particle case, one obtains
Ψ (r, t ) = Ψ (r )e − iEt / η

(2.1.2)

Consequently, the energies and wave functions of stationary states of the system are
given by the solution of the time-independent Schrödinger equation.
HΨ(r) = EΨ(r)
(2.1.3)
For a general N-particle system, the Hamilton operator contains kinetic (T) and
potential (V) energy operators for all particles (e.g. electrons and nuclei).1-4
H=T+V
(2.1.4)

2
2
2
2
2
N
N
N
∂
η
η ⎛ ∂
∂ ⎞
⎜⎜ 2 + 2 + 2 ⎟⎟
(2.1.5)
∇ i2 = −∑
T = ∑ Ti = −∑
∂y i ∂z i ⎠
i =1
i =1 2m i
i =1 2m i ⎝ ∂x i
N

N

N

N

V = ∑∑ Vij =∑∑
i =1 j>i

i =1 j>i

qiq j
rij

(2.1.6)

with mi the mass, qi the charge of particle i, and rij the distance between particles i and j.
Nuclei are much heavier than electrons, and thus move much slower. Hence, the
electrons will adjust rapidly to any change in nuclear positions. Consequently, the
Schrödinger equation can be approximately separated into one part describing the
electronic wave function for a fixed nuclear geometry, and another part expressing the
nuclear wave function, in which the energy from the electronic wave function plays the
role of the potential energy (Born-Oppenheimer approximation). Accordingly, the
electronic wave function depends only on the position of the nuclei, not their momenta.


14

Chapter 2

Denoting nuclear coordinates with R and subscript n, and electron coordinates with r
and e, the Schrödinger equation can be written in the following way.
HtotΨtot(R,r) = EtotΨtot(R,r)
(2.1.7)
Htot = He + Tn
He = Te + Vne + Vee + Vnn
(2.1.8)
Ψtot(R,r) = Ψn(R)Ψe(r;R)

Note that the role of R in Ψe(r;R) is that of a parameter.
The electronic Schrödinger equation becomes
HeΨe(r;R)= Ee(R)Ψe(r;R)
(2.1.9)
Finally, the nuclear Schrödinger equation has the form
{Tn + Ee(R)}Ψn(R) = EtotΨn(R)
(2.1.10)
In this thesis we only concern with the electronic Schrödinger equation (2.1.9).

2.1.2 The Hartree-Fock theory
The goal of the wave function ab initio methods is to find the wave function Ψ, which
satisfies the equation (2.1.9) and thus determines the electronic energy of the molecule.
One approach is the Molecular Orbital (MO) theory, which uses one-electron functions
or orbitals to approximate the full wave function.
The spatial function termed molecular orbital, ψ(x, y, z), is a function of the cartesian
coordinates x, y, z of a single electron. Its square, ψ2 (or ⏐ψ⏐2 if ψ is complex) is
interpreted as the probability distribution of the electron in space. To describe the spin
of an electron, it is necessary to specify a complete set of two orthonormal spin
functions α(ξ) for spin up and β(ξ) for spin down. The full wave function for a single
electron is the product of a molecular orbital and a spin function, ψ(x, y, z)α(ξ) or ψ(x,
y, z)β(ξ). It is termed a spin orbital, χ(x, y, z, ξ). One important property of the wave
function is that it must satisfy the anti-symmetry principle (the Pauli exclusion
principle), which states that a wave function must change sign when the spatial and spin
components of any two electrons are exchanged.
To account for this problem, in the Hartree-Fock theory, the spin orbitals are arranged
in a determinantal wave function, called a Slater determinant.
χ1 (1) χ 2 (1) ...

Ψ(χ1,χ2,…, χN) =

1

χ N (1)

χ1 (2) χ 2 (2) ... χ N (2)

Μ
Μ
N! Μ
χ1 ( N) χ 2 ( N) ... χ N ( N)

(2.1.11)

The (N!)-1/2 factor is a normalization constant. For convenience, a shorthand notation is
often used for (2.1.11). This notation uses the anti-symmetry operator A to represent the
determinant and explicitly normalizes the wave function. 1,3
(2.1.12)
Ψ = A[χ1(1)χ2(2)…χN(N)] = AΠ
A=

1

N −1

∑ (−1)
N!
p=0

p

P=

1
N!

[1 − ∑ Pij + ∑ Pijk − ...]
ij

ijk

The 1 operator is the identity, whereas Pij generates all possible permutations of two