theoretical organic chemistry

A
THEORETICAL AND COMPUTATIONAL CHEMISTRY
Theoretical
Organic
Chemistry
THEORETICAL AND COMPUTATIONAL CHEMISTRY
SERIES EDITORS
Professor P. Politzer
Department
of Chemistry
University of New Orleans
New Orleans, LA
70418,
U.S.A.
Professor Z.B. Maksid
Ruder B0s'k0vi~
Institute
P.O.
Box
1016,
10001 Zagreb, Croatia
VOLUME 1
Quantative Treatments of Solute/Solvent Interactions
P. Politzer and
J.S. Murray
(Editors)
VOLUME 2
Modern Density Functional Theory: A Tool for Chemistry
J.M.
Seminario and P. Politzer (Editors)

VOLUME 3
Molecular Electrostatic Potentials: Concepts and Applications
J.S. Murray
and
K. Sen
(Editors)
VOLUME 4
Recent Developments and Applications of Modern Density Functional Theory
J.M. Seminari0 (Editor)
VOLUME 5
Theoretical Organic Chemistry
C. Pdrkdnyi (Editor)
@
THEORETICAL AND COMPUTATIONAL CHEMISTRY
Theoretical
Organic Chemistry
Edited by
Cyril P~rk~nyi
Department of Chemistry and Biochemistry
Florida Atlantic University
Boca Raton,
FL 33431-0991,
USA
1998
ELSEVIER
Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo
ELSEVIER SCIENCE B.V.
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P.O. Box 211, 1000 AE Amsterdam, The Netherlands
ISBN: 0 444 82660 2

9 1998 Elsevier Science B.V. All rights reserved.
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Printed in The Netherlands.
FOREWORD
This volume is devoted to the various aspects of theoretical organic chemistry. In the
nineteenth century, organic chemistry was primarily an experimental, empirical science.
Throughout the twentieth century, the emphasis has been continually shifting to a more
theoretical approach. Today, theoretical organic chemistry is a distinct area of research, with
strong links to theoretical physical chemistry, quantum chemistry, computational chemistry, and
physical organic chemistry.
Our objective in this volume has been to provide a cross-section of a number of interesting
topics in theoretical organic chemistry, starting with a detailed account of the historical
development of this discipline and including topics devoted to quantum chemistry, physical
properties of organic compounds, their reactivity, their biological activity, and their excited-state
properties. In these chapters, a close relationship and overlaps between theoretical organic
chemistry and the other areas mentioned above are quite obvious.
Cyril Phrk/myi
Boca Raton,

FL
vi
ACKNOWLEDGMENTS
I greatly appreciate the help, advice, and support provided to me by Anita H.
Buckel, Dr. Jane S. Murray, and Dr. Peter Politzer. I am also very grateful to my wife Marie for
her endless patience, understanding, and encouragement.
vii
TABLE OF CONTENTS
Chapter 1.
Theoretical Organic Chemistry: Looking Back in Wonder,
Jan J.C. Mulder 1
1. Personal Preface
1
2. Introduction 3
3. The First Period (1850-1875) 4
4. Interlude 1 6
5. The Second Period (1910-1935) 8
6. Interlude 2 12
7. The Third Period 14
8. Epilogue 20
Chapter 2. Inter-Relations between VB & MO Theories for Organic r~-Networks,
Douglas J. Klein 33
1. Broad Motivation and Aim - Graph Theory 33
2. VB and MO Models 35
3. MO-Based Elaborations and Cross-Derivations 38
4. HOckel Rule 41
5. Polymers and Excitations 44
6. Prospects 47
Chapter 3. The Use of the Electrostatic Potential for Analysis and Prediction of
Intermolecular Interactions, Tore Brinck 51

1. Introduction 51
2. Methodological Background 51
2.1. Definition and physical significance 51
2.2. Spatial minima in the electrostatic potential 52
2.3. Surface electrostatic potential 55
2.4. Geometries of weak complexes 58
2.5. Polarization corrections to the interaction energy 60
2.6. Charge transfer and the average local ionization energy 61
2.7. Characters of the different interaction quantities 62
3. Analysis of Site-Specific Interactions : 65
3.1. Hydrogen bonding 65
3.2 Frequency shitts 71
3.3. Protonation 71
4. Analysis of Substituent Effects on Chemical Reactivity 73
4.1. Background 73
4.2. Acidities of aromatic systems 73
4.3. O-H bond dissociation energies in phenols 77
o~
Vlll
5. Statistically-Based Interaction Indices 81
5.1. Background 81
5.2. Definitions 82
5.3. Predictions of octanol/water partition coefficients 83
6. Summary 87
Chapter 4. Exploring Reaction Outcomes through the Reactivity-Selectivity Principle
Estimated by Density Functional Theory Studies, Branko S. Jursic 95
1. Introduction 95
2. Computational Methodology 96
3. Basics for the Reactivity-Selectivity Approach 96
4. The Diels-Alder Reaction 101

4.1. Diels-Alder reaction of cyclopropene with butadiene 102
4.2. Diels-Alder reaction of cyclopropene with furan 105
5. Ring-Opening Reactions 108
5.1. Cyclobutene ring opening 109
5.2. Influence of substituents upon the reactivity of cyclobutene
ring opening 111
6. Radical Reactions
117
6.1. Trichloromethyl radical proton abstraction reaction
117
6.2. Intramolecular radical addition to carbon-carbon double bond 119
7. Reactivity and Stability of Carbocations 123
7.1. Hydride affinity as a measure of carbocation reactivity 123
7.2. Strain energies as a measure of reactivity 126
8. Conclusion 127
Chapter 5. A Hardness and Sot~ness Theory of Bond Energies and Chemical
Reactivity, Jos~ L. C~quez 135
1.
Introduction 135
2. Reactivity Parameters 136
2.1. The density functional theory framework 136
2.2. Fundamental concepts 9
137
3. Energy and Hardness Differences 140
3.1. Bond energies
143
3.2. Activation energies 146
4. Catalyzed Reactions and Reactions in Solution 148
5. Concluding Remarks 150
Chapter 6. Molecular Geometry as a Source of Chemical Information for ~-Electron

Compounds, Tadeusz M. Krygowski and Michal K. Cyrafiski 153
Abstract
153
Introduction 154
1. Heat of Formation Derived from the Molecular Geometry: The Bond Energy
Derived from CC Bond Lengths
155
ix
1.1. Energy content of individual phenyl rings in various topological
and chemical embedding 156
1.2. Ring energy content of benzene rings in benzenoid hydrocarbons 157
1.3. Ring energy content in the ring of TCNQ moieties involved in
electron-donor-acceptor (EDA) complexes and salts 160
1.4. Ring energy content depending on the intermolecular H-bonding:
the case ofp-nitrosophenolate anion 161
1.5. Ring energy content as a quantitative measure of fulfilling the HOckel
4n + 2 rule for derivatives of fulvene and heptafulvene 162
1.6. Estimation of H O and H N energy of interactions in H-bonds 163
2. Canonical Structure Weights Derived from the Molecular Geometry 165
2.1. Principles of the HOSE model 166
2.2. Substituent effect illustrated by use of the HOSE model 168
2.3. Structural evidence against the classical through resonance concept
in p-nitroaniline and its derivatives 170
2.4. Does the nitro group interact mesomerically with the ring
in nitrobenzene? 172
2.5. Angular group induced bond alternation - a new substituent effect
detected by molecular geometry i '~. 174
3. Substituent Effect on the Molecular Geometry 177
4. Aromatic Character Derived from Molecular Geometry 180
5. Conclusions 183

Chapter 7. Average Local Ionization Energies: Significance and Applications,
Jane S. Murray and Peter Politzer 189
1. Introduction 189
2. Average Local Ionization Energies of Atoms 190
3. Average Local Ionization Energies of Molecules 191
3.1. Applications to reactivity 191
3.2. Characterization of bonds 198
4. Summary 199
Chapter 8. Intrinsic Proton Affinity of Substituted Aromatics, Zvonimir B. Maksi6
and Mirjana Eckert-Maksi6 203
1. Introduction 203
2. Absolute Proton Affinities 203
2.1. Experimental basicity scales 203
2.2. Theoretical models for calculating absolute
PAs
204
2.3. Proton affinities in monosubstituted benzenes 206
2.4. Proton affinities in polysubstituted benzenes - the additivity rule 211
2.4.1. Increments 211
2.4.2. Disubstituted benzenes- the independent substituent
approximation 214
2.4.3. Polysubstituted benzenes 215
2.4.4. The ipso protonation 217
2.4.5. Limitations of the MP2(I) model - the aniline story 222
2.4.6. Proton affinities of larger aromatics - naphthalenes 223
3. Miscellaneous Applications of the Additivity Rule 225
4. Conclusion 228
Chapter 9. Dipole Moments of Aromatic Heterocycles, Cyril Phrkhnyi and
Jean-Jacques Aaron 233
1. Introduction 233

2. Experimental Ground-State Dipole Moments 235
2.1. Dielectric constant methods 235
2.2. Microwave methods 238
2.3. The Stark effect method 239
2.4. Molecular beam method 239
2.5. Electric resonance method 239
2.6. Raman spectroscopy 239
2.7. Sign and direction of the dipole moment 239
3. Calculated Ground-State Dipole Moments 241
3.1. Empirical methods 241
3.2. Semiempirical methods 244
3.3.
Ab initio
methods 245
3.4. Semiempirical and
ab initio
methods - a comparison 245
4. Experimental Excited-State Dipole Moments 245
5. Calculated Excited-State Dipole Moments 249
6. Conclusion 251
Chapter 10.
New Developments in the Analysis of Vibrational Spectra. On the Use
of Adiabatic Internal Vibrational Modes, Dieter Cremer, J. Andreas
Larsson, and Elfi Kraka 259
1. Introduction 259
2. The Concept of Localized Internal Vibrational Modes 260
3. The Basic Equations of Vibrational Spectroscopy 263
4. Previous Attempts of Defining Internal Vibrational Modes 266
5. Definition of Adiabatic Internal Modes 267
6. Definition of Adiabatic Internal Force Constant, Mass, and Frequency 271

7. Characterization of Normal Modes in Terms of Internal Vibrational Modes 273
8. Definition of Internal Mode Amplitudes ,~ 277
9. Analysis of Vibrational Spectra in Terms of Adiabatic Internal Modes 281
10. Correlation of Vibrational Spectra of Different Molecules 288
11. Derivation of Bond Information from Vibrational Spectra 297
12. Adiabatic Internal Modes from Experimental Frequencies 302
13. A Generalization of Badger's Rule 308
14. Intensities of Adiabatic Internal Modes 312
15. Investigation of Reaction Mechanism with the Help of the CNM Analysis 316
16. Conclusions 324
xi
Chapter 11. Atomistic Modeling of Enantioselection: Applications in Chiral
Chromatography, Kenny B. Lipkowitz
Introduction
1. Stereochemistry
2. Chromatography
3. Molecular Modeling
4. Chiral Stationary Phase Systems
5. Modeling Enantioselective Binding
6. Type I CSPS
6.1. Motifbased searches
6.2. Automated search strategies
7. Type II CSPS
8. Type III CSPS
9. Type IV CSPS
10. Type V CSPS
Summary
Chapter 12. Theoretical Investigation of Carbon Nets and Molecules,
Alexandru T. Balaban
1. Introduction

2. Infinite Planar Nets ofsp2-Hybridized Carbon Atoms
2.1. Graphite: two-dimensional infinite sheets
2.2. Other planar lattices with sp2-hybridized carbon
2.3. Tridimensional infinite lattices with sp2-hybridized carbon atoms
2.4. Graphitic cones with sp2-hybridized carbon atoms
3. Infinite Nets of sp3-Hybridized Carbon Atoms
3.1. Diamond: three-dimensional infinite network
3.2. Other systems with sp3-hybridized carbon atoms
3.3. Holes bordered by heteroatoms within the diamond lattice
4. Infinite Nets with Both
sp 2-
and sp3-Hybridized Carbon Atoms
4.1. Local defects in the graphite lattice
4.2. Local defects in the diamond lattice
4.3. Block-copolymers of graphite and diamond (diamond-graphite
hybrids)
4.4. Systems with regularly alternating
sp2/sp3-hybridized
carbon atoms.
5. Infinite Chains ofsp-Hybridized Carbon Atoms
5.1. Chains of sp-hybridized carbon atoms: one-dimensional system
5.2. Heteroatom substitution inside polyacetylenic chains
6. Molecules with sp2-Hybridized Carbon Atoms
6.1. Fullerenes
6.2. Nanotubes and capsules
6.3. Carbon cages and nanotubes including oxygen, nitrogen or boron
heteroatoms
7. Molecules with
sp-
and sp2-Hybridized Carbon Atoms

7.1. Cages with
sp-
and sp2-hybridized carbon atoms
329
329
330
332
335
335
336
336
337
341
354
363
370
371
375
381
381
381
381
382
384
384
385
385
386
386
387

387
389
390
390
391
391
391
391
391
393
395
398
398
oo
Xll
7.2. Molecules with sp-hybridized carbon atoms 3 98
7.3. Covalently-bonded nested cages with
sp-
and/or sp3-hybridized
carbon, or carbon and silicon atoms 399
8. Conclusions: from Radioastronomy to Remedying Dangling Bonds
Carbon Nets 400
Chapter 13. Protein Transmembrane Structure: Recognition and Prediction by Using
Hydrophobicity Scales through Preference Functions, Davor Jureti6,
Bono Lu~i6, Damir Zuci6, and Nenad Trinajsti6 405
1. Introduction 405
2. Methods 407
2.1. Selecting protein data bases for training and for testing 407
2.2. Main performance parameters used to judge the prediction quality 409
2.3. Hydrophobic moment profile 410

2.3.1. The training procedure for the preference functions method 411
2.3.2. The testing procedure 411
2.3.3. Decision constants choice 411
2.3.4. Collection of environments and smoothing procedure 412
2.3.5. Filtering procedure 412
2.3.6. Predicting transmembrane 13-strands (TMBS) 413
2.3.7. Adopted cross-validation technique 414
3. Results 414
3.1. Conformational preference for transmembrane a-helix is strongly
dependent on sequence hydrophobic environment for most amino
acid types 414
3.2. Expected and predicted length distribution for transmembrane
helical segments 416
3.3. What is the optimal choice of the sliding window size? 418
3.4. How do the results depend on different devices used in the SPLIT
algorithm? 418
3.5. What are the best scales of amino acid attributes? 420
3.6. The prediction results with Kyte-Doolittle preference functions 422
3.7. Testing for false positive predictions in membrane and soluble
proteins of crystallographically known structure 424
3.8. Cross-validation, overtraining and sensitivity to the choice
of protein data base 427
3.9. Comparisons with other methods 429
3.10. Using prediction profiles with both a and 13 motifs 432
4. Discussion 434
Chapter 14. Polycyclic Aromatic Hydrocarbon Carcinogenicity: Theoretical
Modelling and Experimental Facts, Lhszl6 von Szentphly
and Ratna Ghosh 447
1. Introduction to Chemical Carcinogenesis 447
2. PAH Carcinogenicity and Theoretical Models 450

xiii
2.1. The bay-region theory
2.2. The MCS model
2.2.1. Metabolic factor
2.2.2. Carbocation formation
2.2.3. Size factor
2.2.4. Performance and limitations
3. DNA Binding of Carcinogenic Hydrocarbon Metabolites
4. Hydrolysis and PAH Carcinogenicity
5. Molecular Modelling of Intercalated PAH Triol Carbocations
5.1. Ab initio
calculations on PAHTC conformations
5.2. AMBER modelling of intercalated PAHTC-DNA complexes
6. Conclusion
Chapter 15. Cycloaddition Reactions Involving Heterocyclic Compounds as Synthons
in the Preparation of Valuable Organic Compounds. An Effective Com-
bination of a Computational Study and Synthetic Applications of Hetero-
cycle Transformations, Branko S. Jursic
1. Introduction
2. Computational Methodology
3. Diels-Alder Reactions with Five-Membered Heterocycles with One
Heteroatom
3.1. Furan, pyrrole, and thiophene as dienophiles in reaction with
acetylene, ethylene, and cyclopentadiene
3.2. Addition of benzyne to furan, pyrrole, and thiophene
3.3. Cycloaddition reactions with pyrrole as diene for Diels-Alder
reaction
3.4. Diels-Alder reactions with benzo[b]- and benzo[c]-fused hetero-
cycles
4. Diels-Alder Reactions with Five-Membered Heterocycles with Two Hetero-

atoms
4. I. Addition of acetylene, ethylene, and cyclopropene to heterocycles
with heteroatoms in the l and 2 positions
4.2. Addition of acetylene, ethylene, and cyclopropene to heterocycles
with heteroatoms in the I and 3 positions
5. Diels-Alder Reactions with Five-Membered Heterocycles with Three Hetero-
atoms
5.1. Addition of acetylene, ethylene, and cyclopropene to heterocycles
with heteroatoms in 1, 2, and 3 positions
5.2. Addition of cyclopropene to heterocycles with heteroatoms in the
1, 2, and 5 positions
5.3. Addition of acetylene, ethylene, and cyclopropene to heterocycles
with heteroatoms in the 1, 2, and 4 positions
5.4. Further investigation of the role of 1,3,4-oxadiazole as a diene in
Diels-Alder reactions
453
454
455
456
458
458
461
472
477
478
481
487
501
501
502

502
502
513
518
529
539
542
546
549
552
554
555
558
xiv
6. Cycloaddition Reactions with Activated Heterocycles That Have Two
or Three Heteroatoms 563
6.1. Activation of 1,2-diazole as a diene for Diels-Alder reaction 563
6.2. Transformation of cyclic malonohydrazides into the Diels-Alder
reactive 1,3-diazole 567
6.3. Quaternization of nitrogen atom as a way to activate 1,3-diazole,
and 1,3,4-triazole as a diene for the Diels-Alder reaction 569
6.4. Oxidation of a sulfur atom: a way to activate 1,3-thiazole and
1,3,4-thiadiazole as dienes for the Diels-Alder reaction 571
7. Conclusion 574
Chapter 16. Triplet Photoreactions; Structural Dependence of Spin-Orbit Coupling
and Intersystem Crossing in Organic Biradicals, Martin Klessinger 581
1. Introduction 581
2. Basic Theory 582
2.1. Wave functions and operators 582
2.2. Matrix elements between bonded functions 584

2.3. Evaluation of spin-orbit integrals 586
3. Spin-Orbit Coupling and Intersystem Crossing in Biradicals 587
3.1. Carbene 588
3.2. Ethylene 590
3.3. Trimethylene 592
3.4. 1,2-Dimethyltrimethylene 595
3.5. Tetramethylene 596
3.6. Oxatetramethylene 599
4. Models for Spin-Orbit Coupling 600
4.1. The 2-in-2 model 600
4.2. Symmetry considerations 603
4.3. The "through-space" vector model 603
5. Conclusions 606
Index 611
C. P~irkb.nyi (Editor) /
Theoretical Organic Chemistry
Theoretical and
Computational Chemistry, Vol. 5
9 1998 Elsevier Science B.V. All rights
reserved
Theoretical Organic Chemistry: Looking Back in Wonder
Jan J.C.Mulder, Gorlaeus Laboratories, P.O.Box 9502,
Leiden University, 2300 RA, Leiden, The Netherlands
1. Personal preface
In 1958 the Chemical Society organized the "Kekul6 Symposium" in London. The papers
presented at the meeting were published under the auspices of the International Union of
Pure and Applied Chemistry, Section of Organic Chemistry, under the title "Theoretical
Organic Chemistry" [1]. Indeed Kekul6 regarded his contribution [2] as theoretical,
and as it was concerned with "the chemical nature of carbon" it was certainly organic.
In 1958 I started studying with L.J.Oosterhoff ~ who had been professor of theoretical

organic chemistry in Leiden since 1950. It was an auspicious moment to enter the field.
Computers started to make an impact in the beginning of a period measured between 1955
and 1980 that marked the heyday of theoretical and physical organic chemistry.
In the course of this introductory chapter on the history of theoretical organic chemistry I
will have occasion to comment on demarcation lines that separate these disciplines, and on
the relation between chemistry and physics. These questions have been discussed by
Walker [3] and Theobald [4] and recently at length by Nye [5] and van der Vet
[6]. Nye's book especially has been a valuable source of information.
This manuscript is dedicated to the memory of an unforgettable teacher.
On a lighter tone, I cannot resist the temptation to mention two characterizations that
concern the difference between physics and chemistry. The first one, due to Oosterhoff
[7], states that "the difference between chemistry and physics is in essence the
difference between chemists and physicists". The second one [8] is expressed as
follows: "The theoretical physicist moves like a swallow with elegant swerves through the
thin air of abstract thought, whilst the theoretical chemist on most occasions rummages in
the earth like a dung-beetle, that only exceptionally is able to raise itself above the
ground, albeit with a loud whirr".
The idea of revolutionary progress in certain periods as developed by Kuhn [9] and
very recently by McAllister [10], has some bearing on what I will discuss. It will be
argued that theoretical organic chemistry has known three periods of dramatic change. The
first of these periods (1850-1875) witnessed the birth of the structural formula and its
development from formal representation to a reflection of physical reality. The second
(1910-1935) saw the advent of quantum mechanics and the concepts of the electron pair,
resonance and mesomerism, and hybridisation. In the third one (1955-1980), already
mentioned, it is perhaps the succesful application of molecular orbital theory to chemical
reactions, made possible by a very fruitful interplay of calculations and concepts, which is
most significant.
A word of warning before starting my exposition is in order. Although this is a chapter on
the history of theoretical organic chemistry, and as such has a beginning and an end, this
certainly is not the case in the literature. Having been in and with this subject for almost

40 years, it is unavoidable that my appreciation for the contributions of many of my
colleagues has become idiosyncratic. Only the future can decide whether my nostalgia
coincides in a more than trivial way with truly historic developments.
2. Introduction
The objective of theoretical organic chemistry has always been to correlate systematic
variation in physical, chemical and (eventually) biological properties of organic molecules,
with systematic variation in their molecular structure. This, of course, is only a relative
correlation that was already possible long before the advent of quantum mechanics. The
formulation of structure-colour correlation rules by Witt [11], Dilthey [12] and
Wizinger [13], forms an impressive example. In inorganic chemistry the periodic
system provided correlation via "isocolumn" substitution. An absolute correlation of
properties with structure becomes possible, at least in principle, within the application of
quantum mechanics to chemical problems. Probably this has been called quantum chemis-
try for the very first time in a curious application of the general theory of relativity to
molecular systems by de Donder [14]. In 1929 a little book by Haas appeared
[15], which may have been the first with the title Quantum Chemistry.
Theoretical organic chemistry is principally concerned with the structure of molecules and
- in reactions - of transition states. In contrast physical chemistry and theoretical chemistry
are also tackling the bulk properties and, more importantly, are bridging the gap that
separates them from the molecular properties. Physical organic chemistry, invented by
Hammett [16], occupies an intermediate position and has in time become the
experimental partner of theoretical organic chemistry. As far as the covalent bond,
ubiquitous in organic molecules, can only be understood using quantum mechanics, it
follows that for instance in the textbooks by Streitwieser [17] and Dewar [18],
theoretical organic chemistry becomes almost synonymous with quantum chemistry,
exemplified in the application of molecular orbital theory to organic molecules. The early
books by Henrich [19] and Branch and Calvin [20] had little or no quantum
mechanics whatsoever. Wheland [21] and Walter Hfickel [22] wrote influential
texts, that contained almost no molecular orbital theory. Pullman and Pullman's book
[23] has a balanced treatment of valence bond and molecular orbital methods. Her-

mans [24], Staab [25], Liberles [26] and Lowry and Richardson [27] are
really all physical organic chemistry texts. The book by Sandorfy [28] quite rightly
had a huge success and was translated into German and English. Very recently a hybrid of
physical and theoretical organic chemistry appeared [29], written by Shaik, Schlegel
and Wolfe, and especially concerned with the valence bond configuration mixing model
for SN2-reactions, which in itself had a forerunner in Salem's [30] beautiful little
book. These last two references, together with new trends in organic photochemistry that
will be discussed, constitute an important core area of theoretical organic chemistry at the
present time. Naturally the qualitative explanations will always lean heavily on the
quantitative calculations.
With the foregoing, theoretical organic chemistry has been positioned in its scientific
environment and the analysis of its development can now be undertaken.
3. The First Period (1850-1875)
The understanding of the behaviour of organic molecules which follows upon Couper's
introduction of the structural formula [31] can hardly be overrated. At first - as
emphasized by Frankland - the line between two atoms only meant the mutual saturation
of valencies [32], but soon, due to Crum Brown [33], the graphical display of the
physical positions of the atoms with respect to one another crept into play. This sequence
of discoveries culminated with the realisation by van't Hoff [34] and Le Bel [35]
that molecules exist in a three-dimensional space. Of course the history of these events has
been described many times. Mackle [36] and Rouvray [37] have given brief
reviews with emphasis on the concepts of valence and bond symbolism, that are
enlightening. In a very short time the transition was made from the constitutional formula
to the structural formula, elucidating the constitution
via
the mutual saturation of
valencies. From there the step towards the true meaning of the structure,
i.e.
the
demonstration of physical connectivity, was made, and finally the so constructed network

became an edifice in three dimensions. The debate amongst the leading organic chemists
of the day, exemplified by the extremely critical Kolbe [38] forms ample testimony of
the significance of this revolutionary change in concepts. An important aspect of the
existing problems was the confusion about atomic weights and the concept of equivalents.
It was only through Cannizzaro's [39] introduction of the true atomic (and molecular)
weights, due to the earlier work by Avogadro, that the situation was clarified.
Then, in the middle of this period, it is discovered - again by Kekul6 - that there are cases
in which a single structural formula does not account for the chemical properties of the
molecule [40]. His explanation has been called the "oscillation hypothesis" and has
been quoted by Staab [41] in another 100 years remembrance. Had it been the NH 3
structure going through the
D3h
planar form, that Kekul6 was discussing, his reasoning
would have been entirely correct. The real state of affairs will become the central issue in
the second period (5.). In fact it was only during the third period (7.), that the structures
for
C6H 6
originally proposed by Dewar [42], HiJckel [43], and Ladenburg
[44], were shown by van Tamelen [45], Wilzbach [46], and Katz [47],
with their colleagues, to be different molecules, perfectly capable of existence. Incidental-
ly, benzvalene was mentioned by Hiickel only as a possible non-canonical bond eigenfunc-
tion and not as a real structural formula. The theoretical development in organic chemistry
might have taken a different and possibly faster route, had all this been known at the time.
The elusive Claus' [48] structure of benzene may also be called "octahedral" benzene
and would - with one of the diagonal bonds uncoupled - be a candidate for existence in the
triplet state if suitable precursors for a photochemical transformation could be found.
4. Interlude 1
The fruits of the eventful 25 years in which the molecule became tangible in organic
chemistry had to be digested and explanations repeated. The precise contents of the
structural formula,

i.c.
the meaning of the bar representing the bond, prompted the
interest of others. As reviewed by Rouvray [49] hundred years later, Cayley [50]
was the first to apply graph theory to isomer counting. The mathematicians Clifford
[51] (Clifford algebra), Sylvester [52] and Gordan [53] (the Clebsch-Gordan
series!) were concerned with invariant theory, and it is interesting that the analogy was
discovered this early, because the subsequent development of valence bond theory in the
hands of Weyl and Rumer [54] showed the connection to be not only formal in
character, but a source for a viable theory of chemical bonding. Many years later,
Clifford's contributions were rediscovered and exploited by Paldus and Sarma [55].
They showed the utility of U(2") over U(n) and the use of spinor invariants in chemistry.
The geometry of molecules has been an essential element of theoretical organic chemistry
from the beginning. An important part has been played by the cycloalkanes. The strain
theory developed by Bayer [56] may be viewed as the start of conformational analysis,
mainly because Sachse [57] was able to show the flaw in the assumption that these
molecules were planar. Later Molar [58] completed the argument and the "chair" and
"boat" forms of cyclohexane were born. The idea of easily interconvertible isomers is
already present in substituted ethanes and the calculation of the barrier of rotation in the
parent molecule is a foremost problem in quantum chemistry. Finally, in the third period,
Kern and coauthors [59] were able to show that the main effect is the exchange
repulsion between the C-H bonding pairs.
Reactivity of strongly bonded molecules was considered by Thiele [60], who
introduced the concept of residual valence. This is tied in with Bayer's strain theory in the
sense that a solution for the same question was sought. Whereas the stereochemistry of the
cycloalkanes made Bayer's theory obsolete, the later introduction of resonance more or
less confirmed Thiele's intuition.
Notwithstanding new attempts by Bamberger [61] and Armstrong [62] the
structure of benzene remained a stumbling block. One of the problems that plagued the
theoreticians when analyzing the effect of substituents, was the difference between polarity
and polarizability, but Vorl~inder saw it clearly and early [63]. Here one discerns the

seeds of the later inductive and mesomeric effects. Chemistry as a whole was dominated
by the gradual filling of the periodic table and the debate on its (ir)regularities, as
discussed in detail in van Spronsen [64]. Early ideas by Abbegg [65] and Drude
[66] called attention to the electronic character of valence using the positions of
elements in the system.
5. The second period (1910-1935)
Nobody will argue the importance of the idea of the electron pair bond, introduced by
Lewis [67], in chemistry. Together with the Bohr theory of the electronic structure of
the atom [68] and its connection with the periodic system [69], one has the
ingredients for a true chemical theory. The octet model introduced by Langmuir [70]
soon demonstrated its immense explanative power for organic and inorganic structure
alike.
The electronic character of the chemical bond opened the door to polarity, and this was
exactly the concept needed for the understanding of chemical reactions. The great schools
of the study of organic reaction mechanisms took off immediately and their development
took place independently of the creation of quantum mechanics. One concept though,
became a link between the two, and this of course was resonance. The way that this
connection was made is interesting because of the different views of the participants
[71]. There can be no question about the fact that organic chemists like Weitz [72]
and Arndt [73] did discover the necessity of describing the structure of certain
molecules as intermediate between extreme formulae before the resonance concept was
introduced in quantum mechanics by Heisenberg [74]. The main difference between
the chemical and the quantum-mechanical significance of resonance lies in the reactivity
versus
the stability argument. The general impression though, that it was Ingold [75]
who invented mesomerism is wrong, as discovered by Eistert [76]. The difference
between mesomerism and tautomerism took some time to be recognized but is in essence
connected to the Born-Oppenheimer approximation [77].
In the second period the electronic structure of benzene - but not naphthalene! - was
finally understood due to Robinson [78], but interestingly it was not Pauling but

Htickel, who first applied the valence bond method to benzene [79]. On the other
hand, Wheland and Pauling [80] were the first to apply the Hiickel method
systematically. The regularities in the properties of substituted benzenes were known and
interpreted for instance by Vorl~inder [81], but the empirical rules following from this
knowledge met with frequent criticism, as exemplified by Lowry [82]. Much later
Heilbronner and Grinter [83] succeeded in bringing physical and chemical properties
together and explaining them correctly.
The story of resonance, which starts in the middle of this period, is an intriguing one.
There are at least two but perhaps three directions to discuss. Pauling pushed the concept
mainly as a qualitative method to gain insight into the stability and reactivity of molecules.
This is the line followed in "The Nature of the Chemical Bond" [84]. Together with
the curved arrow, introduced by Robinson, it became for many years the preferred way of
thinking for organic chemists. At the same time Pauling and his collaborators created the
qualitative valence bond calculations for r-electron systems [85]. This became the
method of choice in the pre-computer era because the number of structures could be
controlled, whereas in the Htickel molecular orbital method the number of n-atomic
orbital centers automatically fixed the dimension of the secular equation. Both methods led
into a dead alley for large systems, but the Htickel method was superior as soon as
computers became available. Moreover, as it turned out, the molecular orbital method was
easier to generalize into programs and large basis sets presented no special problems.
In between, the relationship of the two main quantum-chemical methods was established in
the general sense by Slater [86] and later by Longuet-Higgins [87]. The fact that
molecular orbital and valence bond methods must, if used with the same basis set and the
10
same approximations, but with full configuration interaction or inclusion of all structures,
lead to the same results, was of little help if this process was impractical. Thus a number
of examples arose in the literature where the methods gave different results. The first of
these was the oxygen molecule where the MO method in the hands of Lennard-Jones
[88] was superior in predicting the triplet ground state, with respect to the first order
VB result as discussed by Wheland [89]. The second example is cyclobutadiene where

again the MO method easily predicts the ground-state triplet, but the interaction of the two
covalent structures in the VB model gives a singlet state. In this case extensive
calculations [90] made even before computer technology was fully developed,
indicated that the VB result is probably the right one. In fact, if one realizes that the
oxygen molecule is isoelectronic with ethylene and also takes into account that orthogonal
ethylene is equivalent to cyclobutadiene because of the isomorphism of the D2d and
D4h
symmetry groups [91], the two examples become almost identical. There is, however,
one important difference between 02 on the one hand and orthogonal ethylene and
cyclobutadiene on the other. The last two can lower their symmetry and so remove the
orbital degeneracy which is present, and which favors the triplet configuration. This is the
pseudo-Jahn-Teller effect [92], to be distinguished from the JaM-Teller effect
[93], that describes the fate of a state degeneracy. It has become clear later that the
Jahn-Teller situation, being a conical intersection, will in fact only be affected in two (or a
combination of two) symmetry-lowering coordinates, but will persist in other degrees of
freedom. The symmetry of the intersection geometry makes it easy to find but plays no
further role. The relationship between symmetry and degeneracy is taught to students by
means of the first example where it exhibits itself, the two-dimensional square well.
Nevertheless, the same example also demonstrates the simplification that is involved, as