Oktay Sinanoglu
Book: Sigma Molecular Orbital Theory (1970)

Preface
Many of our colleagues have shared our feeling that the time was ripe
for a look at the present state of the recently developed
"sigma molecular orbital" methods. These methods
have already made quantum chemistry broadly useful in a practical way
in organic chemistry.
It is to be expected that such methods will become more and more everyday
tools for the practicing chemist. At the moment, the methods are still
in the developmental stage. Much effort is being expended on comparisons
and tests of the reliability of the various approximations used.
We hope that researchers and graduate students with diverse interests from
organic chemistry, theoretical chemistry, molecular biophysics, and inorganic
chemistry will find this "stateofthescience" book useful in seeing what
methods are available, what the limitations are, and where one may expect
them to apply. We thank our many colleagues, themselves the originators
and developers of many of the methods, for their encouraging remarks as to
the timeliness and desirability of this project and for their
taking part in it.

We also acknowledge with gratitude the support of the project by the
Yale administration through an NSF institutional grant.
Our special thanks in this regard go to President Kingman Brewster,
Provost Charles Taylor,
Dean John Perry Miller,
and Dr. Arthur Ross. At the production stage, it was a pleasure to
work with Miss Jane Olson and Mrs. Anne Wilde of the Yale University Press,
and with Miss Marie Sarkes and Mrs. Miriam Bess.
Oktay Sinanoglu and Kenneth B. Wiberg
New Haven, Conn.
November 1969
Contents of "Sigma Molecular Orbital Theory" (1970)
Preface ................................................................ v
I Introduction ................... Read it here ..................... 1
II Semiempirical Sigma Molecular Orbital Theories .................... 3
1 General Remarks .............. Read them here ..................... 3
2
LCAO MO Calculations on Saturated Hydrocarbons and Their
Substituted Derivatives.
C. Sandorfy, reprinted from
Can. J. Chem. 33, 1337 (1955) ..................................... 5
3 An Extended Hückel Theory. Hydrocarbons, R. Hoffmann,
reprinted from J. Chem. Phys. 39, 1397 (1963) ..................... 20
4 Approximate SelfConsistent Molecular Orbital Theory.
CNDO Results for AB_{2} and AB_{3} Systems,
J. A. Pople and G. A. Segal, reprinted from
J. Chem. Phys. 44, 3289 (1966) ..................................... 36
III Energetics with Sigma Molecular Orbital Theory ..................... 45
1 General Remarks ....... Read them here ............................. 45
2 Binding: Heats of Formation, Ionization Potentials,
and Hydrogen Bonding ............................................... 49
a Semiempirical AllValenceElectron SCFMOCNDO Theory, M. A.
Whitehead ......................................................... 49
b Ground States of SigmaBonded Molecules.
A Semiempirical SCF MO Treatment of Hydrocarbons,
M. J. S. Dewar and G. Klopman, reprinted from
J. Am. Chem. Soc. 89, 3089 (1967) ................................. 81
c Application of the PopleSantrySegal Complete Neglect of
Differential Overlap (CNDO) Method
to Some Hydrocarbons and Their Cations, K. B. Wiberg,
reprinted from J. Am. Chem. Soc. 90, 59 (1968) .................... 91
d Molecular Binding Energies, C. Hollister and 0. Sinanoglu,
reprinted from J. Am. Chem. Soc. 88, 13 (1966) .................... 96
e Simplified SCF Calculations for SigmaBonded Systems:
Extension to Hydrogen Bonding, D. J. Mickish and H. A. Pohl ....... 105
3 Transition States and Chemical Reactivity ........................... 115
a The Chemical Reactivity of SigmaBonded Molecules  A Generalized
Perturbation Treatment for Transition States, G. Klopman .......... 115
b HybridBased Molecular Orbitals and Their Chemical Applications,
K. Fukui .......................................................... 121
4 Electronic Spectra .................................................. 130
a The Electronic Spectra of SigmaElectron Systems, C. Sandorfy ..... 130
b Electronic Spectra and Structure of Sulfur Compounds,
S. D. Thompson, D. G. Carroll, F. Watson, M. O'Donnell,
and S. P. McGlynn, reprinted from J. Chem. Phys. 45, 1367 (1966) .. 137
IV Sigma Molecular Orbital Theory and Organic Chemistry ................ 151
1 General Remarks, with an annotated bibliography of recent
organic chemical applications ....................................... 151
2 Molecular Orbital Calculations and Organic Chemistry.
K. B. Wiberg ........... Read it here ................................ 159
3 Ab initio Calculations and Organic Chemistry, A. Streitwieser, Jr. ... 161
4 Trimethylene and the Addition of Methylene to Ethylene,
R. Hoffmann, reprinted from J. Am. Chem. Soc. 90, 1475 (1968) ....... 168
5 a Some Organic Chemical Applications of
Sigma Molecular Orbital Theory, K. B. Wiberg ...................... 179
b Application of the PopleSantrySegal CNDO Method to the
Cyclopropylcarbinyl and Cyclobutyl Cation and to Bicyclobutane,
K. B. Wiberg, reprinted from Tetrahedron 24, 1083 (1968) .......... 183
6 A CNDO Treatment of the Arylmethyl Cations, A. Streitwieser, Jr.,
and R. G. Jesaitis .................................................. 197
V Local Orbitals and Hybridization ..................................... 209
1 Semiempirical Orbital Localization and Its Chemical Applications,
C. Trindle and 0. Sinanoglu ......................................... 209
2 Correlations between Tetrahedrally Localized Orbitals,
0. Sinanoglu and B. Skutnik,
reprinted from Chem. Phys. Letters 1, 699 (1968) .................... 221
VI Tests and Comparisons of Sigma Molecular Orbital Theories and Their
Approximations ....................................................... 225
1 General Remarks ..................................................... 225
2 Why ThreeDimensional Hückel Theory Works and Where it Breaks Down,
L. C. Allen ......................................................... 227
3 A Derivation of the Extended Hückel Theory from an Overlap Expansion
of the HartreeFock Hamiltonian Matrix for
DistortedAtom Orbitals, T. L. Gilbert .............................. 249
4 Atomic Orbitals for Semiempirical Molecular Orbital Calculations,
L. C. Cusachs and J. H. Corrington .................................. 256
5 Approximate SelfConsistent Molecular Orbital Theory.
Invariant Procedures, J. A. Pople, D. P. Santry, and G. A. Segal,
reprinted from J. Chem. Phys. 43, S129 (1965) ....................... 273
6 Sigma Electrons in Conjugated Heterocycles, with Special Emphasis
on Biological Purines and Pyrimidines, A. Pullman ................... 280
7 Semiempirical Molecular Orbital Calculations: OpenShell
Computations on Pyridine, B. J. Bertus and S. P. McGlynn ............ 293
VII Nonempirical Methods and Theory ...................................... 301
1 General Remarks ...................................................... 301
2 Chemistry from Computers: A New Instrument for the Experimentalist,
A. C. Wahl ........................................................... 304
3 Automation of Molecular PointGroup Theory, T. D. Bouman,
A. L. H. Chung, and G. L. Goodman .................................... 333
4 Study of the Electronic Structure of Molecules. Pyrolle GroundState
WaveFunction, E. Clementi, H. Clementi, and D. R. Davis,
reprinted from J. Chem. Phys. 46, 4725 (1967) ........................ 350
5 a Subminimal ab initio Calculations, A. A. Frost ..................... 356
b A Simple Floating Localized Orbital Model of Molecular Structure,
A. A. Frost, B. H. Prentice, III., and R. A. Route,
reprinted from J. Am. Chem. Soc. 89, 3064 (1967) .................. 358
c A Floating Spherical Gaussian Orbital Model of Molecular Structure.
Hydrocarbons, A. A. Frost and R. A. Rouse,
reprinted from J. Am. Chem. Soc. 90, 1965 (1968) .................. 360
6 Electron Correlation and How it Supplements Molecular Orbital Theory 365
a ManyElectron Theory of Atoms and Molecules—Shells,
Electron Pairs vs. ManyElectron Correlations,
0. Sinanoglu, reprinted from J. Chem. Phys. 36, 706 (1962) ........ 366
b Reducible and Irreducible Pair Correlations in Benzene,
0. Sinanoglu and J. Cicek,
reprinted from Chem. Phys. Letters 1, 337 (1967) .................. 378
c Nonempirical Calculations of Correlation Effects in the
Diatomic Hydride Molecules, E. R. Davidson ........................ 381
7 The PiElectron Approximation and Coulomb Repulsion Parameters,
0. Sinanogu and M. K. Orloff, reprinted from Modern Quantum
Chemistry, Vol. 1, Academic Press, New York, 1965, p. 221 ........... 390
8 Sigma and Pi Electronic Reorganization in Acetylene,
M. G. Griffith and L. Goodman,
reprinted from J. Chem. Phys. 47, 4494 (1967) ....................... 403
VIII Sigma Molecular Orbital Theory in Inorganic Chemistry ................ 415
1 a Sigma Molecular Orbital Theory: An Inorganic Chemist's
Perspective, J. W. Faller ......................................... 415
b Molecular Orbital Theory for Octahedral and Tetrahedral Metal
Complexes, H. Basch, A. Viste, and H. B. Gray,
reprinted from J. Chem. Phys. 44, 10 (1966) ....................... 426
c ParameterFree Molecular Orbital Calculations,
R. F. Fenske and D. D. Radtke,
reprinted from Inorg. Chem. 7, 479 (1968) ......................... 436
d Selection Rules for the Isomerization and Substitution Reactions of
Transition Metal Complexes,
D. R. Eaton, reprinted from J. Am. Chem. Soc. 90, 4272 (1968) ..... 445
2 Nonempirical SCFM0 Calculations on Transition Metal Complexes,
H. Basch, C. Hollister, and J. W. Moskowitz ......................... 449
Chapter I
Introduction
Quantum chemistry may be considered to be entering a new phase. There was a time when nonempirical calculations were carried out on the smallest of molecules, and semiempirical ones on the pi electrons of conjugated systems alone. Recently, semiempirical molecular orbital (MO) methods have been extended to include all electrons, sigma and pi, and to apply to saturated molecules as well as conjugated. Purely nonempirical MO calculations, although still in general far from the desired HartreeFock MO result, are being made on sizable organic molecules, too.
Clearly, for predictions on chemical reactions, sigma electrons are essential. Inclusion of sigma electrons in conjugated systems shows that although some qualitative conclusions based on pi alone remain valid, in general the picture changes. Sigma and pi are not as clearly separable as once used to be thought.
In the present book an attempt is made to present an overall view of this rapidly developing and still very fluid field with the help of contributions from our colleagues and with occasional inclusion of articles reprinted from the original literature. Chapters II and III contain the main semiempirical methods with applications to different properties. Throughout, attention is drawn to the limitations of the methods as well. In spite of considerable advance, both the semiempirical and nonempirical methods are still in a rudimentary stage.
Chapter IV includes an annotated bibliography of recent organic chemical applications. In Chapter VI semiempirical methods are compared with each other and with nonempirical calculations. The chapter also includes some theoretical results which attempt to justify the use and approximations of the simpler semiempirical methods. In Chapter IV the reader will find discussions of some experimerstal problems in organic chemistry, and in Chapter VIII in inorganic chemistry, which are called to the attention of theorists. Streitwieser gives examples of qualitative notions in organic chemistry that could now be tested by nonempirical calculations.
Chapter VII presents a view of what computers can do at their best, used as powerful instruments of a priori prediction and how they may even do group theory from scratch. Applicability of MO methods, especially to energetics, depends an the error that would remain even after the MO's are calculated at the HartreeFock level, that is, an electron correlation and its behavior. This question is examined in Chapter VIl6 and 7. Sigmapi separation, or rather nonseparation, has been studied in the papers included in Chapter VIl7 and 8. In the last part of the book, Faller gives an inorganic chemist's view of the state of usefulness of sigmaMO theory with selected recent applications.
Chapter II
Semiempirical Sigma Molecular
Orbital Theories
Semiempirical methods allow calculations on a large number of molecules at little cost. They have been useful as guides in chemical applications, und have gained more und more importance in both organic and inorganic chemistry. However, these methods often involve drastic and asyet untested approximations. They need, therefore, to be used judiciously. Although a user may often be interested only in applications to his own chemical problems, he would nevertheless be well advised to look into the foundations of the method that is being used in some detail and to famiiarize himself with the limitations.
For a long time, M0 theory was applied to only the pi electrons of conjugated molecules. For a survey of the pielectron methods and how useful they have been, the reader is referred to the following books:
 R. G. Parr, Quantum Theory of Molecular Electronic Structure. Benjamin, New York, 1961,and to
 0. Sinanoglu, ed., Modern Quantum Chemistry, Vol. 1, Otbitals, Academic Preis, New York, 1965.
For applications of Hückeltype methods in organic chemistry, the reader is referred to the book by
 A. Streitwieser, Jr., Molecular Orbital Theory for Organic Chemists, Wiley, New York, 1961.
Recently, the analogues of these various semiempirical M0 methods have been developed for systems containing sigma electrons. This is a very important development, as almost all molecules involve sigmatype electrons. As in the pielectron methods, the sigmaMO theory has also evolved over various stages of approximations. The Hückel method has been extended in a number of ways, as has the selfconsistentfield (SCF) method, the latter to include electronelectron repulsions in an approximate way.
In a historically very important paper (Chapter II2), Sandorfy applied Hückeltype approximations to saturated hydrocarbons, for the first time including the hydrogens, and concluded that MO methods of the linear combination of atomic orbitals type (LCAO) would be capable of giving as good charge distributions in such molecules as on conjugated systems.
In Hückeltype theories, the total energy is assumed to be a sum of oneelectron orbital energies, and only the oneelectron Hamiltonian matrix is diagonalized to obtain these. The H'_{ r s }, one , and twocenter Hamiltonian matrix elements are obtained either from atomic properties and/or related to overlap integrals S _{r s} in a number of ways. Further, the LCAO may be that of the regular atomic orbitals (AO's) such as the 2s's and 2p's and the hydrogen 1s's, or of hybridized valence atomic orbitals (LCVO). Fukui and coworkers, in their pioneering applications, used especially an LCVO method without overlaps. They obtained charge distributions and sigma dipole moments for a large number of saturated and unsaturated molecules, and they studied with this method chemical reactivities und phenomena auch as the breakup of hydrocarbons under electron impact. These applications, as well as references to the literatur. up to 1965, have been surveyed by Fukui in Modern Quantum Chemistry, Vol. 1, 0. Sinanoglu, ed., Academic Preis, New York, 1965. More recent applications and a brief discussion of the hybridbased MO method will be found in Chapter III3.
A strong impetus to the treatment of a systems has developed from the "extended Hückel" work of Hoffmann (Chapter II3). Hoffmann used a Hückel method with all the oneelectron matrix elements H'_{ r s }, and all the overlaps S_{ r s } included. The method was applied with the same parametrization to a large class of saturated and unsaturated hydrocarbons. Hoffmann concluded that with such a method the geometries of molecules could be well predicted. In later papers, Hoffmann has used his extended Hückel method as a guide for organic chemistry (see Chapter IV4). The success obtained from simple MO calculations in predicting geometries, as was the case with Walsh's rules for smaller molecules, has stimulated work on the reasons of this success by a study of more complete and nonempirical methods (see Chapter VI).
It is interesting that another, much simplified method, which, however, differs from the Hückel approach in important aspects, the subminimal ab initio method of Frost (Chapter VII5), also gives remarkable success in the predictions of geometries. In the method of Frost, the full exact Hamiltonian and all the matrix elements that it gives rise to are used, but, in turn, the orbitals themselves are chosen in die simplest possible manner.
The Hückeltype methods do not include electronelectron interactions and the adjustments of the parameters that would result from these. Such changes in the parameters are particularly important in ionic species and with heteroatoms, where straight extended Hückel calculations run into more difficulty.
As in the pielectron theory, one way to go beyond the Hückel methods whule retaining their basic simplicity and lack of difficult integrals has been to introduce iterations to the parameters, dependent an charge distribution. Such iterated extended Hückel methods (IEHC) are discussed and compared with other methods by Pullman in Chapter VI6. Cusachs and McGlynn have been among the main proponents of this method (see Chapter VI4 and 7).
A very important development in sigmaMO theory involved the inclusion of electronelectron repulsions to achieve a selfconsistency of the orbitals. A number of versions of approximate SCF have been developed. With sigma systems, additional problems concerning parameters and the rotational invariance of atomic orbitals on each center come up which were not present in pielectron theory. Some of these problems and the often drastic approximations they necessitate have been discussed by Pople, Santry, and Segal (Chapter VI5). A hybridbased MO theory, but including electronelectron repulsions, has been given by Katagiri and Sandorfy [Theoret. Chim. Acta 4, 203 (1966)].
Although most of the other methods have been applied mainly to ground states, Katagiri and Sandorfy have been concerned wilth applications to electronic spectra as well. A version of approximate SCF is the CNDO/2 (complete neglect of differential overlap) method of Pople and Segal (Chapter II4). Computer programs for the CNDO/2 method as well
as for the extended Hückel method of Hoffmann are avaiable in the Quantum Chemistry
Program Exchange (Department of Chemistry, Indiana University, Bloomington, Ind.).
These semiempirical methods give considerable success for molecular charge distributions and geometries. They fail, however, in other properties, when used with the same parameters, such as heats of formation. One of the severest approximations in the CNDO/2 method is that 2s and 2p electrons are treated as equivalent to achieve rotational invariance in Coulomb repulsion parameters.
In later chapters of this book the reader will find extensive comparisons of the various semiempirical methods with each other as well as wilth nonempirical calculations (see Chapter VI6). A number of articles and discussions on the nature of the approximations are also included. That often different parametrizations must be used for different properties is a crucial and suggestive aspect. Some discussion on this point will be found in Chapter III, where examples of applications to diverse properties are also given.
Chapter III
Energetics with Sigma Molecular
Orbital Theory
As in pielectron theory, semiempirical sigma MO methods have been used by
and large for charge distributions, dipole moments, and conclusions that can be
drawn from chargc distributions, such as die inductive effects of substituents
and reactivity of sites. A challenge to MO methods is posed by energy properties.
Are MO methods as such capable of yielding heats
of formation, ionization potentials, activation energies, and die energies of
transition in electronic spectra?
Considerable progress on the basic aspects of MO theory as to which
properties it should yield to quite good accuracy, and where it is expected
to fail, has been wade in recent years. A framework for molecular orbitals is
provided by die HartreeFock method, which yields the best single determinantal
wave function made up of spin orbitals, each detersnined in the SCF
of all the electrons in the system. Properties which are expectation values of
oneelectron operators ("oneelectron properties") are expected to come out
well when calculated by HartreeFock MO theory or reasonable approximations
to it.
[See 0. Sinanoglu and D.F. Tuan,
Ann. Rev. Phys. Chem. 15, 251 (1964).]
Equilibrium distances in the geometry, and force constants, have also been related
to oneelectron properties. Properties of the type of energy differences, such as
heats of formation or binding energies, are, however, a different
matter. The binding energy of a molecule is the difference between its total
energy and its atoms, each in its ground state, separated out to infinity.
In obtaining the experimental binding energy, die energy of zeropoint
vibrations is corrected for.
The exact total energy of the system is givcn, barring relativistic effects,
by
E = E_{HF} + E_{ corr}
where E_{corr} , the correlation energy, is die difference between the
exact nonrelativistic Nelectron energy and the HartreeFock energy.
Similarly, the binding energy equals
B.E. = ΔE_{HF} + Δ_{ corr}
Thus the binding energy of a molecule may be described as being due to a
HartreeFock binding and a correlation binding.
The correlation binding constitutes a large fraction of the total binding energy
as shown in Chapter III2d. The flourine molecule F_{2} is an extreme
example, whlch comes out unstable with rcspect to two flourine atoms when
calculated nonempirically by an accurate HartreeFock method. Correlation
binding fractions of 20 to 30 per cent are more typical figures in
other molecules. The paper by Hollister and Sinanoglu gives, by two semiempirical
methods, estimates of correlation binding fractions. It is observed that the
correlation binding fractions are quite constant within classes of molecules,
which gives the hope that it may be possible to predict the actual binding energy
itself using such a ratio, from some molecules of a class and a correlation energy
estimate on the unknown molecule, which is obtainable from simple MO coefficients
and atomic data. The simple correlation estimates have been compared with
experiment and actual HartreeFock on small molecules.
No accurate HartreeFock MO results, however, are available on molecules larger
than ethane. It is not clear, therefore, how well the estimates work on larger
molecules, as it is as yet not possible to compare with experimental
correlation energies, which require a knowledge of accurate HartreeFock values.
Much more work is needed on the correlation energies of sizable molecules for
which additional and more detailed semiempirical methods are under development.
How do the theoretical conclusions above, as to what may be expected from
HartreeFock molecular orbitals (SCF) and the role of electron correlation
in various properties, fit in with the semiempirical sigmaMO methods?
The article by Whitehead (Chapter II2a) studies a wide range of properties
using different versions of a CNDO theory. If the parameters are fixed as in
the PopleSantrySegal CNDO/2 method, the binding energies obtained come out
three to eight times too large. The ionization potentials obtaincd are also
not satisfactory when compared with the experimental ones, including the inner
ionization potentials obtained by ultraviolet photoelectron spectroscopy
(D. Turner et al.). If, on the other hand, the parameters are fitted empirically
using valencestate ionization potentials and the binding energies of small
diatomic and polyatomic moleculcs, then on other systems the binding energies
obtained come out quite well. With these empirical parameters, however, the
orbital populations, charge distributions, and other properties change. Success
with parameters obtained from binding properties on heats of formation
is obtained also by Dewar and Klopman (Chapter III2b) and by Wiberg (Chapter
IIl2c). Wiberg examines the parameters of CNDO/2 theory as to how they need
to be modified to yield better bond distances and straightline correlations
with experimental heats of formation. Dewar and Klopman, it may be noted, use a
different version of approximate MOSCF theory, in which 2s and 2p orbitals
have different repulsion integrals, as they should, at the expense of
rotational invariance not preserved, but this, they show, does not make any
practical difference.
It is clear from these results that semiempirical MO theory may he made
to yield satisfactory results for a given type of property if its parameters
are chosen for that property. But then the success with other propertics is
spoiled. This apparent incompatibiity is understandable, at least qualitatively,
on the basis of HartreeFock and correlation theory. It has been
shown that in ground states electron correlation does not affect charge
distributions and the molecular orbitals much
[O. Sinanoglu and D. F. Tuan, J. Chem. Phys. 38, 1740 (1963)]. One
should therefore obtain the charge distributions and the molecular orbitals from
a semiempiricized theory approximating the HartreeFock SCFM0, in the energy,
excluding any portion of correlation from the parameters. (For an analogous
situation in pielectron PariserParrPople approximate SCF theory, See Chapter
VII7.) When, in a CND0type theory, the parameters are fitted from
bindingenergy data, the orbitals obtained may end up fortuitously altered
from what they should be at the HartreeFock level. The theory would indicate,
therefore, that if one can obtain a simple approximate SCF theory which would
yield a satisfactory approximation to just the HartreeFock total energy, the
molecular orbitals would yield good charge and oneelectron properties. To get
bindingenergyrelated properties, one would then add separately
correlationenergy corrections obtained by other semiempiriczal methods, such
as the ones given in Chapter III2d.
One question in calculating binding energies semiempirically, as in the work of
Dewar and Klopman, Wiberg, and Whitehead, is : Should the energy be calculated for
the known geometry of the molecule, or should one seek the minimumenergy geometry
that would result from the method used? If the geometry comes out close to
experimental, with parameters appropriate for charge distributions, then a
different geometry would be expected to result, with new parameters used
appropriate zo binding energies. The question, therefore, is probably susceptible
to a theoretical analysis, which, however, has not been carried out.
In Chapter III2e Mickish and Pohl show that properties of the hydrogen bond
such as the equiibriumn distances and force constants agree satisfactorily with
experiment when obtained by semiempirical MO calculations.
Reactivity
To obtain the rate of a chemical reaction, the entropy of activation,
ΔS^{‡}, and the enthalpy of activation, ΔH^{‡}, are
needed. This requires an educated guess of die geometry of the activated complex.
For obtaining the entropy of activation, simple formulas based on classical
mechanics with quantum corrections have been developed, at least for classes of
reactions such as "abstraction"
[O. Sinanoglu and K.S. Pitzer, J. Chem. Phys. 30, 422 (1959)].
The activation enthalpy, ΔH^{‡}‚ on die other hand, is even more
difficult than heats of formation to predict. In an activated complex, there are
stretchedout bonds. As ordinary, closedshell, MO theory often gives dissociation
to die wrong atomic states where there are situations near dissociation, an
openshell MO method must be used. This is a difficulty already at the
framework HartreeFock MO theory level, compounded by difficulties in
semiempiricism. An important attempt to tackle this problem with sigmaM0 theory
has been made by Klopman (Chapter III3a).
As mentioned in Chapter II, Fukui and coworkers pioneered the use of sigmaM0
theory for chemical reactivities, using a hybridbased Hückel approach.
(See K. Fukui in Modern Quantum Chemistry, Vol. I,
0. Sinanoglu, ed., Academic Press, New York, 1965, for a detailed prcsentation.)
This approach gives a qualitative guide to reactivities, based on the highest
occupied and lowest unoccupied molecular orbitals, their shapes, and their charge
distributions. The reader interested in reactivity will also find organic chemical
applications, along these lines, of sigmaMO theory discussed in Chapter IV.
Electronic Spectra
The transition energies in electronic spectra constitute another property
difficult to obtain with semiempirical MO theory. The energy differences in
general depend strongly on electron correlation. In excited states, both the
HartreeFock MO theory and the correlation theory are more complex than in ground
states. The excited states involve novel and sizable correlation effects not
present in the ground states, and therefore the correlation energy corrections
are in general not expected to cancel out. Such correlation effects and how they
affect both the transition energies and the transition probabilities have been
studied recently in detail for many atomic states
[O. Sinanoglu in Atomic Physics, V. Hughes et al., edi., Plenum Press, New
York, 1969, and O. Sinanoglu and 1. Öksüz,
Phys. Rev. Letters 21, 507 (1968)].
However, little is known about these effects in molecules, where they may be
even more important. It is also well known that in the orbital theory itself one
needs to minimize the energy of each state separately to obtain orbitals
appropriate to that state. The relatively small amount of data available on
transition energies of saturated and nonconjugated, unsaturated
compounds, coupled with the difficulty in making assignments of the observed
bands, makes it difficult to find experimental data against which to test the
calculations. This is an area which clearly needs much more work, both
experimentally and theoretically.
In his interesting article (III4a), Sandorfy calls attention to the need
for sigmaMO calculations on excited states. Most calculations and methods have
dealt with groundstate properties only. He reviews the new experimental results
on normal and branched paraffin hydrocarbons and the available but inconclusive
interpretations of the UV spectra.
In Chapter III4b, McGlynn et al. study experimentally and theoretically the
electronic spectra and structure of sulfur compounds, where the presence of sulfur
poses additional problems in parametrization. A Hückeltype approach is used
which works better on single sulfur compounds than on those with several sulfur
atoms. McGlynn and coworkers have also studied the spectra of molecules such as
pyridine with openshell calculations of excited states (Chapter VI.7).
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