Oktay Sinanoglu

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 "state-of-the-science" 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 Self-Consistent Molecular Orbital Theory.
              CNDO Results for AB2 and AB3 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 All-Valence-Electron SCF-MO-CNDO Theory, M. A.
               Whitehead .........................................................  49

             b Ground States of Sigma-Bonded 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 Pople-Santry-Segal 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 Sigma-Bonded 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 Sigma-Bonded Molecules - A Generalized
               Perturbation Treatment for Transition States, G. Klopman .......... 115

             b Hybrid-Based Molecular Orbitals and Their Chemical Applications,
               K. Fukui .......................................................... 121

           4 Electronic Spectra .................................................. 130

             a The Electronic Spectra of Sigma-Electron 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 Pople-Santry-Segal 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 Three-Dimensional 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 Hartree-Fock Hamiltonian Matrix for 
             Distorted-Atom Orbitals, T. L. Gilbert ..............................  249

           4 Atomic Orbitals for Semiempirical Molecular Orbital Calculations,
             L. C. Cusachs and J. H. Corrington ..................................  256

           5 Approximate Self-Consistent 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: Open-Shell
             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 Point-Group Theory, T. D. Bouman,
             A. L. H. Chung, and G. L. Goodman .................................... 333

           4 Study of the Electronic Structure of Molecules. Pyrolle Ground-State
             Wave-Function, 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 Many-Electron Theory of Atoms and Molecules—Shells, 
               Electron Pairs vs. Many-Electron 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 Pi-Electron 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 Parameter-Free 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 SCF-M0 Calculations on Transition Metal Complexes,
             H. Basch, C. Hollister, and J. W. Moskowitz .........................  449
 

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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 Hartree-Fock 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 Hartree-Fock level, that is, an electron correlation and its behavior. This question is examined in Chapter VIl-6 and 7. Sigma-pi separation, or rather nonseparation, has been studied in the papers included in Chapter VIl-7 and 8. In the last part of the book, Faller gives an inorganic chemist's view of the state of usefulness of sigma-MO theory with selected recent applications.

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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 as-yet 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 pi-electron 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 Hückel-type 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 sigma-type electrons. As in the pi-electron methods, the sigma-MO theory has also evolved over various stages of approximations. The Hückel method has been extended in a number of ways, as has the self-consistent-field (SCF) method, the latter to include electron-electron repulsions in an approximate way.
  
  In a historically very important paper (Chapter II-2), Sandorfy applied Hückel-type 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 Hückel-type theories, the total energy is assumed to be a sum of one-electron orbital energies, and only the one-electron Hamiltonian matrix is diagonalized to obtain these. The H' _{r s} , one- , and two-center 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 co-workers, 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 hybrid-based MO method will be found in Chapter III-3.
  
  A strong impetus to the treatment of a systems has developed from the "extended Hückel" work of Hoffmann (Chapter II-3). Hoffmann used a Hückel method with all the one-electron 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 IV-4). 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 VII-5), 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 Hückel-type methods do not include electron-electron 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 pi-electron 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 VI-6. Cusachs and McGlynn have been among the main proponents of this method (see Chapter VI-4 and 7).
  
  A very important development in sigma-MO theory involved the inclusion of electron-electron repulsions to achieve a self-consistency 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 pi-electron theory. Some of these problems and the often drastic approximations they necessitate have been discussed by Pople, Santry, and Segal (Chapter VI-5). A hybrid-based MO theory, but including electron-electron 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 II-4). 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 VI-6). 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 pi-electron 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 Hartree-Fock 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 one-electron operators ("one-electron properties") are expected to come out well when calculated by Hartree-Fock 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 one-electron 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 zero-point 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 N-electron energy and the Hartree-Fock 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 Hartree-Fock binding and a correlation binding.

The correlation binding constitutes a large fraction of the total binding energy as shown in Chapter III-2d. The flourine molecule F₂ is an extreme example, whlch comes out unstable with rcspect to two flourine atoms when calculated nonempirically by an accurate Hartree-Fock 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 Hartree-Fock on small molecules.

No accurate Hartree-Fock 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 Hartree-Fock 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 Hartree-Fock molecular orbitals (SCF) and the role of electron correlation in various properties, fit in with the semiempirical sigma-MO methods?

The article by Whitehead (Chapter II-2a) studies a wide range of properties using different versions of a CNDO theory. If the parameters are fixed as in the Pople-Santry-Segal 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 valence-state 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 III-2b) and by Wiberg (Chapter IIl-2c). Wiberg examines the parameters of CNDO/2 theory as to how they need to be modified to yield better bond distances and straight-line correlations with experimental heats of formation. Dewar and Klopman, it may be noted, use a different version of approximate MO-SCF 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 Hartree-Fock 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 Hartree-Fock SCF-M0, in the energy, excluding any portion of correlation from the parameters. (For an analogous situation in pi-electron Pariser-Parr-Pople approximate SCF theory, See Chapter VII-7.) When, in a CND0-type theory, the parameters are fitted from binding-energy data, the orbitals obtained may end up fortuitously altered from what they should be at the Hartree-Fock 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 Hartree-Fock total energy, the molecular orbitals would yield good charge and one-electron properties. To get binding-energy-related properties, one would then add separately correlation-energy corrections obtained by other semiempiriczal methods, such as the ones given in Chapter III-2d.

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 minimum-energy 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 III-2e 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 stretched-out bonds. As ordinary, closed-shell, MO theory often gives dissociation to die wrong atomic states where there are situations near dissociation, an open-shell MO method must be used. This is a difficulty already at the framework Hartree-Fock MO theory level, compounded by difficulties in semiempiricism. An important attempt to tackle this problem with sigma-M0 theory has been made by Klopman (Chapter III-3a).

As mentioned in Chapter II, Fukui and co-workers pioneered the use of sigma-M0 theory for chemical reactivities, using a hybrid-based 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 sigma-MO 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 Hartree-Fock 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 (III-4a), Sandorfy calls attention to the need for sigma-MO calculations on excited states. Most calculations and methods have dealt with ground-state 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 III-4b, 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 Hückel-type approach is used which works better on single sulfur compounds than on those with several sulfur atoms. McGlynn and co-workers have also studied the spectra of molecules such as pyridine with open-shell calculations of excited states (Chapter VI.7).