Oktay Sinanoglu

Preface This book is the result of the joint efforts of a group of lecturers who came together in Istanbul in the summer of 1964 to lecture on Modern Quantum Chemistry. The lectures follow a definite sequence and attempt to present a detailed, up-to-date, and coherent picture of modern quantum chemistry to graduate students and researchers. The book is in three parts, Part I on orbitals, Part II on interactions and effects of electron correlation, and Part III on action of light and organic crystals. The parts are connected, though each is quite self-contained. The book should be useful for advanced quantum chemistry courses, as well as a reference. Parts I, II, and III may be used individually or in combination. Each lecture, by and large, starts with an introduction, before proceeding to current developments and problems. Many lectures contain new work and approaches not published before. The over-all theoretical picture that emerges applies to electronic properties, stabilities, and spectra of saturated and unsaturated molecules, sigma and pi systems, and also to intermediate species, radicals, and triplet states.

Both orbitals and electron correlation are involved. Effects in the gas phase and in condensed phases are treated. These effects include intermolecular forces, solvent effects, orbitals and electron correlation in metals, and action of light on organic crystals. Interplay of theory and experiment appears throughout; theory is compared against experiment, and attention is also drawn to new phenomena which require theoretical investigation.

The lectures constituted the course given at the Istanbul International Summer School of Quantum Chemistry, August 16 - September 5, 1964, to a group of researchers and graduate students from about sixteen countries. The school was sponsored by The Pure Science Bureau of NATO and was organized with the cooperation of Orta Doğu Teknik Üniversitesi (Middle East Technical University) of Ankara, Turkey. Additional support came from The Science Bureau of the Turkish Ministry of Foreign Affairs, from Orta-Doğu T. Ü., and from The U.S. National Science Foundation Fellowships Section. The University of Istanbul, the "Çekmece Araştırma Merkezi" (Çekmece Research Center) of Istanbul, and Robert College col- laborated in the establishment of the school. Thanks are due to each of the sponsoring sud collaborating institutions sud especially to President Kemal Kurdaş of Orts Doğu T.Ü., Dr. Hans Jørgen Helms and Mr. R. Canha e Sá of the Pure Science Bureau of NATO, Professor Fikret Kortel (University of Istanbul), Professor Erdal Inönü and Professor Vedat Enüstün (Orta-Doğu T.Ü.), and Mr. Sadun Illez (Orta-Doğu T.Ü.). They in turn, I am sure, join me, along with other participants of the school, in thanking the lecturers for their hard work both during the school and in the preparation and writing of these lectures.

Oktay Sinanoğlu

New Haven, Connecticut.

A prototype orbital theory for molecules is provided by the Hartree- Fock (H.F) method. Hartree-Fock molecular orbital wave functions may be used for both saturated and unsaturated systems, stable or transient molecular species. They usually represent the electronic charge distributions well, and also sufficiently simplify the treatment of the remaining correlation effects.

The fact that calculation of accurate H.F. orbitals for any sizable molecule is still in the future should not detract from the conceptual usefulness of the orbitals. Further approximations, such as the Hückel molecular orbital theory, may be obtained starting from the prototype in a systematic way.

Stable molecules, most ground states, require the closed shell H.F. orbitals. For electronic excited states, free radicals and radical ions, triplet states, and also for the prediction of potential entergy surfaces of chemical kinetics, nonclosed shell H.F. molecular orbital theory provides a starting point.

Part I of this book is concerned mainly with the orbital theory of molcules. The application of molecular orbitais {MO's) to systems with localized and delocalized sigma electrons is treated in Part I {note O.S.: For the authors of each section mentioned in this introduction see Table of Contents (Parts I-III)}. Sections A.3 and A.2, Sigma MO theory, mainly of the Hückel type, has been used also in connection with the effect of sigma-electrons on the pi-parts of aromatics.

In saturated molecules, localized bonds are recovered from a Lennard- Jones transformation of the MO wave function into the localized description (LO's>. Though in a molecule like CH₄ , the transformation is determined purely by symmetry, in general (H₂O, C₃H₈, etc.) a calculation is required which involves the effects of electrons on each other. In Part I, Section A.4, is discussed the localization of H.F. orbitals from a minimization of exchange interactions (maximization of self-repulsions). The more approximate sigma orbitals obtained from one of the present Hückel procedures may be transformed into localized ones by criteria which replace the electron repulsion integrals with others of similar geometric behavior (2).

One difficulty in treating sizable molecules in terms of valence electrons alone is the requirement of orthogonaiity to inner orbitals. The "pseudo- potential" method developed in solid state physics replaces this requirement by a potential which keeps the valence electrons outside the inner shells. The method may be useful in obtaining MO's of large molecules, and is discussed in Part II, Sections B.2 and B.3 (see also Part II, Sections B.1 and C.5).

Molecular fragments with sigma electrons require a nonclosed shell H.F. MO theory. Recent work (3) has shown that improved accuracy in pi-electron spectra too, is obtained by a nonclosed shell H.F. M0 theory. Hartree- Fock orbitals, nominally the same, may differ appreciably from state to state. Several forms of nonclosed shell H.F. theory (4) are found in Part I, Sections B.3 and B.5, and in Part II, Section A.7.

A series of lectures in Part I, Sections B.6a - f (see also Part III. Section B.13) examine both the formal foundations and the experimental verification of pi electron theories. The nature of pi electron approximations, the prediction of electronic spectra, and charge distributions in hetero- molecules are discussed. Solvent effects are treated in Part II.B. In Section A.4 of Part III is given a survev of experimental singlet-triplet separations and their prediction. Experimental determination of dipole moments of organic molecules in excited states is discussed in Part III. Section A.3. The results of nonclosed shell excited state MO calculations may be compared against these quantities. The experiments are for solutions.

Excited state dipole moments of smaller molecules like formaldehyde have also been obtained recently from gas phase measurements (5). In connection with pi electron spectra, the reader may also wish to consult Sections B.3, B.8, and B.7 of Part III on vibronic effects and the molecuiar exciton model.

Aside from comparison with experiment, final justification of orbital theory lies in the comparison of an orbital wave function and energy with the exact wave function Ψ and energy E (Part II. Section A: see also Part I, Section B.6f). If orbitals are obtained from an H.F. theory, the remaining effects are due to electron correlation. Correlation may shift energy levels in electronic spectra and distort the H.F. orbitals, but its effect is most drastic on binding energies and on forces in gases and in dense media. These effects are surveyed in Part II. The emphasis is on properties where correlation may change even the qualitative picture based on orbitals alone. Recent developments are stressed (6).

Interactions between electrons and dense media, also forces acting between the molecules of a gas, liquid, or solid, strongly depend on correlation. They are treated in Part II, Sections B and C. Electron correlation in metals and systems of infinite extent is discussed in Part II, Sections C.4 and C.5. Part II, Section C.4 includes a compact exposition of zone and H.F. orbital theorv of metals. Part II, Section C.4 includes a treatment of liquid. alkali metal alloys. (See also Part II, Section C.4 in connection with crystal theory for Part III. Section B). The reader will find techniques from manny- body physics outlined and applied. in Part II, Sections A.4, C.4. and C3, and in Part III. Section B.5.

Part III, Section B, of the hook is devoted to organic crystal phenomena, both theoretical and experimental aspects. The lectures in Part III, Section A on some effects of light on molecules and media, are related to those in Part III, Section B on the one hand, and to those in Parts I and II, in ways mentioned above, on the other. Detailed background and theory on excitons and excitation transfer are given in Part III. Sections B.1 and B.2. Alternate wavs of treating excitons, various coupling cases, and the role of charge transfer on excitons and vibronic effects are discussed in Sections B.3 - 7 of Part III. Experimental and theoretical work on the related phenomenon of photoconductivity will be found in Part III, Seetions B.8 - 10. Brief treatments of surface and impurity states, significant for an understanding of organic crystal phenomena, are included (Part III, Sections B.11 and B.12). In the last section. Part III, Section B.13, is discussed the question of the possible semiconductivity of proteins.


(2) See C. Edmiston and K. Ruedenberg. Rev. Mod. Phys. 35, 457 (1963).
For localized Hartree-Fock theory see also T.L. Gilbert, in: "Molecular Orbitals in Chemistry, Physics and Biology - A Tribute to R. S. Mulliken." (B. Pullman and P. 0. Lowdin. eds.), Academic Press, New York, 1964.

(3) See e.g. L Goodman and J.R. Hoyland, J. Chem. Phys. 39, 1068 (1963).

(4) See also C.C.J. Roothaan. Rev. Mod. Phys. 32, 179 (1960).

(5) W. Klemperer et al. (to be published.)


ACKNOWLEDGMENT The Editor's share of the work in the preparation of this book has been aided by grants from the U.S. National Science Foundation and the Alfred P. Sloan Foundation. Both grants are gratefully acknowledged.

For some other theoretical aspects on atoms and molecules on which there are alreadv extensive reviews see, e.g. 0. Sinanoglu, in: "Advances in Chemical Physics" (I. Prigogine. Ed.). Vol. VI, pp. 315 - 412. Wiley Interscience, New York, 1964; and 0. Sinanoglu and D.F. Tuan, Ann. Rev. Phys. Chem. 15, 251 (1964).

                      Modern Quantum Chemistry - Istanbul Lectures 1965

                                    CONTENTS
         
         
          List of Contributors to Part I ................................     v                              
          Preface .......................................................   vii  
          Condensed Table of Contents of Parts I - III ..................  xiii
          Introduction, Parts I - III, O. Sinanoğlu .....................     1
         
 
        
                          Section I. A. Saturated Compounds


          1. Present Status of the Theory of Electronic Structure of Molecules
             ROBERT G. PARR
            1. The Problem ...............................................     5
            2. One- and Two-Electron Cases ...............................     6
            3. Preliminaries for Many-Electron Cases .....................     9
            4. Many-Electron Cases .......................................    10
            3. Implementation ............................................    13
            6. Conclusion ................................................    14
         
         
          2. Chemical Predictions by MO Theory : The Rare Gas Halides
             JOSHUA J0RTNER and STUART A. RICE
            1. Introduction ..............................................    15
            2. The Electron-Correlation Model ............................    16
            3. The Molecular Orbital Model ...............................    18
            4. The Valence Bond Model ....................................    25
            5. Interpretation of Physical Properties .....................    28
            6. Excited Electron States ...................................    33
            7. Discussion of the Theoretical Models ......................    43
               References ................................................    45
         
         
          3. Sigma Molecular Orbital Theory and Chemical Reactivity
             KENICHI FUKUI
            1. Introduction ..............................................    49
            2. Sigma Molecular Orbital ...................................    49
            3. Chemical Reactivity Theory ................................    59
            4. Electron Delocalization at the Transition State ...........    63
            5. Simple Interpretation of Reactivity of Saturated Compounds     70
            6. Conclusion ................................................    81
               References ................................................    63
               

         
          4. Localized Self-Consistent Field Orbitals in Atoms ond Molecules
             KLAUS RUEDENBERG
            1. Introduction ..............................................    85
            2. Arbitrariness of Hartree-Fock Orbitals ....................    86
            3. Fixation of Hartree-Fock Orbitals .........................    88
            4. Canonical SCF Orbitals ....................................    89
            5. Externally Localized SCF Orbitals .........................    89
            6. Intrinsically Localized SCF Orbitals ......................    90
            7. Choice of Separation Function f(r12 ) ......................    92
            8. Construction of Localized Orbitals from an Arbitrary Set
                   of SCF Orbitals .......................................    93
            9. Localized Orbitals and Molecular Symmetry .................    93
           10. Localized Orbitals in the Absence of Symmetry .............    95
           11. Localized Molecular Orbitals in Delocalized Electronic Systems 98
               References ................................................    99
         
         
          5. Integral Hellmann-Feynman Theorem, Barriers to lnternal Rotations,
                 and Isoelectronic Processes
             ROBERT G. PARR
            1. Integral Hellmann-Feynman Theorem .........................   101
            2. Barriers to Internal Rotation .............................   102
            3. Isoelectronic Processes ...................................   104
               References ................................................   105
  

       
         
                        Section I. B. Pi-Electron Systems
 
        
          1. General Survey of Pi-Electron Methods and Problems
             ROBERT 0. PARR
            1. Pi-Electron Approximation .................................   107
            2. Pi-Electron Methods .......................................   109
            3. Pi-Electron Problems ......................................   110
               References ................................................   112
         
         
          2. Three-Dimensional and One-Dimensional Free-Electron Molecular
                Orbitals
             RICHARD L. HUMMEL and KLAUS RUEDENBRRG
            1. Introduction ..............................................   113
            2. General Solution ..........................................   114
            3. Determination of Eigenvalues as Functions of Delta ........   116
            4. One-Dimensional Model .....................................   118
            5. Comparison of Energies ....................................   119
            6. Comparison of Wavefunctions ...............................   120
            7. Conclusion ................................................   121
               Appendix ..................................................   122
               References ................................................   123


         
          3. Self-Consistent Field Theory of Noncloned Shell Systems with
                 Application to Pi-Electron Systems
             R. LEFEBVRE
            1. Introduction ...............................................  125
            2. Self-Consistent Field Equations for s Closed Shell System.
                   The Brillouin Theorem ..................................  126
            3. Self-Consistent Conditions for a Doublet State with One
                   Nonclosed Shell ........................................  128
            4. Self-Consistent Conditions for a Triplet State with Two
                   Nonclosed Shells .......................................  131
            5. The Lowest Triplet Excitation Energies of Some Even Alternant
                   Hydrocarbons Calculated to Various Degrees 
                   of Self-Consistency ....................................  132
               Summary ....................................................  134                                                 
               Referestces ................................................  134

         
         
          4. Charge Transfer and Radical lons
             L. J. OOSTERHOFF
            1. Introduction ...............................................  137
            2. Formulae ...................................................  139
            3. Loosely Bound and Semi-ionic Complexes:
                 Benzene-Iodine and Trimethylamine-Iodine .................  142
            4. Ionic Compounds: Sodium Iodide .............................  145
            5. The Organic Chemist's View of the Problem ..................  148
            6. Radical Ions ...............................................  151
            7. Photoionization ............................................  152
               References .................................................  154
                                       


          5. Some Properties of Pi-lons and Triplets
             A. T. AMOS
           1. Introduction ................................................  157
           2. Restricted Hartree-Fock .....................................  157
           3. Unrestricted Hartree-Fock ...................................  158
           4. Energies and Charge Densities ...............................  159
           5. The Transformation Properties of the Orbitals ...............  161
           6. Spin Properties of Psi(UHF) .................................  164                                   
           7. Zero-Field Splitting in Triplet States ......................  167
           8. Conclusion ..................................................  169
              References ..................................................  169
         
         

          6. Critical Examination of Pi-Electron Theories

            a. Applicability of the Hückel and Pariser-Parr-Type Methods
              J. KOUTECKÝ
               Text .......................................................  171
               References .................................................  182                                                 

             b. Orbital Basis of Zero Differential Overlap
               INGA FISCHER-HJALMARS
          1. Introduction .................................................  185
          2. Expansion Method .............................................  187
          3. Applications to the Fock Operator ............................  189
          4. Reformulation of the ZDO Assumption ..........................  192
             References ...................................................  193

             c. Electron Distribution In Heteromolecules
               R. DAUDEL
          1. Importance of the Notion of Charge ...........................  195
          2. Pariser, Parr, and Hückel (or Pauling and Wheland) 
                   Approxinsations ........................................  195
          3. The Nature of the Pariser and Parr Approximations ............  196
          4. Effect of the Introduction of OAO's on the pi-Electron
                   Distribution ...........................................  197
          5. Comparison between Pariser, Parr. and Pople Method and
                   Hückel Method .....................................  199
             References  ..................................................  202
         
         
             d. Semiempirical Parameters in MO Theory
               INGA FISCHER-HJALMARS
          1. Introduction .................................................  203
          2. One-Center Integrals .........................................  203
          3. Two-Center Integrals .........................................  210
             References ...................................................  213


             e. Extended CI Calculations on Benzene
               J. KOUTECKÝ
               Text .......................................................  215
               References .................................................  220


             f. The Pi-Electron Approximation and Coulomb Repulsion Parameters
               0. SINANOGLU and M. K. ORLOFF
          1. The Pi-Electron Approximation ................................  221
          2. Coulomb Repulsions Parameters ................................  225
             References ...................................................  231

          AUTHOR INDEX ....................................................  233
          SUBJECT INDEX ...................................................  239