Molecular Orbital Theory - An Intro. Lect. Note and Reprint Volume

283 Pages·1965·10.794 MB·English

by  C. Ballhausen, H. Gray

MOLECULAR ORBITAL
THEORY
An Introductory Lecture Note and Reprint Volume
C.J . BALEHAUSEN
i.1 F
Kmbenhavns Universitet
and
HARRY B. GRAY
Columbia University
W. A. BENJAMIN, INC. 1965
New York Amsterdam
MOLECULAR ORBITAL THEORY: An Introductory Lecture
Note and Reprint Volume
Copyright @ 1964 by W. A. Benjamin, Inc.
All rights reserved
Library of Congress Catalog Number 65-12062
Manufactured in the United States of America
This manuscript was put into production on May 7,1964;
this volume was published on December 7,1964;
second printing with corrections September 20,1965
W. A. BENJAMIN, INC.
New York, New York 10016
Preface
These notes are based on lectures on molecular orbital theory that we
have presented at the University of Copenhagen and Columbia University.
They were designed primarily for advanced-undergraduate and first-year
graduate students as an introduction to molecular orbital theory.
It is apparent that the molecular orbital theory is a very useful method
of classifying the ground and excited states of small molecules. The tran-
sition metal complexes occupy a special place here, and the last chapter
is devoted entirely to this subject. We believe that modern inorganic chem-
ists should be acquainted with the methods of the theory, and that they
will find approximate one-electron calculations as helpful as the organic
chemists have found simple Hiickel calculations. For this reason, we have
included a calculation of the permanganate ion in Chapter 8. On the other
hand, we have not considered conjugated pi systems because they are
excellently discussed in a number of books.
Our intuitive approach in the use of symmetry methods is admittedly
nonrigorous and therefore will be unsatisfactory to purists, but we believe
this is the best way to introduce symmetry ideas to the majority of students.
Once the student has learned how to use symmetry methods, it will be
easier for him to appreciate more formal and rigorous treatments.
Several reprints of papers on molecular orbital theory are included in
the back of the book. The papers treat a substantial number of the impor-
tant molecular geometries. The reader should be able to follow the discus-
sions after reading through the lecture notes.
We thank our colleagues in New York and Copenhagen for help with
the manuscript. We gratefully acknowledge the help of Dr. Arlen Viste
and Mr. Harold Basch in preparing Appendix 8-B. Finally, it is a plea-
sure to acknowledge the expert assistance of Mrs. Diane Celeste in pre-
paring the final manuscript.
C. J. BALLHAUSEKNG,b enhavn
HARRBY. GRAYN, ew York
October 1964

Contents
Preface
1 Atomic Orbitals
1-1 The Schrodinger Equation
1-2 "Hydrogen-Like" Orbitals
1-3 The Pauli Exclusion Principle
2 Diatomic Molecules
2-1 Molecular Orbitals for Diatomic Molecules
2-2 Symmetry Considerations
2-3 Diatomic Molecules with Different Atomic Nuclei
3 Electronic States of Molecules
4 Hybridization
5 Band Intensities
6 Triatomic Molecules
6-1 The C02M olecule
6-2 The H20M olecule
6-3 NO2
6-4 0:(a nd SO2
7 Selected Molecules with Four or More Atoms
7-1 Hz02
7-2 Formaldehyde, H2C0
7-3 The Boron Hydride BzHG
vii
viii CONTENTS
8 Molecular Orbitals Involving d Valence Orbitals
8- 1 General Considerations
8-2 Molecular Orbitals for an Octahedral Molecule
8-3 Ligand-Orbital Representations
8-4 Group Overlap of Metal and Ligand Orbitals
8-5 Energy Calculations
8-6 Electronic Spectra of Metal Complexes
Appendix 8A Evaluation of G[eR(cr)]
Appendix 8B Example Calculations 107
8-7 Basis Functions 107
8-8 Normalization Including Ligand-Ligand Overlap 107
8-9 Evaluation of a Group Overlap Integral: GT2( d, crs) 111
8-1 0 Radial Functions 117
8-1 1 Bond Distances 117
8-1 2 Overlap Integrals 117
8-1 3 Coulomb Integrals (Hii) 118
8-14 Exchange Integrals (Hij) 118
8-15 Overlap Correction for Hiio f Ligands 118
8- 16 Calculation of MnO; 123
8- 17 Calculation of CrFi- 128
References 132
Problems 133
Suggested Reading 138
Reprint Collection
General Papers
1. C. A. Coulson and I. Fischer, "Notes on the Molecular Orbital
Treatment of the Hydrogen Molecule," Phil. Mag., 40,386-393
(1949). 139
2. G. E. Kimball, "'Directed Valence," J. Chem. Phys., 8, 188-198
(19 40). 147
CONTENTS ix
3. R. S. Mulliken, C. A. Rieke, D. Orloff, and H. Orloff, "For-
mulas and Numerical Tables for Overlap Integrals," J. Chem.
Phys., 17, 1248-1267 (1949). 158
4. J. A. Pople, "The Molecular-Orbital and Equivalent-Orbital
Approach to Molecular Structure," Quart Revs., 11, 273-290
(1957). 178
5. A. D. Walsh, "The Electronic Orbitals, Shapes, and Spectra of
Polyatomic Molecules. Part I. AH2 Molecules," pp. 2260-
2265; "Part 11. Non-hydride AB2 and BAC Molecules," pp.
2266-2289, J. Chem. Soc. (1953). 196
Transition Metal Complexes
1. C. J. Ballhausen and H. B. Gray, "The Electronic Structure of
the Vanadyl Ion," Inorg. Chem., 1, 111 -122 (1962). 226
2. H. B. Gray and C. J. Ballhausen, "A Molecular Orbital Theory
for Square Planar Metal Complexes," J. Am. Chem. Soc., 85,
260-265 (1963). 238
3. H. B. Gray and N. A. Beach, "The Electronic Structures of
Octahedral Complexes. 1. Metal Hexacarbonyls and Hexacy-
anides," J. Am. Chem. Soc., 85,2922-2927 (1963). 244
4. W. Moffitt, "The Electronic Structure of Bis-cyclopentadienyl
Compounds," J. Am. Chem. Soc., 76, 3386-3392 (1954). 250
5. J. H. Van Vleck, "The Group Relation Between the Mulliken
and Slater-Pauling Theories of Valence," J. Chem. Phys., 3,
803-806 (1935). 257
6. M. Wolfsberg and L. Helmholz, "The Electronic Structure of
MnOc, Cr0z;and ClO4," J. Chem. Phys., 20,837-834 (1952). 261
Corrections
Index
The publisher wishes to thank the American Institute of Physics, the American
Chemical Society, Taylor and Francis, and the Chemical Society (London) for per-
mission to reprint material from their journals.

MOLECULAR ORBITAL THEORY