Notes on molecular orbital calculations

169 Pages·1961·8.746 MB·English

by  John D Roberts

Molecular Orbital
Calculations
BOOKS BY JOHIC' D. ROBERTS
Basic Organic Chemistry, Part I
Nuclear Magnetic Resonance, Applications to Organic
Chemistry
An Introduction to the Analysis of Spin-Spin Splitting
in High-Re solution Nuclear Magnetic Resonance
Spectra
Notes
on
Molecular O r b i t a l
~ a l c u l aito ns
John D. Roberts
Professor of Organic Chemistry
California Institute of Technology
Illustrated by the Author
1961
THE BENJAMINICUMMIMGS PUBLlSHING COMPANY, INC.
ADVANCED BOOK PROGRAM
Reading, Massachusetts
. . .
London Amsterdam Don Mills, Ontario Sydney Tokyo
NOTES ON MOLECULAR ORBITAL CALCULATIONS
First printing, 1961
Second printing, with corrections, 1962
Third printing-Twelfth printing, 1963-1 970
Thirteenth printing, 19 74
Fourteenth printing, 1978
The publisher wishes to express his appreciation to Dr. Roberts,
who, in addition to writing the manuscript, prepared all the
illustrations. The author was also responsible for the editing
and composition; final pages, ready for the camera, were typed
at the California Institute of Technology under Dr. Roberts'
supervision.
International Standard Book Number: 0-8053-8301-8(paperback)
Library of Congress Catalog Card Number: 61-1 81 59
Copyright @ 1961 by W. A. Benjamin, Inc.
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher, W. A. Benjamin,
Inc., Advanced Book Program, Reading, Massachusetts, 018 67, U.S.A.
Manufactured in the United States of America.
ISBN 080538301-8
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NOTES ON MOLECULAR ORBITAL CALCULATIONS
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Preface
For practicing organic chemists the simple, linear-
combination-of-atomic-orbitals (LCAO), molecular-orbital
method permits useful calculations of semi-empirical elec-
tronic energies of unsaturated molecules with no more than
high school algebra. Anyone who can find the roots of
- +
x4 5x2 4x = 0 graphically, analytically, or-by successive
substitutions can obtain the energy levels and calculate the
IT-electron energy of bicycle[ 1.1. 01 butadiene.
bicyclobutadiene
-
If in addition he can solve x4 4x2 = 0, then he can compare
bicyclobutadiene with cyclobutadiene and predict what changes
the 1, 3 bond would make in the a-electron energies. With no
more advanced mathematics, one can compute bond orders,
charge distributions, and reactivity parameters for both free-
radical and polar processes. The results may be crude, but
they are often highly suggestive; there is no excuse for a mod-
ern organic chemist not to be able to use the LCAO method.
The notes that make up this book have been used for
many years at the California Institute of Technology to intro-
duce seniors and graduate students to the elements of the
simple LCAO method. A fairly large number of exercises
are interspersed in the text to illustrate important points. It
is recommended that these be solved as encountered. Some
of the problems are hoped to be suggestive of possible research
problems in the field.
These Notes are not intended as a complete course of
study and shouldibe supplemented by the reference works listed
v
in the Bibliography. No attempt has been made to survey the
recent literature. The purpose has been to provide a practical
introduction. As a result ho appropriate acknowlkdgment to
either the priority of ideas or to their development has been
given.
This set of notes would never have been written without
the generous contributions of Professor W. G. McMillan and
Dr. V. Schomaker to the author's education in the subject
matter. Camera copy was prepared by Mrs. Allene Luke with
the aid of Miss Joy Matsumoto.
JOHN D. ROBERTS
Table of Contents
.............................................
Preface v
. .......................
1 ATOMIC ORBITAL MODELS 1
..........................
Hydrogen-like Orbitals 1
............
Bond Formation Using Atomic Orbitals 6
............................
Hybrid Bond Orbitals 11
Bond Orbitals for Atoms Carrying Unshared
..............................
Electron Pairs 14
......................
Orbitals for Multiple Bonds 15
. .
2 MOLECULAR ORBITAL CALCULATIONS ELEC-
.........................
TRONIC ENERGY LEVELS 23
+. ..........................
The Wave Equation. 23
...........
Molecular Orbitals. The LCAO Method 25
..........................
The Overlap Integral. S 28
1J. ........................
The Coulomb Integral. a 31
The Resonance Integral. P ....................... 32
...........................
Energy Levels of Hz@ 33
.................
Bonding and Antibonding Orbitals 36
..........................
The Hydrogen Molecule 39
................................
Localized Bonds 40
...................
Ethylene by the LCAO Method 42
,. .................................
Butadiene. E 43
.....................
Butadiene Resonance Energy .47
...................
The Butadiene Wave Functions 48
.
3 BOND ORDERS. FREE-VALENCE INDEXES.
.....................
AND CHARGE DISTRIBUTIONS 53
........................
The Mobile Bond Order. p 53
1J ....................
The Free-Valence Index. % 56
.........................
Charge Distributions. qi 58
...........................
Self-consistent Fields 59
vii