Electron Distributions and the Chemical Bond

470 Pages·1982·20.87 MB·English

by  Vedene H. Smith Jr. (auth.), Philip Coppens, Michael B. Hall (eds.)

Electron
Distributions and
the Chemical Bond
Electron
Distributions and
the Chemical Bond
Edited by
PHILIP COPPENS
State University of New York
Buffalo, New York
and
MICHAEL B. HALL
Texas A & M University
College Station, Texas
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Main entry under title:
Electron distributions and the chemical bond.
"Proceedings of a Symposium on Electron Distributions and the Chemical Bond for the na
tional meeting of the American Chemical Society, held March 28-April 2, 1981, in Atlanta,
Georgia" -po
Bibliography: p.
Includes index.
1. Chemical bonds-Congresses. 2. Electron distribution-Congresses. I. Coppens, Philip.
II. Hall, Michael, B. III. Symposium on Electron Distributions and the Chemical Bond (1981:
Atlanta, Ga.) IV. American Chemical Society.
QD461.E45 541.2'24 82-5390
ISBN-13: 978-1-4613-3469-9 e-ISBN-13: 978-1-4613-3467-5 AACR2
DOl: 10.1007/978-1-4613-3467-5
Proceedings of a Symposium on Electron Distributions and the
Chemical Bond held at the National Meeting of the American
Chemical Society, March 28-April 2, 1981, in Atlanta, Georgia
© 1982 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1982
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All rights reserved
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PREFACE
This book represents the proceedings of a symposium held at
the Spring 1981 ACS meeting in Atlanta. The symposium brought
together Theoretical Chemists, Solid State Physicists, Experimen
tal Chemists and Crystallographers. One of its major aims was to
increase interaction between these diverse groups which often use
very different languages to describe similar concepts. The devel
opment of a common language, or at least the acquisition of a
multilingual capability, is a necessity if the field is to prosper.
Much depends in this field on the interplay between theory
and experiment. Accordingly this volume begins with two introduc
tory chapters, one theoretical and the other experimental, which
contain much of the background material needed for a through under
standing of the field. The remaining sections describe a wide
variety of applications and illustrate, we believe, the central
role of charge densities in the understanding of chemical bonding.
We are most indebted to the Divisions of Inorganic and Phy
sical Chemistry of the American Chemical Society, which provided
the stimulus for the symposium and gave generous financial support.
We also gratefully acknowledge financial support from the Special
Educational Opportunities Program of the Petroleum Research Fund
administered by the American Chemical Society, which made exten
sive participation by speakers from abroad possible.
We would like to thank all the authors for their cooperation
in preparing the manuscripts, the staff of Plenum Press for the
pleasant collaboration which led to the completion of this volume,
and Mrs. Carol Reinhardt for the skillful typing of several of
the manuscripts.
P.C.
M.B.H.
v
CONTENTS
Section 1
INTRODUCTION
Concepts of Charge Density Analysis: The Theoretical
Approach • . . . • .. .. • .. .. .. .. .. .. .. .. .. .. .... 3
Vedene H. Smith, Jr.
Concepts of Charge Density Analysis: The Experimental
Approach .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .... 61
Philip Coppens
Section 2
THEORETICAL CONSIDERATIONS
Density Functional Theory • • • • • • • • • • • • • • • • • •• 95
Robert G. Parr
Quantum Model of the Coherent Diffraction Experiment:
, Recent Generalizations and Applications • • 101
C.A. Frishberg, M.J. Goldberg, and L.J. Massa
The Influence of Relativity on Molecular Properties: A
Review of the Relativistic Hartree-Fock-Slater
Me thad .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 111
J.G. Snijders and E.J. Baerends
Section 3
EXTENDED SOLIDS: THEORETICAL AND EXPERIMENTAL RESULTS
Theoretical Determination of Electronic Charge Densities
in Covalently Bonded Semiconductors ••••••• 133
C.S. Wang and B.M. Klein
vii
viii CONTENTS
Fermi Gas Approach to X-Ray Scattering by Metallic
Solids . . . . . . . . . . . " " " " " " " " " " " " " " " 153
Pierre Becker
Theoretical and Experimental Charge Distributions in
Euclase and Stishovite • • • • • • • • • • • • • • • • • • 173
J.W. Downs, R.J. Hill, M.D. Newton, J.A. Tossell,
and G.V. Gibbs
Electron Deformation Density in Calcium Beryllide • • • • • • • 191
D.M. Collins and M.C. Mahar
Section 4
MOLECULAR SOLIDS: THEORETICAL RESULTS
Computation and Interpretation of Electron Distributions
in Inorganic Molecules ••••••••••••••••• 205
Michael B. Hall
Electron Deformation Density Distributions in Binuclear
Complexes of Transition Metals: Computation and
Interpretation from ab initio Molecular Orbital
Wavefunctions •••• • • ., • • • • • • • • • • • • • • • 221
Marc Benard
Experimental Versus Theoretical Electron Densities:
Methods and Errors • • • • • • • . • • • • •• ••••• 255
Martin Breitenstein. Helmut Dannohl. Hermann Meyer,
Armin Schweig, and Werner Zittlau
Section 5
MOLECULAR SOLIDS: EXPERIMENTAL RESULTS
Experimental Observation of Tellurium Lone-Pair and
Molybdenum-Molybdenum Triple and Quadruple Bond
Densities """ " " " " " " " " " " " " " " " " " " 285
J.M. Troup, M.W. Extine, and R.F. Ziolo
Deformation Density Determinations (X-X, X-N) of
Organometallic Compounds • • • • • • • • • • • • • • • • • 297
Richard Goddard and Carl Kruger
CONTENTS ix
Analysis of Electronic Structure from Electron Density
Distributions of Transition Metal Complexes • • • 331
Edwin D. Stevens
Neutron Scattering by Paramagnets: Wave Functions of
Antibonding States in Transition Metal Complexes 351
Ronald Mason
Electron Density Distribution in the Bonds of Cumulenes
and Small Ring Compounds • . • • • • • . • • • • 361
Hermann Irngartinger
Section 6
ELECTROSTATIC PROPERTIES
Pseudomolecular Electrostatic Properties from X-Ray
Diffraction Data 383
Grant Moss
Refinement of Charge Density Models Using Constraints
for Electric Field Gradients at Nuclear Positions 413
D. Schwarzenbach and J. Lewis
The Study of Molecular Electron Distribution by X-Ray
Photoelectron Spectroscopy • • • . 431
William L. Jolly and Albert A. Bakke
Electron Density Functions in Organic Chemistry • • . • . 447
Andrew Streitwieser, Jr., David L. Grier, Boris A. B.
Kohler, Erich R. Vorpagel, and George W. Schriver
Index 475
Section 1
INTRODUCTION
CONCEPTS OF CHARGE DENSITY ANALYSIS:
THE THEORETICAL APPROACH
Vedene H. Smith, Jr.
Department of Chemistry
Queen's University
Kingston, Ontario K7L 3N6, Canada
1. INTRODUCTION
Over the past twenty years the realization has become more and
more wide spread that our understanding of chemical bonding and
chemical reactions is based upon the electron density or the one
electron density matrix. This extends beyond the mere interpreta
tion of the phenomena and the provision of a theoretical framework
for the analysis of the data, to the fact that theoretical calcula
tions can provide data about the electronic structure and -structural
properties of systems that are not measured readily.
It is the purpose of the present article to focus on those con
cepts from the theoretical framework and from computational quantum.
chemistry and solid-state physics which are needed for electron
density studies. To do this some equations are unfortunately needed
and many terms need to be defined, hopefully clearly, to bridge the
gap between the experimental scientist, the quantum-chemist and the
solid-state physicist. Phrases such as ab initio and "first prin
ciples" are used to describe calculations* and a veritable alphabet
*The expressions ab initio and "first principles" are used respec-
tively by quantum chemists and solid-state physicists to describe
calculations which are made without using any empirical data save
the nuclear charges and geometries. The use of basis set parameters
and exchange parameters determined on the basis of computational
experience do not cause a calculation to lose its description as
ab initio. Semi-empirical calculations are those where certain
matrix elements of the Fock operator are approximated in terms of
experimental or other data and hence sometimes ab initio means that
all the matrix elements (integrals) are calculated exactly for a
given basis set. The origin of the phrase ab initio is attributed
by Mullikenl to Parr, Craig and Ross.2
3
4 VEDENE H. SMITH, JR.
soup of acronyms and abbreviations are used as parts of the standard
vocabulary. To emphasize the origins of these latter combination
of letters, we shall write them in the following form, the first
time they appear, e.g. L(ocalized) M(olecular) o (rbital) •
2. WAVEFUNCTIONS AND THE HAMILTONIAN OPERATOR
"The wavefunction is the physicist's description of reality,,3
The time independent SChrodinger equation
A
H'¥ = E'¥ (1)
relates the quantized"energy values (eigenvalues) E to the
H
Hamiltonian operator by means of the wavefunction '1'. From wave
functions we can derive theoretical electron densities. In most
cases exact solutions to the Schrodinger equation are unobtainable
due to the complicated nature of the Hamiltonian. As a result we
are forced to rely on approximations to the correct wavefunctions.
These are usually obtained by means of the variational principle
which selects from a set of approximate wavefunctions, the one of
lowest energy for the given problem. Unfortunately, it is not
necessarily the one of this set which gives the best description
of a given physical property, such as the electron density.
The Hamiltonian operator for a system of nuclei (a,S, ... ) with
coordinates X, and the electrons (i,j, .•. ) with coordinates x, is
2 2
HA (x, X) L:L 1/2 - t'l- 1/2 + V (x,X)
N2M a .2m. i ne
"" a 1. 1.
+ V (x) + VA (X), (2)
ee nn
~here Ma is the mass of nucleus a, m. is the mass of electron i,
V = L:.L: (-Z e2/4TI£° )ria is the nuclear-electron attraction term, Z
1..nS e the 1ato.ma1..Ca n umber 0 f nuc 1 eus a, e 1.. S the e 1 ectron1.. c c h arge, and a
r. the distance between electron i and nucleus a. Similarly,
V1.a = E>~ e 2 /4TI£ r .. and VA = L:<E ZQZ e 2 /4TI£ rQ .
ee 1. J 0 1.J nn a ~ fJ a 0 fJa
The Hamiltonian in this form is far too complicated to be
solved exactly, except for the simplest systems. An important
simplification can be made because of the large difference between
the mass (more than three orders of magnitude), and hence velocities,
of electrons and of nuclei. During a single vibration of the nuclei
the electrons repeat their motions many times; hence, it is usually
possible to treat nuclear and electronic motions as virtually in
dependent of each other. The Hamiltonian operator may therefore
be decomposed: