Progress in Inorganic Chemistry, Volume 10

523 Pages·1968·11.796 MB·English

PROGRESS IN
INORGANIC CHEMISTRY
Volume 10
Advisory Board
L. BREWER
UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA
E. 0. BRIMM
LINDE AIR PRODUCTS COMPANY, TONAWANDA, NEW YORK
ANTON B. BURG
UNIVERSITY OF SOUTHERN CALIFORNIA, LOS ANGELES, CALIFORNIA
J. F. GALL
PENNSYLVANIA SALT MANUFACTURING COMPANY, PHILADELPHIA,
PENNSYLVANIA
H. B. JONASSEN
TULANE UNIVERSITY, NEW ORLEANS, LOUISIANA
J. KLEINBERG
UNIVERSITY OF KANSAS, LAWRENCE, KANSAS
RONALD S. NYHOLM
UNIVERSITY COLLEGE, LONDON, ENGLAND
P. L. ROBINSON
HARWELL, ENGLAND
E. G. ROCHOW
HARVARD UNIVERSITY, CAMBRIDGE, MASSACHUSETTS
L. G. SILLEN
ROYAL INSTITUTE OF TECHNOLOGY, STOCKHOLM, SWEDEN
E. J. W. VERWEY
PHILLIPS RESEARCH LABORATORIES, EINDHOVEN, HOLLAND
C. W. WAGNER
MAX PLANCK INSTITUTE, GOTTINGEN, GERMANY
G. WILKINSON
IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY, LONDON, ENGLAND
PR- 0 G R ESS I N
IN 0 RGANI C C H E M I S T R Y
EDITED BY
F. ALBERT COTTON
DEPARTMENT OF CHEMISTRY,
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY, CAMBRIDGE,
MASSACHUSETTS
VOLUME 10
INTERSCIENCE P U B L I S H E R S 1968
a division of JOHN WILEY & SONS New York * London . Sydney * Toronto
. Copyright 8 1968 by John Wiley & Sons, Inc.
All rights reserved. No part of this book may be reproduced by any means, nor trans-
mitted, nor translated into a machine language without the written permission of the
publisher.
Library of Congress Catalog Card Number 59-13035
SBN 470 17669
Printed in The United States of America
Contents
Covalence and the Orbital Reduction Factor, k, in Magnetochemistry
BY M. GERLOCAHN D J. R. MILLERD, epartment of Chemistry, The
University of Manchester, Manchester, England . . 1
Metal 172-Dithiolenea nd Related Complexes
BY J. A. MCCLEVERTYU,n iversity of Shefield, Shefield, England 49
Complexes of Simple Carboxylic Acids
BY C. OLDHAM,C hemistry Department, University of Lancaster,
.
England 223
Absorption Spectra of Crystals Containing Transition Metal Ions
BY N. S. HUSHA ND R. J. M. HOBBS,D epartment of Inorganic
Chemistry, University of Bristol, Bristol, England . 259
Author Index . 487
.
Subject Index 507
Cumulative Index, Volumes 1-10 . . 521
Progress in Inorganic Chemistry; Volume 10
Edited by F. Albert Cotton
Copyright © 1968 by John Wiley & Sons, Inc.
Covalence and the Orbital Reduction Factor.
k. Magnetochemistry
in
BY M . GERLOCH*A ND J . R . MILLER?
Department of Chemistry. The University of Manchester.
Manchester. England
.
I Introduction . . . . . . . . . . . . . . . . . . 2
I1. Definitions . . . . . . . . . . . . . . . . . . 8
A . Wavefunctions . . . . . . . . . . . . . . . . 8
B . Operators . . . . . . . . . . . . . . . . . 9
111 . k in Octahedral Complexes . . . . . . . . . . . . . 10
.
A Pure Metal Orbitals . . . . . . . . . . . . . . 10
B . Molecular Orbitals . . . . . . . . . . . . . . . 12
C . The Matrix Element <zx\L,\ yz> . . . . . . . . . . . 13
D . Properties of k in Octahedral Complexes . . . . . . . . 15
IV . k in Tetrahedral Complexes . . . . . . . . . . . . . 18
A . Ligand Orbital Mixing . . . . . . . . . . . . . 18
B . Ligand Field Potentials in the Octahedron . . . . . . . . 20
C. Ligand Field Potential in the Tetrahedron . . . . . . . . 22
D . The Crystal Field Wavefunctions in the Tetrahedron . . . . . 24
E . Matrix Elements of L, for d-p Hybrid Orbitals . . . . . . 27
.
F A Pictorial View of the Orbital Reduction by Configurational Mixing 28
G . Isomorphism of the d,- and p-Orbital Sets . . . . . . . . 29
H . Quantitative Aspects of the Orbital Reduction for d-p Hybrids . . 31
I . A More Complete Model for the Tetrahedron . . . . . . . 32
V. Conclusion . . . . . . . . . . . . . . . . . 33
A . Spin-Orbit Coupling . . . . . . . . . . . . . . 36
VI. Appendix I . The Secular Determinant . . . . . . . . . . 38
VII . Appendix I1 . Matrix Elements of the Type (ligandl L, Iligand’) in Oh . 40
A . The Function i(t3/&)(pZ) for the Second Principal Quantum Shell . 41
VIII . Appendix 111 . Matrix Elements of the Type (ligandl Jligand) in Td . 44
Lz
References . . . . . . . . . . . . . . . . . . . . 46
* Present address: Department of Chemistry. University College. London .
t Present address: Department of Chemistry. University of Essex. Colchester .
1
2 M. GERLOCH AND J. R. MILLER
INTRODUCTION
The successful application of quantum mechanics to atomic spectros-
copy in the 1920’s led inevitably to studies directed to the understanding
of similar phenomena in molecules and crystal lattices. It was Bethe (1)
who, in 1929, wrote a now classic paper in which the framework of crystal
field theory was set out. In this approach, the energy of an ion is taken to
be modified by a potential field set up by its neighbors that are assumed to
be described by point charges, or simple dipoles. For idealized systems
involving high symmetry, Bethe made full use of group theory to establish
the nature of crystal field terms arising from a given configuration. His
work was put to good use by Van Vleck (2) in the field of magnetism. Van
Vleck and also Penney and Schlapp (3) developed the theory of the mag-
netic susceptibilities of transition metal ions including some particularly
fruitful studies of the lanthanides.
Meanwhile Pauling (4), who had been studying the bonding in tran-
sition metal complexes, had established his “magnetic criterion for bond
type” from which a measurement of the magnetic moment of a complex
might lead to a knowledge of the stereochemistry of the ions in it. A sub-
sequent aim of magnetochemistry was to establish something of the
character of bonds in complexes. About the same time as the appearance
of Pauling’s magnetic criterion, Van Vleck (5) showed how the change
from a spin-free to a spin-paired situation in iron(II1) complexes could
be achieved by a smooth increase in the strength of the crystal field set up
by the coordinating groups. He did not say, as was asserted by Pauling,
that FC!(CN)~~io-n s involved more ionic bonds than FeFC3-,b ut merely
that the low spin of the cyanide could be explained on the basis of a higher
crystal field strength. Detailed calculations of the magnetic anisotropy of
potassium ferricyanide by Howard (6) in 1934 based on Van Vleck’s
model were in fair, and now famous agreement with experiment.
The success of the crystal field approach, particularly in the case of
the lanthanide ions, prompted many more studies of the magnetic sus-
ceptibilities and anisotropies of complex ions throughout the transition
series. It was apparent that the descriptions of the lanthanide energy levels
as those of the free ion perturbed only by spin-orbit coupling effects, or
of the first-row transition elements perturbed only by a cubic field potential,
were essentially correct. But the finer details of magnetic susceptibilities
could not be accounted for so simply. The inclusion of spin-orbit coupling
effects into strong-field configurations throughout the transition block by
Kotani (7) made a considerable advance toward explaining the often
large differences between magnetic moments of the Ist-, 2nd-, and 3rd-row
COVALENCE AND ORBITAL REDUCTION FACTOR, k 3
elements for a given configuration and their behavior with temperature.
Despite these improvements in magnetochemical theory, there remained
significant and sometimes large deviations from experiment, most par-
ticularly in complexes having a formal orbital triplet ground state. Such
ions make an important orbital contribution to the total moment by virtue
of their orbital degeneracy-a degeneracy which, in the first row at least,
is lifted only a little by the effects of spin-orbit coupling. Experimentally,
these ions usually possess somewhat lower moments than expected, sug-
gesting some additional quenching of the orbital contribution. A mecha-
nism is not hard to find, for it was originally invoked by Howard in his
calculations on potassium ferricyanide : namely, that distortions from
perfect cubic symmetry will reduce the orbital degeneracy of some of
the electronic states and cause the magnetic moments to tend to spin-only
values.
Figgis (8) has examined in detail the magnetic properties of ions with
formal cubic field orbital triplet ground states, perturbed simultaneously
by the effects of an axial ligand field distortion and spin-orbit coupling.
The energy level scheme involved in such calculations is summarized in
Figure 1. The splitting A of the cubic triplet state by the low-symmetry field
components was not calculated from a knowledge, often unavailable
anyway, of the geometric molecular distortion, although its idealized
relationship with the cubic field parameters Dq has been discussed recently
(9): rather, it was taken as an independent parameter of the system to be
x
cubic spin-orbit spin-orbit axial cubic
+
field coupling axial field field field
Fig. 1. Perturbation of a 2Tz,,te,r m by spin-orbit coupling and an axial crystal field.
Numbers in parentheses are total degeneracies.
4 M. GERLOCH AND J. R. MILLER
adjusted by comparison with experiment. The same is true of A, the spin-
orbit coupling coefficient, which cannot be assumed to have the same value
as in the free ion. It proves convenient algebraically to express these
variables as v (equal to A/A) and A instead of A and A. The magnetic
moment computation begins with a calculation of the wave functions and
energy levels which result from the combined effects of the axial crystal
field and spin-orbit coupling acting on the pure metal d wavefunctions of
the cubic field triplet. The energy separations between the three Kramers
doublets which result lie commonly in the range 50-5000 cm The per-
~ l.
turbations induced by the magnetic field-the Zeeman effect-are of the
order of 1 cm-l. Accordingly, the Zeeman perturbation calculation is
performed sequentially rather than simultaneously; this is a time-saving
procedure which involves trivial loss of accuracy. The final calculation (10)
of the magnetic susceptibility or moment at any temperature involves a
Boltzmann distribution of molecules among the Zeeman levels as expressed
in the well-known Van Vleck equation. Figgis has performed these calcula-
tions for the cubic field terms 2T2,3 T1,4 T1,a nd 5T2.F or the doublet and
quintet terms, the moments may be expressed in terms of the two param-
eters 21 and X and are usually plotted as a family of curves, one for each
value of v, of magnetic moment versus kT/X (/is the BoItzmann factor and
T is the temperature). Some results for the 2T2t erm, of octahedral tita-
nium(II1) or tetrahedral copper(I1) ions, for example, are shown in Figure
2a. These calculations clearly show the sensitivity of the effective moment
to the degree of distortion and how the removal of orbital degeneracy with
increasing u leads to moments closer to the spin-only value.
This theoretical approach allowed much closer agreement between
calculated and observed moments than before, especially for complexes of
the first-row transition metals where ligand field perturbations are most
significant. Improvement was less marked, and less necessary, in the third
row where spin-orbit coupling is relatively much more important. Up to
this point, magnetochemistry involved no more than a continuous refine-
ment of the crystal field model as first put forward by Bethe: up to this
point, no explicit account had been taken of the undoubted covalence of
the bonds in these complexes. Some implicit recognition of the molecular
nature of the bonds was inherent in the parameterization of the quantities
Dq, A, and A, of course, but in essence the theory was still a crystal field
one and it had worked very well.
The inadequacy of the crystal field approach was first demonstrated
by Owen (11) and Stevens (12) in 1954. Their work grew out of the diffi-
culty of explaining the low ESR g values for NiC164- and IrC1,'- ions. In
these highly symmetrical ions, the mechanism for quenching some of the
COVALENCE AND ORBITAL REDUCTION FACTOR, k 5
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