Table Of ContentSTRUCTURE
AND
BONDING
1
Volume
C. K. Jergensen Recent Progress in Ligand Field Theory
D. F. Shriver The Ambident Nature of Cyanide
J. B. Neilands Naturally Occuring Non-porphyrin Iron
Compounds
B. B. Buchanan The Chemistry and Function of Ferredoxin
R. E. Feeney/St K. Komatsu The Transferrins
S1. Ahrland Factors Contributing to (b)-behaviour in
Acceptors
R. F. Hudson Displacement Reactions and the Concept
of Soft and Hard Acids and Bases
C. K. Jergensen Electric Polarizability, Innocent Ligands
and Spectroscopic Oxidation States
R.J. P. Williams/J. D. Hale The Classification of Acceptors and
Donors in Inorganic Reactions
Springer-Verlag Berlin Heidelberg NewYork 1966
STRUCTURE AND BONDING is intended to the publication of papers dealing with
problems in all fields of modern inorganic chemistry, chemical physics and biochemistry,
where the general subject are problems ofchemical structureand bonding forces.
STRUCTURE AND BONDING is issued at indefinite intervals, according to the material
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textshouldbeclearand concise as possible, the manuscript written on one side ofthe paper
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Manuscripts will be accepted by the editors:
Dr. C.K.J"Kemen, Cyanamid European Research Institute,
91, Route de la Capite, 1223 Cologny (Geneva)/Switzerland
ProfessorJB.NeiIands, University ofCalifornia, Biochemistry Department,
Berkeley, California/USA
ProfessorR5.Nyholm, University College London, Department ofChemistry,
Gower Street, London WC 1/Great Britain
Dr. DirkReinen, Anorganisch-Chemisches Institut der Universitiit Bonn,
53 Bonn, Meckenheimer Allee 168/Germany
Professor RJP. Wtlliams, Wadham College, Inorganic Chemistry Laboratory,
Oxford/Great Britain
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CONTENTS VOLUME1
Preface 1
C.K.Jergensen Recent Progress in Ligand Field Theory 3
D.F.Shriver The Ambident Natu.re ofCyanide 32
JB.Neilands Naturally Occuring Non-porphyrin Iron Compounds 59
B.B.Buchanan The Chemistry and Function ofFerredoxin 109
REFeeney/5tK.KDmatru The Transferrins 149
5tAhrland Factors Contributing to (b)-behaviourin Acceptors 207
RF.Hutbm Displacement Reactions and the Concept ofSoft and Hard
Acids and Bases 221
C.K.J"Kemen Electric Polarizability, Innocent Ligands and Spectroscopic
Oxidation States 234
RJP. Wtlliams/JD.Hale The Classification ofAcceptors and Donors in Inorganic
Reactions 249
Allrights,especiallythatoftranslationintoforeign languages,reserved.Itisalso forbidden
to reproduce this book, either whole or in part, by photomechanical means (photostat,
microfilm and/or microcard) or by other procedure without written permission from
Springer-Verlag.©bySpringer-VerlagBerlinHeidelberg1966.Library of Congress Catalog
Card Number 67-11280. Printed in Germany.
Title-No. 4525
Preface
During the past few years we have seen the starting of many new scientific
journals and the emergence of perhaps an even greater number of periodic
review volumes which set out to provide a "Survey of Recent Progress
in..." various fields. It was therefore with some hesitation that we ac-
cepted the invitation to become coeditors of this new series entitled,
"Structure and Bonding".
However, after some reflection we believe that a valuable service is
performed by bringing together up-to-date authoritative reviews from
the different fields of modem inorganic chemistry, chemical physics and
biochemistry, where the general subject of chemical bonding involves
(usually) a metal and a small number of associated atoms. These ar-
rangements are of importance for symmetry considerations by crystal-
lographers, for the application of group theory and molecular orbital
theory to chromophores and because of their widespread occurrence in
polyatomic molecules, in complex ions in solution, in vitreous materials,
in minerals and, not least, in biological materials and organisms. We are
specially interested in the role of the "complex metal - ligand" moiety
and are purposely avoiding the more classical organic chemistry and
even organo-metallic chemistry - for which many review journals are
already available - and wish to direct attention towards borderline
subjects.
We are convinced that these borderline areas receive less attention than
they justify; academic studies tend too often to be compartmentalized
whereas technological interest too often lacks sufficient fundamental
understanding. We hope that this series may help to bridge the gaps
between some of these different fields and perhaps provide in the process
some stimulation and scientific profit to tile reader.
.C K. Jcrgensen
J. B. Neilands
R. S. Nyholm
D. Reinen
R. J. P. Williams
Recent Progress in Ligand Field Theory*
.rD .C .K Jorgensen
Cyanamid European Research Institute, Cologny (Geneva), Switzerland
Table of Contents
I. Ligand Field Theory and Interpretation of Spectra .................. 3
.1 Octahedral d -a and de-systems and tctrahedral d~-systems .......... 4
2. Octahcdral and tctrahedral high-spin dS-systcms .................. 8
3. Octahedral low-spin d6-systems ................................. l0
4. Generalized results and evidence necessitating the extension of the
original electrostatic model .................................... 11
II. Extension of the Ligand Field Theory by Consideration of Molecular
Orbitals ....................................................... 13
.1 Central-field covalency ........................................ 41
2. Symmetry-restricted covalency ................................. 15
3. Nephelauxetic effect in L.C.A.O.M.O. approximation ............ 16
4. Relativistic effect (spin-orbit-coupling) in L. C. A. O,M. O.
approximation ................................................ 17
5. Electron transfer spectra and M.O. theory ....................... 19
III. Conclusions ................................................... 22
IV. Note on Recent Progress: The Angular Overlap Model and the Influence
of Madelung Potentials on Wolfsberg-Helmholz Calculations ............ 26
References .......................................................... 30
I. Ligand Field Theory and Interpretation of Spectra
The great progress in ligand field theory in the last decade has only been
concerned with the aspects of a semiempirical theory built on induction
from experiments. The effort concentrated on a priori calculations has
been nearly useless. This is a quite general phenomenon in theoretical
chemistry; at the same time, a priori calculations for more than some
four electrons are nearly impossible, and a classification of energy levels
aCcording to suitably chosen one-electron model configurations is very
SUccessful both in atoms and molecules. This experience was gained in
atomic spectroscopy some 30 years ago, and has now become clarified in
the case of transition group complexes, the subject of ligand field theory.
* The origin of this contribution were notes distributed at lectures given at the
~tlmmer School on Ligand Field Theory (Director: H. Hartmann) in Konstanz
fl~Bvodensee, Septembcr 1962. However, the text was considerably extended,
y according to the advice of Dr. K. H. Hansen, and is made up to date to 1966.
t* 3
C.K. Jorgensen
.1 Octahedral d -3 and dS-systems and tetrahedral dT-systems
The choice of this example may seem unnecessarily complicated to start
with. However, we have the choice between tile mathematical complica-
tions of calculating interelectronic repulsion parameters and the physical
complications that for instance d -1 and rig-systems such as Ti(H~O)e ~+
and Cu(H~O)e ++ are .detrotsid-relleT-nhaJ Whether one has a static
relleT-nhaJ effect where the stereochemical configuration of the ground-
state is distorted, or one has a dynamic Jahn-Teller effect where the
potential surfaces of the excited and groundstates are covered by un-
symmetric vibrations, is a subtle question we do not need to treat here.
However, it is an empirical fact that these elbatsnu-relleT-nhaJ molecules
do not have the simple spectra expected from higher symmetries such as
the octahedral Oh.
On the other hand, one understands only ligand field theory very
incompletely if one concentrates all attention on the effective one-electron
energies alone. The two-electron operator producing the parameters of
interelectronic repulsion is an intrinsic part of the description of transition
group compounds, both because the energy levels have positive and
varying values of the total spin quantum number S and because the
average radius <r) of the partly filled shell is relatively small, making the
parameters proportional to <r -1) important.
We compare our observed spectra with onaguS-ebanaT diagrams,
such as Fig. 1 for octahedral d 3 and tetrahedral d 7 and Fig. 2 for octa-
hedral d 8 (and tetrahedral d2). The variable in this diagram is not an
energy but the ratio A/B between the subshell energy difference A (called
(El- E2) or 10 Dq by certain authors) and the Racah parameter of in-
terelectronic repulsion B. Hence, a higher value of A/B does not neces-
sarily mean a blue-shift of the absorption spectrum; if B decreases, it
may sometimes correspond to a red-shift.
Tables 1 and 2 gives the numerical data for a series of vanadium (II),
chromium (III), manganese (IV), molybdenum (III), rhenium (IV),
iridium (VI), cobalt (II), and nickel (II) complexes. The first spin-allowed
absorption band, caused by an internal transition in the partly filled shell,
has the wavenumber equal to A. If spin-forbidden transitions are super-
posed on this band, a certain distortion from the usual shape of naissuaG
error curve can be observed, and one takes the centre of gravity of
intensity as the corrected wavenumber el. One has to be careful not to
confuse electron transfer or other strong bands with the internal transi-
tions discussed here. Obviously, one has also to watch for absorption due
to other coloured species, produced e. g. by oxidation or hydrolysis of the
solutions. In the case of certain octahedral nickel (II), and nearly all
tetrahedral cobalt (II) complexes, the first band has not actually been
4
Recent Progress in Ligand Field Theory
observed, and A and B are derived from the two next bands as and as.
Hence, one has to be careful not to neglect possible bands in the infra-red.
Racah's parameter B is determined from the implicit equations
as -- ~z = 12B -- x % -- 2~ 1 = 3B + x (1)
where x = 36B~/(.1 -9B + x). If all three absorption bands are ob-
served, the simple relation obtains
as + 3~ = 3~z + ISB = 3A + ISB (2)
/
~,T3b
\\ _ . - - - - ' -." "g 2 T ~ t ,
3 F ~ ~ " g ~ 1 T 3 t C
T + ' ~ ) , H N ( t N ~ X,
. ~ .gEI.o\
.,.~....~,o
\
I+++6),HN(rC
Fig. 1 Fig. 2
Fig. 1. onaguS-ebanaT diagram for octahedral d3-complexes and tetrahedral d -~
complexes. (In the latter case, the parity quantum number g = "gerade" is removed
from the symmetry types of the energy levels.) The independent variable is not an
energy but the pure number A/B, the ratio between the sub-shell energy difference
A (actually -- A for tetrahedral d )7 and s'hacaR parameter of interelectronic re-
pulsion B. Each individual complex can be characterized by a vertical line crossing
the energy levels, the arrows indicating a few actual examples. The levels with
lower total spin S than the groundstate are punctuated; the corresponding transi-
tions from the groundstate are spin-forbidden.
Fig. 2. onaguS-ebanaT diagram for octahedral dS-complexes and tetrahedral d -2
complexes. Notation as in Fig. .1
5
C. K. Jorgensen
0 0 0 0 ~ O ~ O O ~ O O 0 0 O O 0 0
~ ~ ~ ~ ~ i i i I ~ ~
d d d d d o d d d o d d d ~ d d d o d d d ~ d d
d d d d d d d d d d d d d d d d d d d d d d d d
~ ~ ~ d ~ d d d
I d d d ~ d
1 4 ~
O ~ ~ ~ ~ ~ m > b ~ ~
~
~s 7
~ ~ ~ ~ ~ ~ O~
Recent Progress in Ligand Field Theory
i
~ ~ 1 I
~ ~ ~ ~ ~ I I ~ I
~ ~ I ~ I
~ ~-
~
~ u u ~ o o o ~
.~ ~
-t-
-I-
~+
~ ,, o ~.~,~
C.K. Jorgensen
The nephelauxetic ratio ~3 is then defined*
~ = suoes,agB/xelpmocB )3(
The relativistic effects of intermediate coupling are important in the case
of superposition of spin-forbidden and spin-allowed transitions (chromium
(III) in the cases when A ~ 21B, most nickel (II), 3a of tetrahedral cobalt
(II)) and in the cases of the 5d group (Re (IV), IrF6 etc.).
The spin-forbidden transitions in d 3 complexes determine another
nephelauxetic ratio .55~ It is here most appropriate to express the lowest
level of a given symmetry type in Tanabe and Sugano's determinants by
second-order perturbation theory assuming C ~ 4B, giving
~fl (a2Eg): 21B -- 90B2/A
~f2 (a2Tlg) : 21B -- 24B2/A
gr, :)gzT~a( B53 - A/2B671 )4(
though, as Dr. W. Schneider from ETH, Ziirich pointed out, special
circumstances make the correction coefficient 90 from the first line nearly
twice its actual size in usual Cr(III) complexes. The ratio between B
obtained from eq. )4( and the value in the gaseous ion is called .55~ As
we shall see below, there are good reasons to expect that this ratio is
larger than ,533 though below ,1 and indeed, Table 1 confirms this expec-
tation. However, Schneider's phenomenon probably decreases the values
of 553 some 0.05 unit.
The spin-forbidden transitions in octahedral d s complexes are less
influenced by sub-shell configuration intermixing and are for instance:
lf~ )gEla( : B61 -- 6B2/A
ora )g2Tla( : A + B61 -- A/2B21 )5(
The nephelauxetic ratio for the B-value obtained from eq. )5( is called
8a~ of reasons to be discussed below. Terms with the same S and symme-
try type are called a, b, c ....
2. Octahedral and tetrahedral high-spin dS-systems
The nephelauxetic effect is conspicuous in the transitions to the very
nearly coinciding excited states 4Alg and a4Eg belonging to exactly the
same sub-shell configuration teg 3 e, * as the groundstate eAlg. The nephel-
auxetic ratio 5s~ is the ratio between this wavenumber and the energy
difference G4( above eS) in the corresponding gaseous ion, 26.85 kK in
* Though the Mulliken-Griffith nomenclature is used here, the sub-scripts 3 and
5 on various quantities are reminescences of Bethe's original notation 3Y and sY for
the two sub-shells.
8
Recent Progress in Ligand Field Theory
u~
{
I ~ ~ ~ ~ ~
~k
++
z ..-
r
L I ~ ~ " ~ ~ I ~'~0 ~
9
