Table Of ContentINORGANIC
COMPLEXES
CHR., KLIXBULL J0RGENSEN
Cyanamid European Research Institute
Cologny, Geneva, Switzerland
1963
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Copyright © 1963 by Academic Press Inc. (London) Ltd.
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Preface
This book attempts to describe the particular features of inorganic
complex chemistry, as it has developed since about 1950. The more
chemical information recorded here is intimately connected with the
theoretical approach applying M.O. theory (also called ligand field theory
in the special case of transition group complexes with a partly filled shell)
for classification of the energy levels and rationalization of th e £a£bsorption
spectra. Hence, reference is frequently made to the writer's Orbitals in
Atoms and Molecules " (O.A.M. in the text), published by Academic Press
in 1962. In comparison with inorganic chemistry before 1950, the
greatest difference nowadays is probably that, without some qualitative
understanding of spectroscopy and quantum chemistry, a chemist may
frequently miss the really interesting part of new developments in his
field. This is by no means reducing chemistry to a sub-division of physics,
and even less making it a defenceless victim of Don Quixote-like pseudo-
mathematical and metachemical theorists; a fundamental knowledge
of natural history is still an essential condition for any further progress
in an understanding of chemical bonding.
I am exceedingly grateful to Dr. Claus E. Sehàffer, Chemistry Depart
ment I of the University of Copenhagen, for extended discussions about
this book. I would like to thank my collaborator, Dr. Hans-Herbert
Schmidtke, for his careful reading of the proofs, and also all my colleagues
for their stimulating discussions and helpful comments.
October 1963 Chr. Klixbull Jorgensen
CHAPTER 1
Introduction
The division line between inorganic and organic chemistry is not as
sharp as it used to be. We shall here frequently consider organic molecules
as ligands and we reflect vaguely the cynical attitude of a transition
group spectroscopist who believes that the purpose of organic chemistry
is to make new ligands and of solid state physics to make transparent
host lattices. The division into carbon and non-carbon chemistry is not
all that clear-cut ; after all, nearly all hydrogen, nitrogen, oxygen and
sulphur chemistry is organic because it involves carbon atoms somewhere
in the molecule. We shall make the separation by only parenthetically
referring to complexes involving metal-carbon bonds; the organo-
metallic complexes are outside our scope. This does not mean, of
course, that several concepts originating in organic chemistry have been
highly useful also for the recent development in the study of inorganic
complexes, and we shall here concentrate on the ideas of inorganic
chromophores and of various aspects of electronegativity.
Historically, ligand field theory started as an electrostatic model
where the ligands bound to a given central atom M were represented, in
their action on the partly filled shell, by an external electrostatic field.
This is essentially the assumption of a monatomic chromophore M per
turbed by the environment. In a certain sense, this is a good approxi
mation in lanthanides with a partly filled 4f-shell and in heavy elements
with a partly filled 5f-shell, though it is believed (O.A.M., Chapter 11)
that the weak perturbations observed are due to very weak covalent
bonds rather than to electrostatic fields. In the three ordinary transition
groups characterized by a partly filled 3d-, 4d- or 5d-shell, it is a much
better approximation to consider the atoms X in the first coordination
sphere as participating in a chromophore, a cluster of atoms, such as
octahedral MX or regular tetrahedral or square-planar MX . Though
6 4
Mulliken, Van V8le84ck and various other authors previously had hinted at
this fact, Orgel was presumably the first, in 1955, to stress the import
ance of molecular orbital (M.O.) formation in such cluste8rs45. Orgel has
written an excellent introduction to ligand field theory. It is worth
mentioning that the approximate invariance of the absorption spectra
and many other properties of a given chromophore MX when occurring
q
in different solvents, in different crystalline solids or glasses does not
ι* ι
2 INORGANIC COMPLEXES
suggest M.O. theory in the strictest sense as the one-electron operator
approximation in the symmetry of the total system. This is the reason
why the energy band description, involving the translational symmetry
of infini6te31 crystals, is not always appropriate for spectroscopic assign
ments. It is hence necessary to 6d12i stinguish between relevant and
irrelevant symmetry components.
The transitions in a chromophore MX can be divided into those pre
6
dominantly localized on M and the electron transfer transitions usually
involving a jump from filled orbitals mainly localized on X into the
higher orbitals on M. Among the more or less localized transitions can be
mentioned the internal transitions in the partly filled shell (3d, 4d, 5d,
4f or 5f according to M), 4f->5d known in Ce(III), Pr(III), Sm(II,)
Eu(II), Tb(III), Tm(II), Yb(II), 5f->6d known in Pa(IV), U(III),
U(IV), Np(III), Np(IV) and Pu(III), 5s->5p occurring in Sn(II) and
Sb(III), 6s->6p in T1(I), Pb(II) and Bi(III), and even, to a certain
extent, 3p->4s in Cl( — I), 4p-^5s in Br( —I) and 5p->6s in I( — I).
Electron transfer bands can occur even if the d-shell is empty, such as
Ti(IV), V(V), Cr(VI), Mn(VII), Mo(VI), Tc(VII), Ru(VIII), W(VI),
Re(VII), Os(VIII), or to the empty 5s- and 6s-orbitals when the d-shell is
completely filled, such as in Sn(IV), Sb(V), Hg(II), Tl(III) and Pb(IV).
The theory of chromophores developed in the empirical description of
organic dyes, and typical examples are R CO, RN0 , RNNR, where
2 2
R represents other atomic groups bound by σ-bonds to the chromophore,
and also the C benzene or C naphthalene ring systems. The individual
6 10
chromophores are perturbed to some extent by the environment, and
they also interact if more than one is present in the system. It is, of
course, a matter of judgment how strongly two chromophores may
interact before they are considered as one, larger chromophore. H7ow59451
ever, it is quite evident that thousands of absorption spectra *
demonstrate that M.O. theory is more appropriate in terms of individual
chromophores than the formal treatment of the whole system, and ligand
field theory is in exactly the same situation.
When we are considering molecular architecture as constructed from
individual chromophores, it may legitimately be asked whether we also
can consider it as a set of valence bonds. This is using M.O. theory applied
together with the principle of micro-symmetry on each bond region
having approximately linear symmetry and hence constituting a part of
a chromophore AB. The present writer is much more reluctant to accept
valence-bond descriptions in general, though there may be cases of
nearly homopolar bonds of bond-order exactly one, i.e. pure σ-bonds,
where this model is not too bad. This special situation is realized in
alkanes C H and is one of the reasons why valence-bond theory
n 2 n2 +
1. INTRODUCTION 3
appeals especially to organic chemists. However, the most common
situation in inorganic compounds is either fractional bond orders or
strongly heteropolar bonds (between elements of greatly differing electro
negativities) or a combination of both (which is quite frequent in octa
hedral complexes). For descriptions of spectroscopic properties, the
valence-bond theory is quite inadequate, and the M.O. theory is the only
appropriate instrument when combined with some form of the principle
of micro-symmetry isolating the individual chromophores. Note
especially that the ligand field theory is a one-electron approximation,
classifying the low-lying energy levels according to well defined con
figurations (O.A.M., Chapter 4) and allowing the partly filled shell to
become delocalized on the atoms in the chromophores MX or MX . The
6 4
electronegativity is a very valuable concept in the description of inorganic
complexes though it certainly has to be further elaborated. One of the
big differences from organic chem95istry is that a definite element has
very different electronegativities according to its oxidation number,
Mn(VII) higher than Mn(IV) which again is higher than Mn(II). Actually,
as long as a chromophore is mononuclear MX (and not certain cases of
q
binuclear X MYMX or X MY MX complexes) and contains only +one
5 5 4 2 4
partly filled shell (i.e. does not contain ligands such as NO", NO, NO or,
with low oxidation number of M, dipyridyl dip, dip", dip ), the oxida
tion number of M is extremely well defined. This must not be confused
with the actual charge distribution in the complex. The derealization of
the partly filled shell and the other orbitals participating in the chemical
bonding produce fractional values of the atomic charges, insofar as it is
possible to define them. There is mu6c1h 4evidence from spectroscopic
studies (e.g. the nephelauxetic effect ) that the actual charge of M in
typical transition group complexes frequently is between +1 and + 2
and of the X atoms between — 1 and 0. It is not completely certain
whet3her the iridium atom has higher charge in IrF than in IrF^" ~ or
6
IrFj but it has completely well defined oxidation numbers Ir(VI),
Ir(IV),and Ir(III).
In complexes outside the transition groups, not containing a partly
filled shell, spectroscopic studies cannot as directly suggest the charge
distribution. This is essentially connected with the fact that in a system
with positive total spin quantum number S, the density of uncompen
sated spin (i.e. the density of the partly filled shell) is, at least hypo-
thetically, an observable, whereas only the total electronic density can
be known in the closed-shell systems. However, some estimates of the
charge distribution can be obtained from X-ray spectra (O.A.M.,
Chapter 12).
A quite interesting rule was derived by Pauling from the original
4 INORGANIC COMPLEXES
thermochemical electronegativities, where it was assumed that the bond-
energy E is a parabolic function of the electronegativity difference
AB
between x and x :
A B
2
EAB = *(ΕΔΑ + ΕΒ) +Β Κ(*Α-*Β) (1.1)
If this function is universally valid, four elements with the order of
electronegativities
ί£Α <C X-Q <C XQ <C Xjy (1.2)
tend to combine in such a way that one of the products exhibits the most
extreme distribution of ^-values :
AC + BD -> AD + BC (1.3)
and, a fortiori,
AB + CD -> AD + BC (1.4)
Equations (1.3) and (1.4) have a few exceptions, but they are relatively
rare. Frequently, of course, reactions obeying eq. ( 1.3) are related to lattice
energies and solubilities besides ordinary electronegativity differences,
such as
NaCl + AgF -> NaF + AgCl (1.5)
and in aqueous solution, the over-all reaction
NaF + HCl -> NaCl + HF (1.6)
is an exception to eq. (1.3).7 97569
However, as Mulliken » pointed out, the electronegativity scale
has much more to do with the average value (A + I)/2 of the electron
affinity A and the ionization energy I of a given atom. The thermo
chemical behaviour expressed in eq. (1.1) seems to be a secondary effect
of something more fundamental. Mulliken refined this concept for use in
simpler molecules containing atoms of the 2p-group (B, C, N, O) by
considering the valence states formed by promotion, say of electrons from
2s-to 2p-orbitals, necessary for the formation of covalent bonds. Another
refinement, which is much more important in the compounds of metallic
elements, is the variation of # as a function of positive 5 c1h4arge residing
M
on M. It has been proposed by Iczkowski and Margrave that χ be con
sidered 6a0s2 a measure of ionization energy per electron, and the present
writer introduced the differential ionization energy I(z) as a function
of the charge ζ of the atom considered. It is, however, very important
to correct this expression (derived from data of atomic spectra) with a
differential quotient of the Madelung energy favouring charge separation
at small internuclear distances. In this way, one obtains quantities I*(z),
1. INTRODUCTION 5
larger for the anionic and smaller for the cationic constituents of 5a 11
complex (O.A.M., Chapter 7). (See also Hinze, Whitehead and Jaffe. )
The interesting question is now whether electronegativities are
equilibrated in a compound MX , in other words whether 1^ is so much
q
increased by the positive charge assumed by the heteropolar bonding
and Ιχ so much decreased by the negative charge acquired by the more
electronegative constituent X that 1^ = Ιχ. There is no doubt that this
is not the case in lanthanides with a strongly shielded, partly filled 4f-
shell, and, on the other hand, there is much to be said at least for the
qualitative validity in compounds with bonds formed by ρ orbitals. Thus,
the inductive effects by substitution of more or less electronegative atoms
(CH F, CH C1, CH ) and variation of the ionization energy of the mole
3 3 4
cules can be understood. The d transition groups seem to form an inter
mediate case, the equilibration of electronegativities not being perfect.
In the latter complexes, a set of observable quantities is the optical
electronegativi6tie1s 600x2 varying strongly with the oxidation number of a
ovt
given atom. * The values of # are derived from the observation
otp
that the electron transfer bands of a given chromophore MX invariably
6
shift to lower wavenumbers in a regular way, when X varies among the
halogens F, Cl, Br, I. These variations permit the fixing of values of x :
ovt
F-3-9, Η 0 3·5, SOr-3-1, Cl~ 3-0,
2
Br" 2-8, CN-2-8, (C H 0) PSi 2-7, I" 2-5 (1.7)
2 5 2
and to define # of M by
otp
E = (30 kK) [* (X)-* (M)] (1.8)
C0II o p t o p t - 1
where E is the wavenumber (in units of lkK = 1000 cm ) of the first
C0TT
strong electron transfer band corrected for (the rather small) effects of
spin-pairing energy on the partly filled shell
D[(S{S+1)>-S(S+1)] (1.9)
The pointed qbrackets denote the average value of 8(8 + 1) of the con
figuration Z considered, and the spin-pairing parameter D is roughly
inversely proportional to the average radius of the par6t7l1y filled shell. The
numerical values of D are 4-6 kK i6n 70the 3d-group, 2-3 kK in the 4d-
and 5d-groups, ~ 6 kK in the 4f- and ~ 4 kK in the 5f-group.
There is no doubt that # is closely related to Mulliken's concept of
otp
electronegativities, but many detailed questions remain to be solved. The
contributions of charge separation effects to eq. (1.8) have been discussed
(O.A.M., Chapter 7) and may be considerable in the case of electron
transfer from one to another chromophore at some distance. In general,
the values of x for central atoms derived from eq. (1.8) increase when
ovt
6 INORGANIC COMPLEXES
57
the internuclear distances decrease (e.g. by high pressure ) and tetra-
hedral chromophores MX of the 3d-group show higher values of x for
4 ovt
M than th6e71 corresponding MX with slightly larger internuclear
6
distances.
It is a common misunderstanding that there exists a biunique relation
between ionicity of a bond and the difference x — x. This is only true
x M
in the extreme cases, homopolar bonds for x ~ x and entirely electro-
x M
valent bonding for very large differences. The existence of a biunique
relation would essentially correspond to a nearly constant non-diagonal
element in the Wolfsberg-Helmholz approximation (O.A.M., Chapter 7)
which is highly improbable because already the non-diagonal matrix
elements for homonuclear diatomic molecules, loosely speaking repre
senting half the bond energy, vary strongly.
A classification of central ions somewhat connected w16ith electro
negativities was proposed by Ahrland, Chatt and Davies. The A-type
is characterized by forming much stronger complexes with ligand atoms
of high x, whereas the B-type prefer strongly polarizable ligand atoms
with lower χ :
A-type B-type
F" > CI" > Br~ > I- I" > Br" > Cl" > F"
OH" > NH > RS" > H 0 RS- > NH > OH" > H 0 (1.10)
3 2 3 2
The A-type central ions have very clear-cut electrovalent bonding,
such as all the alkaline earths, the rare earths, and Th(IV). In the
transition groups, there exist a long series of intermediate cases. Mn(II),
Cr(III) and U(IV) are nearly pure A-type, Fe(III), Co(II), Zn(II),
Ir(III), Co(III), Ni(II), Cu(II) show more and more B-characters, and
the purest cases of B-type known are Pt(II), Au(III), Cu(I), Ag(I),
Hg(II) and, at the extreme, Au(I). It cannot simply be said that B-
behaviour corresponds to high electronegativity and hence strong
tendency to form covalent bonds. The B-class contains at least three
different groups which seem to have different reasons for their allegiance :
1. The family Sn(II), Sb(III), Te(IV), T1(I), Pb(II), Bi(III), where the
corresponding gaseous ions contain two 5s- or 6s-electrons. This family
only shows B-character towards halides and sulphur-containing ligands,
but not towards NH , amines and CN". The reason seems to be that the
3
filled s orbital would become strongly σ-anti-bonding with respect to the
latter type of ligand. Actually, the aqua ions are probably also de
stabilized by this σ-anti-bonding and contribute to strongly increased
formation constants for the halide c8omplexes in aqueous solution.
2. The square-planar, low-spin d -systems Pd(II), Pt(II), Au(III) and
1. INTRODUCTION 7
10
the d -systems with low oxidation number Cu(I), Ag(I), Au(I) and
Hg(II). This family exhibits the highest complex formation constants
known 1of16 h6eavy halides and of sulphur-containing ligands. Yatsi-
mirski and Chatt have offered the explanation of 7r-back-bonding
from the filled d shell to empty orbitals of the halides. It is clear that such
an effect would only occur at low oxidation numbers (like the formation
of carbonyls) and nearly disappear in Zn(II) and In(III). However logical
this explanation, it does not appeal too much to the present writer
because of the remarkable absence of spectroscopic data suggesting low-
lying empty orbitals in these halide complexes. (Similar arguments can
be brought against extensive 77-back-bonding in cyanide complexes of
metals in not too low oxidation numbers.) An explanation involving
polarizabilities and the continuum orbitals above the ionization limit, as
originally suggested by Fajans, mig8ht7 9be more plausible. The criticisms
recently made by Poë and Vaidya of the mere concept of A- and B-
types cannot solve this problem; it is an experimental fact that the
relative tendencies expressed in eq. (1.10) subsist.
3. It is frequently felt that all elements in higher oxidation numbers
become more B-like, quite in contrast to the special family 2. This is a
question open to considerably more investigation. It is true that all
halide complexes tend to become much stronger in a series such as
K(I), Ca(II), Sc(III), Ti(IV), V(V), but it is doubtful whether this series
discriminates against fluoride, as demanded by evolving Β-tendencies.
For a given element, say Cr(III) and Cr(VI), it is not _all that clear
whether the difference between the stabilities +of +Cr0 F and Cr+Og+Cl" is
3
so much smaller than that between Cr(H 0) F and Cr(H 0) Cl . In the
2 5 2 5
case of high oxidation numbers, such as Mn(VII) or Os(VIII), it is usually
only possible to prepare the fluorides and/or oxides, and we cannot know
how comparatively more stable the bromides would be if they did not
decompose to Br and compounds with lower oxidation numbers. There
2
are characteristic differences between Ca(II), Sc(III), Ti(IV) on one side
and Zn(II), Ga(III), Ge(IV) on the other; or much more pronounced
La(III) and Lu(III) compared to Ir(III) and Tl(III), which tend to
suggest that, under equal circumstances, the smaller ionic radii corre
spond to the stronger B-tendency (quite contrary to Poë and Vaidya's
arguments). This does not explain the behaviour of family 2 but,
nevertheless, rationalizes some of the effects of the "iron group con
traction" and "lanthanide contraction" on the chemistry of the
elements just before and just after the transition groups.
Readers may very often find frustrating those text-books giving
a very lengthy description of the chemistry of the non-metallic elements
followed by short notes on the metals. Nevertheless, it was decided to
