Table Of ContentABSORPTION SPECTRA
AND CHEMICAL BONDING
IN COMPLEXES
C. K. Jorgensen
Cyanamid European Research Institute
Cologny, Geneva, Switzerland
PERGAMON PRESS
OXFORD · LONDON · NEW YORK · PARIS
PERGAMON PRESS LTD.
Headington Hill Hall, Oxford
4 & 5 Fitzroy Square, London W.l
PERGAMON PRESS INC.
122 East 55th Street, New York 22, Ν Y.
GAUTHIER-VILLARS ED.
55 Quai des Grands-Augustins, Paris, 6
PERGAMON PRESS G.m.b.H.
Kaiserstrasse 75, Frankfurt am Main
Copyright
©
1962
PERGAMON PRESS LTD.
First published 1962
Second (revised) impression 1964
Library of Congress Card Number 61-12437
Se t in Time sNew Roma n10 on 12p atn. dPrint edin Grea tBritain
PAGE BROS. (NORWICH) LTD.
PREFACE
OUR knowledge of the electron clouds of gaseous atoms and ions is
based on the energy levels, studied in atomic spectroscopy. It has not
been generally realized among chemists that the study of energy
levels, i.e. the absorption spectra, is equally fruitful in helping our
understanding of the chemical bonding, not only in transition
group complexes, but in every type of molecule. Actually, these
spectra have yielded very much useful information in the last few
years, and the development has only been delayed because physicists
are generally more interested in nuclei than in bound electrons, and
because chemists think that spectroscopy is a matter for physicists
and group theorists.
The main purpose of this book is to summarize the results of this
recent development and attempts to win over some of the mental
inertia which has caused most chemists to think of chemical bonds
in terms of a valency-bond and hybridization description. Actually,
this approximation does not agree at all with the knowledge gained
from absorption spectra, while molecular orbital theory is shown to
be an adequate aid to the classification of energy levels. It will
probably be argued that the treatment presented is too complicated
and too mathematical. The present writer originally intended to
gather the detailed arguments into separate appendixes. However,
he soon realized that nearly all the text would have to be put into
these appendixes, which would not be a great advantage. Hence, the
reader should not feel himself obliged to read the chapters con-
secutively; less difficulties would probably arise by reading different
chapters several times.
I am very grateful for many valuable discussions with Dr. Claus
Ε. Schäifer, Kemisk Laboratorium A, Danmarks tekniske Hojskole,
Copenhagen, to my other colleagues there and to the Director,
Professor Jannik Bjerrum. Further, I am much indebted for most
illuminating visits to Dr. Per-Olov Löwdin, Kvantkemiska Gruppen,
Uppsala, Dr. Leslie E. Orgel, Department of Theoretical Chemistry,
Cambridge, and Professor Marcel Delépine, Collège de France,
Paris.
vii
LIST OF SYMBOLS
(Page numbers indicate the positions where the symbol is first defined.)
A angular function, p. 25
A proportionality constant for interelectronic repulsion, p. 154 (eqn. 146)
A activation energy, p. 260 (eqn. 222)
A Racah parameter, p. 40 (eqn. 35)
A homogeneous polynomium in x, y, z, p. 25 (eqn. 3)
P
a coefficient to Δ, p. 74
a number of y-electrons
5
a Bohr radius, p. 22
0
a activity, p. 248
n
Β Racah parameter, p. 40 (eqn. 35)
b coefficient to B, p. 74
b number of y-electrons
3
C Racah parameter, p. 40 (eqn. 35)
CM and CL total concentrations of M and L, p. 252 (eqn. 202)
Coov linear symmetry without centre of inversion, p. 48
c coefficient to C, p. 74
c velocity of light in vacuo
c molar concentration, p. 89 (eqn. 98)
D term with L = 2
D optical density, p. 89 (eqn. 98)
D proportionality constant for spin-pairing energy, p. 154 (eqn. 146)
D dielectric constant, p. 267
D orthorhombic symmetry, p. 68
2
D h tetragonal symmetry, p. 68
4
Dooh linear symmetry with centre of inversion, p. 51
d orbital with / = 2
Ε energy
3
E Racah parameter, p. 40 (eqn. 36)
(E — Ej) expression equivalent to Δ
x
E polynomium, corresponding to secular determinant, p. 37
p
e electric charge of proton
e degeneracy number, pp. 24, 30
eV electron volt, p. 85
F term with L = 3
2 4 k
F , F ,. . ., F Slater-Condon-Shortley parameters of interelectronic repulsion,
p. 39 (eqn. 32)
f orbital with / = 3
f spectrochemical function of ligands, p. 113 (eqn. 123)
fn activity coefficient, p. 248
G term with L = 4
G free energy, p. 246
AG change of free energy at a reaction
G exchange integral according to Slater, p. 185
t
g two-electron operator, p. 38 (eqn. 27)
g spectrochemical function of central ion, p. 113 (eqn. 123)
ix
LIST OF SYMBOLS
g gerade = even, as subscript, p. 59
g gyromagnetic factor, p. 106
H term with L = 5
H enthalpy (heat content), p. 246
AH change of enthalpy at a reaction
h Planck's constant
h nephelauxetic function of ligands, p. 138 (eqn. 137)
H change of enthalpy of hydrogen ion formation (eqn. 186, p. 237)
h
I term with L = 6
I ionization energy
/ and I light intensities, p. 89 (eqn. 98)
0
J total angular momentum quantum number of system, p. 30
J(aa) or J(ab) Coulomb integral, p. 39 (eqn. 31)
j total angular momentum quantum number of orbital
-1
Κ kayser = cm , wave number unit
°K degree Kelvin, unit for absolute temperature
Κ absorption spectrum, caused by X-ray excitation of ls-electrons, p. 189
K(ab) exchange integral, p. 39 (eqn. 31)
Κ η stepwise formation constant, p. 245 (eqn. 189)
k various constants
k Boltzmann constant (when multiplied by T)
k nephelauxetic function of central ion, p. 138 (eqn. 137)
1
kK kilokayser = 1000 cm"
L ligand in general formulae, p. 245
L orbital angular momentum quantum number of system, p. 31
1 layer thickness, p. 89 (eqn. 98)
/ orbital angular momentum quantum number of orbital, p. 22 (eqn. 1)
M central ion in general formulae, p. 245
M molar concentration, before a chemical formula
Ms magnetic quantum number of system, p. 70
m electronic mass
m effective mass, p. 95 (eqn. 106)
m, magnetic quantum number of electron, p. 38
Ν maximum co-ordination number, p. 245
N characteristic co-ordination number, p. 245
c
η principal quantum number of orbital, p. 22
η formation number, p. 253 (eqn. 205)
Oh cubic-octahedral symmetry, p. 51
Ρ term with L = 1
Ρ perturbation, p. 32
Ρ pressure
Ρ oscillator strength, p. 92 (eqn. 102)
ρ orbital with 1=1
pK acid strength constant p. 247 (eqn. 199)
q various numbers, e.g. of electrons in a shell
R radial function, p. 25
R gas constant (when multiplied by T)
r distance from nucleus
r n ionic radius
i0
TL internuclear ligand-central ion distance, p. 55
ry Rydberg constant, p. 22
S term with L = 0
S entropy, p. 246
χ
LIST OF SYMBOLS
Δ5 change of entropy at a reaction
Sab overlap integral between a and b, pp. 60, 64
S spin quantum number of a system, p. 30
AS change of spin
s orbital with / = 0
Τ absolute temperature
Td tetrahedral symmetry, p. 128
U potential, p. 98 (eqn. 109)
U electrochemical potential, p. 246 (eqn. 197)
U standard oxidation potential, p. 246 (eqn. 197)
0
U(r) central field, p. 27 (eqn. 4)
u ungerade = odd, as subscript, p. 59
V volt
V ligand field of spherical symmetry, p. 55
0
Voct ligand field of octahedral symmetry, p. 55
ν seniority number p. 73
W expression for average value of r~\ p. 39 (eqn. 33)
χ various quantities, pp. 35, 82
x characteristic amplitude vibration, p. 95 (eqn. 107)
e
Xi Rydberg correction, p. 23
x electronegativity of atom A, p. 309
A
Ζ atomic number
Z effective charge, compared to hydrogenic ions, p. 28
#
Zff effective charge, compared to data of atomic spectroscopy, p. 142
e
Z — 1 ionic charge in spectroscopic arguments, p. 23
0
ζ ionic charge as a chemical property, p. 248
8
 Angstrom unit of wavelength = 10~ cm, p. 85
Brackets on chemical symbols, [Ne], [A], [Kr], [Xe], and [Em], indicate closed-
shell cores in electron configurations, and otherwise in the last chapters, molar
concentrations of a given species for use in mass-law expressions,
α Racah-Trees correction, p. 46
α Madelung constant, p. 235 (eqn. 185)
α correlation factor, p. 211 (eqn. 174)
β nephelauxetic ratio, p. 77, 134
βη total formation constant, p. 245 (eqn. 191)
Γ group-theoretical quantum number (analogous to L) for systems, p. 51
η
γ group-theoretical quantum number (analogous to /) for orbitals, p. 51
η
Γj (analogous to J) for systems, p. 51
yj (analogous to j) for orbitals, p. 51
Γ and y for tetragonal symmetry, p. 68 (eqn. 65).
ιη tn
Δ orbital energy difference in octahedral complexes, p. 54, 132
Δ term with Λ = 2
δ half width, p. 92 (eqn. 100)
δ(—) half width towards smaller wave numbers
δ(+) half width towards larger wave numbers
δ orbital with λ = 2
δ disproportionation constant, p. 256 (equ. 212)
η
€ molar extinction coefficient, p. 89 (eqn. 98)
c molar extinction coefficient of maximum
0
ζ multiplet splitting factor
ζι Lande multiplet splitting factor, characteristic for the partly filled n, /-shell,
η
p. 48 (eqn. 41)
η scaling parameter, p. 29
xi
LIST OF SYMBOLS
Θ quantity related to M.O. deviation from / = 2, p. 79 (eqn. 84)
& „ ,p.79
θ Weiss correction, p. 182 (eqn. 157)
Λ orbital angular momentum quantum number in linear symmetry, for
system, p. 57 (eqn. 52)
λ „ , for orbital, p. 57
λ wave length, p. 85
μ magnetic moment in Bohr units, p. 182 (eqn. 157)
μ ionic strength, p. 248
7
ntyi wave length unit (= 10~ cm)
ν frequency, p. 85
Π term with Λ = I
π orbital with λ = 1
Ρ ligand field stabilization parameter, p. 98, 125
Σ summation sign
Σ term with Λ = 0
σ orbital with λ = 0
σ wave number, p. 85
o characteristic wave number of a vibration, p. 95 (eqn. 106)
c
τ variables for wave function, p. 38
9 an angle, p. 36 (eqn. 23)
Xm magnetic (molar) susceptibility, p. 182 (eqn. 157)
Xcorr diamagnetic correction, p. 182 (eqn. 157)
Ψ wave function of system, p. 20
φ wave function of orbital, p. 25
Ω quantum number (analogous to J) of system in linear symmetry, p.. 57
ω quantum number (analogous to j) of orbital in linear symmetry, pp. 57,
159
xii
CHAPTER 1
HISTORICAL INTRODUCTION
IN THE nineteenth century, chemists realized that Dalton's atomic
theory gave a fair description of the composition and reactions of
the chemical compounds, assuming their molecules to consist of a
small number of different atoms. It was clear that some of the bonds
between the atoms were much stronger than others. Thus, it became
convenient to talk about sub-entities, "radicals", in the molecules;
and before the determination of atomic numbers, it was hard to
prove that the entities, assumed to be atoms, were not themselves
radicals, composed of several atoms. For many years, uranium
dioxide UO was considered to be an element, while chlorine Cl
a 2
was thought to be a higher oxide of the hypothetical element, mur-
ium, forming hydrochloric acid HCl (since all acids were thought to
contain oxygen).
Even before Arrhenius' theory of electrolytic dissociation, in-
organic qualitative analysis described properties of the individual
metals and acid radicals in salts. Thus, NaOH, NH , Na S, H S,
3 2 2
Na2C0 , etc., give characteristic precipitates of different colours,
3
which may dissolve in an excess of the reagent. While K S0 or
2 4
BaCl are relatively simple compounds, containing only one metal
2
and one acid radical each, it was discovered that some compounds
having a constant composition (thus proving that they are not
simple mixtures) contain several metals or acid radicals. Thus, the
alums of the type K S0 A1 (S0 ) -24H 0 or the Tutton salts of the
2 4 2 4 3 2
type K S0 -NiS0 -6H 0 give in solution all the reactions of their
2 4 4 2
respective metals and of sulphate. They were called "molecular
compounds" or "double salts". However, other compounds exist,
which must have a type of chemical bonding different from that in
the simple salts. The formula 4KCN-Fe(CN) does not indicate
2
that the ferrocyanides show none of the reactions of cyanide, are
not poisonous, and react very slowly with acids (where KCN im-
mediately forms the volatile acid HCN). Further, a large number of
ferrocyanides can be isolated, all containing the group Fe(CN) as
e
if it were a tetravalent acid radical. It was decided to call such salts
1
2 HISTORICAL INTRODUCTION
"complex" compounds. Actually, the sulphate group S0 has
4
distinctly the same character, i.e. it is extremely difficult to remove
oxygen atoms from it.
It is not easy to give a consistent definition of a complex without
including nearly every type of molecule. In view of the phenomenon
of ionic dissociation, we may say that a complex ion or molecule
(the neutral "inner-salts") contains one or more central atoms,
bound rather strongly to a well-defined number of ligand groups.
The central atom is for most practical applications of the word
"complex" a metal atom; but there is no logical distinction between
this case and the sulphur atom in the sulphate ion. The ligands may
either be single atoms (of the type, which in ionic salts would be
2 2 a
Cl~, F~, O ", etc.) or polyatomic anions (S0 ~, C0 ~, N0 ~) or
4 3 3
neutral molecules (H 0, NH , CO, pyridine C H N, etc.). It is nearly
2 3 5 5
always one definite atom of the polyatomic ligands which is directly
attached to the central atom, e.g. the oxygen atom of the oxo-anions
mentioned and of water and the nitrogen atom of ammonia and of
pyridine. The number of such atoms directly attached to the central
atom is called its co-ordination number, A given ligand may occupy
more than one such co-ordination place. Thus, the ligands oxalate
2
OOCCOO -, glycinate NH CH COO-, and ethylenediamine
2 2
NH CH CH NH are all bidentate (bound by an oxygen or nitrogen
2 2 2 2
atom in each end), diethylenetriamine NH CH CH NHCH CH NH
2 2 2 2 2 2
3
is tridentate (bound by the three N), nitrogentriacetate N(CH COO) ~
2 3
is quadridentate (one Ν and three O), and ethylenediaminetetra-
4
acetate (OOCCH ) NCH CH N(CH COO) - may be sexadentate
2 2 2 2 2 2
(two Ν and all four O) or quinquedentate (two Ν and three O). These
multidentate ligands are said to form chelate complexes. However, a
given complex may very well contain both multidentate and uni-
dentate ligands, e.g. one ammonia and two ethylenediamine mole-
cules and one chloride anion.
The description of chemical bonding has for more than a century
oscillated between two extreme points of view, corresponding to
the division of the old valency concept into the concepts of oxida-
tion number and bond number. Inorganic chemists have nearly always
conceived valency as having a sign. The atoms in the salts NaCl or
KBr are not sufficiently described merely as univalent; the electrical
charges are definitely +1 for the sodium and potassium ions and — 1
for the chloride and bromide ions, and they can freely be substituted
in the other salts NaBr and KCl. Admittedly, the molecules Cl ,
2
HISTORICAL INTRODUCTION 3
ClBr, Br and the metallic alloy NaK exist, but they have properties
2
very different from those of the ionic salts. In modern times oxida-
tion number is defined in the following way :
(1) The sum of oxidation numbers of the atoms in a molecule or an
ion equals its electrical charge in units of the proton charge. The
oxidation number of a monatomic entity always equals its charge.
(2) The oxidation number of hydrogen is +1 (except in H and
2
metallic hydrides, where it is 0, and in salt-like hydrides, where it is
- i ).
(3) The oxidation number of oxygen is —2 (except in 0 , where it
2
is 0, in some rare superoxo compounds, where it is — |, and in
+
H 0 and other peroxo compounds, where it is —1, 0 Ρ + F ~
2 2 2 6
where it is £, and in OF , where it is +2).
2
(4) The oxidation number of fluorine is — 1 (except in F where it
2
is 0).
These rules do not specify the oxidation numbers in every discrete
compound (such as N S or Pb(CH ) ), but, generally, reasonable
4 4 3 4
analogies can be established with well-known cases. It must be
remembered that the oxidation numbers are useful concepts in the
classification of chemical compounds, but they are not measurable
quantities (except in the case of monatomic entities). A very electro-
statically minded chemist may perhaps think of the carbon atom in
C0 or the silicon atom in Si0 as bearing a hypothetical charge of
2 2
+4, because the oxidation number is +4 according to rule (3)
above. However, there is no doubt that the actual electron distribu-
tion inside the molecule C0 and the crystalline SiO does not
2 a
correspond to such a charge distribution, but rather approaches
electroneutrality, having about the same number of electrons in
the neighbourhood of each nucleus, as indicated by its atomic
number. On the other hand, as will be shown later, the concept of
oxidation number has deteriorated much less than the argument
about electrical charges might indicate, and we shall use the Roman
numerals in parentheses after the symbol or name of each element
when giving the oxidation number. We will commit the anachron-
ism of using a minus sign for negative values, Cl(—I), and the
Arabic zero, Pd(0).
Criticism of the concept of oxidation numbers generally comes
from organic chemists. The compounds CH , CHC1, CH C1, CHC1
4 3 2 2 3
and CC1 do not have essentially different properties, but the oxida-
4
tion number of the carbon atoms rises in stages, —4, —2, 0, +2 and
