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Gamma Resonance Spectroscopy and Chemical Bonding.

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where $k is an antisymmetric eigenfunction of an atom or
of a group of atoms. The complete function (11) is not
completely antisymmetric under these conditions.
+
From the standpoint of the valence structure approximation“], the assumption of only local antisymmetrization is
equivalent to ignoring exchange interactions between
different atoms or groups. Empirical parameters, e.g.
“ionic radii”, are introduced in some cases to compensate
for this.
This group of theories includes in particular the Madelung
theoryrg1of ionic crystals and its extension by Hund and
Heisenberg through the inclusion of polarization effects”’].
The crystal field theory[12], which acquired new life from
the success of the methodically equivalent ligand field
theory“ ‘I, deals with polarization effects in incomplete
shells.
As I pointed out a long time ago[’31, the interatomic
exchange effects become less important on purely combinatorial grounds in lattices with high coordination numbers. In principle, therefore, a theory of metallic phases can
be developed on the basis of only local antisymmetrization.
Investigations on magnesium and zinc are in progress. An
investigation on inert-gas crystals[’41 also belongs to this
field.
Interatomic as well as intraatomic exchange effects are
taken into account in the statistical treatments of solids,
which ultimately arise from the work of Lenz and Jen~en[”~.
However, since quantum mechanics is used only for
averaging in statistical studies, these again cannot be
described as complete polyelectron theories.
Received: April 24,1971 [A 829 I€]
German version: Angew. Chem. 83, 521 (1971)
Translated by Express Translation Service, London
[I] M . Born and J . R. Oppenheimw, Ann. Physik 84,457(1927).
[2] H. Hartmann: Theorie der chemischen Bindung auf quantentheoretischer Grundlage. Springer, Berlin 1954, p. 185ff
[3] A. Sommerfeld, W !I Houston, and C. Eckart, Z. Physik 47,1(1928).
[4] R. Peierls, 2. Physik 53,255 (1929).
[5] F. Bloch, Z. Physik 52, 555 (1928).
161 E. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933).
[7] J. C. Slater: Quantum Theory of Molecules and Solids, Vol. 2.
McGraw-Hill, New York 1965, p. 228ff.
[8] H . Hartmann, [2], p. 154ff.
[9] E . Madelung, Nachr. Ges. Wiss. Gottingen, 100 (1909).
[lo] W Heisenberg, Z. Phys. 26,196 (1924); F. Hund, ibid. 31.81 (1925);
32, l(1925).
[ I l l F. E. llse and H . Hartmann, Z. Physik. Chem. 197, 239 (1951).
[12] H . Bethe, Ann. Physik ( 5 )3, 133 (1929).
[I31 H. Hartmann, [2], p. 311 ff.
1141 H. Hartmann and E. 0. Steinborn, Theoret. Chim. Acta 5,29 (1966).
[15] W: Lenz, 2. Physik 77, 713 (1932); H. Jensen, h i d . 77, 722 (1932)
Gamma Resonance Spectroscopy and Chemical Bonding [**I
By Rudolf L. Mossbauer [*I
Gamma resonance spectroscopy makes it possible to observe directly hyperfine interactions in
solids. I n the field of chemistry the feature of greatest interest is the measurement of isomeric
shifts of gamma lines because these shifts are proportional to the electron density at the nucleus
and can thus give detailed information about the electronic structure of the chemical bond.
After a brief introduction to gamma resonance spectroscopy, this paper deals with the fundamental problem of the interpretation of measured isomeric shifts in t e r m of electron densities
and then gives representative examples of chemical information that can be obtained for transition
elements from the shifts and the splitting ofthe gamma lines.
1. Introduction
Gamma resonance spectroscopy is based on the possibility
of observing in solids gamma emission and absorption
lines of natural width, i. e. lines with a frequency definition
as much as ten orders of magnitude sharper than that
achieved in the commonly observed broadening of gamma
lines due to the Doppler effect“]. The method is restricted
to relatively low-energy gamma transitions and often
Prof. Dr. R. L. Mossbauer
Physik-Department der Technischen Universitat
8 Munchen 2, Luisenstrasse 37a (Germany)
Translated by Express Translation Service, London, from a paper
presented to the “Solid State Chemistry” Group of the GDCh on
October 2, 1970, Bonn.
requires the use of low temperatures to minimize the background of nonresonant gamma radiation which is always
present outside the range of the natural line widths[’].
Figure 1 gives a summary of those elements for which
gamma resonance spectroscopy has so far been possible.
A characteristic feature is the absence of any light elements.
Figure 1 also shows, however, that gamma resonance
spectroscopic measurements can be carried out in all
series of transition elements. Figure 2 illustrates the principle of measurements of this kind.
[**I
The hyperfine interactions between the electric and magnetic moments of the atomic nuclei and the fields which
act on them in solids lead to shifting and splitting of the
nuclear levels, which can appear as isomeric shifts and
462
Angew. Chem. infernat. Edrf. J Vol. 10 (1971) J N o . 7
59Pr 60Nd
62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm 70Yb 71Lu
1
92U 93Np
1
Fig. 1. Summary of those elements with which gamma resonance spectroscopy has so far been possible. For many elements
usable gamma transitions exist in several isotopes and at different energies.
magnetic dipole or electric quadrupole splitting of the
gamma lines. While under normal circumstances these
changes in the frequency of gamma lines due to hyperfine
interactions are completely swamped by the latter’s Doppler broadening, the method of resonance spectroscopy
Measuring principie
often makes it possible to observe directly the frequency
changes because of the increased resolution due to the
use of natural line widths. In chemistry it is primarily the
study of isomeric shifts and quadrupole splitting of the
gamma lines that is of interest. In what follows we shall
Measured resu!t
I
I
I
I
1000
Source
Absorber
I _
1
Detector
-t
,--“
u
995
c
0
I /
w
‘J,
E,
* 99 0
m
I
Fig. 2. Principle of the measurements in gamma resonance spectroscopy. The left-hand part of the figure shows the experimental
arrangement, consisting of a radioactive source and a resonance absorber with atomic nuclei identical to those in the gamma
source. The source and the absorber are often placed in a low-temperature cryostat. The detector measures the gamma radiation
passing through the absorber as a function of the relative velocity between the source and the absorber, which is generally
produced by means of an electromagnetic drive system. The result of such a measurement is shown on the right-hand side
of the figure: a resonance absorption maximum, i. e. a minimum in the intensity received at the detector, occurs at zero relative
velocity of the source and the absorber, at which the source and the absorber are exactly in resonance and thus have the same
fundamental frequency. This perfect resonance absorption can be disturbed by exploiting the linear Doppler effect : a change
in the relative velocity of the source and the absorber causes a reduction of the resonance absorption and hence a corresponding
increase in the intensity recorded by the detector. In this way with an emission line having a natural line width r we spread
an absorption line of the same natural line width and obtain for the recorded intensity, in the ideal case, a line width 2 r [Zb].
Angew. Chem. internat. Edit. 1 Val. 10 (1971) 1 No. 7
463
discuss the methods and the chemical information content
of such studies. The discussion of practical examples will
be restricted to stable compounds of the 3d-, 4d-, and 5d
transition
2. Isomeric Shifts of Gamma Lines
A system consisting of a nucleus and an electron shell will
be in a state of minimum energy if the nuclear charge is
concentrated at a point. Any increase in the charge radius
of a nucleus, or indeed any increase in the electron density
at a nucleus of finite extent, leads to an increase in the
energy of the total system. Thus, the energetic position of
any nuclear level of a nucleus incorporated in a solid
depends both on the nuclear radius and an the electron
density at the nucleus. There is a similar dependence for
the frequencies of the gamma transitions between the
individual nuclear levels. In analogy to the optical isotopic
shift, the isomeric shift is given by :
the pljZshells, so that the contribution of the pli2 electrons
to isomeric shifts can be neglected in most cases.
While the s electrons make direct contributions to the
electron density at the nucleus, the electrons in partially
filled shells, such as occur in the transition elements, contribute indirectly to the isomeric shifts, by the “screening
effect” they have on the s electrons.
As will be explained later, it is often difficult to break down
a measured isomeric shift into the contributions originating
directly from s electrons and indirectly from screening
non-s-electrons.
A study of isomeric shifts can be carried out in all series of
nd-transition elements. For this purpose the most suitable
transition in the range of 3d-elements is the 14.4-keV
transition in 57Fe, in the 4d-element range the 90-keV
transition in 99Ru, while in the range of 5d elements the
most suitable are the 73-keV transition in 1931r,the 36-keV
transition in Is9Os, and the 77-keV transition in I9’Au.
2.1. The Problem of Calibrating the Isomeric Shift
where S,- S, is the energy shift of two gamma lines, with
respect to one another, for a gamma transition of energy
E , in one and the same nuclear isotope, situated in two
different chemical environments a and b, while u,-ub
represents the difference of the Doppler velocities for the
two compounds. The quantity i$(0)12represents the total
nonrelativistic electron density at the site of the nucleus.
The constant C, which is a characteristic of the nuclear
radiating transition in question, is a function of the charge
distributions of the nucleus in the initial and final states.
Assuming a uniform nuclear charge distribution, a good
approximation is :
C = ( 2 x / 5 ) Z e 2 ( R :- R ~ ) ~ ( Z ) = ( 4 ~ / 5 ) Z e 2 R 2 ( A R / R ) ~ ( Z )
(2)
where R, and R , denote the charge radii of the ground
state and of the first excited state respectively;
R = ( R , + R,)/2. S’(Z) is a correction factor calculated
approximately by Bodrnerr4l,which takes into account the
modification of the nonrelativistic electron density due
to relativistic effects, in particular the variations in the
wave functions in the region of the nucleus. A table of
values of S ’ ( Z )for all atomic numbers 2 has been given
by Shirley1’]. It must be emphasized that the factor S’(2)
does not in any way represent a conversion factor that
would allow a conversion of the nonrelativistic wave
functions occurring in equation (1) at the position of the
nucleus into a relativistic type.
Only the s electrons of the outermost electron shell, i.e.
the shell which directly takes part in chemical bonding,
contribute directly to the total electron densities appearing
as a difference in eq. (1). Measurements of the isomeric
shift thus give direct information on the proportion of
s electrons in a chemical bond. In the case of heavy nuclei
the relativistic pIi2 electrons can also give considerable
probability densities at the nucleus, but in many cases
there will be no substantial difference in the occupancy of
464
Measurements of isomeric shifts yield, as can be seen in
equation (I),
a factor C which originates in the physics of
the nucleus and an electronic factor A1+(0)12, the total
nonrelativistic electron density difference at the nucleus
for two different compounds. There is as yet no known
method of measuring these two factors separately. To
determine one of the two factors, therefore, one is obliged
to find the other by calculation. In practice, in the present
state of the art, a measurement is first carried out of the
isomeric shift of a selected nuclear isotope for two different
valence states of the electron shells. Comparison of the
measured values with the electron densities calculated for
the two valence states then gives directly the value of C
which is specific to the particular nuclear transition, i. e .
essentially the quantity AR/R. This determination of C
is a central problem in the interpretation of measured
isomeric shifts. Solution of this problem makes it possible
to establish for the nuclear transition considered a practically linear relationship between the isomeric shifts and
the electron densities at the nucleus, a process usually
described as calibration of the isomeric shift. Once the
calibration constant C has been determined, total electron
densities can be found directly for the whole enormous
complex of chemical compounds in which the nuclear
transition concerned can be measured. The electron densities at the nucleus are often a sensitive indication of the
effective valence state of the atom measured. In this way
information on the nature of chemical bonding can be
obtained directly from the isomeric shifts.
The difficulty that arises in the method of calibration described above lies in the fact that while it is possible in
principle to carry out reliable Hartree-Fock calculations
of electron densities at the nucleus, such calculations
presuppose a knowledge of the real electron configurations
of the atoms or ions considered. While these configurations
are generally known for free particles, the corresponding
information is often lacking in the case of ions incorporated
in solids, in which the isomeric shifts are actually measured.
For calibration purposes therefore, as a general principle,
Angew. Chem. internat. Edit. / Vol. 10 ( 1 9 7 1 )
1 No. 7
compound pairs in which the electron configurations are
more or less certain are chosen, as for example in purely
ionic compounds. Deviations from this ideal state, which
is never achieved in practice, give rise to errors in the calibration constant C. Such errors, are however, of secondary
importance if one is mainly interested in drawing qualitative
conclusions about the nature of the chemical bonding, for
example in systematic trends in a large series of compounds.
For quantitative conclusions a precise determination of C
is essential, and this problem has not so far been satisfactorily solved.
a condition that seems to be very difficult to realize. In
fact, on the basis of X-ray absorption measurements,
Goldanskii[*]arrived at effective charges of + 1.9 for Fe"
and only + 1.2 for Fe"'. Jrnrgensen"31 calculated, from
optical data, an effective charge of + 1.7 for Fe"' in highspin complexes. From self-consistent charge and con~
among
figuration MO calculations, Viste et u I ! ' ~obtained,
other things, for [Fe"'F,]'a 4s population of iron equal
to 0.32. On the basis of these results, Dunon''] used a
configuration for [Fei'iF,]3- and a 3d6 configuration for the Fe" complex ofhighest ionicity, and hence
arrived at the value of ARIR given in Table 1.
2.2. Isomeric Shifts in 3 d Transition Elements:
The 14.4-keV Transition in 57Fe
Special interest attaches to the low-spin iron complexes,
which are often distinguished by the absence of isomeric
shifts between the formal di- and trivalent states of the
iron. Classicexamples ofthisare thecomplexes [Fei'(CN),yand [Fe'''(CN),]3-, which exhibit only a slight mutual
isomeric shift. A possible interpretation is back bonding,
i. e. the transfer of electrons from the metal ion to empty
K* antibonding orbitals of the ligands. A transfer difference
of one electron between Fe" and Fe3+ might explain the
absence of isomeric shifts in the low-spin 3d5- and 3d6
configurations of the cyano-complexes but, as will be shown
in greater detail later, this hypothesis is surely too simple.
As an illustration of the difliculty of the calibration problem
Table 1 gives a collection of diverse values given for the
ratio ARIR in the 14.4-keV transition in 57Fe by various
investigators. Table 2 gives values of nonrelativistic electron
densities IJl(0)l' for the most important configurations of
iron. The differences in the s-electron densities at the nucleus
are due to the screening effect of 3d electrons on the s electrons. This screening effect apparently acts mainly on the
3s electrons, while the s electrons in the two inner shells
are hardly affected by it.
Table 1. Relative change in the nuclear radius A R / R for the 14.4-keV
transition in 57Fe.
Method
ARJR
Measurements on Fe" and Fe"' compounds
of highest ionicity
- 1.8 x
[6]
Deduction using effective charges from X-ray
absorption measurements
- 5.0 x
[S]
Combination of optical data and M O
calculations
-8.5 x
[9]
M O calculation taking into account the
screening by 4d- and 4p electrons
-9.ox 1 0 - ~
~
Ref
2.3. Isomeric Shifts in the 4d Transition Elements:
The 90-keV Transition in 99Ru
Measurements of the isomeric shift in ruthenium compounds enable observations to be made over an unusually
wide range of different valence states. Figure 3 shows three
[lo]
~~~
Comparison of the calculation of inner
electron polarization with high-pressure
measurements
- 4 . 0 ~lo-'
[Ill
- 5 . 2 ~ 1 0 - ~ [i2]
I
-f
The values of A R / R given were calculated with the aid of the nonrelativistic wave functions calculated by Watson [7]. To take into
account the relativistic corrections for the s-electron densities, all
values of A R / R in the table must be reduced by the factor S'12)=1.33.
Table 2. 1$(0)[' in units of the cubic Bohr radius ug for electrons with
the same spin orientation, after Watson [7].
Configuration
Fe(3d"4s2)
Fez '(db)
Fe3'(d')
is
2s
3s
4s
5377.873
493.968
68.028
3.042
5377.840 5377.625
493.196 493.793
68.274
69.433
I JI (0)l'(d6)- I $J(0)l2(ds)
0.215
0.003
- 1.159
In their calibration of the isomeric shift in 57Fe, Wufker
et a/.[61assumed that the iron ions in the complex salts of
highestionicity,e.g.inFe,(SO,),~6H,OorinFeSO,~ 7H,O,
can be associated with pure d5- or d6 configurations. For
Fe"' at least this assumption is very suspect, since in this
case the iron ion would have to carry three units of charge,
Angew. Chem. internat. Edit.1 Vol. 10 (1971) 1 N o . 7
I
-15
-10
-05
-
0
05
v [rnrnlsl
10
15
Fig. 3. Gamma resonance spectra of ruthenium compounds, measured
at 4.2"K for the 90-keV gamma transition in 99Ru,using a metal source
exhibiting no hyperfine splitting [IS].
465
representative spectra and Figure 4 a graphical representation of the results of some measurements of isomeric
The isomeric shift is decisively influenced by the
charge transfers which arise in the formation of molecular
I
1
30~10-'
&do
Ru
measured at the nucleus of M, insofar as s electrons are
transferred ; otherwise there is a decrease. The individual
effects that occur can best be seen from an MO scheme,
as represented in Figure 6 for the case of an octahedral
8+
1.5~10-~
0
-1 5 ~ 1 0 - ~ - + -
sleV1
4d'
LdZ
LdL
4d5
Ld'
Ru7+
Ru6'
Ru'*
Ru3'
Ru2*
Fig. 4. Isomeric shifts of the 90-keV gamma radiation from "Ru for various compounds of ruthenium, relative to metallic Ru
(reference point). The lower part of the figure shows the formal valence states and the formal electron configurations of the
Ru ions in the compounds investigated [IS].
orbitals from the metal orbitals and ligand orbitals. This
is demonstrated in Figure 5, where a metal orbital and a
ligand orbital, both of which belong to the same irreducible
representation, combine to form a bonding and an antibonding molecular orbital. An increase in the bonding
increases the distance between the two molecular orbitals.
environmental symmetry. This type of symmetry is found
in the majority of the compounds given in Figure 4. It
should be observed that the position of the metal orbital
M
MO
t 1" IO*,TT*l
/
alglo*i
,
/
,
f
;'
I\
'\
\
\
\
\
\
\
\
\
I
\
\
\
\
I
\
\
,i/\ b'
\
\
\
\
,
I
'
n=10oq
I
u
Metal
M
MoLecular
orbitals
tigand
L
Fig. 5. Combination of a metal orbital and a ligand orbital to form a
pair of molecular orbitals (MO). The coupling increases with increasing
h. Overlap contributions have been neglected. In the bonding M O an
increase in h corresponds to an L-M charge transfer, in the antibonding orbital to an M-L transfer
The bonding orbital here assumes a more marked M
character, this corresponding to a charge transfer L+M,
while the opposite applies to the antibonding orbital. For
the same occupancy of the two orbitals there is no charge
transfer at all with increasing coupling. A lower occupancy
of the metal orbital, placed higher by chance in Figure 5,
on the other hand, leads to increasing charge transfer on
coupling, which is in the direction L-M in the example
chosen. The result is an increase in the isomeric shift
466
Fig. 6. M O level scheme for octahedral metal complexes for ligands
with internal n-bonding [16].
in Figure 6 is determined by the actual electron configuration of the metal ion, and therefore does not correspond
to the configuration of the free ion. Details of the level
structure, for the given case of n = 4 for ruthenium, are
certainly considerably influenced by the strong spin-orbital
Angew. Chew. internat. Edit. 1 Vol. 10 (1971)
1 No. 7
2.4. Isomer Shift Measurement under High Pressure
coupling, so that the following remarks can only have a
qualitative character.
For an octahedral environmental symmetry of the central
R u ion, there is a splitting of the 4d shell, which is relevant
to the optical and magnetic characteristics, leading to
t2,(x) and e,(o) molecular orbitals. The different states of
oxidation are distinguished by different occupancies of the
t,, state. Thus, for example, for the octahedral complexes
of Ru", Ru"', and Ru'" the formal configurations (t2,)6,
(t2,I5, and (t2,I4 apply.
The rise in the electron densities IJr(O)I2 with increasing
valence which can be seen in Figure 4 can be ascribed
qualitatively to the parallel process of a decrease of 4d
electrons i. e. the progressive reduction of the screening of
s electrons, in the inner shells. However, this view is in no
way conclusive, for increasing occupancy of 5s orbitals
could equally be assumed. In fact, in a quantitative description all electron-transfer processes between the ligands
and the metal ion must be taken into account. Table 3
gives a summary of the more important of these processes,
which in ruthenium can appear as a result of the coupling
of ligand and metal orbitals to molecular orbitals and
thereby lead to a change in the electron density at the
nucleus. It is the differences in the contributions of these
different electron-transfer processes which give rise to
differences between the isomeric Shifts of compounds
having the same formal valence. Leaving this aside, Figure 4
demonstrates the possibility of classifying the valences of
ruthenium in its complexes from measurements of the
isomeric shifts. Only K,[Ru(CN),]. 3H,O, K,[Ru(CN),],
and RuBr, appear to behave differently. For the first two
compounds a marked occurrence of a type of bonding
designated as back-bonding can be assumed, in which the
t,, orbitals undergo considerable coupling with initially
unoccupied antibonding n*-ligand orbitals. According to
Shulman et a[.1171,
such an effect can cause a marked abstraction of electrons from the metal ion and thus explain
the fact that isomeric shifts of the two hexacyano-complexes
should not be associated with the nominally divalent but
with the nominally tetravalent state of ruthenium, corresponding to the transfer of two electronic charges from the
metal to the ligands. In fact, measurements of isomeric
shifts directly point to the existence of marked backbonding. Thus, isomeric shift data are really predestined
for a classification of chemical valences.
Table 3. Change of electron density at the nucleus and electron-transfer
process for octahedral symmetry.
_____
Electron-transfer procc\a
_______
I.
2.
3.
4.
5.
OL
-t
XL
-*
nd4d)
0'
O L . XL
-
+
f
AI+(0)Iz
<O
0,.,,(4d)
nM(4d)
10
XL
20
OM(5S)
r-J,.,,(5P),XM(5P)
>O
tO
The measured isomeric shift in RuBr, corresponding to a
nominally divalent state cannot be interpreted at all
unambiguously. However, this compound exhibits diamagnetic behavior, which is quite unusual for a formal
(t,,)5 configuration.
Angew. Chem. internal. Edit. 1 Vol. 10 (1971) 1 No 7
Isomeric shifts are usually observed in different chemical
compounds, the bonding state, which is characterized by
a large number of parameters, being varied in steps. If,
however, the isomeric shifts are measured as a function
of pressure, continuous variation of the bonding parameters over a wide range in one and the same compound
can be achieved. Such high-pressure studies have so far
been almost exclusively restricted to those isotopes that
can be measured at normal temperatures, since the considerable experimental problems of low-temperature highpressure resonance spectroscopy have not yet been satisfactorily solved.
Drickamer et a/.[181
carried out a study of isomeric shifts, in
particular on compounds of iron, and by comparison with
optical studies obtained valuable information on the
chemical behavior of iron. For example, in many cases
the measurements showed increasing reversible reduction,
as the pressure was increased, of high-spin Fe"' into Fe",
for example in Fe,(SO,),, FePO,, and Fe(w) citrate. They
interpret this reduction as the result of a progressive
lowering with compression of the ground state orbitals of
the metal relative to the ligand orbitals, which facilitates
thermal electron transfer, i. e. an L-tM electron transition
from a ligand orbital bonding weakly or not at all to a
3d-metal orbital, with the establishment of thermal
equilibrium. The pressure-induced reduction is thus not
associated with a transition point; instead the electron
transfer made possible by the pressure causes reduction
at a single ion, with simultaneous electrical and mechanical
disturbance of the adjacent ions, the reducibility of which
is thereby decreased. Increasing pressure thus favors electron transfer, but on the other hand it leads to an increased
inhibition of reduction in adjacent ions.
The strongly covalent low-spin iron complexes exhibit a
particularly interesting pressure-dependent behavior, the
most striking representatives being the cyanoferrates(i1)
and -(III), and their derivatives. At pressures around
200 kbar and temperatures around 150°C, Drickamer's
experiments with salts such as K4X, Na,X, Zn,X, Ni,X,
and Cu2X (where X=[Fe(CN),]), showed a low-spin
high-spin conversion. This is contrary to the naive
expectation that with increasing pressure an increase in
the crystal electric field should favor a high-spin + low-spin
] , precisely
transition. According to Drickamer et ~ 1 . [ ' ~ this
opposite effect is due to a lowering of the metal orbitals
relative to the weakly bonding or nonbonding ligand
orbitals. This also signifies an increase in the energetic
distance between metal orbitals and antibonding (x')
ligand orbitals. In parallel with this process there is a
reduction of the back-bonding effect, whereby the metalcyanide bonding is weakened.
---f
In the case of the high-spin iron complexes, Drickamer et
found that the electron density at the nucleus increases with increasing pressure. To interpret this they
assumed a radial expansion of the 3d electrons increasing
with pressure, with a consequent reduction of the 3d-3s
screening and hence an increase in the s-electron density
at the nucleus. In this interpretation the predominant part
467
in the variation of the isomeric shift with pressure is ascribed
to the screening 3d electrons. Making the reasonable
assumption of increasing covalency with increasing pressure, with purely 3d-electron participation in the bonding
we are really dealing with an M+L electron transfer in the
antibonding orbitals which is also manifested in a reduction
of the optically observed Racah parameters. At the same
time, however, an overcompensating L+M transfer occurs
in the bonding orbitals, so that overall there is an increase
in the screening effect and hence a reduction of the electron
density lJl(0)12,contrary to the experimental findings. It
is therefore reasonable to assume participation of 4s electrons in the bonding, so that a small L+M transfer is
sufficient to explain the sign of the pressure dependence
of the isomeric shift observed experimentally. The assumption of 4s participation in the bonding is indeed the basis
of the calibration of the isomeric shift in 57Fecarried out
by Danon, Goldanskii, and Simanek et al. and given in
Table 1.
metal ions and ligands. This is indeed valid if a contribution
due to 4s electrons can be neglected, as is the case with
many compounds of Fe”. On the other hand, in ionic
compounds of trivalent iron the contribution of the 4s
electrons cannot be neglected. Here the overlap effect even
leads to an increase in the direct contribution of the 4s
electrons to the isomeric shift, so that the contribution of
the 4s electrons becomes preponderant. Quantitative
follow-up of this reasoning, such as was carried out by
Sitnbnek et al. for the examples of FeO and KFeF,, suffers
especially from the inadequate knowledge of the modifications which the ligand orbitals used for the calculation of
the overlap undergo in solids as compared with the atomic
case.
Finally, it should be emphasized that the overlap effect
described by Sirnhnek et al. differs basically from the
phenomena occurring within the framework of an MO
description. It is not possible to exclude a priori the possibility that MO considerations may indeed yield relatively
good values for energy levels which are amenable to
optical experiments, but only a poor approximation for
the interpretation of isomeric shift data if overlap effects
of the kind outlined here really make the predominant
contribution.
h u n e k et al?1’”21attempted a calibration of the isomeric
shift in the case of the 14.4-keV transition in ”Fe by
comparing experimental data with theoretical calculations
of the variation with pressure. This work is of interest
mainly because the calculations gave as the preponderant
effect for the occurrence of the isomeric shift the overlapping of the ligand orbitals with the closed Is-, 2s-,
and 3s shells of the iron ion. Such overlap contribution
to the isomeric shift is a direct consequence of the Pauli
principle, which would exclude the electrons from the
overlap region of s-metal orbitals and ligand orbitals and
hence cause an increase in the electron density at the
nucleus due to s-metal orbitals. Mathematically, this overlap effect, which can be calculated on the basis of the
Heitler-London model, can be described by orthogonaliza-
I-<Br--=CI-<
iidonors
SCN-<
I
2.5. Isomeric Shift and Chemical Systematics
In qualitative interpretations it is frequently attempted to
correlate the measured isomeric shifts of a large range of
chemical compounds of one and the same nuclear isotope
systematically with suitable parameters. In this way it is
often possible to establish a relationship between the iso-
F - -==O H -
<H,O
<
weak
-donors
1
bond! ng
T
NH,<
no ii-
NO, -= CN-
i ii-acceptors
increase i n A
>
decrease in ’il - donor effect
increase in u - donor effect
c
_
__
2-
>
R- bonding increase in
TIO)ILon nd-electron transfer-
’ii-bonding : decrease
IYI 01I * on (n+lls-e[ectron transfer-
in
2
-(J - bonding : decrease in YIOJI on nd-electron transferW O I I* on /n+ljs-electron transfer__ u - bonding : increase rn
7-1
Fig. 7. Spectrochemical series of frequently occurring ligands and variation of the electron density lJr(0)12
at the nucleus for transition elements.
tion of the ligand orbitals relative to the filled s-metal
orbitals. According to Sirnhnek et a[.[’ l2], the predominant
mechanism for the increase ofelectron density at the nucleus
with increasing pressure is also given by the overlap effect,
through its strong dependence on the distances between
‘3
468
meric shifts and electronegativity differences. However,
such a single-parameter correlation is only meaningful,
if at all, when it is restricted to isomorphous compounds
which differ only in the degree of ionization and not in the
nature of the bond.
Angew. Chem. internat. Edit. 1 Vol. 10 (1971) J No. 7
For many transition-element complexes it is possible to
establish for the isomeric shifts of the central metal a correlation with spectrochemical behavior, the systematics of
which have resulted in the formulation of the spectrochemical series of ligands. The active parameter of this
series is the splitting of the d orbitals in the ligand field,
observed in absorption spectra. For example, for a given
metal ion in octahedral and also in the square environmental symmetry, the splitting A of the d orbitals increases
in accordance with the spectrochemical series given in
Figure 7 . This series is probably valid for other environmental symmetries.
The variation of A can be understood directly from the
coupling constants h (see Fig. 5). The ligands occurring
in the spectrochemical series differ in their o or x donor or
acceptor properties, i. e. in their ability to effect electron transfers of the L-M type (donor) or M + L type
(acceptor). Strongly covalent compounds are distinguished
by their approximately obeying the principle of electroneutrality, this leading to a synergic coupling between
the o- and x-orbitals, in which the M L transfer associated with strong n-acceptor capacity is more or less
compensated by a correspondingly large L-M o-donor
transfer. G r a h ~ r n ~ deduced
'~~
the existence of such a
synergic coupling principle from the behavior of Mn
complexes. At the start of the spectrochemical series there
are ligands with predominant x-donor properties, which
leads to destabilization of the antibonding orbitals (see
Figs. 5 and 6),and hence results in smaller values of A. Toward the end of the series the n-donor capacity decreases,
and finally changes to a x-acceptor capacity, which goes
along with a o-donor capacity; both effects lead to an
increase of A, since the x-acceptor action stabilizes the
antibonding x-orbitals while the o-donor effect destabilizes
the o-orbitals. In connection with the isomeric shift, in
charge transfers of this kind, we have to make a clear
distinction between the opposing effects of d- and s electrons. Progression along the spectrochemical series involves a reduction of the L-M charge transfer caused by x
bonding, and hence an increase in the isomeric shift. In
parallel with this, however, there is an increase in the
L-M charge transfer caused by o bonding, which can
occur by means of both s- and d-electron transfer. When
the synergic coupling principle is strictly maintained,
the result is in the normal case an increase in the isomeric
shift in the spectrochemical series.
-
The optically measurable spectrochemical behavior is
directly influenced by the transfer of s- and d electrons
changing with the bonding. As far as the isomeric shift is
concerned, s-electron transfers have a considerably larger
influence than d-electron transfers. The ratio of nonrelativistic electron density changes at the nucleus which occur
on the addition of an nd-electron or the subtraction of an
(n l)s-electron can be determined by Hartree-Fock calculations. If, for example, we define the change of configuration
(And}={ndb(n+l)s1)-{nd5(n+ 1)s')
or
{A(n 1)s)= (nd6(n+ l)s'] - {nd6),we obtain for the ratio
c= 61$(0)1&+ l,s,/61$(0)~&ndivalues of approximately 2.5
for Fe, 3.1 for Ru, and 3.4 for Ir. While the proportions of
s- and d-electron transfers must be given much the same
weight in respect of the effective charge, in respect of the
+
isomeric shift the s-electron transfers have the stronger
effect.
Measurements of isomeric shifts do not make it possible
to determine directly the relative proportions of s- and
d-electron transfers as we progress along the spectrochemical series. Such a separation might, however, be
possible with a knowledge of the effective charge difference,
which is associated with a charge transfer n,(M-L)
- nd(L 4 M) - n, (L- M).
To illustrate the correlation between the isomeric shift
and the spectrochemical series, Figure 8 shows a collection
of the isomeric shifts for compounds of gold, using the
77-keV transition in I9'Au. The Au' complexes have linear
structures almost throughout, whereas the Au"' compounds
exhibit a square arrangement of the ligands. The change
of the isomeric shift substantially follows the spectrochemical series. A striking exception is the position of
tetrafluoroaurate, although this may be due to the different
coordination (CN=6). A characteristic feature of the data
given in Figure 8 is that the compounds of Au' and Au"'
with the same ligands exhibit relatively small isomeric
shifts with respect to one another.
Au I
A"=
50/
KAuICNI~
t
KAu ICN lI
1
30
AuCN
2 ?o=]j
E
L
1
J
-2.0
m
1
-2 0
Fig. 8. Isomeric shifts of the 77-keV gamma transition in I9'Au for
compounds of mono- and trivalent gold; after 1201.
+
Angew. Chem. internal. Edit. 1 Vol. 10 (1971) No 7
Rough estimates show that these shifts are an order of
magnitude smaller than would correspond to the 5d" - 5d8
transition, so that the actual configurations differ substanti469
ally from the formal ones. Since in the Au' compounds the
3d-molecular orbitals are fully occupied, and the differences
in the isomeric shift must therefore be ascribed to charge
transfers to 0 orbitals, it can be concluded on the basis of
an MO description that in respect of the isomeric shift the
screening effect of d-electron transfer is overcompensated
by the direct effect of s-electron transfer.
nuclear states participating in a gamma transition has a
nuclear spin >4 and if at the same time the environment
of the nucleus exhibits a symmetry lower than cubic. The
component qii of the tensor of the electric field gradient is
given by
An analogous correlation between isomeric shifts and the
spectrochemical series can in general be expected for the
strongly covalent complexes of the transition elements,
especially the low-spin complexes. Buncroji et u1.'' '1 confirmed this for a long series of low-spin complexes of Fe".
For the high-spin complexes, with their often lower
covalence, there should rather be a correlation with the
nephelauxetic series of ligands, since this series substantially
reflects the electronegativity'22! Danon for example, established such a correlation for the high-spin complexes of
Here the contributions qn (lattice) due to the surrounding
lattice ions and the contribution qir(ion) due to the valence
electrons are each multiplied by Sternheimer factors,
which describe an induced charge polarization of the
electrons in closed shells. Table 4 contains the relative
contributions of qii (ion) for p- and d orbitals.
Y,,= (1 - Y, )q,,(lattice)+(I
- R&,, (ion).
Table 4. Electric field gradients for p- and d orbitals.
~ ~ 1 1 ~ 3 1 ,
3. Relativistic Line Shifts
Relativistic time dilatation leads to a quadratic Doppler
effect, which is also manifested in a shift of the gamma lines
and which must therefore be taken into account in the
interpretation of isomeric shifts. This relativistic line shift
can be made clear on the basis of quantum mechanic~['~1.
The emission ofa gamma quantum ofenergy E , corresponds
to a mass loss Am=Ei/rnc2 on the part of the emitting
nucleus. This results in a slight increase in the internal
energy of the lattice, with an equal decrease in the energy
ofthe emitted quantum, i. e. the relativistic line shift AE. The
applicable relation is AE = - E,AE,,,/(2N,rnc2)), where
AE,,, is the change of internal energy of the crystal per
mole, N L is Avagadro's number, and rn is the mass of the
emitting nucleus. Expressed in terms of Doppler velocities
u and the internal energies of two compounds 1 and 2,
u , ~ , ~ , ,=
~ ,Emo1(TJ
~ , , ~ - Emo,(T2)/(2NLm).
A relativistically determined Doppler shift of this kind occurs in principle
even when the temperatures of the source and the absorber are the same, if the compounds studied have
different bonding strengths and hence have different
internal energies at the same temperature. Relativistic line
shifts are generally small compared to the normally observed isomeric shifts. For example, in the 14.4-keV
transition in 57Fe, a temperature difference of 100°C
corresponds to a relativistic line shift which is about an
order of magnitude smaller than the isomeric shift between
two typical high-spin compounds of Fe" and Fe"'. The
contribution of the relativistic line shift to the total line
shift need therefore only be taken into account in extreme
cases, say the case of a large temperature difference or of
very different bonding strengths of the test substances used.
4. Electric Quadrupole Splitting of the Gamma Lines
In addition to the isomeric shifts, electric quadrupole
splitting of the gamma lines can provide independent
information concerning the nature of the chemical bonding.
Such quadrupole splitting occurs if at least one of the
470
In many cases in compounds of the transition elements
both nd- and (n+ 1)p orbitals make direct contributions
to the electric field gradient. The lattice component of the
field gradient q,i is then generally small compared to that
of the valence electrons. This latter contribution depends
on the degree of overlap of the partially filled molecular
orbitals and the ligand orbitals, and is thus influenced by
the degree of covalence of the bond. In addition, however,
a contribution from the formally closed electron shells of
the metal ion to the field gradient at the nucleus is possible
if these shells have sufficient overlap with the ligand orbitals.
The perturbation of mainly closed p shells caused by such
overlapping-essentially an orthogonalization effect-can
lead to substantial quadrupole splitting insofar as closed
p shells exhibit particularly large values of the ( r - 3, radial
integral which determines the quadrupole splitting.
Calculations by Sawutzki et ~
1for 27Al
. inAI20,
~
~ showed
~
~
that there the effect of overlapping with closed shells makes
the predominant contribution to the electric field gradient.
In a way these discussions represent a parallel case to the
calculations made by Simanek et al.*". 'I, which demonstrated the significance of the overlap effect for isomeric
shifts.
The qualitative magnitude of quadrupole splitting can
often be derived from the symmetry of the particular
orbitals. Thus, the 3d shell of iron in the high-spin Fe"'
complexes has a spherical symmetry and the result may
be a smaller field gradient qii (lattice) originating in the
ligands. Conversely, in the analogous case of Fe" complexes a highly nonspherical symmetry exists, which
typically gives rise to large quadrupole splitting. In the
low-spin compounds of iron, as is to be expected, the Fe"
complexes exhibit a very small and the Fe"' a somewhat
larger quadrupole splitting.
Angew. Chem. inrernat. Edit. / Vol. 10 (1971)
1 No. 7
By way of illustration, Figure 9 shows for complexes of
mono- and divalent gold, a correlation between the quadrupole splitting and the isomeric shift. Such a correlation
is understandable if we again start from the assumption
of a synergic coupling of cs- and n-bonds. The increase
of the isomeric shift with increasing rank of the ligand in
the spectrochemical series corresponds to a transfer of
s electrons due to strengthened cs, bonding. This increase
must necessarily go together with an intensification of o,,
bonding whereby the quadrupole interaction is directly
influenced. However, this argument has only a qualitative
character, and it is not, for example, in any way possible
to conclude that a linear relation exists between the isomeric
shift and quadrupole interaction, since even with proportionality of the s- and d contributions in the o-bonds, the
electron transfers always affect the isomeric shift and the
quadrupole splitting to a different degree. Direct proportionality between the two quantities measured can perhaps
be assumed for small transfers.
K AuICNJ,
+
t
/-
!NCuA
+
K A u ICN),
of the sign of the electric field gradient in this case requires
either the use of single crystals or splitting of the nuclear
level by means of strong external magnetic fields.
5. Final Remarks
To sum up, it can be said that the method of gamma
resonance spectroscopy is capable in a unique manner of
yielding information concerning the nature of the chemical
bond. Measurements of isomeric shifts can be used directly
for the classification of chemical valence states. At the
present stage of development, however, the interpretation
of these measurements is first and foremost of a very
qualitative nature. So far there are no reliable experimental or theoretical methods of determining the relation
between the isomeric shift and the electron density at the
nucleus. In other words, the problem of calibration of the
isomeric shifts still awaits a satisfactory solution. A closely
associated problem is that in most cases it has not, so far,
been possible to resolve the indirect contribution of the
screening electrons from the direct contribution of the
s electrons. For a solution of this problem, direct determination of the effective charges of the bound metal ions
would above all be of great interest. Unfortunately knowledge of the molecular orbital energies yields this information only very indirectly. High-pressure experiments should
in future assume increasing importance for detailed interpretation of isomeric shift data. Systematic comparisons
with force constants and with bond lengths and angles-in
many cases still unknown-are further possible aids to
interpretation. Notwithstanding the often qualitative nature
of its statements, gamma resonance spectroscopy has in a
few years substantially contributed to our understanding
of chemical bonding.
Received: October 27, 1970 [A 830 IE]
German version: Angew. Chem. 83,524 (1971)
Translated by Express Translation Service, London
C12H10N2AUC[3\
20 -
00-
NaAuCC, 2 H 2 0
\ ,~IKAu
K A u Br,
CSAUF~
Rb AU F,,
AuOiOHl
*+&\
+ 4
As(C~HSJLAU
+ , I($A: $d* 2\ ' !
KAuISCNI,
K\
$zAu203
H2°
(C, H 9 k N A U c ( 4
\NH,A~CI,
AvCCI,
HAUL(, 4H7O
AuiAc14 ,
I
I
In principle, the sign of the electric field gradient can be
taken from the difference in the intensity of the components
of the split hyperfine spectrum. However, this method fails
for nuclear transitions of the type I = h I = i , as for
example in the 14.4-keV transition in 57Fe.Here, in polycrystalline substances with more or less isotropic bonding
forces, all that is observed as a result of quadrupole interaction is two gamma lines of equal intensity. Determination
Angew. Chem. internat. Edit. 1 Vol. 10 (1971) 1 NO. 7
[l] R. L. Miissbauer, 2. Physik 151, 124 (1958); Z. Naturforsch. 14a.
211 (1959).
[2] a) A detailed introduction to the fundamentals and applications
of gamma resonance spectroscopy is given, for example, in: H . Frauenfelder: The Mossbauer Effect. W. A. Benjamin, New York 1962;
A . Abragam: L'Effet Mossbauer. Gordon and Breach, New York 1964;
G. K . Wertheim: Mossbauer Effect, Principles and Applications.
Academic Press, New York 1964; H . Wegmer: Der Mossbauer-Effekt
und seine Anwendungen in Physik und Chemie. Bibliographisches
Institut Mannheim, 1965; R. L. Mossbauer and M . J . Ciauser in A. J.
Freeman and R. B. Frankel: Hyperfine Interactions. Academic Press,
New York 1967, Chapter 11; 1! I . Goldanskiiand R. H . Herber. Chemical
Applications of Mossbauer Spectroscopy. Academic Press, New York
1968; J . Danon: Lectures on the Mossbauer Effect. Gordon and Breach,
New York 1968.-b) Cf. also: E. Fluck, W Kerler, and W Neuwirth,
Angew.Chem. 75,461 (1963);Angew. Chem. internat. Edit.2,277(1963);
K I . Goldanskii, ibid. 79, 844 (1967) and 6 , 830 (1967), respectively.
[3] For a discussion of unstable chemical intermediates such as those
y decay or K-capture preceding a gamma resonance
arising in @-, @+,or
transition, which are not dealt with here, see: W Diftshiiuser and P. P.
Craig, Phys. Rev. 162, 162 (1967); 162, 274 (1967); G. K . Wertheim, ibid.
124, 764 (1961); J . G. Mutlen and H . N . Ok, ibid. 168, 550 (1968); G. J.
Perlow and H . Yoshida, J. Chem. Phys. 49, 1474 (1968); P. Rother,
F . Wagner, and U.Zahn, Radiochim. Acta 11,203 (1969).
[4] A. R . Bodmer, Proc. Phys. SOC.(London) A 66, 1041 (1953).
[5] D. A . Shirley, Rev. Mod. Phys. 36, 339 (1964).
[6] L. R. Walker, G. K . Wertheim, and V. Jaccarino, Phys. Rev. Lett. 6 ,
98 (1961).
47 1
[7] R . E . Watson: Solid State and Molecular Theory Group. Tech.
Rep. No. 12, MIT 1959; Phys. Rev. 118,1063 (1960).
[S] K I . Goldanskii, At. Energy Rev. I , 3 (1963).
[9] J . Danon: Applications of the Mossbauer Effect in Chemistry and
Solid State Physics. Tech. Rep. Ser. Int. At. Energy Agency 50,89 (1966).
[lo] V 1. Goldanskii, E. F . Makarov, and R . A . Stukan, Teor. Eksp.
Khim. Akad. Nauk. Ukr. SSR 2, 504 (1966).
[ll] E. Simanek and 2. Scroubek, Phys. Rev. 163,275 (1967).
1121 E . Siriidnek and A . Y. C. Wong, Phys. Rev. 166, 348 (1968).
[13] C. K . Jbrgensen, Progr. Inorg. Chem. 4,73 (1962).
[14] A . Viste and H . B. Gray, Inorg. Chem. 3,1113 (1964).
[l5] G. Kaindl, E! Porzel, F. Wagner, U . Zithn, and R. L. Mossbauer,
Z. Physik 226, 103 (1969).
[I61 H . B. Gray and N . A. Beach, J. Amer. Chem. SOC.85,2922 (1963).
[17] R. C. Shulman and S . Sugano, J. Chem. Phys. 42,39 (1965).
[IS] H . G. Drickamer, R. W Vaughan, and A. R. Champion, Accounts
Chem. Res. 2.40 (1969); S. C. Fung and H.G. Drickamer, J. Chem. Phys.
51,4353, 4360 (1969); H . G. Drickamer, G . K . Lewis, jr., and S . C. Fung,
Science 163, 885 (1969).
1191 U! A. Graham, Inorg. Chem. 7,315 (2968).
[20] H . D. Bartunik, W Potzel, R. L. Mossbauer, and G . Kaindl, Z .
Physik 240, 1 (1970).
[21] G. M . Bancroft, M . J . Mays, and 8. E. Prater, J. Chem. SOC.A 1970,
956.
[22] C. K. Jmgensen: Absorption Spectra and Chemical Bonding in
Complexes. Pergamon Press, Oxford 1962.
[23] J. Danon in K I . Goldanskii and R. H . Herber: Chemical Applications of Mossbauer Spectroscopy. Academic Press, New York 1968,
Chapter 3.
[24] B. D. Josephson, Phys. Rev. Lett. 4, 341 (1960).
[25] G. A . Sawatzky and d . Hupkes, Phys. Rev. Lett. 25, 100 (1970).
Methods and Applications of Nuclear Magnetic Double Resonance
By Wolfgang von PhiIipsbornr''
In double resonance spectra, transitions between energy levels of a nuclear spin system are
measured in the presence of two (or more) oscillating magneticfields. Experiments of this nature
form the basis of what is nowadays one of the most important techniques of N M R spectroscopy.
Depending on the method selected, they can be used to unravel complex spectra, to measure
hidden or weak resonances, or to determine the relative signs of coupling constants, as well as in
stereochemical or kinetic studies. This wide and steadily growing range of applications of double
resonance is described with the aid of specific examples.
1. Introduction
NMR spectroscopy is nowadays an essential part of molecular spectroscopy and an indispensable aid in the investigation of the structures of organic and inorganic compounds.
Several progress reports on various aspects of the field
have appeared in this journal" -61. Particularly great
progress has been made in recent years in the development
and application of double and multiple resonance methods.
An effort is therefore made below to describe the methods
that are of most interest to chemists, and to demonstrate
their use in spectral analysis and for the solution of structural problems. As the literature is extremely abundant,
a comprehensive review is impossible here, and the examples were therefore chosen for their illustrative character.
turbation of a second type of nucleus. The method is based
on a proposal made by Bloch in 1954, and was successfully
realized in the very same year[71.This first reported experiment was concerned with the determination of the Larmor
frequency (o=yH,) of I3C in 13CH31;the procedure used
2. Phenomenology and Instrumental Principles
I
In double resonance experiments, transitions between
energy levels Of a
'pin system in a polarizing static
magnetic field HO are measured in the Presence of two
oscillatingmagnetic fields H, and H,. H, is used to observe
the resonance of one type of nucleus, and H, for the per[*] Prof. Dr. W. v. Philipsborn
Organisch-chemisches Institut der Universitat
CH-8001 Zurich, Ramistrasse 76 (Switzerland)
472
EmJ
w,
1
WC
Fig,1, Schematic illustration ofthe proton spectrum of13CH31(bottom)
and Royden's 1H-{13C] double resonance experiment [7]. Observing
field H I , perturbing field H,.
was to look for the frequency w, of the perturbing field
H, that simplifies the proton doublet observed with H I
to an optimal singlet (Fig. 1). The experiment is thus also
Angew. Chem. internat. Edit. 1 Vol. 10 (1971)
/ No. 7
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