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Polarized Low-Temperature Crystal Spectra of Inorganic Complexes.

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Polarized Low-Temperature Crystal Spectra of Inorganic
By Peter Day[*]
The electronic spectra of complexes are especially informative if they are recorded for crystals
at low temperature or at varying temperature with polarized light. This straightforward technique frequently permits reliable band assignment. Such assignments, being independent of
the assumptions of any particular theoretical model, then provide a basis for testing theories of
electronic structure.
1. Introduction
When chemists want to measure the electronic spectrum of
a molecular complex ion or molecule in the visible or ultraviolet, they usually dissolve it in some suitable solvent and
run the spectrum of the solution at room temperature. Under
these circumstances, absorption bands are generally broad
(rarely less than lo3 cm-') and unstructured. In that case,
the experimental information content of each band consists
of its energy at the absorption maximum, its intensity (often
defined as the maximum molar extinction coefficient, but
better taken as the integrated band area) and its halfwidth or
shape function. We can use all three of these observables to
help assign the band, for example to a charge transfer or a
ligand field transition, and by matching its energy to the results of some calculation to try and define the electronic symmetry of the excited state. However, even with such a well established procedure as ligand-field theory, the results are often ambiguous. Many generalizations about electronic structures of metal complexes have foundered because of wrongly
assigned spectra.
A simple illustration of this fact is the case of the purple
permanganate ion, MnO;. Across the visible and near ultraviolet it has four main absorption bands, plus another
much weaker one in the near infrared. Since the oxidation
state of the manganese is + 7, with an effective electron configuration 3d0, they cannot be d-d (ligand field) transitions
but must be of charge transfer type, i. e. excitations of electrons from molecular orbitals mainly localized on the oxygen
atoms into the empty d orbitals. In the tetrahedral ion the d
orbitals are split into two-fold (e) and three-fold (t2) degenerate subsets, while the eight 2p orbitals of m-symmetry on the
four oxygen atoms are also split into sets labeled e, t,, and t2,
with degeneracies 2, 3, and 3. In principle, therefore, we
could have electronic transitions of any of the filled levels to
either of the empty ones, giving a total of six possibilities,
even without taking into account splitting of the excited configurations by electron repulsion. From 1952 up to the present, at least a dozen attempts have been made, using various
kinds of molecular orbital calculation, to assign the five observed bands to permutations of these orbital excitations.
The point I wish to make here is that the seven assignments
reported between 1952 and 1970 were all different! Yet the
low temperature polarized crystal spectrum described in Sec-
Dr. P Day
Oxford Universrty, Inorganic Chemistry Laboratory
South Parks Road, Oxford OX1 3QR (England)
0 Verlog Chemie, GmbH, 0-6940 Weinheim, 1980
tion 6.1 contains experimental evidence which uniquely assigns most of the observed bands.
In this article, I want to show how much more information, often of a very precise and unambiguous kind, one can
get about the electronic excited states of inorganic molecules
and complexes by measuring the spectra of single crystals using polarized light and low temperatures. Figure 1 is a dramatic illustration of the extra information gained by lowering the sample temperature.
298 K
Fig 1 A ligand field transition in Cs,CoC1, at rcom temperature, 77 K, and 4
Most of the examples come from our own work, but they
are quite representative of many now found in the literature.
Also, I shall only deal with complexes, by which I mean molecular species, whether charged or not, which retain their
chemical integrity when isolated in dilute solution just as
when they are placed in a crystal lattice. Electronic spectroscopy of transition metal ions in continuous lattice solids, like
Ni2+in MgO or pure NiO for example, forms a large subject
of its own, traditionally closer to solid state physics, although
many of the principles I shall describe here apply equally to
continuous lattices. There is a very large literature on the
electronic spectra of inorganic compounds. Thus, no attempt
is made here to treat the theoretical background of the subject, for which reference should be made to textbooks''' and
review articles[']. Rather, I wish to give an overview, albeit
$ 02.SO/O
Angew. Chem. Int. Ed. Engl 19, 290-301 (1980)
brief, of some of the methods used to obtain precise and experimentally based assignments of ligand field and charge
transfer states on which, ultimately, the tests for theories of
electronic structure depend.
2. Why Measure the Spectra of Single Crystals?
There are several answers to this question. The most
straightforward is that one may wish to know about the spectrum of a complex which does not exist in solution, perhaps
because it is hydrolyzed or transformed to a complex with a
different stoichiometry or stereochemistry. A simple example
is CuCl:-. However large an excess of chloride ions one puts
into a solution of CuC12either in water or dipolar aprotic solvents, the highest complex formed in any appreciable
amount is CuCl:-. Because of lattice energy considerations
though, use of a tripositive counterion like [CO(NH3)6]3+allows one to crystallize the pentachlorocuprate. Its ligand
field spectrum has been recorded for comparison with that of
Another reason which motivates much work on inorganic
crystal spectra is that one may be interested in the interactions between complex ions, due either to magnetic exchange
or to charge transfer. For instance, the color of Magnus'
Green Salt, [Pt(NH,),]PtCL, tells one at once that molecular
interactions are present in the crystal since the constituent
ions [Pt(NH3W2 and PtC1:- are respectively colorless and
redl41. Mixed valency is another frequent source of "non-additive" colors'51.Several examples of fine structure due to
magnetic exchange and the much broader intervalence
charge transfer transitions are given later (cf. Sections 6.4
and 4).
Probably the most valuable consequence of building complex ions into a crystal is that the orientations and geometries
of the molecules are thereby fixed, so that the polarization
vector of the incident light can be defined with respect to the
molecular axes. For the detailed quantum mechanics of the
interaction between electromagnetic radiation and molecules, reference should be made to the standard quantum
chemistry textbooks such as Eyring, Walter, and KimbaIl'6].
Suffice it to say here that when an electromagnetic wave
passes by, the molecule is subjected to simultaneous electric
and magnetic fields, oscillating with the frequency Y of the
radiation. If this frequency coincides with the energy difference between the ground state 0 and an excited state n of the
molecule through the relationship En, = hvo,, the resulting
time-dependent perturbation can be thought of as "mixing
together" the two wavefunctions +o and 9,. Integrating over
time one finds that radiation is absorbed and the molecule
undergoes a transition from $0 to +". The probability of light
absorption, represented experimentally by the peak molar
extinction coefficient or the oscillator strength, is related theoretically to the magnitude of the off-diagonal matrix element of the appropriate perturbation operator between the
two states 0 and n. Now the transition may be brought about
by the oscillations of either the electric or the magnetic component of the radiation. In the former case the perturbation
operator is the electric dipole operator m = 2 er, where the
matrix elements like J+,mJlodr and jJl;gJlOdr are observable properties of the molecule, like the ground state dipole
moment J+im+odr. Consequently, their absolute values
have to be independent of the molecular coordinates used to
define the wave functions Put another way, the matrix elements must be totally symmetric to all transformations of the
molecular coordinate system or, in the language of group
theory, they must span the totally symmetric representation
A,, within the point group of the molecule (for nomenclature
see ref. ['I; a very useful compilation of group theoretical tables is ref. [*I).In a cubic system the vector r appearing in the
electric dipole operator is three-fold degenerate: r = x + y + z,
for example TI, in the group Oh.Light absorption is then isotropic. However, when the symmetry is lowered from cubic
to tetragonal one axis, e. g., z is no longer equivalent to x and
y. In the D4h point group z transforms as Azu and x, y as
A particularly simple example of the assignment of an absorption band using polarized light is provided by the square
planar PtC1:- ion. This is a low spin d8 ion with a diamagnetic closed shell ground state, which therefore transforms as
A,, in D4h. The crystal KzPtCI, contains stacks of PtC1:ions with their planes all parallel or perpendicular to the
planes of the ions (Fig. 2a). For a transition to take place, the
arguments just given lead to the general rule
rox roPx r, c A,,
summation goes over all the electrons, and in the latter it is
the magnetic dipole operator p =(e/2m) 1I,. In principle,
Angew. Chem. Inl. Ed. Engl. 19. 290-301 (1980)
Fig. 2. a) Arrangement of PtCIz- ions in the K2PtCL crystal (schematic); b) directions of polarization of incident light; c) polarized absorption spectra.
where the T's are irreducible representations of the ground
state, the electronic or magnetic dipole operator and the excited state, respectively. For the two orientations of the electric vector of the incident light, shown in Figure 2b, we
therefore have
The former is satisfied for r, = A2,, the latter for r, = E,. Experimentally one finds''] that in the ultraviolet there is a very
intense band in the crystal spectrum of K,PtC1, at 42500
cm-' when the electric vector of the incident light is parallel
to z, but which is absent when EIIx,y (Fig. 2c). Thus, the upper state in question is 'A,,, and probably results from a
5d,2-6pz transition. On the other hand, the first intense band
in the spectrum of the isostructural crystal K2PdCl4only appears in E[lx,y so it has to be assigned to a 'E, state, most
likely a Cl(pa)+Pt5dxz- "2 charge transfer transition. Such
information could never have been found from a solution
Strictly speaking, in the example we have just given, no
definitive judgment could be made from the two polarized
29 1
spectra as to whether the transition was being allowed by the
electric or magnetic dipole mechanism. However, because of
the relative magnitudes of the electronic charge and the Bohr
magneton, it turns out that even fully allowed magnetic dipole transitions are many orders of magnitude weaker than
electric dipole transitions. For uniaxial crystals though, there
is a simple test to determine whether a transition is allowed
by the electric or magnetic dipole operator. As shown in Figure 3, we measure three polarized spectra, one called the axial (a)spectrum, with the light incident parallel to the unique
crystal axis (in which case both electric and magnetic vectors
are perpendicular to the axis) and two with the incident light
perpendicular. In the latter case, one has the choice of placing the electric vector parallel or perpendicular to the axis
(called respectively the a and cr spectra), Compare the three
spectra: two will be similar, the other different. Depending
on whether the transition is induced by the oscillating electric or magnetic component of the light, the axial spectrum
coincides with the u- or with the a-spectrum, because then
these two vectors are parallel. An example, shown in Figure
4, is one of the ligand field transitions of the CoC1:- ion in
Cs3CoC1,. In this tetragonal crystal we see clearly that the
axial and u-spectra coincide, demonstrating the electric dipole character of the transition.
Fig. 3. Measurement of polarized spectra for a uniaxial crystal.
3. Why Measure the Spectra of Crystals at Low
A fundamental problem with any kind of spectroscopy is
that information about two states, ground and excited, is
convoluted into one observable, the energy of the transition
between them. How can one uncouple that information and
find out about the two states separately? The simplest experiment along these lines is to change the temperature because
changes of thermal population among closely spaced sublevels only affect the ground state. In the limit, as we approach
absolute zero, all the molecules in the ensemble are in their
lowest states and any fine structure observed in the spectrum
relates to sublevels of the excited state. There are many
sources of sublevels within the electronic ground states of
inorganic complexes which, if thermally populated, confuse
and broaden the optical spectrum. Bearing in mind that the
thermal energy kT corresponding to room temperature is
about 200 cm-I, we can cite the following:
Skeletal vibrations in the range 100-300 cm-', (v(CoN)
is about 350 cm-' in Co(NH3)2+ and u(Hg-I) is about
120 cm-l in HgIz-);
Lattice vibrations and librations of complex ions in the
range 20-100 cm-';
Low symmetry splittings due to the distortion of the complex when placed in the crystal, usually in the range 1-10
cm-' (usually referred to by ESR spectroscopists as
"zero-field splittings");
Splittings of the order of 5-50 cm- ' due to magnetic exchange interactions in dimeric or cluster complexes.
At liquid helium temperature (4.2 K), kT is only about 3
cm- I , so broadening due to the population of these kinds of
sublevels is almost entirely eliminated, often with dramatic
effects on the resolution and hence on the information content of the spectrum. An example, shown in Figure 5, is a
A final reason for measuring the spectra of crystals is that
it gives us much the most convenient way of examining the
spectra at low temperatures.
1 lnml
Fig. 5. The spin-forbidden ligand field bands of Cs3CoBrsat r w m temperature
(top) and 4.2 K (bottom) (after [lo]).
27 0
26 6
26 2
Fig. 4. Axial (a),u- and n-polarized spectra of a ligand field transition in
portion of the ligand field spectrum of CoBrZ- in
Cs3CoBr5["I. In favorable cases such as this one, even very
small perturbations of a few cm - I can be used as assignment
Apart from cooling the sample to the lowest available temperature, another approach is to measure the spectrum as a
Angew. Chem. I n ( . Ed. Engl. 19, 290-301 (1980)
function of temperature and monitor the changing populations of the ground state sublevels. This can be done in two
different ways: if the spectrum is well resolved one can simply monitor the areas of the separate peaks and fit the results
to a Boltzmann distribution equation to extract the energy
separation between the ground state sublevels directly. For
example in CoC1:- the ground state of the Co" is 4AZ,but in
the crystal of Cs3CoC15the anion is slightly distorted in such
a way that the fourfold degeneracy (U' in the double group
Ti) is lifted and two doublet states result, split apart by 8.4
cm - ' . Looking at some of the ligand field bands under high
resolution, one sees pairs of bands with just this separation,
one member of each pair increasing in intensity with increasing temperature and the other decreasing. On fitting the intensities to the Boltzmann populations in a two-level model
an estimate of the separation of the two levels is easily made
(Fig. 6)I1li.
when it is formed by absorbing a photon it must be in a
strongly vibrationally excited state.
0 1300KI
fLKI 85 180 2
Fig. 7. Treatment of broad absorption bands: HgI:- doped into a crystal of
(N(C2H5)&ZnI+a) Axil absorption spectrum at temperatures from 300 to 4.2
K, b) band shapc at 300 and 4.2 K, c) halfwidth as a function of temperature
190 L
Fig. 6. Temperature dependence of the intensity (oscillator strength, arbitrary
units) of a pair of ligand field bands in Cs,CoBr, [ 111. The full Line is fitted to 11
cm-' separation between the ground state levels.
4. Band Shapes of Broad Absorption Bands
Unfortunately, it sometimes happens that absorption
bands remain broad and unstructured, even at very low temperatures. In such cases it may still be possible to extract useful information from the spectrum by measuring it as a function of temperature. For example, Figure 7a shows the first
transition of Hg1:- doped in a crystal of [(C2H5)4N]ZZnL
from room temperature to 4.2 K[12J.On cooling it shifts
somewhat and narrows, but otherwise remains featureless.
What we can measure, though, is its shape or, more particularly, its halfwidth. As we shall describe in more detail below, the band is broadened because the electronic excitation
couples to molecular vibrations: the transition obeys the
Franck-Condon principle, i. e., it is vertical on a potential energy diagram because the nuclei remain at the same positions
in space as an electron is transferred from an occupied to an
unoccupied orbital. If the equilibrium geometry of the excited state differs substantially from that of the ground state
Angew. Chem. Int. Ed. Engt. t9, 290-301 (1980)
If the motions of the electron and the nuclei are not coupled (i. e., the Born-Oppenheimer approximation is valid) the
total wavefunctions of the ground and excited states may be
factored into products of electronic and vibrational wavefunctions: e. g., = Jln xy, where x is a vibrational function.
If, as suggested above, we get the total oscillator strength of
the band by integrating the band area, this amounts to summing over all transitions from the thermally populated vibrational levels of the ground state to each vibrational level of
the excited state:
Given that the electric dipole operator operates only on the
electronic part of the wavefunction, the shape function G(v)
of the band envelope is obtained by summing over the set of
overlap integrals between the vibrational wavefunctions x.,
and xi. the purely electronic matrix element (+nlerl+o) acting as a constant multiplier:
In Eq. (4) P(v) represents the probability that the vth vibrational level of the electronic ground state is occupied. Of
course, there are many different modes i with frequencies q.
v'= 2
For any general case G (v) cannot easily be computed. However, by making some rather drastic simplifying assumptions,
a tractable expression results. In particular, one assumes that
all the modes i have the same frequency or alternatively, and
more realistically, that only one mode contributes to the
broadening. Furthermore, one supposes that the ground and
excited state potential energy surfaces are both harmonic,
and merely displaced Aq from one another as shown in Figure 8. The shape function G (v) then simplifies to a Gaussian
with a halfwidth H which is quite a simple function of temperature
HL CK (hw)'Scoth(hw/2kT)
v =o
v =o
Fig. 8. Ground and excited state potential energy surfaces. a) No change of dimensions in the excited state; b) small change; c) large change.
where w is the "effective" vibrational frequency in the
ground state and S , called the Huang-Rhys factori131,is the
ratio of the vibrational energy excited in the upper state to
the energy of a single vibrational quantum, i e., (1/2) w2Aq2/
h w. Measuring H as a function of T is thus a means of determining w, whilst the value of H at T=O gives S and hence
Aq, the expansion of the excited state compared with the
ground state.
To test Eq. (6) we first have to be sure that the band is well
represented by a Gaussian and that the shape does not
change with temperature. This is done by plotting
ratio of the absorption constant to its maximum value,
against v/H. A Gaussian curve converts to a parabola, as
shown in Figure 7b, which also shows that for Hg1:- the
shape is indeed constant with temperature. To obtain w one
then plots coth-'(H/H,)' against 1/T, giving a straight line
passing through the origin, from whose slope w is found (Fig.
7c). For HgIi- the value of w found in this way is 116 cm-',
remarkably close to the frequency of the totally symmetric
Hg-I stretching vibration as found by Raman spectroscopy.
The charge transfer spectrum of the ion Co1:- behaves in
exactly the same wayr141.
The ultraviolet spectrum of HgL- remains broad because
it results from transfer of an electron from non-bonding orbitals localized OR the halogen atoms to the highly antibonding empty 6s orbital on Hg. Even broader are the bands
which, in mixed valency compounds, arise from electron
transfer between two complex ions containing metals in different oxidation states. For instance, compounds containing
the two complex ions SbCI, and SbCl2- are dark blue because of an absorption band which does not occur in compounds containing either ion ~eparately"~'.
The new band is
a charge transfer Sb"'+Sb". As can be seen from Figure 9a,
it is at least 5000 cm-' wide['61.This is because we are removing an electron completely from one complex ion and
placing it on another, a process which must lead to an excited state having an equilibrium geometry very different
from that of the ground state. In Figure 9b the variation of
halfwidth with temperature is compared with that calculated
from eq. (6) with w = 2 1 0 cm-' and S = 130['61.The fit, which
is quite good. corresponds to the bond length change (about
0.2 A) expected on going from MCl2- to MCli-. On the
other hand, the frequency is not that of either SbCk- or
SbCl a .
[ 1o3~m-'I
Fig. 9. Intervalence Sb"'-rSbV absorption band in (CHaNH3]1Sb,Snt- X I 6 [16). a) Transmission spectra of two crystals of different thickness, A at 300 K, B at 6 K; b) observed and calculated half-width of
the intervalence band as a function of temperature.
Angew. Chem. In?. Ed. Engf. 19, 290-301 (i980)
5. How to Measure the Spectra of Crystals at Low
We have discussed some of the types of information which
are potentially accessible by measuring crystal spectra at low
temperatures. How then does one go about it? Technical details of optical spectroscopy are given in a number of
books('71;here I will describe some general principles.
5.1. Cryostats
Liquid helium is now found much more often in chemistry
laboratories than it was a few years ago, so we shall not consider any other cryogenic fluids such as liquid nitrogen (b. p.
77 K) or liquid hydrogen (b.p. 20 K). Cryostats for optical
spectroscopy are of two main types: static or flow. Also available, though more expensive than cryostats, are various types
of closed-cycle or open-cycle refrigerators which are usually
based on the Joule-Thomson effect. However, they are much
cheaper than conventional cryostats to operate, since they
only need gas or, in the case of the closed-cycle systems, only
electricity, and are very suitable for laboratories where supply of liquid refrigerants is a problem. On the other hand, they
rarely work below about 10 K, and have only a limited cooling capacity.
Static cryostats, nowadays mostly made of metal, consist
of an outer vacuum casing within which the can containing
the liquid helium is further isolated from heat entry by surrounding it with a copper radiation shield cooled by liquid
nitrogen. The sample is then suspended on a rod so that it is
immersed in the liquid helium for experiments at 4 K, or in
cold flowing gas for work above 4 K. The sample rod usually
contains a small heating element, as well as a temperature
sensor such as a carbon resistor or a gold/0.03 atomic percent
iron us. chrome1 thermocouple, to enable the temperature to
be controlled by a feed-back device. A typical form of static
cryostat is shown in Figure 10a. To reach temperatures below 4 K, a second liquid helium container is placed within
the main container, insulated from it by another vacuum
space but connected to it by a siphon tube. The inner chamber is filled through the siphon from the outer, then closed
off, and the pressure above the liquid is reduced by a rotary
pump. In this way, temperatures down to about 1.4 K are accessible. To go lower, more specialized methods are needed.
A very convenient form of small cryostat for carrying out
short experiments down to about 3.6 K is the continuous
flow system shown in Figure lObI"1. Here the liquid helium
is sucked from a storage vessel through the cryostat by a
small pump, the flow rate being controlled by a needle
5.2. Sample Mounting
Unless condensing optics are used to focus the light onto
the crystal, the minimum crystal dimensions for optical spectroscopy are about 1 mm2 in area. Of course, the thickness
depends upon the extinction coefficients of the bands being
measured and the concentration of active chromophore in
the crystal. Most conventional double beam spectrophotometers can measure an optical density of about 3 without the
effects of stray light becoming too noticeable. Pure solids
may have an effective concentration of light absorbing species as high as 5-IOM.
so if the molar extinction coefficient
of the band in question is 10 1 mol-' cm-' the crystal should
not be thicker than about 0.2 mm. On the other hand, if one
wishes to measure a charge transfer transition, with a molar
extinction coefficient of several thousands, the best way is to
dilute the chromophore by making a solid solution with an
isomorphous but non-absorbing host lattice, for example
MnO; in KC104. If necessary, crystals can be thinned either
on a lapping wheel using diamond paste, or with successively
finer grades of emery paper, followed by polishing with
After determining its orientation by taking an oscillation
or a Laue back-reflection X-ray photograph, the crystal is
usually mounted in the cryostat by fixing it over a hole in a
copper plate with a small amount of silicone grease, taking
care that it is not strained, and that no light passes around its
5.3. Spectrophotometers
Fig. 10. a) Static cryostat. 1 , helium level indicator, 2, liquid nitrogen reservoir; 3,
liquid helium container; 4, copper block; 5, quartz windows; 6, copper radiation
shield; 7, to vacuum pump; 8, transfer tube; 9, to helium Dewar. b) Flow cryostat
Angew. Chem. Inl. Ed. Engl. 19, 290-301 (1980)
Commercial double beam ratio recording spectrophotometers are quite suitable for all except the most sophisticated
measurements of polarized low temperature crystal spectra.
Important factors to bear in mind are the resolution of the
monochromator, determined by the length and the number
of lines/mm of the grating; the stray light level, which determines the maximum optical density which can be measured,
and the sensitivity and wavelength range of the detection
system, which governs the slit width at which one can work,
and hence the ultimate resolution possible with a crystal of
given size. Taking the Cary 14 or 17 as an example, these in-
struments have monochromators containing both a prism
and a grating. The quality of the monochromation is usually
expressed as the reciprocal dispersion, in this case about 30 A
mm- ' in the visible. The ability of the instrument to resolve
closely spaced peaks depends on the width of the entrance
and exit slits: at the minimum values usually employed in the
Cary (about 0.02-0.05 mm) it has a resolution, or spectral
band-pass, of about 1 A. Normally visible-ultraviolet spectra
are expressed in wavenumbers (cm-'), so it is of interest to
note that at 4000 A, on the edge of the ultraviolet, 1 A is
equivalent to about 6 cm-', while in the red, at 7000 A, it is
about 3.5 cm-'.
More sophisticated monochromators may do considerably
better than this. For example, a standard 1 m Czerny-Turner
monochromator with a grating having 1200 lines mm-' has
a reciprocal dispersion of 8.3 A mm-' in first order, and can
be used to obtain spectral bandpass nearer 0.1 A, i. e., about
0.5 cm-' in the visible. Quite a different way of obtaining
highly monochromatized radiation, now having a large impact on many fields of spectroscopy, is the tunable dye laser.
With a given dye one can usually tune the radiation over
about 300 A but dyes are now available to cover the whole
range from the near infrared (9500 A) to the ultraviolet (3500
A) or, with frequency doubling, to about 2200 A. As in a
monochromator the spectral bandpass of the radiation depends upon the size and quality of the grating used in the laser cavity, but around 0.1 A is quite readily obtained. Further,
by fitting an etalon in the cavity this may be reduced by a
further factor of 100.The uses of such very narrow bandpass
radiation for inorganic spectroscopy are only now beginning
to be explored.
6. Fine Structure in Low Temperature Crystal
Earlier on in Section 3 we listed some of the sublevels
within the electronic ground state which, by becoming thermally populated at room temperature, serve to confuse the
absorption spectrum. It is important to realize that such sublevels exist for every excited state, so at low temperatures the
fine structure we see in the spectra reflects the sublevel structure of the excited state, and is extremely valuable for assigning the transition. Let us now consider some sources of fine
structure, and the kind of information that we can get from
them. First of all, we take the fine structure which comes
from co-excitation of molecular vibrations.
6.1. Vibrational Structure
The three parts of Figure 8 indicate the three broad subdivisions of behavior when a transition occurs between a
ground state and excited state potential energy surface. They
correspond to increasingly strong coupling between the electron being excited and the nuclear framework of the complex, a distinction which was originally made a long time ago
by Herzberg in the spectra of small molecules in the gas
phaser'''. We have already discussed in Section 4 the extreme
form of case c, when only a broad unstructured envelope is
seen, In the other limiting case, when the equilibrium dimensions and the force constants of the molecule are unchanged
by the electronic transition, one would anticipate only a single sharp line corresponding to v=O+v'=O, because the vibrational wave functions form an orthonormal set. Only
when v = u' is the vibrational overlap integral in Eq. (4) nonzero. Case a of Figure 8 applies when the electrons involved
in the transition scarcely influence the molecular binding; an
extreme example would be an f+f transition in a lanthanoid
or actinoid complex. However, there is a complicating factor
here because the electronic transition itself is not electric dipole-allowed if the complex is centrosymmetric, owing to the
fact that Jlo and Jln share the same parity. For an electric dipole transition to be observed, the electronic excitation has to
be accompanied by creation (xo+x;) or annihilation ( x , +&)
of a quantum of some non-totally symmetric vibrational
mode. An extension of Eq. (1) is then
r,, r;b x roDx r. x r:b c A,,.
Applying Eq. (7) to an octahedral complex of an f-block element, for example, roand r, would both be u-functions, rOp
is the u while if the temperature is low enough for all the molecules in the crystal to be in their vibrational ground states
rp is g. Hence, has to be u.
Just such a situation, which represents a particularly neat
example of these arguments, is the UC1,'- ion, whose spectrum was measured some years ago by Satten and his colleagued2']. The electron configuration of the ion is 5P and
the ground term is 3H4.Fine structure of one of the f-if transitions in [N(CH3)4]2UCb,in which the UCli- occupies a
centrosymmetric site, is shown in Figure 11. There is a clear
symmetry about this band system, corresponding components lying at equal frequency intervals on either side of a
central point, marked with the arrow. The latter represents
the frequency of the purely electronic f - + ftransition which,
because it is u-u, does not appear. What we do see, though,
are narrow bands corresponding to the frequency of the
purely electronic transition plus or minus the frequencies of
single quanta of each of the odd-parity vibrational modes of
the octahedral complex. Sum and difference bands are easily
distinguished by varying the temperature because the xl -+ xb
bands lose intensity when the crystal is cooled and the u = 1
levels become depopulated. The way their intensities vary
with the temperature provides an additional check on the
ground state vibrational frequencies via the Boltzmann population expression [Eq. (5)].
Usually, d-electrons in transition metal complexes are
thought of as more heavily engaged in molecular binding
than f-electrons in complexes of the lanthanoids and actinoids. In analyzing vibrational fine structure accompanying
the d-d transitions of centrosymmetric transition metal complexes we meet the same problem we have just described for
UCl,'-, namely that the absorption is electric dipole-forbidden, this time because it is g+g. However, we can avoid this
complication by looking at the spectrum of a tetrahedral
complex. If the equilibrium position along a vibrational
coordinate in the excited state is slightly (but only slightly)
displaced from its position in the ground state, or if the force
constant is slightly altered by the excitation, the ground and
excited state vibrational wavefunctions no longer form a
strictly orthonormal set so that transitions other than u=u'
become allowed. On the other hand, the vibrational overlap
Angew. Chem. IRI. Ed. Engl. 19, 290-301 (1980)
integrals ( x J x v ) , whose squares are called Franck-Condon
factors, fall off rapidly in magnitude as v and u’ diverge. At
low temperature then, we find the x o - + x i band strongest, but
followed by a “progression” of increasingly weaker bands
from excitation to x;, &, ... etc. If the potential energy surface
remains reasonably harmonic in the excited state, the intervals between its vibrational levels are constant. The progression then manifests itself in a very obvious way, as a series of
equally spaced bands. In fact, one of the first things which a
spectroscopist does when confronted by a highly structured
band system is to search for some constant energy intervals.
Fig. 1 1 . Part of the f+f spectrum of [(CH3)4N]2UC4at various temperatures.
showing fine structure due to odd-parity vibrational modes [20].
He is often aided by the fact that the vibrational frequencies
in the excited state are not more than 10% or so different
from those of the ground state. Consequently, a good knowledge of the crystal’s infrared and Raman spectra is a great
Nevertheless, even such a simple molecule as a tetrahedron has four intramolecular vibrational modes (a, e, t,, and
t2), not to mention vibrations of the molecules against one
another, or against the wunterions in the crystal. Which of
them are likely to show up as progressions? The answer is
mostly the totally symmetric ones. This is because of the operation of the Born-Oppenheimer approximation. Even if we
remove the orthonormality requirement from the vibrational
wavefunctions, only multiple quanta can be excited of those
modes which are totally symmetric in the point group both of
the ground and the excited electronic state. Should the complex change shape on excitation, i. e. if the point group of the
excited complex, at its equilibrium geometry, is different
from the ground state, one may find w-excited modes which,
while non-totally symmetric in the ground state’s point
group, become totally symmetric in that of the excited state.
The most common consequence of the breakdown of the
Angew. Chem. Int. Ed. Engl. 19, 290-301 (1980)
Born-Oppenheimer approximation is the Jahn-Teller effect:
as Liehr rernarkedI2‘1many years ago “observation of a progression in a non-totally symmetric mode is a sure sign of
Jahn-Teller funny business”. However, in this short article, I
do not want to consider this particular complication.
An illustration representative of the vibrational fine structure often seen in ligand field spectra is the band system of
Figure 4. Three sets of repeating bands are observed; they
are separated by intervals of 275 cm-l, very close to the a,
stretching frequency in the ground state of CoC1:(285 cm-’). Further subsidiary intervals correspond to excitation of single quanta of the e molecular mode, and also
various lattice modes. After the vibrational sidebands have
been assigned in this particular case, there remain four closely spaced electronic origin bands. These originate from the
lowering of symmetry in the ground and excited states as a
result of the crystal lattice environment. We shall discuss
them further below.
When the molecule changes its dimensions by a larger
amount on excitation, as for example in a charge transfer
transition when an electron is transferred from an orbital localized on the ligands to one localized on the metal, the first
member of the vibrational progression is no longer necessarily the most intense: as a function of u’ the vibrational overlap integral (xolx;,) may have its maximum value for u’>O.
Figure 12 shows a particularly well resolved progression in
the visible spectrum of the MnO, ion doped into the tetragonal lost lattice K10,[221.The frequency of the repeat interval is 764 cm-‘, which should be compared to the a, Mn-0
stretching frequency in the ground state, 850 cm-‘. Note
that this excited state frequency is reduced by a much larger
factor than was the case for the ligand field band of CoClz-.
By assuming that the potential energy surfaces of the two
states are harmonic, one can use the set of Franck-Condon
factors to calculate how much the molecule is expanded in
the excited state: from the very similar spectra of MnO; in
the orthorhombic host crystal KC104, a figure of 0.10 A has
been estimated[23’.
Sometimes the nature of the vibration co-excited with the
electronic transition can be used to diagnose the type of transition. An interesting set of examples of this way of using vibrational fine structure are the metal-metal bonded dimers
such as Re,CI;-, whose structures consist of two planar
ReC1, moieties placed face-to-face with a very short Re-Re
distance. Two kinds of electronically excited state can be envisaged in this kind of complex. Either electrons are excited
0 45
0.35 0.30 -
2 0.25 -
9 0.15 -
Fig. 12. Part of the axial spectrum of MnOi in tctragonal K I 0 4 1221
from C1 orbitals to empty Re orbitals (charge transfer) or the
excitation is from metal-metal bonding orbitals to antibonding ones, in which case the transition is localized within the
Re2 part of the molecule. If the transition were of charge
transfer type the vibrational coordinate q in Figure 8 along
which the molecule is displaced on going from the ground to
the excited state is that of an Re-Cl normal mode. On the
other hand if the electron remains within the Re2 unit, while
reducing the Re-Re bond order, then it is the Re-Re distance which is most altered on excitation. In the event (Fig.
13) the vibrational mode co-excited with the 680 nm band in
Re2C1i- is the Re-Re stretching mode (350 cm-I), so the
band is assigned to the 6 - 6%transition of the Re-Re quadruple
Similar conclusions were reached about the
visible absorption bands of several complexes containing the
Mo;+ unit, though here there is an interesting complication
because much of the intensity appears to arise from vibronic
ural abundances 75.4% and 24.6%, respectively. The tetrachloromanganate complexes in our crystal therefore consist
. ..etc. in
of [Mn35CL$-, [Mn35C1337C1]2-,
1 [nml
Fig. 14. Isotope fine structure in the vibrational sidebands of a ligand field transition of MnC1:- in Cs,MnCI, [28].
statistically determined proportions. Each Cl, unit has a
slightly different reduced mass (in the a, mode the Mn remains stationary) and so gives a sideband at a slightly different frequency. The calculated frequencies and abundances
are shown as sticks in Figure 14: agreement with the experimental spectrum is clearly excellent.
1 [nml
Fig. 13. Polarized absorption spectra of [N(C4HP)&[Re2CI81
at 5 K [241
6.2. Isotope Vibrational Splittings
A special case of vibrational fine structure occurs when the
ligands can exist in more than one isotopic form. Frequencies of metal-ligand vibrations depend on the masses of the
vibrating atoms and on the force constant of the bond,
which, of course, is unaffected by substituting one isotope for
another. Shifts in the frequencies on isotope substitution
therefore result from the changed reduced mass alone. Sometimes isotope substitutions are made deliberately to assign vibrational fine structure: for exampIe D for H in aquo-complexes[261or 0l8for 0 l 6 in complexes of the uranyl (UO:+)
Sometimes, too, one may simply find two isotopes
present in ordinary natural abundance. An instance of this
effect is shown in Figure 14. One of the ligand field bands of
MnC1:- in the tetragonal crystal Cs3MnC15[actually one of
the spin-orbit components of 4T2(D)] is accompanied by a
progression in the a, Mn-C1 stretching mode, much as in
the band of CoC1:- in Figure 4. However, in the Mn case
the bands are particularly sharp and well resolved, so that
further substructure becomes
In the first vibrational sideband (i. e., one quantum of the a, mode) we see an
envelope of at least three bands, each separated from the
next by 2.1 cm-‘. Chlorine occurs as 35Cland 37C1with nat-
6.3. Site Group Splittings
Although complex ions like CoC1:- and MnO; may be
regular tetrahedral in soIution, when they are incorporated
into a crystal lattice they will almost certainly occupy sites
with lower point symmetry than Td. Taking the absorption
band in Figure 4 as an example, we noticed that after the vibrational sidebands were all accounted for there remained a
group of bands constituting the electronic origin. This is
shown in greater detail in Figure 15. As noted earlier, the
ground state (4A2in Td) is split in the crystal of Cs3CoCl5by
a combination of spin-orbit coupling and a small tetragonal
distortion to give two doublets ( E and E ’ in Did). Ligand
field calculations[“] suggest that the band system in Figures
4 and 15 might be assigned as a transition to a %(Td)state
which, like the ground state, would transform as U’ in the
double group T3. Also like the ground state, this excited U’
state would be split by the tetragonal site distortion, similarly
giving two doublets, E’+ E . In principle, therefore, four
transitions are possible, and they can all be assigned by combining temperature dependence and polarization data as
shown in Figure 16[“’. Eq. (1) applied to the double point
group D;d tells us that E + E and E’-+E’ are allowed only
in xy-polarization while E + E ’ and E ” + E are allowed for
both xy- and z-polarizations. In Figure 15a we see that the
lowest energy band A only appears in the xy-spectra while
temperature variation experiments indicate that it is a “hot”
band; 8.4 cm-’ to higher energy the next band B has mixed
polarization and behaves as a “cold” band. Figure 15b shows
Angew. Chem. Ini. Ed. Engl. 19, 290-301 (1980)
bands A and B in the xy polarization at even higher resolution and lower temperature. At 1.3 K band A has disappeared completely. The temperature variation experiments also
C10; groups but fortunately their mirror planes are all parallel. Permanganate has a closed shell ground state, transforming as ' A . Transitions are allowed to ' A when the electric vector is parallel to the mirror plane and to ' A ' when it
is perpendicular. When one examines the electronic origin of
the visible band at 4 K for these two polarizations[291one
finds that there are two 'A' bands and one 'A". Since T2 in
Td is decomposed into 2 A + A" in Cs, the experiment clearly
defines the tetrahedral parentage of the excited state as IT2.
Ligand field
Ligand fieid
+Site group
Fig. 16. Site splitting of the 'A2-% transition of CoCI:- in CszCoCIs. Labels
A-D refer to Fig. 15.
Fig. 15. Electronic origin region of the "A>+'E(D) transition of CoC1:- in
Cs,CoClS: a) under medium resolution; b) under high resolution. Bands A-D
refer to Fig. 16.
tell us that the hot band A originates from a level 8.4 cm-'
above the lowest, hence the first two bands come from transitions to the same upper level from the two components of the
ground state. The third band C, which is also "hot", is of
mixed polarization while the fourth D, again "cold", is only
seen in the xy-spectrum. ESR spectroscopy[301tells us that
the E' level lies 8.4 cm-' below the E" in the ground state so
the optical data show quite unambiguously that the two levels of the upper state lie in the opposite sequence. The two
cold bands are 33 cm-' apart, which is therefore the sitegroup splitting of the upper 'E state. By applying the same
kind of arguments most of the other dozen or so doublet ligand field states of CoCIi- and CoBri- were definitively located and assigned'". ' ''.
Charge transfer spectra too show many nice examples of
site-group splittings which constitute a most valuable assignment tool for this type of transition. Again the MnO; ion
provides a good illustration. When doped in the orthorhombic crystal KC1o4 the MnO; occupies the C10; sites, having
only Cs point symmetry, i e., only one remaining element of
symmetry, a mirror plane passing through the C1 and two oxygen atoms. Actually in the unit cell of Kclo, there are four
Angew. Chem. Int. Ed. Engl. 19, 290-301 (1980)
A very similar example is MnOi-, a 3d' ion, whose low
temperature charge transfer spectrum in a Cs,SO, host crystal is shown in Figure 17I3'].The site group in this lattice is
again Cs, which splits the *E(Td)ground state into ' A and
that the latter lies
,Af'. From ESR s p e c t r ~ s c o p yit~is
lower by some 200-300 cm - I . Because of the extra electron
the situation is now more complicated than for MnO ;and in
the Td point group transitions would be electric dipole-allowed from 'E to either 'TI or 'T2 states. Our task is thus to
discover which in fact appear in the charge transfer spectrum, and in what order. Selection rules in the Cs2S04lattice
are the same as the ones we have just given for Kclo,. Notice that the origin region of the first charge transfer band in
Figure 1 consists of two bands in the E\lb spectra and one in
the Ella; in the former the electric vector is parallel to the
mirror planes through the Mn atoms, in the latter it is perpendicular. Consequently we have the same result as for
MnO; in KC1o4, namely two A' and one A" origin, and the
tetrahedral parentage of the first charge transfer band is
Y [ern-']
Fig. 17. The polarized charge transfer spectrum of Mn0:[31]. -,
.Ells. . ..-, Ellk
in Cs2S04 at 4 K
again T2. As can be seen from Figure 1 the higher energy
bands are not sufficiently resolved, even at 4 K, for this
means of assignment to be used, but the relative intensities in
the two polarizations give a clue to the fact (confirmed by
more detailed arguments which we shall not reproduce here)
that all except the band near 30000 cm-‘ also have T2parentage.
6.4. Magnetic Interactions
Most metal complexes are monomeric, but a number of
classical examples such as the acid and basic “rhodo-” and
“erythro”-chromium(iI1) salts contain pairs or larger clusters
of transition metal ions, and in recent years an increasing
number of others have been synthesized. If the individual
metal ions in the cluster have unpaired electrons there will be
some magnetic exchange interaction between them, either
ferro- or antiferromagnetic. The ground state of the cluster
then consists of a series of sublevels characterized by various
values of ST,the total spin quantum number of the cluster.
Consider, for example, a dimeric chromium(m) complex. In
the ground state, each Cr atom (3d3, 4A2gin an octahedral
ligand field) labeled 1 and 2 carries a net spin of S , = S2= 3/2
so the total spin quantum number of the complex can take
integral values from Sl - S, to S , + Sz, i. e. from 0 to 3. The
sublevels with different SThave different energies, often described to a good approximation by the Heisenberg hamiltonian
which predicts energy intervals between successive levels
with increasing S, of J, ZJ, 3J. If J i n eq. (8) is negative (antiferromagnetic) the S,=O sublevel lies lowest while if it is
positive (ferromagnetic) S , = 3 is lowest. In the ligand field
spectra of dimeric chromium(Ir1) complexes therefore we expect to see groups of bands representing transitions from
each of the STsublevels of the ground state to various S; sublevels of the excited state. The selection rule A ST=Ois
usually obeyed quite well[331.Changing the temperature will
alter the populations of the S , sublevels and hence the relative intensities of the bands. A quantitative intensity measurement as a function of temperature serves to identify
which S, sublevel the transition originates from, and, in
combination with the observed energy of the band, enables
one to map the ground and excited state exchange sublevels.
A good example[34’ is the acid “rhodo”-chloride
3 H 2 0 in which the hydroxyl
ion forms a bent bridge between the two Cr atoms. Figure 18
“ 0
Fig. 18. Temperature dependence of intensity of two exchange-split ligand field
H,O fitted to the ground state exchange
bands in [(NH3)sCr(OH)Cr(NH3)s]ClS.3
splitting shown inset 1341.
shows the temperature variation of the two most intense
bands in the 680 nm (4A2-’ZE) region of the ligand field
spectrum fitted to fractional populations calculated for the
separations of S , sublevels shown. A value of J of about
- 33 cm-I gives quite a good fit to the experimentally observed energy levels, with the ratio of the intervals between
the sublevels very close to 1:2: 3. Comparable experiments
have been done with several other d i m e r i ~ [and
~ ~ ltrimeric[’“’
chromium(m) complexes, as a testing ground for theories of
magnetic exchange.
7. Conclusion
Electronic absorption spectroscopy is one of the most
widely used tools of the inorganic and coordination chemist
who wants to learn something about the electronic structures
of molecular complexes containing not only transition metal
but also B-subgroup cations. By orienting the complex in a
crystal and then lowering the temperature the amount of information contained in the visible absorption spectrum is
enormously enhanced. Not just the overall polarization of
the bands, but the various kinds of fine structure only resolved at low temperature, contribute to a refined view of the
excited state’s electronic structure. In particular in this article
we have tried to show how various observable features in low
temperature polarized crystal spectra can give unambiguous
symmetry assignments to transitions using only our knowledge of the crystal structure and the group theoretical selection rules and, further, give information about the equilibrium geometry of the excited state. However, the beauty of
selection rules based only on symmetry requirements is that
they do not depend for their validity on the results of detailed quantum mechanical calculations containing approximations which may or may not be well founded.
It will be clear that such experimentally based assignments, not relying for their validity on the assumptions of
any particular theoretical model, are the only possible starting point for assessing how valid these assumptions are. Fitting absorption band energies to the results of ligand field
calculations is a long standing sport among inorganic chemists, but it is always wise to be sure, from some other experiment, that the bands being being fitted actually have the assignment which is being put on them. Such advice is doubly
necessary in the field of charge transfer spectra, for which no
reliably predictive model exists yet. Only by amassing the results of many experiments of the kind described here on the
widest possible variety of complexes can we arrive at the experimental basis on which a predictive model must be
founded. Basic equipment for measuring low temperature
polarized crystal spectra is readily available commercially,
and is not difficult to use. In our laboratory we have measured temperature dependent spectra down to as low as 0.8 K
using a specially designed cryostat, and spectral bandwidths
as small as 0.001 A could be obtained using a tunable dye
laser containing an intracavity etalon. However, very little
work on the spectra of inorganic complexes has been reported yet with such low temperatures and high resolving
power. More important for the chemist wanting to correlate
his results with structural theories is the accumulation of a
large body of securely assigned spectra. For the simplest tetra- and hexahalide and tetroxo-complexesthe information is
Angew. Chem. Int. Ed. Engl. 19, 290-301 (1980)
at hand, for mixed complexes and complexes of more elaborate ligands it is only now beginning to be accumulated.
Most of this article was written while a Visiting Scientist at
the Xerox Corporation Webster Research Center. I am grateful for the hospitality extended to me by members of the Center.
Received: December 22, 1978;
supplemented: November 12, 1979 [A 314 IE]
German version: Angew. Chem. 92, 290 (1980)
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The Dynamic Behavior of 2,4,6-CycIoheptatriene-lcarbaidehyde["]
By Metin Balci, Hartmut Fischer, and Harald Giintherl'l
Ring inversion and valence tautomerism are well-known
dynamic processes in cycloheptatrienesl". While stenc effects, besides possible electronic factors, play a major rolef21
in determining the position of the conformational equilibrium (la)+(lb) in C7-substituted derivatives, the cycloheptatriene-norcaradiene equilibrium (2)*(3) is largely controlled by the acceptor properties of the substituents RI3].According to MO calculations141this influence should increase
Dr. M.Balci, Dip1.-Chem. H. Fischer, Prof. Dr. H. Giinther
Gcsamthochschule Siegen, FB8, OC I1
Postfach 21 0209, D-5900 Siegen 21 (Germany)
["I This work was supported by the Minister fur Wissenschaft und Forschung
des Landes Nordrhein-Westfalen.
Angew. Chent Int. Ed Engl. 19 (1980) No. 4
0 VerIag Chemie. GmbH, 6940 Weinheim, 1980
05 70-0833/80/04O4-0301
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crystals, inorganic, low, temperature, polarizes, complexes, spectral
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