Isotropic collision-induced scattering by CF 4 in a Raman vibrational band
J.-L. Godet, A. Elliasmine, Y. Le Duff, and T. Bancewicz
Citation: The Journal of Chemical Physics 110, 11303 (1999); doi: 10.1063/1.478004
View online: http://dx.doi.org/10.1063/1.478004
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/110/23?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 23
15 JUNE 1999
Isotropic collision-induced scattering by CF4 in a Raman vibrational band
J.-L. Godet,a) A. Elliasmine, and Y. Le Duff
Laboratoire des Propriétés Optiques des Matériaux et Applications, Université d’Angers, 2 boulevard
Lavoisier, 49045 Angers, France
T. Bancewicz
Nonlinear Optics Division, Institute of Physics, Adam Mickiewicz University, Umultowska 85,
61-614 Poznań, Poland
~Received 10 November 1998; accepted 18 March 1999!
Light-scattering intensities and depolarization ratio data have been recorded at room temperature for
gaseous tetrafluoromethane in the collision-induced band of the Raman vibrational line n 1
5908 cm21. For the first time, binary isotropic intensities of the n 1 -Raman band are reported in
absolute units for Stokes frequency shifts up to 110 cm21. From comparison with theoretical
semiclassical computations of the dipole-multipole spectrum contributions, evaluations of the first
derivatives of the successive dipole-multipole polarizability tensors are provided. These results are
coherent with those obtained from corresponding depolarized intensities. Moreover, the agreement
with ab initio quantum-chemistry calculations of the CF4 multipolar polarizabilities is satisfactory.
© 1999 American Institute of Physics. @S0021-9606~99!52522-1#
I. INTRODUCTION
II. THEORETICAL SPECTRUM
Since a molecule in a gas interacts with its neighbors,
collision processes induce polarizability modifications and
collision-induced scattering ~CIS! may be observed in the
vicinity of spectral lines. For the optically symmetric molecule CF4, depolarized Rayleigh1,2 and n 1 -Raman3 intensities due to CI binary interactions have been reported in absolute units. In these cases, monomolecular depolarized
scattering is forbidden and the CI polarizability anisotropy
may be regarded as responsible for all observed scattered
light. On the contrary, for polarized scattering, Rayleigh and
Raman Q lines due to monomer polarizability contribute to
corresponding spectra. Moreover, Rayleigh and Raman polarized bands are due as well to the trace and to the anisotropy of Rayleigh and Raman CI-polarizability tensors. Recently, the isotropic contribution to the CF4 Rayleigh
scattering has been obtained from the measurement of the
depolarized and polarized scattering intensities around the
laser frequency.4 This procedure needs good accuracy for
intensity data, especially when the depolarization factor
value is high and the isotropic contribution relatively weak.
In the present work, for the first time, we present our results
concerning the CI isotropic intensities in the n 1 -Raman band.
We compare these experimental data with theoretical semiclassical computations. In our analysis, we consider the influence of successive multipolar mechanisms from comparison between the theoretical and the experimental spectra.
Taking into account previous data extrapolated from
Rayleigh2 and n 1 -Raman3 depolarized spectra and from the
isotropic Rayleigh spectrum,4 we deduce the values (A 8 ,E 8 )
of the derivatives of the dipole-multipole polarizability tensors. Then these values are compared with quantummechanical values recently calculated by Maroulis.5,6
We consider a macroscopically isotropic system composed of N-like globular molecules in an active scattering
volume V illuminated by laser radiation of angular frequency
v i 52 pn i , linearly polarized in the direction e. We analyze
the secondary electromagnetic radiation emitted by the system in response to that perturbation. The radiation scattered
with an angular frequency v s 52 pn s is measured at a point
R from the center of the sample located behind an analyzer
of polarization n. Then, the quantum-mechanical expression
for the differential scattering cross section for scattering into
an angular-frequency interval d v and a solid angle dV has
the form7
a!
Electronic mail: [email protected]
0021-9606/99/110(23)/11303/6/$15.00
v i v 3s
] 2s
5 4
]v] V
c
r i u ^ i u e–P–nu f & u 2 d ~ v 2 v f i ! ,
(
i, f
~1!
where r i denotes the density matrix element of the initial
state i and P is the polarizability tensor. Using the Fourier
transform of d ( v 2 v f i ) we rewrite Eq. ~1! as
~2!
where ^ & denotes a canonical average. After Ref. 8, the correlation function F(t) for macroscopically isotropic systems
may be expressed as the sum of components each of which is
the product of two zero rank tensors, one dependent of the
scattering geometry and the other on the internal properties
of the scattering system. The polarizability tensor Pab ,
when completely symmetric to its indexes, decomposes into
an isotropic part and an anisotropic part. Expressing the
same in the language of irreducible spherical tensors, the
polarizability tensor P splits into two irreducible parts of
ranks zero and two:
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© 1999 American Institute of Physics
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Godet et al.
J. Chem. Phys., Vol. 110, No. 23, 15 June 1999
TABLE I. Isotropic Raman light-scattering correlation functions F iso
n 1 (t) for successive multipolar induction
operators. The functions S N (t), R j (t), and F 1 are defined in Refs. 2–4 whereas R 12 is the intermolecular
distance. ~DQ: dipole-quadrupole; DO: dipole-octopole; QQ: quadrupole-quadrupole; QO: quadrupoleoctopole; OO: octopole-octopole.!
Mechanism
Raman case
F iso
n 1 (t)
First-order DID
Second-order DID
DQ
a 8 Ta 1 a Ta 8
a 8 Ta Ta 1...
a 8 TA1 a TA8
a 8 TE1 a TE8
A8 TA1ATA8
A8 TE1ATE8
E8 TE1ETE8
0
216a 4 a 8 2 ^ R 12(0) 26 R 12(t) 26 & F 1
DO
QQ
QO
OO
P⇒P~ 0 ! % P~ 2 ! .
Then the correlation function F(t) reads
1
F ~ t ! 5 ~ e–n! 2 ^ P~ 0 ! ~ 0 ! (P~ 0 ! ~ t ! &
3
31 ~ e–n! 2 ~ 2 !
1
^ P ~ 0 ! (P~ 2 !~ t ! & .
30
~3!
In our experiment, we study the 90° scattering intensities
and we observe scattered radiation without any analyzer.
However, the polarization of the incident laser beam is either
perpendicular or parallel to the scattering plane. In the perpendicular case ~'!, the correlation function becomes
F' ~ t ! 5F iso~ t ! 1 67 F d ~ t ! ,
~4!
where
F iso~ t ! 5 31 ^ P~ 0 ! ~ 0 ! (P~ 0 ! ~ t ! & ,
~5!
F d ~ t ! 5 51 ^ P~ 2 ! ~ 0 ! (P~ 2 ! ~ t ! & ,
~6!
are responsible for the isotropic and the depolarized spectral
intensities, respectively. From Eq. ~2!, we note that the
double differential cross section ( ] 2 s / ]v] V) j of the respective kind of scattered radiation of interest and the appropriate
time correlation function F j (t) are connected by a Fourier
transform
S D
v i v 3s 1
] 2s
5 4
]v] V j
c 2p
E
`
2`
dt e 2i v t F j ~ t ! ,
~7!
with j equal to d, ' or iso. From Eqs. ~4! and ~6! we deduce
the frequency-dependent depolarization ratio for a 90° scattering experiment:
h~ n !5
I d ~ n ! Ft F d ~ t !
I d~ n !
5
5
,
I' ~ n ! Ft F' ~ t ! I iso~ n ! 1 67 I d ~ n !
~8!
where n is the frequency shift that is defined relative to the
incident-beam frequency n i and Ft symbolizes the Fourier
transform. Therefore, the isotropic intensities I iso may be deduced from depolarization ratios and depolarized intensities
as
S
D
1
7
I iso~ n ! 5
2 I d~ n ! .
h~ n ! 6
~9!
160
2
2
7 @ ( a 8 A) 1( a A 8 ) # S 3 (t)R 0 (t)R 3 (t)F 1
224
2
2
9 @ ( a 8 E) 1( a E 8 ) # S 4 (t)R 0 (t)R 4 (t)F 1
2816
2
189 (AA 8 ) S 4 (t)R 3 (t)R 3 (t)F 1
416
2
2
21 @ (AE 8 ) 1(A 8 E) # S 5 (t)R 3 (t)R 4 (t)F 1
110
2
3 (EE 8 ) S 6 (t)R 4 (t)R 4 (t)F 1
Within the multipolar polarizability model and for the
particular case of the CF4 n 1 -Raman band, ~multi!polarizabilities ~dipolar a, dipole-quadrupole A, dipole-octopole E,
etc.! as well as their normal coordinate derivatives are responsible for the incremental CI pair polarizability tensor as
is explained in detail in our previous paper on a depolarized
spectrum.3 In Table I, we provide the successive multipolar
contributions to the correlation function F iso(t) involving the
dipolar polarizability a and independent components (A,E)
of the tensors ~A,E! together with their normal-coordinate
derivatives a 8 , A 8 , and E 8 ~it is worth noting that, contrary
to the depolarized spectrum,3 terms due to hyperpolarizabilities do not contribute to the isotropic spectrum in the firstorder approximation considered here!.
In this work, the Fourier transforms of the successive
multipolar correlation functions provided in Table I ~and
therefore, the theoretical isotropic spectrum! are numerically
computed by the method, the approximations, and the intermolecular potentials9–11 already described, used and justified
in Refs. 2–4.
III. EXPERIMENTAL PROCEDURE
The experiment and the experimental setup used are very
similar to the one described in a recent paper.3 Provided by
L’Air Liquide with an initial purity of 99.995%, the CF4 gas
was pumped at low temperature in order to improve its purity. Then it was compressed inside a four-window highpressure cell at 294.5 K and illuminated by the l L 5514.5
nm line of an argon-ion laser operating at 2 W. The polarization of the laser was adjusted relative to the horizontal
scattering plane defined by the laser beam and the axis of the
90° scattered beam. According to the laser polarization perpendicular or parallel to the scattering plane, we obtained an
experimental polarized spectrum I V or an experimental depolarized spectrum I H , respectively. At each frequency, intensities have been measured at various densities up to 250
amagat and the pair intensities I 2 have been deduced as coefficients proportional to the square density in the virial expansion given by
I5I 0 1I 1 r 1I 2 r 2 1I 3 r 3 .
~10!
IH
2 (n)
From
ization
and I V2 ( n ), we deduce the experimental depolarH
V
ratio h exp
2 (n)5I2 (n)/I2 (n). However, due to the non-
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J. Chem. Phys., Vol. 110, No. 23, 15 June 1999
H
V
FIG. 1. Experimental depolarization ratio h exp
2 (n)5I2 (n)/I2 (n) of the binary
n 1 -Raman band of gaseous CF4 ~d! at 294.5 K in the 0 – 110 cm21
frequency-shift range. The corresponding depolarization ratio for the Rayleigh band is also reported ~1!.
zero value of the collection angle Q used for the scattering
beam, the depolarized intensity I d2 ( n ) is not exactly I H
2 ( n ),
the polarized intensity I'2 ( n ) is not exactly I V2 ( n ), and the
12,13
isotropic intensity I iso
2 ( n ) is not exactly given by Eq. ~9!.
In our setup, Q56.2°. Consequently, according to the
correction formulas calculated in Ref. 13, we get the depolarized pair intensity by using3 I d2 ( n )5 $ 1.006
H
20.006/h exp
2 (n)%I2 (n). In a similar way, we obtain the isotropic pair intensity I iso
2 using an equation derived from Eq. ~9!
for the particular collection-angle value of our setup:4
I iso
2 ~ n !5
S
1.004
h 2 ~ n ! exp
D
21.1695 I d2 ~ n ! .
~11!
IV. RESULTS AND DISCUSSION
We present in Fig. 1 the behavior of the experimental
pair depolarization ratio h exp
measured in the
2 (n)
10– 110 cm21 frequency-shift range of the n 1 -Raman band.
Also in Fig. 1, we show the previously published depolarization ratio for the CF4 Rayleigh band.4 The Raman
depolarization-ratio data are significantly different from
these observed in the Rayleigh band. At low frequencies
(10– 20 cm21) the upper Raman value measured is about 0.5
when we obtained almost 6/7 for the Rayleigh band. At
higher frequencies ( n >60 cm21), h exp
2 (n) is measured at
about 0.2. This is approximately three times less than the
value obtained for Rayleigh scattering in the 60– 100 cm21
frequency region. Such behavior shows first that the diodeinduced-dipole ~DID! interactions alone fail to reproduce
scattering intensities and second that the multipolar polarizability effects and/or other short-range effects contribute differently in the Raman and the Rayleigh bands. From the pair
depolarization-ratio data and the pair depolarized intensities
11305
FIG. 2. Two-body isotropic scattering Stokes spectrum of the n 1 -Raman
band of gaseous CF4 in absolute units at 294.5 K. Closed circles ~d! indicate our experimental data including error bars. Theoretical curves ~DID
– – –, DQ - - -, DO – - –, QQ1QO1OO – - - –, and total theoretical —!
are computed using a Lennard-Jones potential ~Ref. 9!, a 52.93 Å 3 , a 8
54.00 Å 2 , and a set M of multipolarizability values calculated by Maroulis
~Refs. 5 and 6! given in Table II.
given previously in Ref. 3, we deduced from Eq. ~11! the
experimental absolute-unit isotropic intensities I iso( n ) which
are reported together with their error bars in Fig. 2 for the
10– 110 cm21 frequency-shift range. In Fig. 2, we also show
our total theoretical spectrum and its successive multipolar
contributions for a Lennard-Jones potential,9 a set D
5( a , a 8 ) of dipolar polarizabilities, and a set M
5(A,A 8 ,E,E 8 ) of dipole-multipole polarizabilities. The D
values, a 52.93 Å 3 and a 8 54.00 Å 2 , are deduced from CF4
refractive-index measurements14 and from Raman
studies,15,16 respectively. They are close to the static polarizabilities calculated ab initio by Maroulis5,6 ~a 52.89 Å 3 ;
a 8 53.92 Å 2 ! and may be regarded with confidence. The M
values of A, A 8 , E, and E 8 result from quantum-mechanical
calculations of Maroulis.5,6 They are reported in Table II. As
can be seen in Fig. 2, the total theoretical spectrum calculated with these values lies below the lower error-bar limits,
whatever the frequency is. This discrepancy has also been
observed, however to a lesser degree, in the depolarized
n 1 -Raman band, and a fitted value of A 8 is proposed in Ref.
3. In the present work, we test the compatibility of our theoretical model with both depolarized and isotropic Raman
experiments. We check if there exists a new set M8 of
dipole-multipole polarizabilities since both the depolarized
and the isotropic theoretical intensities lie inside the error
bars of the corresponding experimental points. Shortdistance range effects are expected to contribute significantly
at high frequencies. Unfortunately, the overlap and exchange
effects are not yet known in the CF4 case and, therefore,
cannot be taken into account by our model. Besides, at low
frequencies, it is not possible to study both depolarized and
isotropic spectra in order to measure dipole-multipole polarizabilities. First, a first-order DID contribution exists in the
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J. Chem. Phys., Vol. 110, No. 23, 15 June 1999
TABLE II. Theoretical and experimental values of the CF4 multipolarizabilities and of their bond-length R
derivatives ~which are related to normal-coordinate derivatives; see Ref. 3!. Theoretical values ~set M! computed ab initio by Maroulis ~Refs. 5 and 6! and used in Fig. 2 are labeled by an asterisk ~*!. Experimental values
~set M8 ! deduced from our CIS experiments ~Refs. 2–4 and the present work! and used in Figs. 3 and 4 are
labeled by a diamond ( L ). These labels correspond to a CF4 potential given in Ref. 9. The circles ~°! and the
stars ( ! ) refer to two other potentials that are given in Refs. 10 and 11, respectively.
Polarizability
uAu
Theory
Experiment
U U
uA8u5
]A
]R
uEu
U U
uE8u5
]E
]R
CIS spectrum
0.972 Å *
1Å
1.2 Å 4
isotropic Rayleigh ~Ref. 4!
depolarized Rayleigh ~Ref. 2!
4.09 Å 3 *
5 Å 3L
4.7 Å 3 °
4.7 Å 3 !
5.3 Å 3
isotropic Raman ~this work!
isotropic Raman ~this work!
isotropic Raman ~this work!
depolarized Raman ~Ref. 3!
1.15 Å 5 *
1.5 Å 5L
3.5 Å 5
isotropic Rayleigh ~Ref. 4!
depolarized Rayleigh ~Ref. 2!
4
5.53 Å 4 *
4L
,18 Å 4L!
,16 Å 4 °
,28 Å 4
depolarized case, which predominates over all dipolemultipole contributions in the 0 – 30 cm21 frequency range,3
whereas only a weak second-order DID mechanism contributes to the isotropic spectrum. Second, it can be noticed in
Fig. 2 that the line shape of the experimental isotropic spectrum deviates from the corresponding theoretical one as n
tends towards zero. This may be attributed, at least partly, to
the vibrational-rotational coupling present in the n 1 Q line.17
Consequently, it is not possible to fit our theoretical model
and both experimental spectra at lower frequencies as well as
at higher frequencies, and we restrict our study to the
30– 80 cm21 frequency range. As in Ref. 3, we chose for M8
the values of A51.0 Å 4 and E51.5 Å 5 that we previously
deduced from the analysis of both depolarized and isotropic
Rayleigh spectra.4 Then we adopt a fitting procedure related
to the parameter vector (A 8 ,E 8 ) only. Despite the fact that
we study a restricted frequency range, it is not possible to
have theoretical curves through all the error bars, or through
all but one or two. Taking into consideration the fact that
three theoretical points may be slightly outside the error bars
for the two spectra together, the parameter vector ~A 8
'5 Å 3 , E 8 '18 Å 4 ! becomes a solution which completes set
M8 reported in Table II together with previous evaluations
of A, A 8 , E, and E 8 . 2–4 In Figs. 3 and 4, we present experimental depolarized and isotropic n 1 -Raman bands, respectively, and corresponding theoretical spectra computed using
our evaluated M8 values and the same Lennard-Jones
potential.9 In the 30– 80 cm21 frequency range, the theoretical curves lie either near the upper limits of the error bars in
the depolarized case of Fig. 3 or in the vicinity of the errorbar lower limits in the isotropic case of Fig. 4. Moreover ~i!
above 80 cm21, the theoretical model cannot reproduce experimental intensities and ~ii! the fitted value E 8 '18 Å 4 is
far from the E 8 55.53 Å 4 calculated by Maroulis.5,6 We have
checked that, in our experiment, leaking and mixing between
polarized and depolarized components due to experimental
isotropic Raman ~this work!
isotropic Raman ~this work!
depolarized Raman ~Ref. 3!
polarization errors do not significantly affect our data.18
Therefore, deviations in our calculations with regard to experiment may be due to short range effects, to the aforementioned vibrorotational coupling, and/or to uncertainties as to
the potential. Several CF4 potentials exist. Most of them have
been presented in previous papers.3,4 The choice of potential
slightly modifies the integrated intensity for each dipolemultipole contribution.3,4 Moreover, considering the strong
first-order DID contribution to the depolarized Rayleigh and
FIG. 3. Two-body depolarized scattering Stokes spectrum of the n 1 -Raman
band of gaseous CF4 in absolute units at 294.5 K reported in Ref. 3. Closed
circles ~d! indicate experimental data including error bars. The theoretical
curves ~DID – – –, DQ - - -, DO – - –, QQ1QO1OO – - - – and total
theoretical —! are computed using a Lennard-Jones potential ~Ref. 9!, a
52.93 Å 3 , a 8 54.00 Å 2 , and a set M8 of multipolarizability values given
in Table II.
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J. Chem. Phys., Vol. 110, No. 23, 15 June 1999
FIG. 4. The same as in Fig. 2, except that the theoretical curves computed
here are for the multipolarizability set M8 given in Table II.
Raman spectra, we found that several potentials19–22 provide
theoretical integrated intensities which are bigger than the
upper limit of the corresponding experimental ones.3 Only
three available potentials are compatible with these measurements: the Lennard-Jones potential used in Figs. 2–4, a second Lennard-Jones potential reported in Ref. 10, and the
isotropic part of potential calculated ab initio by Palmer and
Anchell.11 On the other hand, whatever the potential is, the
spectral shapes of dipole-multipole contributions are not significantly modified, as can be seen in Figs. 3 and 4 of Ref. 3.
This is due to the fact that potential-independent rotational
stick spectra of the successive light scattering mechanisms
are mainly responsible for the dipole-multipole line
shapes.3,23 The choice of potential simply shifts upward or
downward slightly each theoretical dipole-multipole contribution like those represented in the logarithmic scale of Figs.
2–4. For the three aforementioned potentials, the integrated
intensities of the dipole-quadrupole and dipole-octopole contributions are altered by less than 20%, and the corresponding changes in the dipole-multipole values are less than
10%.3 This may be checked in Table II, where we report
fitted values of (A 8 ,E 8 ) for these potentials.9–11 Moreover,
except for the purely translational DID contribution, the
choice of potential affects both theoretical depolarized and
isotropic intensities in a similar manner. Therefore, in the
30– 80 cm21 frequency range, it could not allow simultaneous ‘‘decreasing’’ of the theoretical depolarized spectrum
and ‘‘increasing’’ of the theoretical isotropic spectrum in order to make them closer to depolarized and isotropic experiments, respectively. With regard to the influence of the rotovibrational coupling of the n 1 Q line on its width at half
intensity, it may be equal to several cm21 at a few amagat.
However, the effect of coupling in the wing of the n 1 line
decreases with density and with frequency. Therefore, we
may estimate that it is negligible in the 30– 80 cm21 frequency region for the density range used in these experi-
11307
ments. A fortiori, it cannot explain the discrepancies beyond
80 cm21, which are observed for both the isotropic and the
depolarized spectra. The discrepancies observed might
mainly be seen as results of short range effects ~such as
overlap and exchange, or molecular frame distortion; the
nonpoint-like size of the CF4 molecule may also play a role,
particularly in the case of the trace-induced isotropic
spectrum24!. The dipole-octopole ~DO! mechanism is the
shortest range effect considered here. It may explain why our
fitting procedure leads to overestimated values of E 8 in comparison to Maroulis’ value. In Figs. 3 and 4, overestimation
of the DO contributions makes up for short-range effects, not
taken into account in our theoretical model. We use E 8
518 Å 4 in these figures, but it is rather an order of magnitude and an upper limit than a real estimate @in Ref. 3, we
only wrote that E 8 ,28 Å 4 #. On the other hand, our measurement of A 8 ~A 8 '5 Å 3 ; in Ref. 3, we found A 8 '5.3 Å 3 ! is
close to the ab initio calculation of Maroulis5,6 (A 8
54.09 Å 3 ). We assume that it is due to two factors: ~i! the
dipole-quadrupole ~DQ! mechanism is predominant from 30
up to 80 cm21 for both depolarized and isotropic spectra; ~ii!
our theoretical model is sufficient in this frequency range.
The measurement of the isotropic n 1 -Raman band thus confirms the conclusion of our previous paper on the depolarized
spectrum.3 At the same time, the lack of theoretical isotropic
intensity not only concerns the frequencies beyond 80 cm21
like in the depolarized case, but all of the frequency range
scanned. This has shed new light on the relative importance
of short-range effects on the trace and on the anisotropy of
the CF4 pair polarizability tensor.
V. CONCLUSION
In the present work, the isotropic intensities of the
n 1 -Raman band measured in absolute units have been reported for the first time in the 10– 110 cm21 frequency range.
Comparison between experiment and theoretical predictions
as well as comparison with previous measurements of the
depolarized n 1 -Raman band3 have shown that CIS Raman
experiments on gaseous CF4 are a good way to measure the
dipole-quadrupole derivative A 8 . The value A 8 '5 Å 3 that
we have deduced from fitting both depolarized and isotropic
Raman spectra is close to the quantum-mechanical computed
A 8 54.09 Å 3 of Maroulis.5,6 Most certainly, short-range effects modify depolarized and, more significantly, isotropic
spectral line shapes at high frequencies. This leads to an
overestimated value of the dipole-octopole derivative E 8 .
However, it does provide a good order of magnitude of E 8 .
In conclusion, the Raman CIS experiment on both isotropic
and depolarized spectra is a suitable technique by which to
measure at least the dipole-quadrupole Raman-polarizability
tensor in the case of a globular molecule such as CF4. Moreover, measurement and theoretical analysis of isotropic Raman spectra has provided us with new information on
mechanisms contributing to the trace of the Raman pair polarizability tensor.
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J. Chem. Phys., Vol. 110, No. 23, 15 June 1999
ACKNOWLEDGMENTS
This work has been supported in part by the University
of Angers, and in part by Grant No. 98086 of French-Polish
Scientific cooperation program POLONIUM.
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