Long known as a fully polarized band with a near vanishing depolarization ratio [ηs = 0.05, W. Holzer and R. Ouillon, Chem. Phys. Lett. 24, 589 (1974)], the 2ν5 Raman overtone of SF6 has so far been considered as of having a prohibitively weak anisotropic spectrum [D. P. Shelton and L. Ulivi, J. Chem. Phys. 89, 149 (1988)]. Here, we report the first anisotropic spectrum of this overtone, at room temperature and for 13 gas densities ranging between 2 and 27 amagat. This spectrum is 10 times broader and 50 times weaker than the isotropic counterpart of the overtone [D. Kremer, F. Rachet, and M. Chrysos, J. Chem. Phys. 138, 174308 (2013)] and its profile much more sensitive to pressure effects than the profile of the isotropic spectrum. From our measurements an accurate value for the anisotropy matrix-element |⟨000020|Δα|000000⟩| was derived and this value was found to be comparable to that of the mean-polarizability

$\left|\left\langle 000020\right|\bar{ \alpha }\left|000000\right\rangle \right|$
000020α¯000000⁠. Among other conclusions our study offers compelling evidence that, in Raman spectroscopy, highly polarized bands or tiny depolarization ratios are not necessarily incompatible with large polarizability anisotropy transition matrix-elements. Our findings and the way to analyze them suggest that new strategies should be developed on the basis of the complementarity inherent in independent incoherent Raman experiments that run with two different incident-beam polarizations, and on concerted efforts to ab initiocalculate accurate data for first and second polarizability derivatives. Values for these derivatives are still rarities in the literature of SF6.

Topics
Raman scattering, Hooke's law, Polarizability, Matrix calculus, Functions and mappings, Monochromators, Second harmonic generation, Chemical physics, Raman spectroscopy, Vibrational spectroscopy
1.
D. A.
 
Long
,
The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules
(
Wiley
, Chichester,
UK
,
2002
).
Google Scholar
Crossref
Search ADS
 
2.
G. C.
 
Tabisz
, in
Molecular Spectroscopy
(A Specialist Periodical Report), edited by
R. F.
 
Barrow
,
D. A.
 
Long
, and
J.
 
Sheridan
, (
Chemical Society
,
London
,
1979
), Vol.
6
, pp.
136
–
173
.
Google Scholar
 
3.
E. B.
 
Wilson
 Jr.,
J. C.
 
Decius
, and
P. C.
 
Cross
,
Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra
(
Dover
,
New York
,
1980
).
Google Scholar
 
4.
L.
 
Frommhold
,
Adv. Chem. Phys.
 
46
,
1
(
2007
).
https://doi.org/10.1002/9780470142653.ch1
Google Scholar
Crossref
Search ADS
 
5.
Collision- and Interaction-Induced Spectroscopy
, edited by
G. C.
 
Tabisz
 and
M. N.
 
Neuman
 (
Kluwer
,
Dordrecht
,
1995
).
Google Scholar
Crossref
Search ADS
 
6.
T.
 
Bancewicz
,
Y. Le
 
Duff
, and
J.-L.
 
Godet
,
Adv. Chem. Phys.
 
119
,
267
(
2002
).
https://doi.org/10.1002/0471231479.ch6
Google Scholar
Crossref
Search ADS
 
7.
J.-M.
 
Hartmann
,
C.
 
Boulet
, and
D.
 
Robert
,
Collisional Effects on Molecular Spectra: Laboratory Experiments and Model, Consequences for Applications
(
Elsevier
,
Amsterdam
,
2008
).
Google Scholar
 
8.
I. A.
 
Verzhbitskiy
,
M.
 
Chrysos
,
F.
 
Rachet
, and
A. P.
 
Kouzov
,
Phys. Rev. A
 
81
,
012702
(
2010
).
https://doi.org/10.1103/PhysRevA.81.012702
Google Scholar
Crossref
Search ADS
 
9.
M.
 
Chrysos
 and
I. A.
 
Verzhbitskiy
,
Phys. Rev. A
 
81
,
042705
(
2010
).
https://doi.org/10.1103/PhysRevA.81.042705
Google Scholar
Crossref
Search ADS
 
10.
I. A.
 
Verzhbitskiy
,
M.
 
Chrysos
, and
A. P.
 
Kouzov
,
Phys. Rev. A
 
82
,
052701
(
2010
).
https://doi.org/10.1103/PhysRevA.82.052701
Google Scholar
Crossref
Search ADS
 
11.
M.
 
Chrysos
,
I. A.
 
Verzhbitskiy
,
F.
 
Rachet
, and
A. P.
 
Kouzov
,
J. Chem. Phys.
 
134
,
044318
(
2011
).
https://doi.org/10.1063/1.3535599
Google Scholar
Crossref
Search ADS
PubMed
 
12.
M.
 
Chrysos
,
I. A.
 
Verzhbitskiy
,
F.
 
Rachet
, and
A. P.
 
Kouzov
,
J. Chem. Phys.
 
134
,
104310
(
2011
).
https://doi.org/10.1063/1.3557820
Google Scholar
Crossref
Search ADS
PubMed
 
13.
I. A.
 
Verzhbitskiy
,
A. P.
 
Kouzov
,
F.
 
Rachet
, and
M.
 
Chrysos
,
J. Chem. Phys.
 
134
,
194305
(
2011
).
https://doi.org/10.1063/1.3580278
Google Scholar
Crossref
Search ADS
PubMed
 
14.
I. A.
 
Verzhbitskiy
,
A. P.
 
Kouzov
,
F.
 
Rachet
, and
M.
 
Chrysos
,
J. Chem. Phys.
 
134
,
224301
(
2011
).
https://doi.org/10.1063/1.3596750
Google Scholar
Crossref
Search ADS
PubMed
 
15.
S. M.
 
El-Sheikh
,
G. C.
 
Tabisz
, and
R. T.
 
Pack
,
J. Chem. Phys.
 
92
,
4234
(
1990
).
https://doi.org/10.1063/1.457781
Google Scholar
Crossref
Search ADS
 
16.
G.
 
Maroulis
,
Chem. Phys. Lett.
 
312
,
255
(
1999
).
https://doi.org/10.1016/S0009-2614(99)00939-2
Google Scholar
Crossref
Search ADS
 
17.
T.
 
Bancewicz
,
J.-L.
 
Godet
, and
G.
 
Maroulis
,
J. Chem. Phys.
 
115
,
8547
(
2001
).
https://doi.org/10.1063/1.1410979
Google Scholar
Crossref
Search ADS
 
18.
J.-L.
 
Godet
,
F.
 
Rachet
,
Y. Le
 
Duff
,
K.
 
Nowicka
, and
T.
 
Bancewicz
,
J. Chem. Phys.
 
116
,
5337
(
2002
).
https://doi.org/10.1063/1.1463421
Google Scholar
Crossref
Search ADS
 
19.
Y. Le
 
Duff
,
J.-L.
 
Godet
,
T.
 
Bancewicz
, and
K.
 
Nowicka
,
J. Chem. Phys.
 
118
,
11009
(
2003
).
https://doi.org/10.1063/1.1575733
Google Scholar
Crossref
Search ADS
 
20.
If the Cartesian coordinates of the XY6 atoms are X(0, 0, 0), Y1(0, 0, R), Y2(0, 0, −R), Y3(R, 0, 0), Y4(− R, 0, 0), Y5(0, R, 0), and Y6(0, −R, 0), and R is the extension of the bond X–Y at equilibrium, then the symmetry coordinate of the ν5 vibration reads
$\frac{1}{2}R(\alpha _{35}-\alpha _{36}-\alpha _{45}+\alpha _{46})$
12R(α35−α36−α45+α46)⁠, where αab is the angle between the bonds X–Ya and X–Yb.
21.
W.
 
Holzer
 and
R.
 
Ouillon
,
Chem. Phys. Lett.
 
24
,
589
(
1974
).
https://doi.org/10.1016/0009-2614(74)80188-0
Google Scholar
Crossref
Search ADS
 
22.
D. P.
 
Shelton
 and
L.
 
Ulivi
,
J. Chem. Phys.
 
89
,
149
(
1988
).
https://doi.org/10.1063/1.455497
Google Scholar
Crossref
Search ADS
 
23.
D.
 
Kremer
,
F.
 
Rachet
, and
M.
 
Chrysos
,
J. Chem. Phys.
 
138
,
174308
(
2013
).
https://doi.org/10.1063/1.4803160
Google Scholar
Crossref
Search ADS
PubMed
 
24.
The meaning of the two double-superscript quantities I(⊥∥) and I(⊥⊥) is scattering intensity recorded at the output when the incident beam is polarized perpendicular (⊥) to the scattering plane (first superscript) and the output beam analyzed in the direction parallel (∥) and perpendicular (⊥) to the scattering plane, respectively (second superscript).
25.
F.
 
Rachet
,
M.
 
Chrysos
,
C.
 
Guillot-Noël
, and
Y. Le
 
Duff
,
Phys. Rev. Lett.
 
84
,
2120
(
2000
).
https://doi.org/10.1103/PhysRevLett.84.2120
Google Scholar
Crossref
Search ADS
PubMed
 
26.
F.
 
Rachet
,
Y. Le
 
Duff
,
C.
 
Guillot-Noël
, and
M.
 
Chrysos
,
Phys. Rev. A
 
61
,
062501
(
2000
).
https://doi.org/10.1103/PhysRevA.61.062501
Google Scholar
Crossref
Search ADS
 
27.
Y. Le
 
Duff
,
Phys. Rev. Lett.
 
90
,
193001
(
2003
).
https://doi.org/10.1103/PhysRevLett.90.193001
Google Scholar
Crossref
Search ADS
PubMed
 
28.
M.
 
Chrysos
,
A. P.
 
Kouzov
,
N. I.
 
Egorova
, and
F.
 
Rachet
,
Phys. Rev. Lett.
 
100
,
133007
(
2008
).
https://doi.org/10.1103/PhysRevLett.100.133007
Google Scholar
Crossref
Search ADS
PubMed
 
29.
S.
 
Dixneuf
,
M.
 
Chrysos
, and
F.
 
Rachet
,
J. Chem. Phys.
 
131
,
074304
(
2009
).
https://doi.org/10.1063/1.3200929
Google Scholar
Crossref
Search ADS
PubMed
 
30.
Confusion between symbols k and ϕ, often used indifferently to denote cubic force constants, is regularly source of errors in matrix-element calculations and of misunderstandings regarding the real physical significance of these constants; in this context, see, for instance, a recent comment by
M.
 
Chrysos
 and
D.
 
Kremer
,
Int. J. Quantum Chem.
 
113
,
2634
(
2013
).
https://doi.org/10.1002/qua.24514
Google Scholar
Crossref
Search ADS
 
31.
B. J.
 
Krohn
 and
J.
 
Overend
,
J. Phys. Chem.
 
88
,
564
(
1984
).
https://doi.org/10.1021/j150647a048
Google Scholar
Crossref
Search ADS
 
32.
D. P.
 
Hodgkinson
,
J. C.
 
Barrett
, and
A. G.
 
Robiette
,
Mol. Phys.
 
54
,
927
(
1985
).
https://doi.org/10.1080/00268978500103271
Google Scholar
Crossref
Search ADS
 
33.
D. P.
 
Hodgkinson
,
R. K.
 
Heenan
,
A. R.
 
Hoy
, and
A. G.
 
Robiette
,
Mol. Phys.
 
48
,
193
(
1983
).
https://doi.org/10.1080/00268978300100141
Google Scholar
Crossref
Search ADS
 
34.
J. J.
 
Hurley
,
D. R.
 
Defibaugh
, and
M. R.
 
Moldover
,
Int. J. Thermophys.
 
21
,
739
(
2000
).
https://doi.org/10.1023/A:1006697620523
Google Scholar
Crossref
Search ADS
 
35.
B. P.
 
Stoicheff
,
Can. J. Phys.
 
35
,
730
(
1957
).
https://doi.org/10.1139/p57-079
Google Scholar
Crossref
Search ADS
 
36.
J.
 
Rychlewski
,
J. Chem. Phys.
 
78
,
7252
(
1983
).
https://doi.org/10.1063/1.444713
Google Scholar
Crossref
Search ADS
 
37.
C.
 
Schwartz
 and
R. J. Le
 
Roy
,
J. Mol. Spectrosc.
 
121
,
420
(
1987
).
https://doi.org/10.1016/0022-2852(87)90059-2
Google Scholar
Crossref
Search ADS
 
38.
The chosen function was given the form g(ν) = H[β(ν − νs)]CG(ν), with H the Heaviside step function, C and β free parameters, and
$G(\nu )\break =\frac{\beta ^{\alpha }(\nu -\nu _{s})^{\alpha -1}}{(\alpha -1)!}\exp [ -\beta (\nu -\nu _{s})]$
G(ν)=βα(ν−νs)α−1(α−1)!exp[−β(ν−νs)] the unity-normalized shape function for a gamma distribution probability density with random variable ν − νs, shape α(= 2) and rate β. This function, whose choice was dictated by probability theory, turned out to faithfully reproduce the exponential decrease of the O and S branches and their rise from the origin (ν = νs). The converged M0 values for the branches O and S are 1.71 × 10−54 cm6 and 1.61 × 10−54 cm6, respectively.
© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
You do not currently have access to this content.