While parity-changing transitions, such as antisymmetric fundamentals in a molecule ha-ving inversion center,
are strictly forbidden in conventional (E1-E1) Raman scattering, they become allowed when dipole magnetic
(M1) or quadrupole electric (E2) couplings are involved between the molecule and one of the Raman photons.
For more than a decade now, there exists a theory which allows one to calculate, on the basis of the generalized
linear polarizability tensors A and G, the scattering cross sections of such “unconventional” E1-M1 and E1-E2
Raman processes [1]. However, calculations now done for those processes in CO2, relying on available as well
as on preliminary quantum-chemically computed numerical data for the vibrational dependence of the tensors
for the ν3 fundamental transition, suggest a Raman E1-E2/M1 cross section seven whole orders of magnitude
weaker than the cross section of a typical conventionally-allowed E1-E1 fundamental such as the ν1 transition
of CO2 [2]. If this is indeed the case, it leaves little hope for the observation of this effect even by using the most
sensitive diagnostic tool available ever. But recent theoretical treatments currently in progress in our group seem
to suggest the occurrence of another type of scattering which comes to accompany the incoherent E1-E2/M1
effect at the frequency of the ν3 vibration. Although in the new mechanism there is still an incident photon “1”
which disappears and a scattered photon “2” which is born, unlike with standard Raman scattering there is now
also a third (emitted) photon “3” thereby ensuring photon energy conservation, ω1 = ω2 + ω3, and causing a
coherent response [3] (referred to hereafter as E1-E2/M1-E1 scattering) from the molecular ensemble. And for
this reason one can readily expect this response to be far more enhanced by the resonance of ω3 with an infrared
dipole-allowed transition than the response of E1-E2/M1 which is both off-resonant and incoherent. Clearly, the
involvement of the photon “3” is instrumental when it is about comparing scattering amplitudes for E1-E2/M1
alone and E1-E2/M1-E1 although its presence should remain ghostly because the infrared photons cannot be
detected with a visible-range Raman experiment. Investigations currently underway in our groups indicate an
integrated intensity for the three-photon scattering which by far exceeds that of the incoherent (two-photon) E1-
E2/M1 Raman scattering even under the most unfavorable conditions, namely, broken phase-matching. A
gratifying agreement with preliminary experiments conducted in Angers with room-temperature CO2 gas in the
region of the ν3 fundamental was found [4].
The Russian co-authors thank RFBR (grant 03-15-04997) for financial support.
References:
[1] N. Egorova, A. Kouzov, M. Chrysos, and F. Rachet, J. Raman Spectrosc. 36, 153 (2005).
[2] A. Haskopoulos and G. Maroulis, Chem. Phys. Lett. 417, 235 (2006); Chrysos et al (unpublished).
[3] D.N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, NY, 1988).
[4] N. Egorova et al (unpublished)