Raman spectroscopy polarizability tensor

Raman spectroscopy is an inelastic light scattering experiment for which the intensity depends on the amplitude of the polarizability variation associated with the molecular vibration under consideration. The polarizability variation is represented by a second-rank tensor, oiXyZ, the Raman tensor. Information about orientation arises because the intensity of the scattered light depends on the orientation of the Raman tensor with respect to the polarization directions of the electric fields of the incident and scattered light. Like IR spectroscopy, Raman... 

In the final column of the character table are given the assignments to symmetry species of nxx, ocyy, ocxy, a.yz and ocxz. Tlicsc are the components of the symmetric polarizability tensor a which is important in vibrational Raman spectroscopy, to be discussed in Section 6.2.3.2. 

It is important to note that the two electric fields that lead to a Raman transition can have different polarizations. Information about how the transition probability is affected by these polarizations is contained within the elements of the many-body polarizability tensor. Since all of the Raman spectroscopies considered here involve two Raman transitions, we must consider the effects of four polarizations overall. In time-domain experiments we are thus interested in the symmetry properties of the third-order response function, R (or equivalently in frequency-domain experiments... 

Classically, Raman spectroscopy arises from an induced dipole in a molecule resulting from the interaction of an electromagnetic field with a vibrating molecule. In electromagnetic theory, an induced dipole is a first-rank tensor formed from the dot product of the molecular polarizability and the oscillating electric field of the photon, (jl = a-E. Assuming a harmonic potential for the molecular vibration, and that the polarizability does not deviate significantly from its equilibrium value (a0) as a result of the vibration... 

We mention that, by contrast, the more familiar Raman spectra arising from the permanent polarizabilities of the individual (noninteracting) molecules of the complex are not considered a part of the supermolecular spectra, or of CILS. In ordinary Raman spectroscopy of rarefied gases the invariants of the permanent molecular polarizability tensor are conveniently considered to be not affected by intermolecular interactions, an approximation that is often justified because induced spectral components are usually much weaker than ordinary allowed Raman bands. 

In addition to the Raman selection rules described above there are surface selection rules that apply for SERS because the process occurs close to metal surfaces [40—42]. The SERS surface selection rule predicts that the vibrational bands that have contributions from the Raman polarizability tensor component where z is the surface normal, will be most intense with weaker contributions from vibrational bands which have contributions from and o. This is essentially because tlic electric field of the exciting hght is enhanced in the direction of the surface normal (Figure 6.2). The surface selection rule for Raman spectroscopy is more complex than that for infrared spectroscopy. Modes with the bond axis paraUel to... 

There have been a number of reports of analogous surface selection rules for Raman spectra [27-29]. However, for SERS, the situation is complicated by the essential roughness of the metal surface and the mixture of enhancement mechanisms, in addition to the facts that the Raman effect depends upon the molecular polarizability tensor and the excitation frequencies are typically high enough to reduce the metal conductivity to levels where finite parallel, as well as perpendicular, electric vectors are established at the surface. An excellent recent review of this subject has been written by Creighton [30]. Suffice it to say here that surface selection rules evidently do exist for Raman spectroscopy but they are more complicated than the rule for infrared and EELS. 

The original Placzek theory of Raman scattering [30] was in terms of the linear, or first order microscopic polarizability, a (a second rank tensor), not the third order h3q)erpolarizability, y (a fourth rank tensor). The Dirac and Kramers-Heisenberg quantum theory for linear dispersion did account for Raman scattering. It turns out that this link of properties at third order to those at first order works well for the electronically nonresonant Raman processes, but it cannot hold rigorously for the fully (triply) resonant Raman spectroscopies. However, provided one discards the important line shaping phenomenon called pure dephasing , one can show how the third order susceptibility does reduce to the treatment based on the (linear) polarizability tensor [6, 27]. 

X HE VIBRATIONAL SPECTRUM of any material consists of two parts the infrared (IR) and Raman spectra. IR spectroscopy is sensitive to the changes in dipole moment that occur during the vibrations of atoms that are forming chemical bonds. Raman spectroscopy detects the polarizability tensor changes of the electron clouds that surround these atoms. These apparent differences in the physical principles of both effects have led to the development of these two distinctly different techniques. IR and Raman spectra complement each other. Because they are sensitive to the vibrations of atoms, they are called vibrational spectra. 

Raman spectroscopy is complementary to the corresponding absorption process because different selection rules are involved. For an absorption of a photon to take place there must be a change in the dipole moment of the molecule in the course of the transition (a non zero transition electric dipole moment). In Raman spectroscopy, however, the requirement for scatering to occur is that there is a change in the molecular polarizability (a second rank tensor) in the course of the transition. 

Normal Raman spectroscopy probes the variations of the polarizability tensor with respect to the degrees of freedom, in the ground electronic state. When an electrical field is applied to a system the electron distribution is modified and the sample acquires an induced dipole moment as the barycenters of the charges are displaced. The polarizability tensor [a] defines the correspondence between the incident electrical field E and the induced dipole moment M = [a]E. The polarizability tensor can be expanded in a Taylor series analogous to Equation (8.8) ... 

JM Femandez-Sanchez, WF Murphy. True and effective polarizability tensors for asymmetric top molecules The rotational Raman spectra of H2S and D2S. J Mol Spectrosc 156 444-460, 1992. H Frunder, R Angstl, D Illig, HW Schrotter, L Lechuga-Fossat, JM Flaud, C Camy-Peyret, WF Murphy. The coherent anti-Stokes Raman spectroscopy spectrum of the Q-branch of the Vi band of hydrogen sulfide. Can J Phys 63 1189-1194, 1985. 

Fig. 1.28c). This preliminary result appears to indicate the FFMD calculated response is sensitive to the intermolecular interaction model chosen and that the node position varies with the model. The corollary to this is that the relative contributions of the anharmonic and nonlinear polarizability terms in the calculation are changing between the two models. As this change in sign along the probe axis is the one discrepancy between experiment and theory for this tensor element it remains an open question as to where the difference originates. Further calculations are in progress with a specific focus on the Dutch Cross tensor element where the experimental results have converged. The primary conclusion that should be drawn, however, is that the overall dynamics of the new simulations is in excellent agreement with previous MD calculations for the all parallel polarization response of CS2. This convergence of both the theory and the experiment is an important milestone in the advancement of fifth-order Raman spectroscopy as a probe of the liquid state.

The information provided by the Raman spectrum of an oriented polymer differs from its infrared counterpart because of the fundamentally different processes involved in the generation of the spectra. In the infrared absorption process, as already noted, the absorption intensity is dependent on the angle between the electric vector and the direction of the dipole moment change. The Raman spectrum results from inelastic photon scattering details of which are determined by changes in the polarizability of the chemical bonds involved. Polarizability is a tensor quantity, which results in complications but, in principle, provides additional information. As we have seen, infi ared spectroscopy involves only one beam of polarized radiation, and the fraction of the nufotion absorbed by a molecule depends only on the orientation of the molecule with respect to the polarisation vector of the radiation. However, Raman scattering involves two beams of radiation, those of illumination and collection, and the scattered intensity depends on the orientation of the molecule with respect to the polarisation vectors of both beams, whidi may, of course, be different. This necessitates more detailed measurements in order to obtain the relevant information. 

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