Theory of a Novel Odd-Parity Raman Scattering Mechanism: Depolarization Ratios and Reversal Coefficients for Random Molecular Systems

Abstract

Raman scattering is treated as a two-photon process. A scattering mechanism that involves one-photon in an electric dipole mode of radiation and one photon in a magnetic dipole mode (or an electric quadrupole mode) has been worked out. The scattering tensors are of odd parity and may be of higher than the second rank. Therefore, this mechanism may be used to study the “silent” modes forbidden in the ir and the conventional Raman effect which is of even parity. When the molecule has inversion or reflection symmetry, this mechanism gives rise to an odd-parity electronic Raman effect between two (different) electronic states of opposite parities. This is in contrast to the recently discovered electronic Raman effect due to antisymmetric tensors which connect states of the same parity. When the molecule is optically active and has no inversion or reflection symmetry, this mechanism gives rise to novel vibrational and rotational Raman effects with symmetry and selection rules which are different from the conventional (even-parity) Raman scattering. Intensities due to scattering by random molecular systems are computed. These will permit the calculation of the depolarization ratios for this odd-parity Raman scattering of linearly polarized incident light into perpendicular directions, and the reversal coefficients for the scattering of circularly polarized incident light into forward as well as into arbitrary directions. Some useful angular factors for this odd-parity scattering have been tabulated (Tables I and II). To average over all random orientations, use is made of the coupling of irreducible spherical (vs Cartesian) tensors, the properties of the rotation matrices, and the symmetry of Clebsch–Gordan vector coupling coefficients, instead of the method of direction cosines used by early workers. Such angular momentum techniques are capable of being extended to multiphoton (hyper) Raman effects and to scattering by quantized rotors. A few examples of the spherical scattering tensors of odd parity and their symmetry in the D2 point group are presented.