Spectral theory of molecular rotation-induced broadening of hyper-Raman lines in liquids

The spectral line shape of hyper‐Raman light scattering in liquids is calculated by the method of irreducible spherical tensors and the theory of rotational Brownian motion. The line broadening due to rotational molecular motion in the liquid is expressed by way of relaxation times τ JM and is found to depend on nonlinear molecular parameters ∣B̃ JM∣2, which are quadratic functions of the derivatives with respect to appropriate normal coordinates of the hyperpolarizability tensor elements b 2ωijk. Tables of ∣B̃ JM∣2 are adduced for all vibration symmetries of spherical‐top and symmetric‐top molecules. The tensor elements of scattered light intensity are calculated for linearly and circularly polarized incident light. Investigation of hyper‐Raman spectral line broadening is seen as a source of new data on the dynamics of molecules in the liquid state and on their nonlinear optical properties.