RELATION OF VIBRATIONAL HYPER-RAMAN INTENSITIES TO GAMMA-HYPERPOLARIZABILITY DENSITIES

Band intensities for nonresonant vibrational hyper-Raman scattering depend on the derivatives of the beta hyperpolarizability, a nonlinear electronic response tenser, with respect to normal mode coordinates. In this work, we derive a new result for the change in beta(-omega(sigma);omega(1),omega(2)) due to small shifts in nuclear positions within a molecule. We prove that the derivative of beta(-omega(sigma);omega(1) omega(2)), taken with respect to the position R(K) of nucleus K, depends on the nonlocal hyperpolarizability density gamma(r,r',r '',r<triple prime>;-omega(sigma)omega(1) omega(2),0) of second order, the charge on nucleus K, and the dipole propagator from R(K) to r<triple prime>. Thus gamma(r,r',r '',r<triple prime>; -omega(sigma);omega(1) omega(2),0) determines the origins of vibrational hyper-Raman intensities on the intramolecular scale. Two observations provide the physical basis for this result: The effective value of beta for a molecule in a static applied held is governed by the gamma hyperpolarizability density. When a nucleus shifts infinitesimally, the electrons respond to the resulting change in the nuclear Coulomb field via the same nonlocal susceptibilities that characterize their response to an applied electric field. (C) 1995 American Institute of Physics.