Time-dependent Hartree-Fock schemes for analytical evaluation of the Raman intensities

Methods for analytical evaluation of the Raman intensities were presented using time-dependent Hartree-Fock schemes. The derivatives of frequency-dependent polarizability with respect to atomic Cartesian coordinates were obtained. The iterative scheme determined the mixed derivatives of the density matrix with respect to atomic Cartesian coordinates and dynamic electric fields. The second scheme expressed the polarizability derivatives in terms of first-order derivatives utilizing the 2n+1 rule. Results indicated large frequency dispersion effects for the proposed methods.