Multidimensional femtosecond spectroscopies of vibrational motions in liquids: Semiclassical expansion

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Abstract
Fifth- (χ(5)) and seventh- (χ(7)) order electronically off-resonant Raman spectroscopies in molecular liquids are investigated using a new semiclassical expansion of the optical response which applies for weak anharmonicities and low temperatures. The leading contribution can be calculated using classical equations of motion for nuclear wave packets, even when the system itself may be highly nonclassical. Two sources of nonlinearities which generate the signals—the nonlinear dependence of the polarizability on nuclear coordinates and vibrational anharmonicities—are identified. Formal analogy between the present equations and the time-dependent Hartree–Fock equations used in electronic nonlinear spectroscopy suggests specific experimental signatures of the various nonlinearities.