Off-resonant fifth-order nonlinear response of water and CS2: Analysis based on normal modes

Off-resonant fifth-order nonlinear response functions of liquid water and liquid ${\mathrm{CS}}_{\mathrm{2}}$ are analyzed based on two normal-mode schemes, quenched and instantaneous normal modes. It was found that the fifth-order response function is very sensitive to the mode mixing in polarization, arising from the quadratic term of polarization with respect to the different modes. The echo signal is drastically reduced by this off-diagonal mode mixing in polarization even without any rapid frequency modulation mechanism. The near absence of echo signal thus obtained for liquids is consistent with the recent experimental results for liquid ${\mathrm{CS}}_{\mathrm{2}}.$ The present calculation yields the different fifth-order signals for different polarization geometries, as experimentally shown by Tokmakoff and Fleming [J. Chem. Phys. 106, 2569 (1997)]. The mode mixing dynamics is investigated in terms of the bispectra of total potential energy and polarizability.