Reduced equations of motion for semiclassical dynamics in phase space

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Abstract
Time-dependent self-consistent equations for semiclassical dynamics in phase space are developed. The method is based on constructing a Gaussian density matrix, whose equations of motion are obtained by requiring that the first two moments of the coordinates and momenta have the correct time evolution. The method can yield, in principle, the exact values of these moments for all time. The present method can be applied for the time evolution of mixed states in phase space and may, therefore, be particularly useful for molecular dynamics in condensed phases. Raman excitation profiles in anharmonic molecules are calculated and show excellent agreement with exact calculations.