Abstract: The mixed-order semiclassical molecular dynamics method is used for the calculation of quantum time correlation functions in extended systems. The method allows the consistent treatment of a selected number of degrees of freedom to second-order in the stationary phase approximation through the Herman and Kluk propagator, while the rest of the system is treated to zeroth-order, using frozen Gaussians. The formulation is applied to calculate the absorption spectrum, of the B $IMP X transition of Cl$- 2$/ isolated in solid Ar, a spectrum that shows zero-phonon lines and phonon sidebands with relative intensities that depend on the excited state vibrational level. The explicit simulation of quantum time correlation functions of the system consisting of 321 degrees of freedom, reproduces the spectrum and allows its interpretation in terms of the underlying molecular motions.IN order to extend the semiclassical methods to longer timescale a new extension of Herman-Kluk propagator is developed, which combines classical propagation of trajectories for length where the initial value propagator remains accurate, followed by Monte-Carlo regeneration of the ensemble of trajectories and continuation of propagation. This new method is tested for the calculation of long time dynamics in a 1D Morse oscillator. !26
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