Mixed-order semiclassical dynamics in coherent state representation: The connection between phonon sidebands and guest–host dynamics

The formalism of mixed-order semiclassical molecular dynamics in coherent state representation is developed and applied to calculations 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←X transition of Cl2 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. Details of the dynamics of a chromophore coupled to lattice phonons are discussed.