Condensed phase spectroscopy from mixed-order semiclassical molecular dynamics: Absorption, emission, and resonant Raman spectra of I2 isolated in solid Kr

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Abstract
A method for spectral simulations in systems of very large dimensionality via semiclassical molecular dynamics is introduced and applied to the spectroscopy of iodine isolated in solid Kr, as a prototype of spectroscopy in condensed media in general. The method relies on constructing quantum correlation functions, C(t), using initial value propagators which correspond to the zeroth‐ and second‐order approximations in stationary phase of the exact quantum propagator. The first is used for treating modes with high thermal occupation numbers, the lattice modes, while the second is used for treating the guest mode. The limits of validity of the bare propagators are tested vs exact treatments of gas phase I2, and shown to be quite broad. The mixed order simulations are then used to reproduce the structured A→X emission, the structureless B←X absorption, and the intensities in resonant Raman (RR) progressions of matrix isolated I2, connecting spectroscopic observables to molecular motions. Decompositions of the supersystem correlations into system and bath are used to provide perspectives about condensed phase spectroscopy. The system correlation can be regarded as the sampling function for the decaying bath correlation, which in turn is a summary of the many‐body dynamics. The B←X absorption spectrum is determined by the coherent ballistic motion of the excited state density: Upon stretching, I2 pushes the cage atoms out of overlap in position density, and C(t) never recovers. Due to the compressive nature of the cage coordinate in the A→X transition, C(t) decays more gently, after being sampled three times. RR spectra, which are reproduced with adiabatic dynamics, sample the complete history of the many‐body correlations, however, due to the breadth in space‐time of scattering into high overtones, the sampling is coarse grained. The specific dynamics that control C(t) cannot be described as dissipative.