Semiclassical molecular dynamics computation of spontaneous light emission in the condensed phase: Resonance Raman spectra

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Abstract
The three-time correlation function that describes resonance Raman (RR) spectra is computed directly using the Herman–Kluk semiclassical propagator. The trace expression for this correlation function {C(t 1 ,t 2 ,t 3 )= Tr [e −βĤ e −iĤ g (t 1 +t 2 ) e −iĤ e t 3 e +iĤ g (t 2 +t 3 ) e +iĤ e t 1 ]} allows forward–backward time propagation of trajectories over closed time-circuits, leading to efficient convergence in multidimensional systems. A local harmonic approximation is used to derive an expression for the density operator in the coherent state representation (〈p 1 q 1 |e −βĤ |p 2 q 2 〉). This allows efficient sampling of phase space as well as simulations at arbitrary temperatures and in arbitrary coordinates. The resulting method is first analyzed for a one-dimensional problem, where the results are shown to be in excellent agreement with exact quantum calculations. The method is then applied to the problem of RR scattering of iodine in the condensed phase. The RR spectrum of an I 2 molecule in a xenon fluid at 230 K is calculated and also found to be in excellent agreement with experiment.