Monte Carlo Evaluation of Forward−Backward Semiclassical Correlation Functions with a Quantized Coherent State Density

Abstract

The derivative formulation of the forward-backward semiclassical dynamics (FBSD) representation of time correlation functions can be expressed as an integral with respect to trajectory initial conditions weighted by the coherent state transform of a corrected density operator. Expressions are derived for evaluating the relevant matrix elements for applications of particular interest, such as normal mode, bond stretching, and velocity correlation functions at zero and at finite temperature by employing the Gaussian approximation and the discretized path integral representation of the initial density operator, respectively. The obtained expressions lend themselves naturally to integration via Monte Carlo sampling techniques. The fully quantum mechanical representation of the appropriate density operator ensures a proper treatment of zero-point effects, and the use of the coherent state representation captures important imaginary components that are absent from purely classical trajectory methods. Applications to clusters of four water molecules at room temperature are presented.