Optimized Monte Carlo sampling in forward–backward semiclassical dynamics

Abstract

Forward-backward semiclassical dynamics (FBSD) provides a rigorous and powerful methodology for calculating time correlation functions in condensed phase systems characterized by substantial quantum mechanical effects associated with zero-point motion, quantum dispersion, or identical particle exchange symmetries. The efficiency of these simulations arises from the use of classical trajectories to capture all dynamical information. However, full quantization of the density operator makes these calculations rather expensive compared to fully classical molecular dynamics simulations. This article discusses the convergence properties of various correlation functions and introduces an optimal Monte Carlo sampling scheme that leads to a significant reduction of statistical error. A simple and efficient procedure for normalizing the FBSD results is also discussed. Illustrative examples on model systems are presented.

Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

“…7 we also present results obtained using the forward-backward semiclassical dynamics ͑FBSD͒ approximation [30][31][32][33][34][35][36][37][38][39][40][41][42] FBSD methodology generates the real-time version of the correlation function C v·v ͑t͒, we had to transform the results to the complex-time form G v·v ͑t͒ in order to compare. In Fig.…”

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation

“…Efforts to mitigate the sign problem have led to the development of more approximate methods such as the linearized (LSC)-IVR [50][51][52][53] that fail to capture quantum coherence effects, a) Electronic mail: na346@cornell.edu and various forward-backward (FB) methods that are either less accurate or computationally expensive. [54][55][56][57][58][59][60][61][62] The recently-introduced Mixed Quantum-Classical (MQC)-IVR method 63,64 employs a modified Filinov filtration (MFF) scheme 45,[63][64][65][66][67][68][69][70][71][72][73][74][75] to damp the oscillatory phase of the integrand and has been shown to improve numerical convergence without significant loss of accuracy. 63,64 Specifically, the filtering parameters employed in MQC-IVR modify the extent to which a particular dof contributes to the overall phase of the integrand, effectively controlling the 'quantumness' of that mode.…”

Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen

“…The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it 28,29 . There are other ways to derive the classical Wigner model (or one may simply postulate it) 9,35,40,41 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 32,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 22,57 (or the still more accurate generalized FB-IVR 58 ) of Miller et al, are needed for this-but it does describe some aspects of the quantum dynamics very well 26,[30][31][32]34,[59][60][61][62] .…”