Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions

Abstract

The thermal Gaussian approximation (TGA) recently developed by Mandelshtam et al [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator ( )for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the 'forward-backward semiclassical dynamics' (FBSD) approximation developed by Makri et al. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.

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

“…In the TGA, the Boltzmann matrix element is approximated by a Gaussian form: specifically, in Eq. and we refer readers to Section IV of our recent paper 32 for more details. We note here that the TGA/LSC-IVR is exact in the classical limit and in the harmonic limit as pointed out in our previous work 32 .…”

“…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] . E.g., the LSC-IVR has been shown to describe reactive flux auto-correlation functions (which determine chemical reaction rates) quite well, including strong tunneling regimes 31 , and velocity auto-correlation functions 26,32,60 and force auto-correlation functions 26,34,61,62 in systems with enough degrees of freedom for quantum re-phasing to be unimportant.…”

“…Section II first summarizes the theory of inelastic neutron scattering and shows how the self-part of the intermediate scattering function and the velocity correlation function are related with each other, and then describes the LSC-IVR formulation of these time correlation functions using the thermal Gaussian approximation (TGA) 26,32 . Section III presents the LSC-IVR simulation results for the incoherent dynamic structure factor of liquid para-hydrogen at 14K T = (under nearly zero external pressure) using different correlation functions, along with the spectral moment test and the comparison to other methods and the recent inelastic neutron scattering experiment data 101 .…”

“…The simplest (and most approximate) version of the SC-IVR is its 'linearized' approximation (LSC-IVR) 9,26,[28][29][30][31][32][33][34][35] , which leads to the classical Wigner model [36][37][38][39] for time correlation functions; see Section IIB for a summary of the LSC-IVR. 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 .…”

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation

“…The SC-IVR provides a way for generating the quantum time evolution operator (propagator) by computing an ensemble of classical trajectories, much as is done in standard classical MD simulations. As is well known from SC developments in the early 1970's 1,[18][19][20][21] , such approaches actually contain all quantum effects at least qualitatively, and in molecular systems the description is usually quite quantitative (see reviews [2][3][4][5]14,22,23 and some recent applications [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] ).…”