Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: Applications to condensed phase systems

Abstract

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne 13 Lennard-Jones (LJ) cluster in its liquid-solid phase transition region (temperature from 4 K to 14 K).Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquid-like) than in the classical case. Liquid

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

“…However, both the CMD and the RPMD models have the desirable feature that the quantum mechanical equilibrium distribution is correctly conserved-i.e., for the case px 1 A = the correlation function (i.e. the canonical ensemble average of operator B ) is time-independent-while this is not the case for the LSC-IVR (though Liu et al 26,54 have demonstrated that this is in fact not a problem in practical calculations so long as the correlation time scale is not too long).…”

“…Fig. 4 of a recent study 26 shows that for the realistic anharmonic system liquid para-H 2 at the state point (25K under nearly zero external pressure), the LSC-IVR is a more faithful approximation to quantum mechanical real time correlation functions at short time (on the order of thermal time β ) than the CMD and RPMD models even for linear operators (such as or ). How generally true this conclusion is must of course await future investigations on other realistic systems.…”

“…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] . 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 .…”