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

Abstract

The linearized approximation to the semiclassical initial value representation (LSC-IVR) is used to calculate time correlation functions relevant to the incoherent dynamic structure factor for inelastic neutron scattering from liquid para-hydrogen at 14 K. Various time correlations functions were used which, if evaluated exactly, would give identical results, but they do not because the

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

“…The degree to which this affects the accuracy of the LSC-IVR in practical applications is subtle, since the LSC-IVR quantizes  β rather than the Boltzmann density operator . A previous investigation 26 suggested that this inconsistency in the LSC-IVR correlation function may be most noticeable at very long time for some systems at quite low temperature.…”

“…There are other ways to derive the classical Wigner model (or one may simply postulate it) 6,44,49,50 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 24,[28][29][30][51][52][53][54][55][56][57][58][59][60][61][62] 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 22,63 , or the still more accurate generalized FB-IVR 64 and exact FB-IVR 5 of Miller et al , are needed for this-but it does describe some aspects of the quantum dynamics very well [24][25][26][34][35][36][37][38]41,42,[65][66][67] . E.g., the LSC-IVR has been shown to describe the strong tunneling regime 42 in reactive flux auto-correlation functions (which determine chemical reaction rates) quite well, and also velocity autocorrelation functions 24,25,66,67 , force autocorrelation functions 25,[34][35]...…”

“…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 22,63 , or the still more accurate generalized FB-IVR 64 and exact FB-IVR 5 of Miller et al , are needed for this-but it does describe some aspects of the quantum dynamics very well [24][25][26][34][35][36][37][38]41,42,[65][66][67] . E.g., the LSC-IVR has been shown to describe the strong tunneling regime 42 in reactive flux auto-correlation functions (which determine chemical reaction rates) quite well, and also velocity autocorrelation functions 24,25,66,67 , force autocorrelation functions 25,[34][35][36][37][38] , and incoherent dynamic structures 26 in systems with enough degrees of freedom for quantum re-phasing to be unimportant.…”

“…Since the LSC-IVR approximation is more accurate in some aspects than RPMD and CMD (e.g., it is exact for harmonic systems for non-linear, as well as linear operators, also see Refs. 26,106 ), it should thus provide an even more useful 'prior' for the MEAC methodology (the accuracy of which depends on having as good a 'prior' as possible). Since the LSC-IVR itself becomes accurate in the high-temperature and the harmonic limits (for both linear and nonlinear operators), the combination MEAC+LSC/IVR will obviously be good in both of these limits, and it should provide some improvement over the LSC-IVR description of strongly anharmonic systems and for lower temperatures.…”

“…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] ).…”