Quantum Diffusion in Liquid Para-hydrogen:  An Application of the Feynman−Kleinert Linearized Path Integral Approximation

Abstract

Quantum effects on diffusion in liquid para-hydrogen at temperatures of T ) 17 and 25 K and saturated vapor pressure is studied by calculating the diffusion coefficient from the standard Green-Kubo formula, using both the ordinary velocity correlation function (CF) and its Kubo-transformed counterpart. All CFs are calculated with a recently proposed linearized path integral expression for general CFs, using an approximate Wigner transformed Boltzmann operator based on Feynman-Kleinert variational path integral theory. Also, the ability of the approximate Wigner transform to predict the radial distribution function and kinetic energy of the liquid is investigated. The conclusions are as follows: (i) The predicted structure of liquid parahydrogen is in excellent agreement with accurate path integral Monte Carlo calculations at both temperatures. (ii) The calculated liquid kinetic energy is in very good agreement with the accurate value at T ) 25 K but deviates somewhat from the accurate value at T ) 17 K. (iii) The diffusion coefficients based on the Kubotransformed CF are in very good agreement with experiment, at both temperatures, whereas results from the ordinary velocity CF are not accurate at T ) 17 K. The reason for the better performance of the Kubo CF approach is attributed to the latter's robustness toward errors in the approximate Boltzmann operator Wigner transform. The kinetic energy derived from the Kubo-transformed CFs is in excellent agreement with accurate values at both temperatures. † Part of the special issue "Frank H. Stillinger Festschrift".

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

“…Some kinds of harmonic approximation 3,6,7 for the elements of the Boltzmann operator is necessary. These approximations have been successfully applied to some complex systems 15,21 . They all, however, encounter problems at low temperature when the potential energy has negative curvature; this shows up most strikingly in regions of potential barriers, but also in the long range region of bounded potentials.…”

“…Semiclassical (SC) theory [8][9][10][11][12] provides one way for adding quantum effects to classical MD simulations, and there is ample evidence that the SC approximation is a usefully accurate description of essentially all quantum effects in molecular dynamics 2,7,[13][14][15][16][17][18] . For systems with many degrees of freedom, various initial value representations (IVRs) of SC theory provide the first step toward a practical way for carrying out SC calculations; this effectively replaces the non-linear boundary value problem of traditional SC theory with a Monte Carlo average over the initial conditions of classical trajectories [9][10][11][12] , a procedure much akin to what is done in classical MD simulations, allowing one to borrow from the great deal of computational development in that field.…”

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach

“…Methods suitable for numerical simulations of real p-H 2 ensembles have been proposed using the path integral Monte Carlo (PIMC), 1, 2 linearized semiclassical initial value representation (LSC-IVR), 7,8 centroid molecular dynamics (CMD), 3,4,6 ring-polymer molecular dynamics (RPMD), 9 and the thermal Gaussian molecular dynamics (TGMD). 10 These all are based on the imaginary-time path-integral theory, and the latter four have been implemented for calculations of time correlation functions (TCFs) accounting for particularly important NQEs such as zero-point energy (ZPE) effect.…”

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

“…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]...…”