Quantum Diffusion in Liquid Para-hydrogen: An Application of the Feynman-Kleinert Linearized Path Integral Approximation † Jens Aage Poulsen and Gunnar Nyman Physical Chemistry, Gøteborg UniVersity, S-412-96, Go ¨teborg, Sweden Peter J. Rossky* Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed: June 10, 2004; In Final Form: October 14, 2004 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 para- hydrogen 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 Kubo- transformed 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. 1. Introduction During the past decade, practical and general methods for calculating liquid-state correlation functions have been devel- oped. Among these, we find the forward-backward semiclas- sical scheme, 34,53 the centroid molecular dynamics (CMD) algorithm, 5,21,22 and a recent implementation of the linearized path integral (LPI) representation of CFs, using a specific Feynman-Kleinert (FK) version of the Boltzmann Wigner transform (hence termed FK-LPI). 36 These methods represent practical schemes that strive for a compromise between the two, apparently incompatible, extremes: a method capable of ac- curately describing the quantum dynamics of large systems and a computational feasibility comparable to that of classical molecular dynamics codes. The aforementioned methods achieve this compromise by sacrificing the description of long-time coherence effects and, instead, focusing only on short-time interference phenomena. The daunting problem of propagating dynamics quantum-mechanically is bypassed by this focus, while retaining quantum mechanical probability distributions. The quantum statistical many-body dynamics then becomes com- putationally accessible. Therefore, it has been possible to apply these methods to dynamical phenomena in liquids where comparisons between theory and experiment are possible. The liquid-state applications of CMD, 3,20 forward-backward semi- classical dynamics, 34,53 maximum entropy analytical continua- tion schemes, 25-27,39,48 and the classical Wigner/LPI method 37,44,45 have demonstrated an acceptable level of accuracy and com- putational practicality of these methods, and that the accurate treatment of only short-time interference effects indeed does not seem to present a basic limitation. The neglect of long-time interference effects is an approxima- tion that works well in condensed phases. It is worth elaborating on this point. There has been much work devoted to the study of the quenching of interference effects when a “system” couples to a dissipative “bath”, the latter mostly modeled as a set of harmonic oscillators (see, e.g., refs 2, 14, and 17). The essence of these studies is that the system-reduced density matrix rapidly becomes diagonal when the system and bath are allowed to interact. This effect, which is known as decoherence, 17 can be shown by a path integral analysis to generate classical and noise- free dynamical behavior for the system degree of freedom, augmented with a Wigner distribution for its initial phase-space distribution, if the system possess a sufficient inertia (see section VI.B. of ref 14). The classical Wigner/LPI model can be derived by a related analysis, which is also justified when decoherence is strong. 36 The chain of reasoning is as follows. One starts from the exact path integral (PI) expression for the desired system CF. First, it is noted, as is also well-known, 14 that forward-backward system paths must inherently be similar to make any significant contribution to the CF value. This occurs because of the assumption of strong system-bath coupling. As a consequence, the PI action functional may be linearized in the system degree † Part of the special issue “Frank H. Stillinger Festschrift”. * Author to whom correspondence should be addressed. Telephone: 512- 471-3555. Fax: 512-471-1624. E-mail address: rossky@mail.utexas.edu. 19799 J. Phys. Chem. B 2004, 108, 19799-19808 10.1021/jp040425y CCC: $27.50 © 2004 American Chemical Society Published on Web 11/16/2004