Feynman-Kleinert Linearized Path Integral (FK-LPI) Algorithms for Quantum Molecular Dynamics, with Application to Water and He(4) Jens Aage Poulsen,* ,† Gunnar Nyman, † and Peter J. Rossky ‡ Physical Chemistry, Go ¨teborg UniVersity, S-412-96, Go ¨teborg, Sweden, and Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, UniVersity of Texas at Austin, Austin, Texas 78712 Received May 11, 2006 Abstract: The Feynman-Kleinert Linearized Path Integral (FK-LPI) representation of quantum correlation functions is extended in applications and algorithms. Diffusion including quantum effects for a flexible simple point charge model of liquid water is explored, including new tests of internal consistency. An ab initio quantum correction factor (QCF) is also obtained to correct the far-infrared spectrum of water. After correction, a spectrum based on a classical simulation is in good agreement with the experiment. The FK-LPI QCF is shown to be superior to the so-called harmonic QCF. New computational algorithms are introduced so that the quantum Boltzmann Wigner phase-space density, the central object in the implementation, can be obtained for arbitrary potentials. One scheme requires only that the standard classical force routine be replaced when turning from one molecular problem to another. The new algorithms are applied to the calculation of the Van Hove spectrum of liquid He(4) at 27 K. The spectrum moments are in very good agreement with the experiment. These observations indicate that the FK-LPI approach can be broadly effective for molecular problems involving the dynamics of light nuclei. 1. Introduction Recently, a variety of computational schemes such as centroid molecular dynamics (CMD), 1,2 ring polymer mo- lecular dynamics (RPMD), 3,4 forward-backward semiclas- sical dynamics, 5 the classical Wigner (CW) model, 6-10 mode coupling theory, 11 and analytic continuation methods 12 have been applied for modeling real many-body quantum dynami- cal processes in the condensed phase. Common to all of these methods is the focus on the time correlation function (CF) formalism: The process of interest is studied by evaluating its corresponding CF. For instance, the dynamic structure factor in neutron or X-ray scattering experiments is described by a Van Hove CF, and the rate of diffusion of a particle is obtained from its velocity CF. The accuracy of the different methods remains difficult to evaluate, but it appears that they are all able to capture the main qualitative quantum effects that are relevant in a condensed phase, where quantum coherences are quenched because of the strong interatomic couplings. The CW model, the subject of this paper, is perhaps conceptually the simplest of the methods considered above and has a rigorous derivation. 9 It has been successfully applied for obtaining vibrational relaxation rates of oxygen in liquid oxygen, determined by the golden rule force-force CF, 10 the diffusion coefficient for liquid para-hydrogen at 17 and 25 K, via the Kubo velocity CF, 8 neutron scattering via the Van Hove CF of liquid He(4) at 27 K, 6 and the diffusion coefficient plus a quantum correction factor for the infrared spectrum of water. 7 In short, the model splits the calculation of the quantum CF into two separate tasks, the generation of initial conditions and the propagation of dynamics. The sampling of the appropriate quantum initial conditions (here assumed to be given by a Boltzmann operator) is done through Wigner’s phase-space distribution, * Corresponding author e-mail: jens72@chem.gu.se. † Go ¨teborg University. ‡ University of Texas at Austin. 1482 J. Chem. Theory Comput. 2006, 2, 1482-1491 10.1021/ct600167s CCC: $33.50 © 2006 American Chemical Society Published on Web 09/28/2006