A fast path integral method for polarizable force fields.

A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. It is however possible to improve on this estimate by decomposing the potential into a sum of slowly and rapidly varying contributions. If the slowly varying contribution changes only slightly over the length scale of the ring polymer, it can be evaluated on a contracted ring polymer with fewer than the full n beads (or equivalently on a lower order Fourier decomposition of the imaginary time path). Here we develop and test this idea for systems with polarizable force fields. The development consists of iterating the induction on the contracted ring polymer and applying an appropriate transformation to obtain the forces on the original n beads. In combination with a splitting of the Coulomb potential into its short- and long-range parts, this results in a method with little more than classical computational effort in the limit of large system size. The method is illustrated with simulations of liquid water at 300 K and hexagonal ice at 100 K using a recently developed flexible and polarizable Thole-type potential energy model.

[1]  David E. Manolopoulos,et al.  A refined ring polymer contraction scheme for systems with electrostatic interactions , 2008 .

[2]  B. Berne,et al.  On path integral Monte Carlo simulations , 1982 .

[3]  Per Linse,et al.  Ewald summation and reaction field methods for potentials with atomic charges, dipoles, and polarizabilities , 2000 .

[4]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[5]  John E. Bertie,et al.  Infrared Intensities of Liquids XX: The Intensity of the OH Stretching Band of Liquid Water Revisited, and the Best Current Values of the Optical Constants of H2O(l) at 25°C between 15,000 and 1 cm−1 , 1996 .

[6]  G. Schenter,et al.  A quantitative account of quantum effects in liquid water. , 2006, The Journal of chemical physics.

[7]  P. Kusalik,et al.  Quantum effects in light and heavy liquid water: A rigid-body centroid molecular dynamics study. , 2004, The Journal of chemical physics.

[8]  D. Ceperley.  Path integrals in the theory of condensed helium , 1995 .

[9]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[10]  Gregory A. Voth,et al.  A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables , 1999 .

[11]  Thomas F. Miller,et al.  Quantum diffusion in liquid water from ring polymer molecular dynamics. , 2005, The Journal of chemical physics.

[12]  B. Thole.  Molecular polarizabilities calculated with a modified dipole interaction , 1981 .

[13]  Sotiris S Xantheas,et al.  Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water. , 2008, The Journal of chemical physics.

[14]  Franz J. Vesely,et al.  N-particle dynamics of polarizable Stockmayer-type molecules , 1977 .

[15]  Sotiris S Xantheas,et al.  The flexible, polarizable, thole-type interaction potential for water (TTM2-F) revisited. , 2006, The journal of physical chemistry. A.

[16]  David E Manolopoulos,et al.  Comparison of path integral molecular dynamics methods for the infrared absorption spectrum of liquid water. , 2008, The Journal of chemical physics.

[17]  L. Dang,et al.  Recent advances in molecular simulations of ion solvation at liquid interfaces. , 2006, Chemical reviews.

[18]  D. Manolopoulos,et al.  An efficient ring polymer contraction scheme for imaginary time path integral simulations. , 2008, The Journal of chemical physics.

[19]  J. A. Barker.  A quantum‐statistical Monte Carlo method; path integrals with boundary conditions , 1979 .

[20]  V. Tipparaju,et al.  An efficient parallelization scheme for molecular dynamics simulations with many-body, flexible, polarizable empirical potentials: application to water , 2006 .

[21]  J. Reimers,et al.  Unit cells for the simulation of hexagonal ice , 1997 .

[22]  Sotiris S. Xantheas,et al.  The parametrization of a Thole-type all-atom polarizable water model from first principles and its application to the study of water clusters (n=2–21) and the phonon spectrum of ice Ih , 1999 .

[23]  D. Manolopoulos,et al.  Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice. , 2008, The Journal of chemical physics.

[24]  Sotiris S. Xantheas,et al.  Development of transferable interaction models for water. IV. A flexible, all-atom polarizable potential (TTM2-F) based on geometry dependent charges derived from an ab initio monomer dipole moment surface , 2002 .

[25]  Peter G. Wolynes,et al.  Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids , 1981 .

[26]  David E Manolopoulos,et al.  On the short-time limit of ring polymer molecular dynamics. , 2006, The Journal of chemical physics.

[27]  Jianshu Cao,et al.  The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties , 1994 .

[28]  Ian R. Craig,et al.  Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics. , 2004, The Journal of chemical physics.

[29]  Thomas F. Miller,et al.  Quantum diffusion in liquid para-hydrogen from ring-polymer molecular dynamics. , 2005, The Journal of chemical physics.

[30]  Rahman,et al.  Molecular-dynamics study of atomic motions in water. , 1985, Physical review. B, Condensed matter.

[31]  G. Voth,et al.  Quantum effects in liquid water from an ab initio-based polarizable force field. , 2007, The Journal of chemical physics.

[32]  M. Parrinello,et al.  Study of an F center in molten KCl , 1984 .

[33]  R. A. Kuharski,et al.  A quantum mechanical study of structure in liquid H2O and D2O , 1985 .

[34]  C. Burnham,et al.  On the origin of the redshift of the OH stretch in Ice Ih: evidence from the momentum distribution of the protons and the infrared spectral density. , 2006, Physical chemistry chemical physics : PCCP.

[35]  Anders Wallqvist,et al.  A molecular dynamics study of polarizable water , 1989 .