Reconsidering Dispersion Potentials: Reduced Cutoffs in Mesh-Based Ewald Solvers Can Be Faster Than Truncation.

Long-range dispersion interactions have a critical influence on physical quantities in simulations of inhomogeneous systems. However, the perceived computational overhead of long-range solvers has until recently discouraged their implementation in molecular dynamics packages. Here, we demonstrate that reducing the cutoff radius for local interactions in the recently introduced particle-particle particle-mesh (PPPM) method for dispersion [Isele-Holder et al., J. Chem. Phys., 2012, 137, 174107] can actually often be faster than truncating dispersion interactions. In addition, because all long-range dispersion interactions are incorporated, physical inaccuracies that arise from truncating the potential can be avoided. Simulations using PPPM or other mesh Ewald solvers for dispersion can provide results more accurately and more efficiently than simulations that truncate dispersion interactions. The use of mesh-based approaches for dispersion is now a viable alternative for all simulations containing dispersion interactions and not merely those where inhomogeneities were motivating factors for their use. We provide a set of parameters for the dispersion PPPM method using either ik or analytic differentiation that we recommend for future use and demonstrate increased simulation efficiency by using the long-range dispersion solver in a series of performance tests on massively parallel computers.

[1]  Rolf E. Isele-Holder,et al.  Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions. , 2012, The Journal of chemical physics.

[2]  C. Kong Combining rules for intermolecular potential parameters. II. Rules for the Lennard‐Jones (12–6) potential and the Morse potential , 1973 .

[3]  Christian Holm,et al.  How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines , 1998 .

[4]  Capillary waves at the liquid-vapor interface and the surface tension of water. , 2006, The Journal of chemical physics.

[5]  Robert D. Skeel,et al.  Multiple grid methods for classical molecular dynamics , 2002, J. Comput. Chem..

[6]  Johann Fischer,et al.  Molecular dynamics simulation of the liquid–vapor interface: The Lennard-Jones fluid , 1997 .

[7]  Pingwen Zhang,et al.  Error estimate of short-range force calculation in inhomogeneous molecular systems. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Berk Hess,et al.  Lennard-Jones Lattice Summation in Bilayer Simulations Has Critical Effects on Surface Tension and Lipid Properties. , 2013, Journal of chemical theory and computation.

[9]  T. Darden,et al.  Liquid–vapour equilibrium of n -alkanes using interface simulations , 2006 .

[10]  R. Good,et al.  New Combining Rule for Intermolecular Distances in Intermolecular Potential Functions , 1970 .

[11]  Paolo Bientinesi,et al.  Multilevel summation for dispersion: a linear-time algorithm for r(-6) potentials. , 2013, The Journal of chemical physics.

[12]  J. Ilja Siepmann,et al.  Transferable Potentials for Phase Equilibria. 1. United-Atom Description of n-Alkanes , 1998 .

[13]  M. Deserno,et al.  HOW TO MESH UP EWALD SUMS. II. AN ACCURATE ERROR ESTIMATE FOR THE PARTICLE-PARTICLE-PARTICLE-MESH ALGORITHM , 1998, cond-mat/9807100.

[14]  Bernard R. Brooks,et al.  Pressure-Based Long-Range Correction for Lennard-Jones Interactions in Molecular Dynamics Simulations: Application to Alkanes and Interfaces , 2004 .

[15]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[16]  G. Saville,et al.  Computer simulation of a gas–liquid surface. Part 1 , 1977 .

[17]  M. P. Tosi,et al.  Ionic sizes and born repulsive parameters in the NaCl-type alkali halides—I: The Huggins-Mayer and Pauling forms , 1964 .

[18]  H. G. Petersen,et al.  An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles , 1988 .

[19]  H. G. Petersen Accuracy and efficiency of the particle mesh Ewald method , 1995 .

[20]  O. Borodin,et al.  A Quantum Chemistry Based Force Field for Perfluoroalkanes and Poly(tetrafluoroethylene) , 2002 .

[21]  Christian Holm,et al.  Interlaced P3M algorithm with analytical and ik-differentiation. , 2010, The Journal of chemical physics.

[22]  Andrew E. Torda,et al.  The GROMOS biomolecular simulation program package , 1999 .

[23]  Alexandre Tkatchenko,et al.  Dispersion-corrected Møller-Plesset second-order perturbation theory. , 2009, The Journal of chemical physics.

[24]  Hans Hasse,et al.  Hydrogen bonding of methanol in supercritical CO2: comparison between 1H NMR spectroscopic data and molecular simulation results. , 2007, The journal of physical chemistry. B.

[25]  Christian Holm,et al.  Removal of spurious self-interactions in particle-mesh methods , 2011, Comput. Phys. Commun..

[26]  Pingwen Zhang,et al.  On the Numerical Accuracy of Ewald, Smooth Particle Mesh Ewald, and Staggered Mesh Ewald Methods for Correlated Molecular Systems. , 2012, Journal of chemical theory and computation.

[27]  R. H. Boyd,et al.  Prediction of polymer crystal structures and properties: polyethylene and poly(oxymethylene) , 1988 .

[28]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Surface Tension , 1949 .

[29]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[30]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[31]  M. P. Tosi,et al.  Ionic sizes and born repulsive parameters in the NaCl-type alkali halides—II: The generalized Huggins-Mayer form☆ , 1964 .

[32]  Ding-Yu Peng,et al.  On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface , 1997 .

[33]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[34]  D. Wolff,et al.  Tabulated potentials in molecular dynamics simulations , 1999 .

[35]  J. Perram,et al.  Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems , 1992 .

[36]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[37]  Bo Shi,et al.  Molecular dynamics simulation of the density and surface tension of water by particle-particle particle-mesh method. , 2006, The Journal of chemical physics.

[38]  R. A. Zubillaga,et al.  Surface Tension of Organic Liquids Using the OPLS/AA Force Field. , 2013, Journal of chemical theory and computation.

[39]  A. Tkatchenko,et al.  Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. , 2009, Physical review letters.

[40]  Gary S Grest,et al.  Application of Ewald summations to long-range dispersion forces. , 2007, The Journal of chemical physics.

[41]  Terry P Lybrand,et al.  Staggered Mesh Ewald: An extension of the Smooth Particle-Mesh Ewald method adding great versatility. , 2009, Journal of chemical theory and computation.

[42]  A. Tkatchenko,et al.  Describing Both Dispersion Interactions and Electronic Structure Using Density Functional Theory: The Case of Metal-Phthalocyanine Dimers. , 2010, Journal of chemical theory and computation.

[43]  Arnold T. Hagler,et al.  New combining rules for rare gas van der waals parameters , 1993, J. Comput. Chem..

[44]  L. An,et al.  A molecular-dynamics simulation study on the dependence of Lennard-Jones gas-liquid phase diagram on the long-range part of the interactions. , 2005, The Journal of chemical physics.

[45]  David L Mobley,et al.  Accurate and efficient corrections for missing dispersion interactions in molecular simulations. , 2007, The journal of physical chemistry. B.

[46]  Jim Glosli,et al.  Comments on P3M, FMM, and the Ewald method for large periodic Coulombic systems , 1996 .

[47]  Dick Bedeaux,et al.  Tail corrections to the surface tension of a Lennard-Jones liquid-vapour interface , 1995 .

[48]  Jirí Janecek,et al.  Long range corrections in inhomogeneous simulations. , 2006, The journal of physical chemistry. B.

[49]  Gary S. Grest,et al.  Surface tension of normal and branched alkanes , 2007 .

[50]  H. Stern,et al.  On mesh-based Ewald methods: optimal parameters for two differentiation schemes. , 2008, The Journal of chemical physics.

[51]  C Holm,et al.  How to Convert SPME to P3M: Influence Functions and Error Estimates. , 2012, Journal of chemical theory and computation.

[52]  Lee G. Pedersen,et al.  Long-range electrostatic effects in biomolecular simulations , 1997 .

[53]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[54]  J. I. Siepmann,et al.  Pressure dependence of the vapor-liquid-liquid phase behavior in ternary mixtures consisting of n-alkanes, n-perfluoroalkanes, and carbon dioxide. , 2005, The journal of physical chemistry. B.

[55]  Peter Wriggers,et al.  Formulation and analysis of a three-dimensional finite element implementation for adhesive contact at the nanoscale , 2009 .

[56]  H. A. Lorentz Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase , 1881 .

[57]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .