Electronically coarse-grained molecular dynamics using quantum Drude oscillators

Standard molecular dynamics (MD) simulations generally make use of a basic description of intermolecular forces which consists of fixed, pairwise, atom-centred Coulomb, van der Waals and short-range repulsive terms. Important interactions such as many-body polarisation and many-body dispersion which are sensitive to changes in the environment are usually neglected, and their effects treated effectively within mean-field approximations to reproduce a single thermodynamic state point or physical environment. This leads to difficulties in modelling the complex interfaces of interest today where the behaviour may be quite different from the regime of parameterisation. Here, we describe the construction and properties of a Gaussian coarse-grained electronic structure, which naturally generates many-body polarisation and dispersion interactions. The electronic structure arises from a fully quantum mechanical treatment of a set of distributed quantum Drude oscillators (QDOs), harmonic atoms which interact with each other and other moieties via electrostatic (Coulomb) interactions; this coarse-grained approach is capable of describing many-body polarisation and dispersion but not short-range interactions which must be parametrised. We describe how on-the-fly forces due to this exchange-free Gaussian model may be generated with linear scale in the number of atoms in the system using an adiabatic path integral molecular dynamics for quantum Drude oscillators technique (APIMD-QDO). We demonstrate the applicability of the QDO approach to realistic systems via a study of the liquid–vapour interface of water.

[1]  B. Leimkuhler,et al.  Adaptive stochastic methods for sampling driven molecular systems. , 2011, The Journal of chemical physics.

[2]  J. Tersoff,et al.  New empirical approach for the structure and energy of covalent systems. , 1988, Physical review. B, Condensed matter.

[3]  O. Seeberg.  Statistical Mechanics. — A Set of Lectures , 1975 .

[4]  T. Whitfield,et al.  Low variance energy estimators for systems of quantum Drude oscillators: treating harmonic path integrals with large separations of time scales. , 2007, The Journal of chemical physics.

[5]  Nohad Gresh,et al.  Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo‐β‐lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry , 2005, J. Comput. Chem..

[6]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[7]  M. W. Cole,et al.  Nanoscale van der Waals interactions , 2009 .

[8]  Mischa Bonn,et al.  Nuclear quantum effects affect bond orientation of water at the water-vapor interface. , 2012, Physical review letters.

[9]  Mark E. Tuckerman,et al.  Explicit reversible integrators for extended systems dynamics , 1996 .

[10]  A. Donchev,et al.  Many-body effects of dispersion interaction. , 2006, The Journal of chemical physics.

[11]  Wilma K. Olson,et al.  The dependence of DNA tertiary structure on end conditions: Theory and implications for topological transitions , 1994 .

[12]  C. F. Curtiss,et al.  Molecular Theory Of Gases And Liquids , 1954 .

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

[14]  Aneesur Rahman,et al.  Correlations in the Motion of Atoms in Liquid Argon , 1964 .

[15]  J. Ilja Siepmann,et al.  Development of Polarizable Water Force Fields for Phase Equilibrium Calculations , 2000 .

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

[17]  A. W. Overhauser,et al.  Theory of the Dielectric Constants of Alkali Halide Crystals , 1958 .

[18]  C. Vega,et al.  Dipole-quadrupole force ratios determine the ability of potential models to describe the phase diagram of water. , 2007, Physical review letters.

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

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

[21]  B. Berne,et al.  Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals , 1993 .

[22]  A. Stone,et al.  Towards an accurate intermolecular potential for water , 1992 .

[23]  J. Crain,et al.  Norm-conserving diffusion Monte Carlo method and diagrammatic expansion of interacting drude oscillators: Application to solid xenon , 2009 .

[24]  Alexander D. MacKerell,et al.  A simple polarizable model of water based on classical Drude oscillators , 2003 .

[25]  J. Crain,et al.  Quantum Drude oscillator model of atoms and molecules: many-body polarization and dispersion interactions for atomistic simulation. , 2013 .

[26]  L. M. Woods,et al.  Many-Body van der Waals Interactions between Graphitic Nanostructures , 2010 .

[27]  Glenn J. Martyna,et al.  A unified formalism for many-body polarization and dispersion: The quantum Drude model applied to fluid xenon , 2006 .

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

[29]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[30]  M. Dixon,et al.  Interionic potentials in alkali halides and their use in simulations of the molten salts , 1976 .

[31]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[32]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[33]  Henry Margenau,et al.  Theory of intermolecular forces , 1969 .

[34]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[35]  Roberto Car,et al.  Nuclear quantum effects in water. , 2008, Physical review letters.

[36]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[37]  Efthimios Kaxiras,et al.  New Insights into the Structure of the Vapor/Water Interface from Large-Scale First-Principles Simulations. , 2011, The journal of physical chemistry letters.

[38]  Bin Chen,et al.  Structure and dynamics of the aqueous liquid-vapor interface: a comprehensive particle-based simulation study. , 2006, The journal of physical chemistry. B.

[39]  Wilson,et al.  Polarization Effects, Network Dynamics, and the Infrared Spectrum of Amorphous SiO2. , 1996, Physical review letters.

[40]  J. Perram,et al.  Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[41]  W. Cochran.  Lattice dynamics of Alkali Halides , 1959 .

[42]  L. Dang,et al.  MOLECULAR DYNAMICS STUDY OF WATER CLUSTERS, LIQUID, AND LIQUID-VAPOR INTERFACE OF WATER WITH MANY-BODY POTENTIALS , 1997 .

[43]  J. Crain,et al.  Electronically coarse-grained model for water. , 2013, Physical review letters.

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

[45]  Mark E. Tuckerman,et al.  Molecular dynamics algorithms for path integrals at constant pressure , 1999 .

[46]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[47]  S. Xantheas,et al.  Development of transferable interaction models for water. I. Prominent features of the water dimer potential energy surface , 2002 .

[48]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[49]  Richard D. Schaller,et al.  Surface relaxation in liquid water and methanol studied by x-ray absorption spectroscopy , 2002 .

[50]  D. G. Pettifor,et al.  Analytic bond-order potentials beyond Tersoff-Brenner. I. Theory , 1999 .

[51]  Glenn J. Martyna,et al.  Constant pressure path integral molecular dynamics studies of quantum effects in the liquid state properties of n-alkanes , 2000 .

[52]  S. Grimme.  Density functional theory with London dispersion corrections , 2011 .

[53]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[54]  R. Wilcox.  Exponential Operators and Parameter Differentiation in Quantum Physics , 1967 .

[55]  C. Poole,et al.  Classical Mechanics, 3rd ed. , 2002 .