Calculation of the group-based pressure in molecular simulations. I. A general formulation including Ewald and particle-particle-particle-mesh electrostatics

A general formulation is given for the calculation of the isotropic or anisotropic group-based instantaneous pressure in molecular simulations under periodic boundary conditions. The equations, derived from the statistical mechanical definition of the pressure, apply to groups defined as single atoms (atomic pressure) or whole molecules (molecular pressure), but also to any other arbitrary atom grouping. Different definitions lead to different pressure fluctuations, but to the same average pressure. Two sets of equations are derived for the calculation of the group-based virial. The “traditional” set, which is the one commonly used to compute molecular pressures in simulations, has two main drawbacks: (i) it requires bookkeeping of group definitions in the inner loop of the nonbonded interaction calculation, (ii) it cannot be applied when electrostatic interactions are computed through lattice-sum methods. The “alternative” set is based on the remarkable result that any group-based virial can be computed ...

[1]  G. Pawley,et al.  Computer Simulation of the Plastic-to-Crystalline Phase Transition in SF 6 , 1982 .

[2]  Hoover,et al.  Time-reversible equilibrium and nonequilibrium isothermal-isobaric simulations with centered-difference Stoermer algorithms. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[3]  Wilfred F. van Gunsteren,et al.  Lattice‐sum methods for calculating electrostatic interactions in molecular simulations , 1995 .

[4]  S. Nosé,et al.  Isothermal–isobaric computer simulations of melting and crystallization of a Lennard‐Jones system , 1986 .

[5]  S. Nosé,et al.  Structural Transformations in Solid Nitrogen at High Pressure , 1983 .

[6]  S. Neyertz,et al.  A GENERAL PRESSURE TENSOR CALCULATION FOR MOLECULAR DYNAMICS SIMULATIONS , 1995 .

[7]  Gary P. Morriss,et al.  The isothermal/isobaric molecular dynamics ensemble , 1983 .

[8]  G. Ciccotti,et al.  Atomic stress isobaric scaling for systems subjected to holonomic constraints , 1997 .

[9]  T. Ruijgrok,et al.  On the energy per particle in three- and two-dimensional Wigner lattices , 1988 .

[10]  D. Heyes,et al.  MOLECULAR DYNAMICS AT CONSTANT PRESSURE AND TEMPERATURE , 1983 .

[11]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[12]  M. Parrinello,et al.  Crystal structure and pair potentials: A molecular-dynamics study , 1980 .

[13]  D. Tildesley,et al.  Molecular dynamics simulation of the orthobaric densities and surface tension of water , 1995 .

[14]  Gerhard Hummer,et al.  Free Energy of Ionic Hydration , 1996 .

[15]  Evans,et al.  Pressure tensor for inhomogeneous fluids. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  G. Hummer,et al.  The pressure dependence of hydrophobic interactions is consistent with the observed pressure denaturation of proteins. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

[18]  Mauro Ferrario,et al.  Constant pressure-constant temperature molecular dynamics for rigid and partially rigid molecular systems , 1985 .

[19]  J. Mccammon,et al.  Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study. , 1999, Biophysical chemistry.

[20]  W. V. van Gunsteren,et al.  Dynamical properties of bovine pancreatic trypsin inhibitor from a molecular dynamics simulation at 5000 atm , 1993, FEBS letters.

[21]  S. Nosé,et al.  A study of solid and liquid carbon tetrafluoride using the constant pressure molecular dynamics technique , 1983 .

[22]  D. Lévesque,et al.  New High-Pressure Phase of Solid 4 He Is bcc , 1983 .

[23]  M. Marchi,et al.  SIMULATION OF A PROTEIN CRYSTAL AT CONSTANT PRESSURE , 1997 .

[24]  D. Y. Yoon,et al.  Novel molecular dynamics simulations at constant pressure , 1992 .

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

[26]  D. H. Tsai.  The virial theorem and stress calculation in molecular dynamics , 1979 .

[27]  Bernard R. Brooks,et al.  Removal of pressure and free energy artifacts in charged periodic systems via net charge corrections to the Ewald potential , 1998 .

[28]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[29]  Wilfred F. van Gunsteren,et al.  A generalized reaction field method for molecular dynamics simulations , 1995 .

[30]  Pressure calculation in polar and charged systems using Ewald summation: Results for the extended simple point charge model of water , 1998, physics/9806038.

[31]  T. Straatsma,et al.  Free energy of ionic hydration: Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations , 1988 .

[32]  H Bekker,et al.  THE VIRIAL OF ANGLE-DEPENDENT POTENTIALS IN MOLECULAR-DYNAMICS SIMULATIONS , 1994 .

[33]  J. Mccammon,et al.  Ewald artifacts in computer simulations of ionic solvation and ion–ion interaction: A continuum electrostatics study , 1999 .

[34]  K. Heinzinger,et al.  Isothermal-isobaric molecular dynamics simulation of polymorphic phase transitions in alkali halides , 1989 .

[35]  Baldomero Oliva,et al.  Calculation of the group-based pressure in molecular simulations. II. Numerical tests and application to liquid water , 2002 .

[36]  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.

[37]  Brad Lee Holian,et al.  Comment on ‘‘Constant pressure molecular dynamics algorithms’’ [J. Chem. Phys. 101, 4177 (1994)] , 1996 .

[38]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .

[39]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[40]  J. H. Weiner,et al.  Bond forces and pressure in diatomic liquids , 1990 .

[41]  Philippe H. Hünenberger,et al.  Optimal charge-shaping functions for the particle–particle—particle–mesh (P3M) method for computing electrostatic interactions in molecular simulations , 2000 .

[42]  S. Yip,et al.  Molecular dynamics study of pressure in molecular systems , 1994 .

[43]  J. Henderson,et al.  Statistical mechanics of inhomogeneous fluids , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[44]  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.

[45]  D. Theodorou,et al.  Stress tensor in model polymer systems with periodic boundaries , 1993 .

[46]  Robert J. Swenson,et al.  Comments on virial theorems for bounded systems , 1983 .

[47]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[48]  J. Mccammon,et al.  Molecular Dynamics Simulations of a Polyalanine Octapeptide under Ewald Boundary Conditions: Influence of Artificial Periodicity on Peptide Conformation , 2000 .

[49]  R. Levy,et al.  Molecular dynamics simulation of solvated protein at high pressure. , 1992, Biochemistry.

[50]  E. Wajnryb,et al.  Uniqueness of the microscopic stress tensor , 1995 .

[51]  M. Klein,et al.  Constant pressure molecular dynamics algorithms , 1994 .

[52]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[53]  R. F. Snider,et al.  Differences in fluid dynamics associated with an atomic versus a molecular description of the same system , 1976 .

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

[55]  J. Clarke,et al.  Molecular Dynamics Modelling of Polymer Materials , 1989 .

[56]  Hoover,et al.  Constant-pressure equations of motion. , 1986, Physical review. A, General physics.

[57]  R. Wood.  Continuum electrostatics in a computational universe with finite cutoff radii and periodic boundary conditions: Correction to computed free energies of ionic solvation , 1995 .

[58]  B. P. Eijck.  Pressure Calculation in Molecular Dynamics Simulations of Molecular Crystals , 1994 .

[59]  Emanuele Paci,et al.  Constant-Pressure Molecular Dynamics Techniques Applied to Complex Molecular Systems and Solvated Proteins , 1996 .

[60]  G. Ciccotti,et al.  Hoover NPT dynamics for systems varying in shape and size , 1993 .

[61]  Lukas D. Schuler,et al.  On the Choice of Dihedral Angle Potential Energy Functions for n-Alkanes , 2000 .

[62]  M. Parrinello,et al.  Strain fluctuations and elastic constants , 1982 .

[63]  Giovanni Ciccotti,et al.  Molecular dynamics simulation of rigid molecules , 1986 .

[64]  R. Wentzcovitch,et al.  Invariant molecular-dynamics approach to structural phase transitions. , 1991, Physical review. B, Condensed matter.

[65]  Gary P. Morriss,et al.  Isothermal-isobaric molecular dynamics , 1983 .

[66]  M. P. Allen.  Atomic and molecular representations of molecular hydrodynamic variables , 1984 .

[67]  Priya Vashishta,et al.  Structural Transitions in Superionic Conductors , 1983 .

[68]  S. Nosé,et al.  Constant pressure molecular dynamics for molecular systems , 1983 .

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

[70]  B. U. Felderhof,et al.  Electrostatic interactions in periodic Coulomb and dipolar systems. , 1989, Physical review. A, General physics.

[71]  H. Berendsen,et al.  AN EFFICIENT, BOX SHAPE INDEPENDENT NONBONDED FORCE AND VIRIAL ALGORITHM FOR MOLECULAR-DYNAMICS , 1995 .

[72]  M. Sampoli,et al.  Parameterizing a polarizable intermolecular potential for water , 1995 .

[73]  Nathan A. Baker,et al.  Polarization around an ion in a dielectric continuum with truncated electrostatic interactions , 1999 .

[74]  R. Bharadwaj,et al.  Effect of Pressure on Conformational Dynamics in Polyethylene: A Molecular Dynamics Simulation Study , 2000 .

[75]  J. A. Barker,et al.  Monte Carlo studies of the dielectric properties of water-like models , 1973 .

[76]  J. H. R. Clarke,et al.  A comparison of constant energy, constant temperature and constant pressure ensembles in molecular dynamics simulations of atomic liquids , 1984 .

[77]  H. Bekker,et al.  Force and virial of torsional‐angle‐dependent potentials , 1995, J. Comput. Chem..

[78]  H. Berendsen,et al.  A systematic study of water models for molecular simulation: Derivation of water models optimized for use with a reaction field , 1998 .

[79]  P. Daivis,et al.  Comparison of constant pressure and constant volume nonequilibrium simulations of sheared model decane , 1994 .

[80]  Giovanni Ciccotti,et al.  Introduction of Andersen’s demon in the molecular dynamics of systems with constraints , 1983 .