A continuum, O(N) Monte Carlo algorithm for charged particles.

We introduce a Monte Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric field on an interpolating lattice. We discuss the theoretical justifications of the algorithm and show that it efficiently equilibrates model electrolytes and polar fluids. In order to reduce lattice artifacts that arise from the interpolation of charges to the grid we implement a local, dynamic subtraction algorithm. This dynamic scheme is completely general and can also be used with other Coulomb codes, such as multigrid based methods.

[1]  J. W. Perram,et al.  Simulation of electrostatic systems in periodic boundary conditions. II. Equivalence of boundary conditions , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[3]  C. Sagui,et al.  Multigrid methods for classical molecular dynamics simulations of biomolecules , 2001 .

[4]  Abraham Pais,et al.  Inward bound : of matter and forces in the physical world / Abraham Pais , 1986 .

[5]  T. Darden,et al.  Molecular dynamics simulations of biomolecules: long-range electrostatic effects. , 1999, Annual review of biophysics and biomolecular structure.

[6]  S. W. Leeuw,et al.  An Iterative PPPM Method for Simulating Coulombic Systems on Distributed Memory Parallel Computers , 1998 .

[7]  J. Caillol,et al.  Comments on the numerical simulations of electrolytes in periodic boundary conditions , 1994 .

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[10]  A. C. Maggs,et al.  Local simulation algorithms for Coulomb interactions. , 2002 .

[11]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[12]  A. C. Maggs.  Dynamics of a local algorithm for simulating Coulomb interactions , 2002 .

[13]  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 .

[14]  Foulkes,et al.  Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions. , 1996, Physical review. B, Condensed matter.

[15]  Laxmikant V. Kale,et al.  Algorithmic Challenges in Computational Molecular Biophysics , 1999 .

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

[17]  A C Maggs,et al.  Auxiliary field Monte Carlo for charged particles. , 2004, The Journal of chemical physics.

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

[19]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[20]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[21]  M Duggan,et al.  Inward bound. , 1993, The Health service journal.