Efficient Algorithms for Electrostatic Interactions Including Dielectric Contrasts

Coarse-grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need to compute exact electrostatic interactions between charges in those systems is computationally demanding. We review here several algorithms developed by us that perform exactly this task. For planar dielectric surfaces in partial periodic boundary conditions, the arising image charges can be either treated with the MMM2D algorithm in a very efficient and accurate way or with the electrostatic layer correction term, which enables the user to use his favorite 3D periodic Coulomb solver. Arbitrarily-shaped interfaces can be dealt with using induced surface charges with the induced charge calculation (ICC*) algorithm. Finally, the local electrostatics algorithm, MEMD(Maxwell Equations Molecular Dynamics), even allows one to employ a smoothly varying dielectric constant in the systems. We introduce the concepts of these three algorithms and an extension for the inclusion of boundaries that are to be held fixed at a constant potential (metal conditions). For each method, we present a showcase application to highlight the importance of dielectric interfaces.

[1]  Axel Arnold,et al.  ICMMM2D: an accurate method to include planar dielectric interfaces via image charge summation. , 2007, The Journal of chemical physics.

[2]  Z. Siwy,et al.  Asymmetric diffusion through synthetic nanopores. , 2005, Physical review letters.

[3]  A. C. Maggs,et al.  Boundary conditions in local electrostatics algorithms. , 2008, The Journal of chemical physics.

[4]  C. Holm,et al.  Effects of dielectric mismatch and chain flexibility on the translocation barriers of charged macromolecules through solid state nanopores , 2012 .

[5]  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.

[6]  Axel Arnold,et al.  Electrostatics in Periodic Slab Geometries I , 2002 .

[7]  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.

[8]  Mathieu Salanne,et al.  New Coarse-Grained Models of Imidazolium Ionic Liquids for Bulk and Interfacial Molecular Simulations , 2012 .

[9]  Igor Pasichnyk,et al.  Coulomb interactions via local dynamics: a molecular-dynamics algorithm , 2004 .

[10]  A. Kornyshev,et al.  Superionic state in double-layer capacitors with nanoporous electrodes , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[11]  Alexander Y. Grosberg,et al.  Electrostatic Focusing of Unlabeled DNA into Nanoscale Pores using a Salt Gradient , 2009, Nature nanotechnology.

[12]  Rui Qiao,et al.  Microstructure and Capacitance of the Electrical Double Layers at the Interface of Ionic Liquids and Planar Electrodes , 2009 .

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

[14]  Jörg Rottler,et al.  Local Monte Carlo for electrostatics in anisotropic and nonperiodic geometries. , 2008, The Journal of chemical physics.

[15]  Andreas Dedner,et al.  The Distributed and Unified Numerics Environment (DUNE) , 2006 .

[16]  Stephan Gekle,et al.  Profile of the static permittivity tensor of water at interfaces: consequences for capacitance, hydration interaction and ion adsorption. , 2012, Langmuir : the ACS journal of surfaces and colloids.

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

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

[19]  Michael Hofmann,et al.  Comparison of scalable fast methods for long-range interactions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Axel Arnold,et al.  MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries , 2002 .

[21]  Christian Holm,et al.  An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries. , 2010, The Journal of chemical physics.

[22]  U. Keyser,et al.  Salt dependence of ion transport and DNA translocation through solid-state nanopores. , 2006, Nano letters.

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

[24]  Axel Arnold,et al.  ESPResSo 3.1: Molecular Dynamics Software for Coarse-Grained Models , 2013 .

[25]  Axel Arnold,et al.  A novel method for calculating electrostatic interactions in 2D periodic slab geometries , 2002 .

[26]  Cees Dekker,et al.  Optical tweezers for force measurements on DNA in nanopores , 2006 .

[27]  E. R. Smith Electrostatic potentials for simulations of thin layers , 1988 .

[28]  D. Heyes,et al.  Electrostatic potentials and fields in infinite point charge lattices , 1981 .

[29]  A. Arnold,et al.  Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions. , 2009, The Journal of chemical physics.

[30]  Christian Holm,et al.  Applying ICC* to DNA translocation: Effect of dielectric boundaries , 2011, Comput. Phys. Commun..

[31]  Axel Arnold,et al.  Electrostatics in periodic slab geometries. II , 2002 .

[32]  Axel Arnold,et al.  Electrostatic layer correction with image charges: a linear scaling method to treat slab 2D+h systems with dielectric interfaces. , 2008, The Journal of chemical physics.

[33]  Axel Arnold,et al.  Efficient methods to compute long-range interactions for soft matter systems , 2005 .

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

[35]  M. Berkowitz,et al.  Ewald summation for systems with slab geometry , 1999 .

[36]  Peter Bastian,et al.  Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE) , 2010, Kybernetika.

[37]  A. de Keizer,et al.  Electrophoretic mobility of a cylinder with high surface charge density , 1979 .

[38]  Albert H. Widmann,et al.  A comparison of Ewald summation techniques for planar surfaces , 1997 .

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

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

[41]  Stephan Gekle,et al.  Dielectric profile of interfacial water and its effect on double-layer capacitance. , 2011, Physical review letters.

[42]  Hans-Jörg Limbach,et al.  ESPResSo - an extensible simulation package for research on soft matter systems , 2006, Comput. Phys. Commun..

[43]  C. Dekker Solid-state nanopores. , 2007, Nature nanotechnology.

[44]  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.

[45]  A C Maggs,et al.  Local simulation algorithms for Coulombic interactions , 2002, Physical review letters.

[46]  C Holm,et al.  Computing the Coulomb interaction in inhomogeneous dielectric media via a local electrostatics lattice algorithm. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  John T. Katsikadelis,et al.  Boundary Elements: Theory and Applications , 2002 .

[48]  Jörg Rottler,et al.  Local molecular dynamics with coulombic interactions. , 2004, Physical review letters.

[49]  R Everaers,et al.  Simulating van der Waals interactions in water/hydrocarbon-based complex fluids. , 2007, The journal of physical chemistry. B.