Harmonic surface mapping algorithm for molecular dynamics simulations of particle systems with planar dielectric interfaces

Abstract

We have developed an accurate and efficient method for molecular dynamics simulations of charged particles confined by planar dielectric interfaces. The algorithm combines the image-charge method for near field with the harmonic surface mapping, which converts the contribution of infinite far-field charges into a finite number of charges on an auxiliary spherical surface. We approximate the electrostatic potential of far-field charges via spherical harmonic expansion and determine the coefficients by fitting the Dirichlet-to-Neumann boundary condition, which only requires the potential within the simulation cell. Instead of performing the direct evaluation of spherical harmonic series expansion, we use Green’s second identity to transform the series expansion into a spherical integral, which can be accurately represented by discrete charges on the sphere. Therefore, the fast multipole method can be readily employed to sum over all charges within and on the sphere, achieving truly linear O(N) complexity. Our algorithm can be applied to a broad range of charged complex fluids under dielectric confinement.

HSMA: An O(N) electrostatics package implemented in LAMMPS

“…The HSMA algorithms for 3D and 2D periodic systems were described in detail in Refs. [42] and [43], respectively. Here we give a brief overview of the most important features of the algorithm.…”

“…To overcome this issue, we introduce the Dirichlet-to-Neumann (DtN) boundary condition in Ref. [43], which transforms the dielectric conditions into a surface integral that only requires knowledge of Φ c and its derivative in z-direction. The coefficients A m n are then obtained by minimizing the residual norm of the DtN boundary condition which is approximated via the 2D-dilation formula [46].…”

“…The HSMA2D style invokes the HSMA algorithm for 2D periodic system with dielectric interfaces [43]. The definitions of λ, P, F w , F, f 1 , and f 2 are the same as in the HSMA3D style.…”

“…To benefit the community, we present a parallel implementation of two previously formulated HSMA methods [42,43] into the popular MD package LAMMPS [44], producing highly efficient solvers for modeling electrostatic interactions in 3D and 2D periodic system. This article describes the new implementation and analyses its performance.…”

A High-Accurate Fast Poisson Solver Based on Harmonic Surface Mapping Algorithm

“…Recently, a harmonic surface mapping algorithm (HSMA), which combines the method of image charges and the boundary integral method to calculate the Green's function, has been proposed and applied to particle systems [27,28]. Its basic idea is that an auxiliary surface is introduced such that the contribution of image charges outside the surface is represented by image charges distributed over the surface.…”