The Symmetry-Preserving Mean Field Condition for Electrostatic Correlations in Bulk

TL;DR

This paper investigates the importance of the symmetry-preserving mean-field (SPMF) condition for accurately simulating electrostatic correlations in bulk ionic and polar systems, demonstrating its necessity and how to enforce it in simulations.

Contribution

The work analytically examines the asymptotic behavior of the charge structure factor and shows how existing methods can be modified to satisfy the SPMF condition for better accuracy.

Findings

Methods violating SPMF fail at small wavenumbers

Simulations confirm the importance of SPMF for accurate charge correlations

Simple amendments can enforce SPMF in existing simulation techniques

Abstract

Accurate simulations of a condensed system of ions or polar molecules are concerned with proper handlings of the involved electrostatics. For such a Coulomb system at a charged planar interface, the Coulomb interaction averaged over the lateral directions with preserved symmetry serves as a necessary constraint in building any accurate handling that reconciles a simulated singlet charge density with the corresponding macroscopic charge/dielectric response. At present, this symmetry-preserving mean-field (SPMF) condition represented in the reciprocal space, is conjectured to be necessary for a simulated bulk system to reproduce correctly the charge structure factor of the macroscopic bulk, as well. In this work, we further examine analytically the asymptotic behavior of the charge structure factor at small wavenumbers for an arbitrary charge-charge interaction. In light of our theoretical predictions, simulations with a length of nearly 0.1 micron are carried out to demonstrate that, typical efficient methods violating the SPMF condition indeed fail to capture the exact charge correlations at small wavenumbers for both ionic and polar systems. However, for both types of systems, these existing methods can be simply amended to match the SPMF condition and subsequently to probe precisely the electrostatic correlations at all length scales.