Zero-multipole summation method for efficiently estimating electrostatic interactions in molecular system

Abstract

The zero-multipole summation method has been developed to efficiently evaluate the electrostatic Coulombic interactions of a point charge system. This summation prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large amounts of energetic noise and significant artifacts. The resulting energy function is represented by a constant term plus a simple pairwise summation, using a damped or undamped Coulombic pair potential function along with a polynomial of the distance between each particle pair. Thus, the implementation is straightforward and enables facile applications to high-performance computations. Any higher-order multipole moment can be taken into account in the neutrality principle, and it only affects the degree and coefficients of the polynomial and the constant term. The lowest and second moments correspond respectively to the Wolf zero-charge scheme and the zero-dipole summation scheme, which was previously proposed. Relationships with other non-Ewald methods are discussed, to validate the current method in their contexts. Good numerical efficiencies were easily obtained in the evaluation of Madelung constants of sodium chloride and cesium chloride crystals.