Generalized Moment Correction for Long-Ranged Electrostatics

Abstract

Describing long-ranged electrostatics using short-ranged pair potentials is appealing because the computational complexity scales linearly with the number of particles. The foundation of the approach presented here is to mimic the long-ranged medium response by cancelling electric multipoles within a small cutoff sphere. We propose a rigorous and formally exact new method that cancels up to infinitely many multipole moments and is free of operational damping parameters often required in existing theories. Using molecular dynamics simulations of water with and without added salt, we discuss radial distribution functions, Kirkwood–Buff integrals, dielectrics, diffusion coefficients, and angular correlations in relation to existing electrostatic models. We find that the proposed method is an efficient and accurate alternative for handling long-ranged electrostatics as compared to Ewald summation schemes. The methodology and proposed parameterization are applicable also for dipole–dipole interactions.

Electrostatic pair-potentials based on the Poisson equation

“…Like in the previous section, the Q(q)=1 and Q(q)=1−q pair-potentials gives fairly erroneous results why we exclude them from further analysis in this section. For results using the latter on the same system as used here we refer elsewhere [19].…”

On short-ranged pair-potentials for long-range electrostatics

“…These will be oppositely polarized and, given that the local region is sufficiently large, perfectly cancel each other. This physical relation is the main idea behind the q-potential, 9 where image charges (or moments) of the local region are used to generate the opposing multipole of the surroundings (see Fig. 1).…”

“…Here P A N index the number of cancelled moments, P p h i q is the q-analogue of the binomial coefficient, and (a;q) P is the q-Pochhammer symbol. 9 Since the multiplicative factor to the original interaction-tensor is a q-analogue, we index the modified interaction-tensor with a superscript q and from here on include the derived potential in the q-potential notation.…”

“…1 differing in how they cancel moments. The first approach, which has previously been validated for ion-ion interactions, 9 uses image charges (l = 0) while the second approach uses image-like dipoles (l = 2) to cancel higher-order moments. We later revisit the meaning of image-like dipoles.…”

“…That is, the effect of long ranged electrostatic interactions is approximated by cancelling one, two, or more electric multipolar moments in the cut-off sphere, 1,3 mimicking polarization of the surroundings. The newly developed q-potential 9 for ion-ion interactions is a generalization of this concept, and allows for cancellation of an arbitrary number of moments while being free from empirical damping parameters. In this work we expand the q-potential model to include any type of higher-order interactions, i.e.…”