Solvation in the Large Box Limit

TL;DR

This paper investigates the asymptotic behavior of solvation models for charged molecules in large systems, revealing how ionic effects influence long-range interactions and identifying different energy scaling regimes.

Contribution

It introduces a comprehensive analysis of the large box limit for solvation models, including ionic effects and various scaling regimes, with rigorous proofs of the limiting behaviors.

Findings

Screening effect causes localization of electrical interactions with ionic effects.

Different energy scaling regimes are characterized depending on the number of molecules.

Long-range electrical interactions are negligible in the presence of ionic effects in the limit.

Abstract

In this paper, the authors study the limit of a sharp interface model for the solvation of charged molecules in an implicit solvent as the number of solute molecules and the size of the surrounding box tend to infinity. The energy is given by a combination of local terms accounting for the physical presence of the molecules in the solvent and a nonlocal electrical energy with or without an ionic effect. In the presence of an ionic effect, the authors prove a screening effect in the limit, i.e., the limit is completely localized and hence electrical long-range interactions of the molecules can be neglected. In the absence of the ionic effect, the authors show that the behavior of the energy depends on the scaling of the number of molecules with respect to the size of the surrounding box. All scaling regimes are identified and corresponding limit results proved. In regimes with many solute molecules this limit includes electrical interactions of $H^{-1}$-type between the molecules.