Function-Space Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT

TL;DR

This paper introduces a novel function-space based Newton method and Green's function preconditioning for solving the size-modified Poisson-Boltzmann equation within full-potential DFT, enabling efficient implicit solvation modeling.

Contribution

It presents a new solution scheme for the MPB equation using a function-space Newton method and Green's function preconditioning, integrated into a DFT code for improved efficiency.

Findings

Accurately describes activity coefficients of KCl solutions.

Demonstrates the method's efficiency over traditional multi-grid solvers.

Highlights the importance of experimental ionic parameters for modeling.

Abstract

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multi-grid solvers this approach allows to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.