Ion Solvation in Dipolar Poisson models in a dual view

TL;DR

This paper reformulates ion solvation models using convex dual functionals, enabling better analysis and parametrization of dipolar Poisson models with applications to water and electron transfer.

Contribution

It introduces a dual convex functional approach to Dipolar-Poisson models, extending the harmonic polarization functional to nonlinear regimes and linking theory with molecular simulations.

Findings

Derivation of convex dual functionals for Dipolar-Poisson models

Extension of Marcus theory to nonlinear polarization regimes

Quantitative parametrization using molecular dynamics simulations

Abstract

We study the classic problem of ion solvation within the continuum theory of Dipolar-Poisson models. In this approach an ion is treated as a point charge within a sea of point dipoles. Both the standard Dipolar-Poisson model as well as the Dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential $\phi$. Applying the Legendre transform approach introduced by A.C. Maggs [A.C. Maggs, Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement and the polarization field. We show that the Dipolar-Poisson-Langevin functional generalizes the harmonic polarization functional used in the theory of Marcus for electron transfer rate to nonlinear regimes and can be quantitatively parametrized by molecular dynamics simulations for SPC/E-water.