Convexity and stiffness in energy functions for electrostatic simulations

TL;DR

This paper analyzes convex energy functionals used in electrostatic simulations of charged systems, examining their physical accuracy and numerical properties like stiffness, to improve simulation methods.

Contribution

It evaluates the physical fidelity and numerical stiffness of various convex functionals for electrostatic simulations, guiding better functional selection.

Findings

Some functionals better reproduce electrolyte fluctuations.

Stiffness varies significantly among functionals.

Choice of functional impacts accuracy and computational efficiency.

Abstract

We study the properties of convex functionals which have been proposed for the simulation of charged molecular systems within the Poisson-Boltzmann approximation. We consider the extent to which the functionals reproduce the true fluctuations of electrolytes and thus the one-loop correction to mean field theory -- including the Deby-H\"uckel correction to the free energy of ionic solutions. We also compare the functionals for use in numerical optimization of a mean field model of a charged polymer and show that different functionals have very different stiffnesses leading to substantial differences in accuracy and speed.