Systematic Study of the Boundary Composition in Poisson Boltzmann Calculations

TL;DR

This study systematically analyzes how boundary shape and size affect Poisson Boltzmann calculations, proposing a method to optimize boundary geometry and achieve accurate results without charge scaling.

Contribution

It introduces a three-stage procedure to determine optimal boundary discretization, geometry, and parameters for Poisson Boltzmann calculations, improving accuracy and consistency.

Findings

Optimal boundary element size for convergence identified

Reference calculations on dipeptides establish baseline accuracy

Default parameters yield close match without charge scaling

Abstract

We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but our results are also of interest to finite difference techniques of Poisson Boltzmann calculations. At first, we identify the critical size of the geometrical elements for discretizing the boundary, and thus the necessary resolution required to establish numerical convergence. In the following two steps we perform reference calculations on a set of dipeptides in different conformations using the Polarizable Continuum Model and a high-level Density Functional as well as a high-quality basis set. Afterwards, we propose a mechanism for defining appropriate boundary geometries. Finally, we compare the classic Poisson Boltzmann description with the Quantum Chemical description, and aim at finding appropriate fitting parameters to get a close match to the reference data. Surprisingly, when using default AMBER partial charges and the rigorous geometric parameters derived in the initial two stages, no scaling of the partial charges is necessary and the best fit against the reference set is obtained automatically