Poisson–Boltzmann Electrostatics and Analytical Approximations

Wei Cai ()
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Wei Cai: Southern Methodist University, Department of Mathematics

Chapter Chapter 2 in Deterministic, Stochastic, and Deep Learning Methods for Computational Electromagnetics, 2025, pp 31-71 from Springer

Abstract: Abstract In this chapter, first, we introduce the Poisson–Boltzmann (PB) equation, which is based on the Debye–Hückel potential of mean force (PMF) approximation for electrostatic interactions for biomolecules in ionic solvents, and second, we introduce the concept of electrostatic solvation energy. Several analytical approximation methods for solving electrostatic solvation problems are discussed. First, the generalized Born approximation is described for the electrostatic solvation energy using Born radii for atoms embedded in molecules. A fast Fourier transform (FFT)-based algorithm for calculating the Born radii is given. Then we present various image approximations to electrostatic reaction fields in the Poisson and Poisson–Boltzmann electrostatic models in the presence of dielectric or perfectly conducting materials with boundaries such as single or multiple planes and spherical and cylindrical geometries.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-96-0100-4_2

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DOI: 10.1007/978-981-96-0100-4_2

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