Electrostatic pair-potentials based on the Poisson equation

Summary, in English

Electrostatic pair-potentials within molecular simulations are often based on empirical data, cancellation of derivatives or moments, or statistical distributions of image-particles. In this work we start with the fundamental Poisson equation and show that no truncated Coulomb pair-potential, unsurprisingly, can solve the Poisson equation. For any such pair-potential the Poisson equation gives two incompatible constraints, yet we find a single unique expression which, pending two physically connected smoothness parameters, can obey either one of these. This expression has a general form which covers several recently published pair-potentials. For sufficiently large degree of smoothness we find that the solution implies a Gaussian distribution of the charge, a feature which is frequently assumed in pair-potential theory. We end up by recommending a single pair-potential based both on theoretical arguments and empirical evaluations of non-thermal lattice- and thermal water-systems. The same derivations have also been made for the screened Poisson equation, i.e. for Yukawa potentials, with a similar solution.

• Author: B. Stenqvist
• Department/s: Physical Chemistry
• Publishing year: 2019
• Language: English
• Publication/Series: New Journal of Physics
• Volume: 21
• Issue: 6
• Links: http://dx.doi.org/10.1088/1367-2630/ab1ec1
• Document type: Journal article
• Publisher: IOP Publishing
• Topic: Physical Chemistry (including Surface- and Colloid Chemistry)
• Keywords: Electrostatics; Gaussian charge-distribution; Pair-potential; Poisson equation; SPC/E-water; Yukawa potential
• Status: Published
• ISBN/ISSN/Other: ISSN: 1367-2630