Electrostatic pair-potentials based on the Poisson equation
(2019) In New Journal of Physics 21(6).- Abstract
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... (More)
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.
(Less)
- author
- Stenqvist, B. LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Electrostatics, Gaussian charge-distribution, Pair-potential, Poisson equation, SPC/E-water, Yukawa potential
- in
- New Journal of Physics
- volume
- 21
- issue
- 6
- article number
- 063008
- publisher
- IOP Publishing
- external identifiers
-
- scopus:85073659861
- ISSN
- 1367-2630
- DOI
- 10.1088/1367-2630/ab1ec1
- language
- English
- LU publication?
- yes
- id
- cb9fd279-2982-4922-9de9-6ac6f100622c
- date added to LUP
- 2019-11-05 09:48:55
- date last changed
- 2022-04-18 18:51:08
@article{cb9fd279-2982-4922-9de9-6ac6f100622c,
abstract = {{<p>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.</p>}},
author = {{Stenqvist, B.}},
issn = {{1367-2630}},
keywords = {{Electrostatics; Gaussian charge-distribution; Pair-potential; Poisson equation; SPC/E-water; Yukawa potential}},
language = {{eng}},
number = {{6}},
publisher = {{IOP Publishing}},
series = {{New Journal of Physics}},
title = {{Electrostatic pair-potentials based on the Poisson equation}},
url = {{http://dx.doi.org/10.1088/1367-2630/ab1ec1}},
doi = {{10.1088/1367-2630/ab1ec1}},
volume = {{21}},
year = {{2019}},
}