Electrostatic pair-potentials based on the Poisson equation

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 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.

An Exact Ewald Summation Method in Theory and Practice

“…Note that the Gaussian function gives a discontinuous splitting function at the real space cutoff distance, whereas a truncated Gaussian yields a smooth splitting function 1 . The obtained real space energy term is similar to that in pair-potential theory, 8,9 as for example both the interaction energy and force are zero at the real space cutoff. This feature ensures no neglected contributions in real space, which also makes the truncated Gaussian screening function an ideal candidate for Ewald summations using isotropic periodic boundary conditions.…”

On short-ranged pair-potentials for long-range electrostatics

“…Accounting for long-ranged electrostatic interactions in computer simulations is an exquisite task [1][2][3][4] and although formally exact theories exist for repetitive structures subjected to periodic boundary conditions (PBC), 5,6 these are computationally expensive and may impose artificial symmetry from periodicity. Finite-ranged or truncated pair-potentials are fast alternatives to such lattice-sum models and can be more relevant (and often only valid) for isotropic systems.…”

Applicability of the Linearized Poisson-Boltzmann Theory to Contact Angle problems and Application to the Carbon Dioxide-Brine-Solid Systems

“…Moreover, the validity of the LPB equation was demonstrated decades ago using the same technique (Tironi, 1995). Electrostatics interactions found in colloidal systems are like those related to surface complexation in geologic systems, where wetting phenomena are associated with surface charge regulation predictable using the PB theory (Stenqvist, 2019). In such systems, for instance, those related to geological carbon storage, pH decrease of formation brine leads to decrease surface charge density/potential (Jung & Wan, 2012).…”