Electrostatic pair-potentials based on the Poisson equation

Electrostatic pair-potentials based on the Poisson equation

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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 Baby Toothbrushes 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 LP Record Sleeves thermal water-systems.The same derivations have also been made for the screened Poisson equation, i.e.

for Yukawa potentials, with a similar solution.