Physical meaning of the Ewald sum method

TL;DR

This paper explains the physical significance of the Ewald sum method by relating it to the electrostatic potential and energy of point charges in a crystal at finite temperatures, emphasizing the role of thermal vibrations.

Contribution

It clarifies the physical meaning of the Ewald sum method by incorporating thermal vibrations, linking the Gaussian width to finite temperature effects.

Findings

Ewald sum corresponds to finite temperature electrostatics.

Gaussian width relates to temperature, often exceeding 10000 K.

Method provides a physical interpretation of electrostatic calculations.

Abstract

The electrostatic potential and energy of point charges in a real crystal, in the presence of thermal vibrations, is obtained as a special case of the Fourier method. Incorporating the role of thermal vibrations in electrostatic energy calculations leads to the physical meaning of the Ewald sum method. The Ewald summation method determines the electrostatic potential and energy of point charges in a crystal at a temperature that is obtained from the width of the Gaussian and not at 0 K. For values of the width of the Gaussian commonly recommended for computational convenience temperatures exceed 10000 K.