Evaluation of Coulomb potential in a triclinic cell with periodic boundary conditions

TL;DR

This paper generalizes the evaluation of Coulomb energy and forces under periodic boundary conditions to triclinic cells, extending previous work limited to orthorhombic cells, thereby enabling more flexible simulations.

Contribution

It introduces a generalized method for calculating Coulomb interactions in triclinic cells, broadening the applicability of previous orthorhombic-based approaches.

Findings

Derived expressions similar to previous orthorhombic cases

Enables use of triclinic cells in 3D simulations

Facilitates more general periodic boundary condition calculations

Abstract

Lekner and Sperb's work on the evaluation of Coulomb energy and forces under periodic boundary conditions is generalized that makes it possible to use a triclinic unit cell in simulations in 3D rather than just an orthorhombic cell. The expressions obtained are in a similar form as previously obtained by Lekner and Sperb for the especial case of orthorhombic cell.