# Molecules with dipoles in periodic boundary conditions in a tetragonal cell

## TL;DR

This paper addresses the challenge of artificial electric fields in periodic boundary condition simulations of dipolar systems with less than three dimensions, extending correction methods to tetragonal geometries and analyzing error terms.

## Contribution

It extends existing correction methods for dipolar systems to tetragonal geometries and introduces an empirical model for exponential error terms.

## Key findings

- Correction for 0D systems extended to tetragonal geometries.
- For a specific c/a ratio, the correction becomes zero.
- Identifies and discusses an exponential error term in the potential.

## Abstract

When a system which contains a dipole, and whose dimensionality is less than three, is studied in a code which imposes periodic boundary conditions in all three dimensions, an artificial electric field arises which keeps the potential periodic. This has an impact on the total energy of the system, and on any other attribute which would respond to an electric field. Simple corrections are known for 0D systems embedded in a cubic geometry, and 2D slab systems. This paper shows how the 0D result can be extended to tetragonal geometries, and that for a particular $c/a$ ratio the correction is zero. It also considers an exponential error term absent from the usual consideration of 2D slab geometries, and discusses an empirical form for this.