Molecules with dipoles in periodic boundary conditions in a tetragonal cell

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.