M. J. Rutter

Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised by the introduction of a uniform neutralising background, are very slow to converge with cell size. The periodicity introduces spurious electric fields which decay slowly with cell size and which also slow the convergence of other properties relating to the ground state charge density. This paper presents a simple self-consistent technique for producing rapid convergence of both energies and charge distribution in the particular geometry of 2D periodicity, as used for studying surfaces.

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.

The c2x code fills two distinct roles. Its first role is as a converter between the binary format .check files from the Castep electronic structure code and various visualisation programs. Its second role is to manipulate and analyse the input and output files from a variety of electronic structure codes, including Castep, Onetep and Vasp, as well as the widely-used `Gaussian cube' file format. Analysis includes symmetry analysis, and arbitrary cell transformations. It continues to be under development, with growing functionality, and is written in a form which would make it easy to extend it to working directly with files from other electronic structure codes. Data which c2x is capable of extracting from Castep's binary checkpoint files include charge densities, spin densities, wavefunctions, relaxed atomic positions, forces, the Fermi level, the total energy, and symmetry operations. It can recreate .cell input files from checkpoint files. Volumetric data can be output in formats usable by many common visualisation programs, and c2x will itself calculate integrals, expand data into supercells, and interpolate data via combinations of Fourier and trilinear interpolation. It can extract data along arbitrary lines (such as between atoms) as 1D output. C2x is able to convert between several common formats for describing molecules and crystals, including the .cell format of Castep. It can construct supercells, reduce cells to their primitive form, and add specified k-point meshes. It uses the spglib library to report symmetry information, which it can add to .cell files. C2x is a command-line utility, so is readily included in scripts. It is available under the GPL and can be obtained from http://www.c2x.org.uk. It is believed to be the only open-source code which can read Castep's .check files, so it will have utility in other projects.

Silicon carbide often grows in the cubic phase under conditions where this is not the most stable phase. Ab initio calculations are presented which determine the energy of a stacking reversal at the (0001) and surfaces of silicon carbide, and thus whether the cubic form is preferred in the vicinity of a free surface. In these calculations the surfaces are not reconstructed but hydrogen terminated, and care is taken to eliminate the spurious dipole - dipole interaction caused by the imposition of periodic boundary conditions, and also in estimating the amount of residual ionic relaxation. These calculations do show a clear distinction of 13 meV per surface pair between the silicon and carbon surfaces, although the results are not in complete agreement with experiment.