Convergence of surface energy calculations for various methods: (001), (012), (100) hematite and the applicability of the standard approach.

Three different methods for the calculation of the surface energy, namely the standard approach, the Boettger relation and the linear-fit method, are applied to the (001), (012) and (100) hematite surfaces. The standard approach was previously shown to suffer from a divergence problem, and the Boettger relation was shown to exhibit quantum size effects. While the linear-fit method, in general, leads to a good convergence behavior of the surface energy, the questions arise whether the relative order of the calculated surface energies depends on the chosen calculation method, and whether there is any merit at all in employing the standard approach. The present work investigates these questions with hematite as a benchmark material system. The simulations show that, for the surface facets and slab thicknesses studied here, the relative order of the surface energies is unaffected by the chosen calculation method. A regime is found where the three methods are in reasonably good agreement with respect to the obtained surface energies. Finally, a procedure is put forward to extract meaningful surface energy values from the standard approach.