Convergence of surface energy calculations for various methods: (0 0 1) hematite as benchmark
Different methods for calculating the surface energy from ab initio simulations are applied to the relaxed (0 0 1) surface of the metal oxide hematite (α-Fe2O3). The simulations are carried out with a rather moderate k-point grid with shrinking factors of (6 6 6) for all bulk and (6 6) for all slab simulations. Very good convergence is obtained if a linear fit of the slab energies with respect to the number of layers in the slab is performed. In comparison to the other methods employed, this procedure is ultimately the most accurate and reliable method for extracting convergent surface energies from (0 0 1) hematite slabs. Additionally, we propose a way to determine the least possible starting point for calculating the surface energy by the linear-fit method. Furthermore, we find the Boettger method to perform nearly equally well, if the bulk energy is extracted from the energy difference per layer between the slabs with 12 and 18 layers thickness. Both methods give a surface energy of 2.43 J m-2 with a deviation of less than ±0.005 J m-2. The standard approach, which uses a separate bulk simulation, instead shows a significant linear divergence with increasing number of layers in the slab. We also carried out bulk simulations with a surface-oriented bulk unit cell, but found it in our case not to improve the convergence of the standard approach.