A method of calculating surface energies for asymmetric slab models

Many essential chemical processes, such as adsorption and catalysis, take place at the surface of a solid material. Hence, accurately determining the energy of a solid surface provides crucial information about the material's potential utility for such processes. The standard method of calculating surface energy yields good approximations for solids that, upon cleavage, expose identical surface terminations (symmetric slabs) but suffers critical shortcomings when applied to the multitude of materials that expose atomically different terminations (asymmetric slabs) due to the inaccurate assumption that the two terminations exhibit exactly the same energy. A more rigorous method of calculating the individual energetic contributions of the two terminations of a cleaved slab was pursued in 2018 by Tian and colleagues, however the approach's accuracy is weakened by a similar assumption that frozen asymmetric terminations contribute exactly the same energy. Herein, a novel technique is presented. The method expresses the slab's total energy in terms of the energy contributions of the top (A) and bottom (B) surfaces in both the relaxed and frozen states. Total energies for different combinations of these conditions are obtained through a series of density-functional-theory calculations alternately optimizing different parts of the slab model. The equations are then solved for the individual surface energy contributions. The method shows improvement over the previously-established approach by exhibiting greater precision and internal consistency, while also providing additional information about the contributions of frozen surfaces.