Ab initio energetics of charge compensating point defects: A case study on MgO

Density functional theory (DFT) calculations using supercells have proven quite successful in predicting defect properties. Although forming defect groups, for example, the Schottky pair V O • • + V Mg ″ in MgO, are usually energetically favorable in many ionic systems, it is useful to obtain the defect energies of such systems without any defect-defect interactions as reference energies. However, determining non-interacting energies through multi-defect supercell calculations is challenging due to interactions between the defects that are difficult to quantify and can only be avoided by using very large supercells. One solution to this problem is to build an effective multi-defect cell through separate isolated defect calculations, with each defect in their own supercell. However, this isolated defect approach requires that the charge compensation be introduced through charged supercells, and a careful treatment of the cell energetics and electron reference energy is required. In this paper we assess the use of an isolated defect approach for modeling charge-compensating defect groups using the test case of MgO. The appropriate asymptotic condition for the electron reference energy shift is formulated and a method to meet the condition is given. We also demonstrate the strong coupling effect between residual strain energy and electrostatic energy in charged cells, demonstrating that these two effects cannot generally be separated and treated in isolation. The key steps in an approach that yields accurate defect group energies from the isolated defect calculations are presented. The non-interacting Schottky defect formation energy in MgO is determined to be 6.1 eV through calculation of separated isolated charged cells containing V O • • and V Mg ″ , respectively, while the binding energy between the charged defects V O • • and V Mg ″ is determined to be 1.5 eV. This approach may also be of value for accurate modeling of general isolated defects. The formation energy of an isolated neutral Mg vacancy is found to be lower than that of a Schottky pair, suggesting that it is possible to have significant thermal cation defect formation in MgO without forming charge compensating Schottky pairs.