Accuracy of density functional theory in predicting formation energies of ternary oxides from binary oxides and its implication on phase stability

The evaluation of reaction energies between solids using density functional theory (DFT) is of practical importance in many technological fields and paramount in the study of the phase stability of known and predicted compounds. In this work, we present a comparison between reaction energies provided by experiments and computed by DFT in the generalized gradient approximation (GGA), using a Hubbard $U$ parameter for some transition metal elements (GGA+$U$). We use a data set of 135 reactions involving the formation of ternary oxides from binary oxides in a broad range of chemistries and crystal structures. We find that the computational errors can be modeled by a normal distribution with a mean close to zero and a standard deviation of 24 meV/atom. The significantly smaller error compared to the more commonly reported errors in the formation energies from the elements is related to the larger cancellation of errors in energies when reactions involve chemically similar compounds. This result is of importance for phase diagram computations for which the relevant reaction energies are often not from the elements but from chemically close phases (e.g., ternary oxides versus binary oxides). In addition, we discuss the distribution of computational errors among chemistries and show that the use of a Hubbard $U$ parameter is critical to the accuracy of reaction energies involving transition metals even when no major change in formal oxidation state is occurring.