Combining density functional theories to correctly describe the energy, lattice structure and electronic density of functional oxide perovskites

Functional oxide perovskites are the pillar of cutting-edge technological applications. Density functional theory (DFT) simulations are the theoretical methods of choice to understand and design perovskite materials. However, tests on the reliability of DFT to describe fundamental properties of oxide perovskites are scarce and mostly ill-defined due to a lack of rigorous theoretical benchmarks for solids. Here, we present a quantum Monte Carlo benchmark study of DFT on the archetypal perovskite BaTiO$_{3}$ (BTO). It shows that no DFT approximation can simultaneously reproduce the energy, structure, and electronic density of BTO. Traditional protocols to select DFT approximations are empirical and fail to detect this shortcoming. An approach combining two different non-empirical DFT schemes, "SCAN" and "HSE06", is able to holistically describe BTO with accuracy. Combined DFT approaches should thus be considered as a promising alternative to standard methods for simulating oxide perovskites.