Synergy of van der Waals and self-interaction corrections in transition metal monoxides

Density functional theory in principle predicts correct ground-state properties for all materials. However, the rocksalt structure of MnO has been obtained only by the high-level random phase approximation and diffusion Monte Carlo (DMC). Here, we propose and test for MnO, FeO, CoO, and NiO that a semilocal density functional can solve this problem by properly including both self-interaction and van der Waals corrections. The importance of the latter was previously unanticipated. The MnO structural energy difference from SCAN+$r\text{VV10+}U$ agrees well with that from DMC. Here SCAN is a recent semilocal exchange-correlation functional, $r\text{VV10}$ is the revised Vydrov-Van Voorhis long-range van der Waals correction, and the onsite Hubbard $U$ is taken from linear response.