Covalency and the metal-insulator transition in titanate and vanadate perovskites

A combination of density functional and dynamical mean-field theory is applied to the perovskites SrVO$_3$, LaTiO$_3$ and LaVO$_3$. We show that DFT+DMFT in conjunction with the standard fully localized-limit (FLL) double-counting predicts that LaTiO$_3$ and LaVO$_3$ are metals even though experimentally they are correlation-driven ("Mott") insulators. In addition, the FLL double counting implies a splitting between oxygen $p$ and transition metal $d$ levels which differs from experiment. Introducing into the theory an \textit{ad hoc} double counting correction which reproduces the experimentally measured insulating gap leads also to a $p$-$d$ splitting consistent with experiment if the on-site interaction $U$ is chosen in a relatively narrow range ($\sim 6\pm 1$ eV). The results indicate that these early transition metal oxides will serve as critical test for the formulation of a general \textit{ab initio} theory of correlated electron metals.