Dielectric properties of correlated oxides: a GGA+U electric-enthalpy approach

The dielectric response of correlated-electron oxides is often overestimated in common density-functional theory approaches, such as the local-density or the generalized-gradient approximations, in a failure that closely mirrors the underestimation of the Kohn- Sham band gap. A Hubbard $U$ correction can greatly improve the description of the electronic ground-state for these difficult systems; in addition, $U$ can be derived fully from first-principles using a linear-response approach,\footnote{M.\ Cococcioni and S.\ de Gironcoli, Phys.\ Rev.\ B {\bf 71}, 035105 (2005)} making the approach parameter-free. Here, we show that an electric-enthalpy formulation allows to straightforwardly calculate the dielectric properties in the presence of a Hubbard $U$ term, leading to much closer agreement with experiments for the paradigmatic case of $3d$ transition-metal oxides.