First-principles Hubbard U and Hund's J corrected approximate density functional theory predicts an accurate fundamental gap in rutile and anatase TiO2

Titanium dioxide (TiO2) presents a long-standing challenge for approximate Kohn-Sham density functional theory (KS-DFT), as well as to its Hubbard-corrected extension, DFT+U. We find that a previously proposed extension of first-principles DFT+U to incorporate a Hund's J correction, termed DFT+U+J, in combination with parameters calculated using a recently proposed linear-response theory, predicts fundamental band gaps that are accurate to well within the experimental uncertainty in rutile and anatase TiO2. Our approach builds upon established findings that Hubbard correction of both the titanium 3d and oxygen 2p subspaces in TiO2, symbolically giving DFT+Ud,p, is necessary to achieve acceptable band gaps using DFT+U. This requirement remains when the first-principles Hund's J is included. We also find that the calculated gap depends on the correlated subspace definition even when using subspace-specific first-principles U and J parameters. Using the simplest reasonable correlated subspace definition and underlying functional, the local density approximation, we show that high accuracy results from using a relatively uncomplicated form of the DFT+U+J functional. For closed-shell systems such as TiO2, we describe how various DFT+U+J functionals reduce to DFT+U with suitably modified parameters, so that reliable band gaps can be calculated for rutile and anatase with no modifications to a conventional DFT+U code.