Titanium dioxide () presents a long-standing challenge for approximate Kohn-Sham density functional theory (KS-DFT), as well as to its Hubbard-corrected extension, . We find that a previously proposed extension of first-principles to incorporate a Hund's correction, termed , 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 . Our approach builds upon established findings that Hubbard correction of both the titanium and oxygen subspaces in , symbolically giving , is necessary to achieve acceptable band gaps using . This requirement remains when the first-principles Hund's is included. We also find that the calculated gap depends on the correlated subspace definition even when using subspace-specific first-principles and 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 functional. For closed-shell systems such as , we describe how various functionals reduce to with suitably modified parameters, so that reliable band gaps can be calculated for rutile and anatase with no modifications to a conventional code.
