The Hubbard-U correction and optical properties of d metal oxide photocatalysts.

We report a systematic investigation of individual and multisite Hubbard-U corrections for the electronic, structural, and optical properties of the metal titanate oxide d photocatalysts SrTiO and rutile/anatase TiO. Accurate bandgaps for these materials can be reproduced with local density approximation and generalized gradient approximation exchange-correlation density functionals via a continuous series of empirically derived U and U combinations, which are relatively insensitive to the choice of functional. On the other hand, lattice parameters are much more sensitive to the choice of U and U, but in a systematic way that enables the U and U corrections to be used to qualitatively gauge the extent of self-interaction error in the electron density. Modest U corrections (e.g., 4 eV-5 eV) yield the most reliable dielectric response functions for SrTiO and are comparable to the range of U values derived via linear response approaches. For r-TiO and a-TiO, however, the U corrections that yield accurate bandgaps fail to accurately describe both the parallel and perpendicular components of the dielectric response function. Analysis of individual U and U corrections on the optical properties of SrTiO suggests that the most consequential of the two individual corrections is U, as it predominately determines the accuracy of the dominant excitation from O-2p to the Ti-3d t/e orbitals. U, on the other hand, can be used to shift the entire optical response uniformly to higher frequencies. These results will assist high-throughput and machine learning approaches to screening photoactive materials based on d photocatalysts.