Use of DFT+ U+ J with linear response parameters to predict non-magnetic oxide band gaps with hybrid-functional accuracy

Abstract

First-principles Hubbard-corrected approximate density functional theory (DFT+U) is a low-cost, potentially high-throughput method of simulating materials, but it has been hampered by empiricism and inconsistent band gap correction in transition metal oxides (TMOs). DFT+U property prediction of non-magnetic systems such as d0 and d10 TMOs is typically faced with excessively large calculated Hubbard U values and difficulty in obtaining acceptable band gaps and lattice volumes. Meanwhile, Hund's exchange coupling J is an important but often neglected component of DFT+U, and the J parameter has proven challenging to directly calculate by means of linear response. In this paper, we provide a revised formula for computing Hund's J using established self-consistent field DFT+U codes. For non-magnetic systems, we introduce a non-approximate technique for calculating U and J simultaneously in such codes, at no additional cost. Using unmodified quantum espresso, we assess the resulting values using two different DFT+U functionals incorporating J, namely, the widely used DFT+(U-J) and the readily available DFT+U+J. We assess a test set comprising TiO2, ZrO2, HfO2, Cu2O, and ZnO, and apply the corrections both to metal- and oxygen-centered pseudoatomic subspaces. Starting from the PBE functional, we find that DFT+(U-J) is significantly outperformed in band gap accuracy by DFT+U+J, the mean-absolute band gap error of which matches that of the hybrid functional HSE06. ZnO, a longstanding challenge case for DFT+U, is addressed by means of Zn 4s instead of Zn 3d correction, whereupon the first-principles DFT+U+J band gap error falls to half of that reported for HSE06 yet remains larger than that for PBE0.