Use of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>DFT</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">J</mml:mi></mml:mrow></mml:math> with linear response parameters to predict non-magnetic oxide band gaps with hybrid-functional accuracy

Abstract

First-principles Hubbard-corrected approximate density functional theory ($\mathrm{DFT}+\mathrm{U}$) 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). $\mathrm{DFT}+\mathrm{U}$ property prediction of non-magnetic systems such as ${d}^{0}$ and ${d}^{10}$ 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 $\mathrm{DFT}+\mathrm{U}$, 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 $\mathrm{DFT}+\mathrm{U}$ 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 $\mathrm{DFT}+\mathrm{U}$ functionals incorporating J, namely, the widely used $\mathrm{DFT}+(\mathrm{U}\ensuremath{-}\mathrm{J})$ and the readily available $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$. We assess a test set comprising $\mathrm{Ti}{\mathrm{O}}_{2}, \mathrm{Zr}{\mathrm{O}}_{2}, \mathrm{Hf}{\mathrm{O}}_{2}, {\mathrm{Cu}}_{2}\mathrm{O}$, and ZnO, and apply the corrections both to metal- and oxygen-centered pseudoatomic subspaces. Starting from the PBE functional, we find that $\mathrm{DFT}+(\mathrm{U}\ensuremath{-}\mathrm{J})$ is significantly outperformed in band gap accuracy by $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$, the mean-absolute band gap error of which matches that of the hybrid functional HSE06. ZnO, a longstanding challenge case for $\mathrm{DFT}+\mathrm{U}$, is addressed by means of Zn $4s$ instead of Zn $3d$ correction, whereupon the first-principles $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$ band gap error falls to half of that reported for HSE06 yet remains larger than that for PBE0.

Topics & Concepts