Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

Abstract

Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initioU parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.

Structural Properties and Magnetic Ground States of 100 Binary d-Metal Oxides Studied by Hybrid Density Functional Methods

“…Even in the case of diamagnetic d-metal oxides such as Cu 2 O, DFT-GGA may describe the electronic properties rather poorly, resulting in a poor description of other properties such as phonons [17]. These challenges arise from the self-interaction error of DFT-GGA, resulting from the over-delocalization of the electrons in the metal d orbitals, in particular 3d orbitals [9,[18][19][20][21]. As a result, the electronic structure can be even qualitatively wrong.…”

“…Hybrid density functionals that incorporate some exact exchange are known to significantly correct the self-interaction error, leading to correct description of the electronic and magnetic structures [15,18,20,21,24,[31][32][33]. In particular, the main improvement of hybrid functionals over GGA functionals is the correct treatment of the valence bands near the Fermi level, leading to correct localization of the electrons [15,21]. The structural and electronic properties are typically described reasonably well, even if the band gap is generally overestimated [34,35].…”

“…Approaches to further improve the band gap prediction of hybrid functionals have also been suggested: dielectric-dependent hybrid functionals do not show real improvement, but the application of so-called charge transition level scheme leads to the further improvement of the predicted band gaps [36,37]. In principle, it is possible to tune the band gap predictions by tuning the amount of exact exchange, but such an empirical approach deteriorates the predictive power of the methodology [21]. In general, hybrid functionals with about 25% exact exchange such as PBE0 have been shown to describe d-metal oxides and their magnetic structures reasonably well [15,21,24,31].…”

“…In principle, it is possible to tune the band gap predictions by tuning the amount of exact exchange, but such an empirical approach deteriorates the predictive power of the methodology [21]. In general, hybrid functionals with about 25% exact exchange such as PBE0 have been shown to describe d-metal oxides and their magnetic structures reasonably well [15,21,24,31]. The screened hybrid functionals such as HSE06 are another very commonly used approach in solid-state DFT studies, and they have been shown to predict band gaps of d-metal oxides and dichalcogenides with good accuracy [38].…”

Effects of the Hubbard U correction on the electronic and magnetic properties of the tetragonal V2P2 sheet

“…The LRA approach has been used successfully for high-performance benchmarking of some wellknown TM systems with greater accuracy that coincides with the available experimental data. 25 In this study, we investigate the stability, electronic and magnetic properties of t-V 2 P 2 sheet based on DFT+U calculations. The t-V 2 P 2 sheet shows excellent vibrational and mechanical stabilities.…”