Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory.

Fabien Tran,Peter Blaha

doi:10.1021/acs.jpca.7b02882

Abstract

Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke–Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke–Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.

Highlights

The calculation of the electronic properties of molecules, surfaces, and bulk solids is done mostly with the Kohn−Sham (KS) scheme of density functional theory (DFT),1,2 which is considered as a fast method especially if the exchange and correlation effects are approximated at the semilocal level, i.e., by using functionals Exc of the local density approximation (LDA), generalized gradient approximation (GGA), or metaGGA (MGGA)
The best agreement with experiment is obtained with the MGGA mBJLDA since the MAE and MARE drop to 0.47 eV and 15%, respectively
The results show that among all semilocal potentials, the mBJLDA potential leads to the smallest values for both the STDE and STDRE

Summary

Introduction

The calculation of the electronic properties of molecules, surfaces, and bulk solids is done mostly with the Kohn−Sham (KS) scheme of density functional theory (DFT), which is considered as a fast method especially if the exchange and correlation effects are approximated at the semilocal level, i.e., by using functionals Exc of the local density approximation (LDA), generalized gradient approximation (GGA), or metaGGA (MGGA). Of high interest is the electronic gap Δg, which is defined as I − A, where I and A are the ionization potential and electron affinity, respectively. The calculation of the electronic properties of molecules, surfaces, and bulk solids is done mostly with the Kohn−Sham (KS) scheme of density functional theory (DFT), which is considered as a fast method especially if the exchange and correlation effects are approximated at the semilocal level, i.e., by using functionals Exc of the local density approximation (LDA), generalized gradient approximation (GGA), or metaGGA (MGGA).. Of high interest is the electronic gap Δg, which is defined as I − A, where I and A are the ionization potential and electron affinity, respectively. It has been shown that the KS band gap (defined as the conduction band minimum minus the valence band maximum) calculated with the exact (but unknown) potential vxc = δExc/δρ discontinuity differs from the band gap Δxc,− which can be of.

Objectives

Methods

Results

Conclusion