Adjustable potential probes for band-gap predictions of extended systems through nonempirical hybrid functionals

Abstract

We describe a nonempirical procedure for achieving accurate band gaps of extended systems through the insertion of suitably defined potential probes. By enforcing Koopmans' condition on the resulting localized electronic states, we determine the optimal fraction of Fock exchange to be used in the adopted hybrid functional. As potential probes, we consider point defects, the hydrogen interstitial, and various adjustable potentials that allow us to vary the energy level of the localized state in the band gap. By monitoring the delocalized screening charge, we achieve a measure of the degree of hybridization with the band states, which can be used to improve the band-gap estimate. Application of this methodology to AlP, C, and MgO yields band gaps differing by less than 0.2 eV from experiment.

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

“…We consider various native defects, such as vacancies, interstitials, and antisites, but decide to focus only on halide vacancies since their single-particle energy levels are found to lie close to mid-gap. Indeed, the present construction scheme works most effectively when the hybridization of the defect states with the delocalized band states is minimized [39]. We remark that in our scheme the defect levels are obtained without structural relaxation [36,39], thereby explaining their different location in the band gap with respect to previous studies of defects in such perovskite materials [69][70][71].…”

“…Indeed, the present construction scheme works most effectively when the hybridization of the defect states with the delocalized band states is minimized [39]. We remark that in our scheme the defect levels are obtained without structural relaxation [36,39], thereby explaining their different location in the band gap with respect to previous studies of defects in such perovskite materials [69][70][71]. The defect calculations in this section are carried out with the pseudopotential set PP1 due to the computational cost entailed by the consideration of supercells.…”

“…For the construction of a hybrid functional that satisfies Koopmans' condition, we use the procedure shown in Fig. 2 [36,39]. We study single-particle energy levels induced by point defects within a supercell of the considered material.…”

“…To support the choice of the halide-vacancy defect, we use the concept of adjustable hydrogenic-like potential probes [39]. We use potentials resulting from a Gaussian distribution of positive charge with width parameters σ ranging from 0.625 to 1.25 bohr.…”

“…However, hybrid functionals remain unsatisfactory because they contain undetermined parameters, such as the amount of incorporated Fock exchange. To overcome this deficiency, two different nonempirical determination schemes are being investigated at present, namely, * thomas.bischoff@epfl.ch dielectric-dependent hybrid (DDH) functionals [22][23][24][25][26][27][28][29][30][31][32] and hybrid functionals enforcing Koopmans' condition [33][34][35][36][37][38][39][40]. Both approaches exhibit great potential due to their promising combination of accuracy and computational cost.…”