Nonempirical hybrid functionals for band gaps and polaronic distortions in solids

Abstract

We construct hybrid functionals in a nonempirical way by fixing the fraction of Fock exchange through either the long-range screening or the generalized Koopmans' condition applied to defect charge-transition levels. These functionals not only give band gaps of solids as accurate as state-of-the-art GW calculations, but are also capable of describing polaronic distortions. The Koopmans' condition is found to be satisfied across a series of defects, to the point of achieving accurate band gaps through a hydrogen probe. Extension to range-separated functionals demonstrates the robustness of the present approach.

Defect Formation Energies of Interstitial C, Si, and Ge Impurities in β‐Ga2O3

“…We use the PBE0 hybrid functional, in which the fraction α of Fock exchange is set to 0.27 in order to achieve a band gap of 4.8 eV for β ‐Ga 2 O 3 . This procedure has recently been shown to be consistent with the enforcement of the generalized Koopmans condition from exact DFT . The calculations are carried out for an optimized monoclinic supercell containing 120 atoms ( a = 12.21 Å, b = 3.05 Å, c = 5.81 Å, and β = 103.89°), in accurate agreement with the experimental lattice parameters ( a = 12.21 Å, b = 3.03 Å, c = 5.79 Å, and β = 103.83°) …”

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

“…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.…”

“…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.…”

“…Both approaches exhibit great potential due to their promising combination of accuracy and computational cost. However, a comparative study of these techniques has so far only been reported for alkali-halide compounds [36].…”

Optical absorption induced by small polaron formation in transition metal oxides: The case ofCo3O4

“…We note that hole polarons do not form for α below 10%, as illustrated in Figure 2b-c). The value of α determined in this manner is an intrinsic property of the bulk system, and the choice of defect used to enforce the Koopmans condition is proper as long as it has minimum hybridization with the bulk Bloch states [61,62,65]. We then determined U parameters based on the hybrid functional results, and the stable formation of electron and hole polarons (see Table S1 for more details).…”