Modified HSE06 functional applied to anatase TiO₂: influence of exchange fraction on the quasiparticle electronic structure and optical response

Abstract

The influence of non-interacting Kohn-Sham Hamiltonian on the non-self consistent GW (G0W0) quasiparticle gap and Bethe-Salpeter-Equation(BSE) optical spectra of anatase TiO2 is systematically evaluated. G0W0 and BSE calculations are carried out starting with HSE06 (Heyd-Scuseria-Ernzerhof) type functionals containing 20, 25 and 30% exact Hartree-Fock exchange. The results are also compared against G0W0+BSE calculations starting from semi-local(PBE) functionals. Our results indicate that the G0W0 and BSE calculations of anatase TiO2 depend critically on the mean-field starting point, wherein its dependence is mainly introduced through the dielectric screening evaluated at the intermediate G0W0. We find that the band dispersion, density of states, and consequently the oscillator strengths of optical excitation and spatial localization of excitons are insensitive to the starting points while the quasiparticle gap, optical gap and exciton binding energies are strongly affected. G0W0 quasiparticle gap of anatase TiO2 computed over hybrid functional starting points is typically overestimated compared to measured values. However, by varying the amount of exact exchange, the dielectric screening can be tuned, and thus the quasiparticle gap. Exciton binding energy is shown to increase in proportion to the increase of the amount of exact exchange. A simple extrapolation of the calculated data leads to the exact match with the recently measured value with 13% of the exact exchange. Systematic analysis of G0W0+BSE calculation starting from screened hybrid functionals provided in this study forms a reference for all such future calculations of pristine anatase TiO2 and its derivatives.

Electronic Bulk and Surface Properties of Titanium Dioxide Studied by DFT-1/2

“…92 These are ∼1 eV below our DFT-1/2 values. Note, however, that the fraction of exact exchange is a system-dependent quantity, 93,94 which was not optimized for TiO 2 in that study, whereas our DFT-1/2 approach was adjusted for TiO 2 , providing bulk band-gap values close to experimental reference values (see Table 1).…”