Optical absorption spectra of metal oxides from time-dependent density functional theory and many-body perturbation theory based on optimally-tuned hybrid functionals

Using both time-dependent density functional theory (TDDFT) and the “single-shot” GW plus Bethe-Salpeter equation (GW-BSE) approach, we compute optical band gaps and optical absorption spectra from first principles for eight common binary and ternary closed-shell metal oxides (MgO, ${\mathrm{Al}}_2{\mathrm{O}}_3$, CaO, ${\mathrm{TiO}}_2, {\mathrm{Cu}}_2\mathrm{O}$, ZnO, ${\mathrm{BaSnO}}_3$, and ${\mathrm{BiVO}}_4$), based on the nonempirical Wannier-localization-based, optimally tuned, screened range-separated hybrid functional. Overall, we find excellent agreement between our TDDFT and GW-BSE results and experiment, with a mean absolute error smaller than 0.4 eV, including for ${\mathrm{Cu}}_2\mathrm{O}$ and ZnO that are traditionally considered to be challenging for both methods.

Figure 1

Imaginary part of the dielectric function, computed with TDPBE (yellow dot-dashed line), $G_0{W}_0$-BSE@PBE (green dotted line), TDWOT-SRSH (purple dot-dashed line), and $G_0{W}_0$-BSE@WOT-SRSH (red dashed line), compared to experiment (gray solid line). Vertical dotted lines indicate the main spectral features in experiment. The anisotropy in ${\mathrm{Al}}_2{\mathrm{O}}_3, {\mathrm{TiO}}_2$, and ZnO is accounted for by considering polarization perpendicular to the optic axis (ordinary component, $c_{\perp }$) and parallel to the optic axis (extraordinary component, $c_{\parallel }$) explicitly. Computed spectra are rigidly shifted in the energy axis by the vibrational renormalization reported in Table 3. They are also shifted in the vertical axis such that the zero absorption tail exactly begins where indicated by an axis tick. Experimental data are taken from the following sources: ${\mathrm{Al}}_2{\mathrm{O}}_3$: Ref. [150]; MgO: Ref. [151]; ${\mathrm{TiO}}_2$: Ref. [152]; CaO: Ref. [153]; ZnO: Ref. [154]; ${\mathrm{Cu}}_2\mathrm{O}$: Ref. [155]; and ${\mathrm{BaSnO}}_3$: Ref. [72].

Figure 2

Same as Fig. 1 but for ${\mathrm{BiVO}}_4$. The anisotropy in the optical response is directionally averaged. Experimental data are taken from Ref. [173].