Comparing time-dependent density functional theory with many-body perturbation theory for semiconductors: Screened range-separated hybrids and the GW plus Bethe-Salpeter approach

We present band structure and optical absorption spectra obtained from density functional theory (DFT) and linear response time-dependent DFT (TDDFT) calculations using a screened range-separated hybrid (SRSH) functional, including spin-orbit coupling, for seven prototypical semiconductors. The results are compared to those obtained from highly converged many-body perturbation theory calculations using the GW approximation and the GW plus Bethe-Salpeter equation (GW-BSE) approaches. We use a single empirical parameter for our SRSH calculations, fit such that the SRSH band gap reproduces the GW band gap at the $\mathrm{\ensuremath{\Gamma}}$ point. We then find that ground-state generalized Kohn-Sham SRSH eigenvalues accurately reproduce the band structure obtained from GW calculations, typically to within 0.1--0.2 eV, and optical absorption spectra obtained using TDDFT with the SRSH functional agree well with those of GW-BSE, with a mean deviation of 0.03 and 0.11 eV for the location of the first and second absorption peaks, respectively, at a fraction of the computational cost.