Time-dependent density functional theory calculations for the excitation spectra of III-V ternary alloys

We adopted the time-dependent density functional theory (TDDFT) within the linear augmented Slater-type orbitals basis and the cluster averaging method to compute the excitation spectra of III-V ternary alloys with arbitrary concentration $x$. The TDDFT was carried out with the use of adiabatic meta-generalized gradient approximation (mGGA), which contains the $1/{q}²$ singularity in the dynamical exchange-correlation kernel $[{f}_{\text{XC,}00}(\mathbf{q})]$ as $q\ensuremath{\rightarrow}0$. We found that, by using wave functions obtained in local density approximation while using mGGA to compute self-energy correction to the band structures, we can get good overall agreement between theoretical results and experimental data for the excitation spectra. Thus, our paper provides some insight into the theoretical calculation of optical spectra of semiconductor alloys.