Ab initio simulations of x-ray emission spectroscopy with the GW+ Bethe-Salpeter equation method

Abstract

In order to calculate x-ray emission spectroscopy (XES) spectra, we apply the $GW+$Bethe-Salpeter equation ($\mathrm{GW}+\mathrm{BSE}$) method on a basis of extended quasiparticle theory, which enables one to treat an arbitrary excited state as an initial state, because the initial state in the XES process is a highly excited state with a core hole. Compared to the preexisting experimental data of XES fluorescence photon energy, the calculated $\mathrm{GW}+\mathrm{BSE}$ results give values with about 1-eV accuracy, which is comparable to the previous results using the time-dependent density functional theory with the short-range corrected exchange-correlation functional, the equation of motion-coupled cluster single and double, and delta self-consistent field methods. Our $\mathrm{GW}+\mathrm{BSE}$ results reproduce corresponding experimental XES spectra without missing any peak. The method can assign the excitonic configuration of each peak in XES spectra with the quasiparticle levels. As a result, the analysis of excitonic structure for each peak gives obvious interpretation concerning the relation between excitonic states and valence states.