Extended quasiparticle approach to non-resonant and resonant X-ray emission spectroscopy

The initial states of the secondary processes of X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS) are highly excited eigenstates with a deep core hole after a X-ray photoelectron spectroscopy (XPS) process and a X-ray photoabsorption spectroscopy (XAS) process, respectively, so that the XES and RIXS calculation offers a good example of extended quasiparticle theory (EQPT) (K. Ohno, S. Ono and T. Isobe, J. Chem. Phys., 2017, 146, 084108) which is applicable to any initial exited eigenstate. We apply the standard one-shot GW + Bethe-Salpeter equation (BSE) approach in MBPT to this problem on the basis of EQPT and analyze XES and RIXS spectra for CH₄, NH₃, H₂O, and CH₃OH molecules. We also suggest a simpler approach only using the GW calculation without solving the BSE to compute the XES and RIXS energies, although it cannot give the spectral intensity. Moreover, according to extended Kohn-Sham theory (T. Nakashima, H. Raebiger and K. Ohno, Phys. Rev. B, 2021, 104, L201116), we give a justification and comment of applying the method relying on time-dependent density functional theory as well as the one-shot GW + BSE approach to this problem.