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 CH 4 , NH 3 , H 2 O, and CH 3 OH 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.