Efficient core-excited state orbital representation for many-body X-ray absorption transitions

X-ray absorption spectroscopy (XAS) is an explicit probe of the unoccupied electronic structure of materials and an invaluable tool for fingerprinting various electronic properties and phenomena. Computational methods capable of simulating and analyzing such spectra are therefore in high demand for complementing experimental results and for extracting valuable insights therefrom. In particular, a recently proposed first-principles approach titled Many-Body XAS (MBXAS), which approximates initial and final states as Slater determinants constructed from Kohn-Sham (KS) orbitals optimized in the absence or presence of the relevant core-hole, respectively, has shown promising prospects in evaluating X-ray transition amplitudes. Here, we re-derive the MBXAS approach using a transition operator expressed entirely in the basis of core-excited state KS orbitals. This reformulation offers substantial practical and conceptual advantages: circumventing previous issues of convergence with respect to the number of unoccupied ground-state orbitals; reducing computational cost by rendering the calculation of such orbitals unnecessary altogether; and providing a direct pathway for comparing the many-body approximation with the so-called single-particle treatment. One can now directly quantify the importance in observed XAS intensity of the relaxation of the valence occupied subspace induced by the core excitation and observe the associated electronic structure changes using auxiliary orbitals to explain the observed spectral intensity.