For the computational
prediction of core electron binding energies
in solids, two distinct kinds of modeling strategies have been pursued:
the Δ-Self-Consistent-Field method based on density functional
theory (DFT), and the GW method. In this study, we examine the formal
relationship between these two approaches and establish a link between
them. The link arises from the equivalence, in DFT, between the total
energy difference result for the first ionization energy, and the
eigenvalue of the highest occupied state, in the limit of infinite
supercell size. This link allows us to introduce a new formalism,
which highlights how in DFT—even if the total energy difference
method is used to calculate core electron binding energies—the
accuracy of the results still implicitly depends on the accuracy of
the eigenvalue at the valence band maximum in insulators, or at the
Fermi level in metals. We examine whether incorporating a quasiparticle
correction for this eigenvalue from GW theory improves the accuracy
of the calculated core electron binding energies, and find that the
inclusion of vertex corrections is required for achieving quantitative
agreement with experiment.