Calculation of multiplet structure of corep-vacancy levels

The multiplet splittings of core $p$-vacancy levels have recently been observed in various transition-metal complexes and in some rare-earth as well as actinide complexes. This paper presents the calculation of the multiplet structure of core $p$-vacancy levels in the Hartree-Fock free-ion approximation. The spin-orbit and crystal-field effects have been included. The cases studied are ${\mathrm{Mn}}^{2+}$ in Mn${\mathrm{F}}_2$ and the free ion ${\mathrm{Fe}}^{3+}$. For $3p$ vacancies these effects appear to be unimportant from the point of view of photoelectron spectroscopy owing to the limited resolution of the technique. For $2p$ vacancies the spin-orbit interaction is comparable to the electrostatic interaction between the electrons and both the interactions must be considered simultaneously. The conclusion is that the x-ray photoelectron spectra of inner-core electrons are more suitable for chemical analysis than those of outer electrons which, in addition, contain large correlation and many-body effects.