Multiplet Splitting of Core-Electron Binding Energies in Transition-Metal Ions

X-ray photoelectron spectra indicate core-electron binding-energy splittings of \ensuremath{\sim}6 eV for the $3s$ levels in Mn${\mathrm{F}}_{2}$, MnO, and Fe${\mathrm{F}}_{3}$, and less pronounced effects on the $3s$ levels in Mn${\mathrm{O}}_{2}$ and Fe metal. These splittings are considerably reduced from free-ion predictions but agree well with calculations for Mn in a cluster environment. The $3p$ multiplet splittings are shown to behave in a quantitatively different fashion.