Multiplet splitting (also termed exchange splitting) is a final state effect which, similar to spin-orbit splitting arises because of interactions between magnetic fields set up by localised spinning charges.
In an atomic system with an unpaired valence electron, the exchange interaction will favour spin-up and spin-down electrons unequally. Core electrons of a parallel spin to that of the unpaired valence electron will exhibit an exchange-potential, whereas those antiparallel will not (since exchange interactions only exist between electrons of the same spin).1 Coulombic repulsion is reduced by exchange interactions, and hence the parallel spin electrons will be energetically favoured, and the effect on the resulting wavefunctions is a slight spatial displacement – for example, Iron 3s wavefunctions are predicted to have a radius of 0.433 Å for the spin parallel core electrons, versus 0.435 Å for the spin anti-parallel electrons.2 The effect on binding energies ought be pronounced, with Hartree-Fock calculations predicting splittings as large as 12 eV for free ion Fe 3s electrons,3 however in practice these splittings are oft reduced significantly due to covalent-bonding effects.4
Multiplet splitting arises from:
a: Unparied electrons remaining in the core-level containing the core-hole
b: Unpaired valence electrons, whether initially present or introduced by relaxation (note these become localised by the newly formed core-hole)
Recall that valence electrons are involved in bonding, so with the valence levels playing a significant role in multiplet splitting, we have a phenomena which is extremely sensitive to the local chemical environment. Such observations are useful, especially for 3d transition metal compounds, to provide fingerprints of metal oxidation states.
3d transition metal compounds exhibiting multiplet splitting are show below (taken from xpsfitting.com)
- HarwellXPS Primer on Multiplet splitting
- Multiplet splitting at XPSfitting and references therein
- Multiplet splitting of heavier elements (Elsevier)
- Multiplet Splitting of Metal-Atom Electron Binding Energies (APS)
- Splitting of core-level lines in photoemission spectra of transition metal compounds
- Slater, John C. Quantum theory of atomic structure. No. 530.12 S53. 1960.
- Fadley, C. S., and D. A. Shirley. “Multiplet splitting of metal-atom electron binding energies.” Physical Review A 2.4 (1970): 1109.
- Bagus, P. S., and B. Liu. “Analytic-Expansion Unrestricted Hartree-Fock Wave Function for the D 5 State of Fe.” Physical Review 148.1 (1966): 79.
- Fadley, C. S., et al. “Multiplet splitting of core-electron binding energies in transition-metal ions.” Physical Review Letters 23.24 (1969): 1397.