Multiplet Splitting

Quick Overview

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.

Multiplet splitting arise 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)

First row transition metal species that show multiplet splitting in their XPS spectra

Fundamentals of Multiplet Splitting

Multiplet splitting, also known as exchange splitting, happens in systems with unpaired valence electrons, like open-shell systems. When these electrons interact with the unpaired electrons left in the core level after photoemission, they create a series of final states with slightly different energies. This means the atom is paramagnetic during photoemission.

The extent of multiplet splitting depends on the number of possible non-degenerate electronic states in the final hole states of these open-shell systems. You can observe this in both solid and gaseous species and across different electron shells that XPS can probe. For example, the s-shell electrons in paramagnetic gases like O₂, NO, and NO₂[1] show multiplet splitting, as do the 3s levels in solids like MnF₂ and MnO.[2]

In transition metals, the 2p levels, such as Mn(2p) in manganese oxides, Cr(2p) in Cr₂O₃, and Cu(2p) in CuO and CuSO₄, exhibit more complex peak shapes due to multiplet splitting. The complexity varies with different materials. For instance, in O₂ and MnF₂, the s-level splitting is easily observable and measurable, but in Cr₂O₃ and Dy, the splitting is more complicated and requires fitting different final states to understand the peak shape.

The energy of multiplet splitting (E_m), the splitting pattern (number of peaks), and the degeneracy (D_m) depend on the orbital angular momentum of the photoemitted electron and the number of unpaired valence electrons. For orbitals where the angular momentum is zero, the energy and degeneracy values scale with the total spin induced by the unpaired valence electrons and the core-level spin.[3]

E_m ∝ 2S_v +1 (1)
D_m ∝ 2(S_v + s_c) +1 (2)

Where:

S_v = Total spin induced by unpaired electrons

s_c = Core level spin (+1/2).

However it is more common to combine these two parameters into total spin (S) of the emitting atom.

When a core-hole forms, it can also excite valence electrons, which might relax back into their original state or into a different state. If this relaxation happens at the same time as photoemission, you’ll see satellite peaks at higher binding energies compared to the main photo peak (which means lower kinetic energies due to energy loss). These satellite peaks are known as shake-up structures, like those seen in CuO.

First Row Transition Metals

Multiplet splitting in p-shells is common in first-row transition metal compounds.[4,5,6,7] Using Hartree–Fock free-ion calculations, Gupta and Sen (GS) figured out how 2p core-holes couple with unpaired 3d electrons in free ion systems.[8,9] Their method’s predicted multiplet peaks match the observed 2p spectral envelope, although complex charge-transfer from ligands can cause deviations and complicate theoretical calculations.

Nickel Oxide XPS Fit — Nickel Oxide multiplet fit using a combination of Gupta-Sen free-ion envelopes and satellite features (Biesinger *et al*).

You can often see multiplet splitting of the 2p level clearly, like in Ni(II) in NiO, but in other cases, like Cu(II) in CuO, it shows up more as peak broadening.[10] The number of multiplet peaks can get pretty complex, but Biesinger and colleagues have shown that well-constrained variations of the GS models can fit transition metal compounds.[11,12] However, Fe compounds are still tricky and full of uncertainties. Bagus and co-workers found that Fe oxides have many multiplet states, many of which are degenerate in energy, making it tough to fully interpret the final electronic state.[13,14]

Copper (I) vs Copper (II) XPS — Copper (I) and Copper (II) Oxides by XPS. Note the peak broadening of the Cu(II) spectra, caused by multiplet splitting.

Heavier Elements

In heavy elements like those in the lanthanide series, this splitting can be very pronounced. For example, in metallic dysprosium (Dy), which has the ground state electronic configuration [Xe] 4f¹⁰ 6s², the 4d orbital is low-lying. When photoemission occurs, it results in a 4d⁹ 4fⁿ final state configuration. This allows the 4d core-hole to couple with the partly filled 4f shell, creating the complex structure we observe.[15]

Other heavy elements like cerium (Ce) and uranium (U) have also been extensively studied, showing similar complexities. Bagus and his team have done a lot of work in this area, providing detailed insights into these phenomena. For a more detailed discussion on these splittings, we recommend reading the works of reference 16 and reference 17.

Cerium 3d XPS fit — Peak model fits for Ce(III) and Ce(IV) highlighting the complex nature following splitting.

Understanding Your Spectra

Multiplet splitting can help identify the chemical state of a material. For example, Junta and Hochella suggested that manganese oxides can be identified by the magnitude of the Mn(3s) peak splitting. However, Ilton and colleagues pointed out that for mixed hydroxides and hydrated species, it’s better to model high-quality spectra using standards rather than just relying on the Mn(3s) splitting magnitude. In manganites like lanthanum strontium manganese oxides (LSMO), the lack of changes in Mn(3s) splitting with different dopant levels suggests that any dopant holes are localized in the O(2p) state.[18]

Multiplet splitting can also indicate the spin state of a material. First-row transition metals can have high-spin or low-spin electronic configurations, explained by crystal-field and ligand-field theory. This isn’t usually an issue for second- and third-row metals, which tend to be low-spin. For example, high-spin Fe(II) shows multiplet splitting, while low-spin Fe(II) does not. Similar effects are seen in Co and Mn complexes.

New XPS practitioners should record spectra of bulk compounds to understand the spectral shapes and note the multiplet (and shake) structure. This helps in accurately modelling experimental spectra and allows for “fingerprinting” the spectral envelope. It also enables fitting spectra through a linear combination approach to determine the concentrations of different chemical states in samples.

Modelling Multiplet Splitting

Multiplet splitting can be modeled using various software packages, often extensions of those used for modeling X-ray absorption spectra. Some of the popular tools include CTM4XAS and QUANTY, which have been discussed in detail by de Groot. For example, there’s good agreement between the calculated and experimental spectra for Ni(II) using these tools. However, they don’t account for shake-satellites or charge transfer final states, so you need to be careful when assigning the origins of XPS features derived from these models. Despite this, these software packages are excellent for understanding the complex line shapes caused by multiplet splitting in different oxidation states.

References

Hedman, J., et al. “Energy splitting of core electron levels in paramagnetic molecules.” Physics Letters A 29.4 (1969): 178-179. Read it online here.
Fadley, C. S., et al. “Multiplet splitting of core-electron binding energies in transition-metal ions.” Physical Review Letters 23.24 (1969): 1397. Read it online here.
Van der Heide, P. A. W. “Multiplet splitting patterns exhibited by the first row transition metal oxides in X-ray photoelectron spectroscopy.” Journal of Electron Spectroscopy and Related Phenomena 164.1-3 (2008): 8-18. Read it online here.
Grosvenor, A. P., et al. “Investigation of multiplet splitting of Fe 2p XPS spectra and bonding in iron compounds.” Surface and Interface Analysis: An International Journal devoted to the development and application of techniques for the analysis of surfaces, interfaces and thin films 36.12 (2004): 1564-1574. Read it online here.
Van der Heide, P. A. W. “Multiplet splitting patterns exhibited by the first row transition metal oxides in X-ray photoelectron spectroscopy.” Journal of Electron Spectroscopy and Related Phenomena 164.1-3 (2008): 8-18. Read it online here.
Briggs, D., and V. A. Gibson. “Direct observation of multiplet splitting in 2P photoelectron peaks of cobalt complexes.” Chemical Physics Letters 25.4 (1974): 493-496. Read it online here.
Nelson, A. J., John G. Reynolds, and Joseph W. Roos. “Core-level satellites and outer core-level multiplet splitting in Mn model compounds.” Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 18.4 (2000): 1072-1076. Read it online here.
Gupta, R. P., and S. K. Sen. “Calculation of multiplet structure of core p-vacancy levels. II.” Physical Review B 12.1 (1975): 15. Read it online here.
Gupta, R. P., and S. K. Sen. “Calculation of multiplet structure of core p-vacancy levels.” Physical Review B 10.1 (1974): 71. Read it online here.
Frost, D. C., A. Ishitani, and C. A. McDowell. “X-ray photoelectron spectroscopy of copper compounds.” Molecular Physics 24.4 (1972): 861-877. Read it online here.
Biesinger, Mark C., et al. “Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn.” Applied surface science 257.3 (2010): 887-898. Read it online here.
Biesinger, Mark C., et al. “Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni.” Applied Surface Science 257.7 (2011): 2717-2730. Read it online here.
Bagus, Paul S., et al. “Origin of the complex main and satellite features in Fe 2p XPS of Fe 2 O 3.” Physical Chemistry Chemical Physics 24.7 (2022): 4562-4575. Read it online here.
Bagus, Paul S., et al. “Combined multiplet theory and experiment for the Fe 2p and 3p XPS of FeO and Fe2O3.” The Journal of Chemical Physics 154.9 (2021). Read it online here.
Morgan, David J. “Core-level spectra of metallic lanthanides: Dysprosium (Dy).” Surface Science Spectra 30.2 (2023). Read it online here.
Bagus, Paul S., et al. “Multiplet splitting for the XPS of heavy elements: Dependence on oxidation state.” Surface Science 643 (2016): 142-149. Read it online here.
Bagus, Paul S., and Eugene S. Ilton. “Theory for the XPS of Actinides.” Topics in Catalysis 56 (2013): 1121-1128. Read it online here.
Junta, Jodi L., and Michael F. Hochella Jr. “Manganese (II) oxidation at mineral surfaces: A microscopic and spectroscopic study.” Geochimica et Cosmochimica Acta 58.22 (1994): 4985-4999. Read it online here.