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# Electronic-Structure Interpretation: How Much Do We Understand Ce L3 XANES?

Kristina O. Kvashnina

► To cite this version:

Kristina O. Kvashnina. Electronic-Structure Interpretation: How Much Do We Understand Ce L3 XANES?. Chemistry - A European Journal, 2024, 30 (46), pp.e202400755. 10.1002/chem.202400755. hal-05098760

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Submitted on 5 Jun 2025

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# Electronic-Structure Interpretation: How Much Do We Understand Ce L₃ XANES?

Kristina O. Kvashnina*<sup>[a, b]</sup>

Historically, cerium has been attractive for pharmaceutical and industrial applications. The cerium atom has the unique ability to cycle between two chemical states (Ce(III) and Ce(IV)) and drastically adjust its electronic configuration: [Xe] 4f¹5d¹6s² in response to a chemical reaction. Understanding how electrons drive chemical reactions is an important topic. The most direct way of probing the chemical and electronic structure of materials is by X-ray absorption spectroscopy (XAS) or X-ray absorption near-edge structure (XANES) in high energy resolution fluorescence detection (HERFD) mode. Such measurements at the Ce L₃ edge have the advantage of a high

penetration depth, enabling in-situ reaction studies in a time-resolved manner and investigation of material production or material performance under specific conditions. But how much do we understand Ce L₃ XANES? This article provides an overview of the information that can be extracted from experimental Ce L₃ XAS/XANES/HERFD data. A collection of XANES data recorded on various cerium systems in HERFD mode is presented here together with detailed discussions on data analysis and the current status of spectral interpretation, including electronic structure calculations.

## Introduction

Among all cerium systems, cerium dioxide has garnered significant attention in the nanotechnology field due to its valuable applications as catalysts, fuel cells, polishing agents, ceramic manufacturing, cancer therapy and imaging. At the same time, various Ce-phosphates, - carbonates, -silicates, and -hydroxide phases have been discovered and investigated in the field of geoscience. Despite this, identifying novel cerium phases remains challenging, highlighting the need for improved analytical methods. X-ray spectroscopy is an element-selective experimental technique used to measure the oxidation state and local structure of compounds under investigation. X-ray absorption spectroscopy (XAS), or X-ray absorption near edge structure (XANES), particularly in high-energy resolution fluorescence mode (HERFD), is now a commonly used method at synchrotron facilities for studying materials containing cerium. XAS or XANES works on the principle of the excitation of core electrons to the first possible unoccupied electronic level. Following the dipole and quadrupole selection rules at the Ce L₃ edge, electrons are excited from the 2p<sub>3/2</sub> core level into the unoccupied 4f and 5d states. Technically, the method involves measuring the transmission or fluorescence signal as a function of X-ray energy close to the absorption edge. The

experimentally recorded XANES features, especially in HERFD mode, are highly detailed and rich in information.<sup>[1,2]</sup>

Figure 1 shows the Ce L₃ XANES spectrum recorded on polycrystalline CeO₂ in total fluorescence yield (TFY) and HERFD modes. Since the first XANES measurement, the oxidation state and ground state configuration of CeO₂ have been the subject of debate. XANES spectrum at the Ce L₃ edge on CeO₂ shows a double profile, which has been hard to understand by considering only 2p→5d excitations. Krill et al.<sup>[3]</sup> suggested that the excitation process of XANES begins from a single Ce(IV) (4f⁴)

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Full Ce L₃ HERFD spectra of CeO₂ and CePO₄ reference compounds, recorded with the X-ray emission spectrometer set to the maximum of the Ce Lα₁ emission line and compared to the spectra recorded in TFY (standard XANES) mode. Top: schematic depicting the origin of the Ce L₃ HERFD transitions; middle: the detailed pre-edge HERFD structure recorded on CeO₂ and CePO₄ with Ce(IV) and Ce(III) oxidation states, respectively.</figcaption></figure>

<footnote>[a] K. O. Kvashnina
The Rossendorf Beamline at ESRF, The European Synchrotron, CS40220,
38043 Grenoble Cedex 9, France
E-mail: kristina.kvashnina@esrf.fr</footnote>

<footnote>[b] K. O. Kvashnina
Institute of Resource Ecology, Helmholtz Zentrum Dresden Rossendorf,
Dresden 01328, Germany</footnote>

<footnote>© 2024 The Authors. Chemistry - A European Journal published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>
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configuration and goes to the final state made up of both 4f¹ and 4f¹ configurations. The final 4f¹5d¹ state of Ce(IV) overlaps with the energy of the final 4f¹5d¹ of Ce(III). Indeed, Figure 1 illustrates that the main peak of Ce L₃ XANES recorded on CePO₄ with Ce(III) aligns with peak A1 in CeO₂ in TFY mode, and has a small shift in HERFD mode.

It should be noted that the oxidation state and the occupation of the valence electron shells (4f and 5d in the case of cerium) are correlated, however, they remain two distinct concepts used to describe the electronic structure and chemical behaviour. The oxidation state represents the hypothetical charge an atom would have if all chemical bonds to different atoms were purely ionic. This concept is used to describe oxidation and reduction processes in chemical reactions and is fundamental to obtaining the charge balance. In this oxidation/ reduction scenario, the transfer of electrons takes place, changing the occupation of the valence shells and the charge on the atoms involved in a process. In reality, the bond is never purely ionic. In the quantum chemical description of the bond, the electrons are shared between atoms because they occupy molecular orbitals formed by mixing the atomic orbitals from atoms in the system. This leads to fractional alterations in electron occupation and orbital configurations. Understanding both concepts is crucial for revising previously reported results on ceria from different scientific groups and communities.

Bianconi and co-authors[4] reported intermediate valence states observed in CeO₂ and Ce(SO₄)₂*4H₂O, both of which are in the Ce(IV) oxidation state but possess different crystal structures. The authors demonstrated that the final states of XANES reflect the interaction between 4f¹ and 4f¹⁺L configurations in the ground state, where L represents the mixing of the 4f localized state with ligand valence orbitals through a hybridization mechanism. Overall, the authors concluded that Ce L₃ XANES of CeO₂ provides direct insight into the mixed 4f¹ and 4f¹⁺L ground state, indicating that a simple one-electron band-structure interpretation is insufficient to explain the entire spectrum. Soldatov et al.[5] provided an interpretation of all spectral features of Ce L₃ XANES based on the full multiple-scattering approach. The crystal field splitting of the 5d states into the *e*<sub>g</sub> and *t*<sub>2g</sub> levels in the final state was found to be approximately 4.0 eV.[4,5] The pre-edge peak in the Ce L₃ edge XANES of CeO₂ corresponds to the transition at the bottom of the CeO₂ conduction band. The complete shape of the Ce L₃ XANES has been calculated by considering a significant mixing between localized 4f levels and more delocalized O 2p levels, described by the mixing of multielectron configurations: 4f⁰ and 4f¹L, while neglecting the 4f¹L² configuration.[5]

It is worth mentioning that the double structure in Ce L₃ XANES on CeO₂ has been named differently by various researchers. Bianconi's and Soldatov's groups[4,5] assigned the lower-energy peak to the 2p→5d transition with 4f¹L configuration, and the higher-energy peak to the 2p→5d transition with 4f⁰L configuration. The term "multi-electron excitations" has been used, which refers to the process where the excitation of more than one electron occurs from the ground state. This contributes to additional features in the XANES spectrum at other energies than the main edge and indicates strong

electron-electron interactions. Two XANES peaks on CeO₂ were also interpreted in terms of screened (low-energy peak) and unscreened (high-energy peak) states.[6,7] Screened states are screening the lower energy required to create a core-hole and generally indicate a strong interaction between the core-hole and valence electrons. Unscreened states correspond to the higher energy features in the spectrum and imply weak electron interaction. From this point of view, it is always challenging to assign where the main edge, multi-electron excitations, or screened and unscreened states appear in the experimental XANES data. It depends on the abbreviation and context used by the authors. In further discussion I will refer to the high-energy peak in CeO₂ XANES as "multi-electron" excitations and to the lower-energy peak as "main edge" transitions. This is because the Ce 5d states plays the key role in the formation of the low-energy peak in CeO₂ XANES at the Ce L₃ edge.[5]

## Results and Discussion

Later, it was shown that Ce L₃ XANES can be recorded in high energy resolution mode by HERFD[8–10] with the help of the X-ray emission spectrometer.[11,12] Figure 2 shows a comparison of XANES data recorded in TFY and in HERFD modes for various cerium compounds in Ce(III) and Ce(IV) oxidation states. Analysis of the spectral features reveals that the pre-edge structure on the low-energy side of XANES is clearly resolved in HERFD mode. This pre-edge structure of Ce L₃ HERFD is associated with quadrupole transitions from the 2p to 4f level.[8,13,14] Additionally, the main edge exhibits fine details of the Ce 5d crystal field splitting and multi-electron excitations, which are also better resolved in HERFD mode.[6,15–28]

The principles of the HERFD methodology were introduced in 1991[13] and are based on the reducing the life-time broadening in XANES by analysing the fluorescence photon energy with energy resolution superior to the natural linewidth. HERFD

<figure><img src="image_6.png" /><figcaption>**Figure 2.** a) and c) Ce L₃ HERFD-XANES spectra of Ce(IV) and Ce(III) reference compounds, recorded with the X-ray emission spectrometer set to the maximum of the Ce Lα₁ emission line. b) and d) Ce L₃ XANES spectra of Ce(IV) and Ce(III) reference compounds, recorded in TFY (standard) mode.</figcaption></figure>
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is a part of the resonant inelastic X-ray scattering (RIXS) process,[1,29–31] and is measured by scanning incident energy near the absorption edge with the help of an X-ray emission spectrometer, aligned at the maximum of the corresponding emission line.[13] Additionally, RIXS can be performed with either valence or core excitations, depending on the chosen energy transfer during the experiment. The intermediate process of RIXS (or final process of HERFD) contains a core-hole, which makes a technique element selective. The final state contains the core-hole in core-to-core RIXS and does not contain core-hole in the valence band RIXS process.

The core-to-core RIXS method is the most frequently utilized, primarily because its intensity is significantly higher compared to valence band RIXS.[32–38] Figure 3 shows the core-to-core RIXS data[8] recorded near Ce $L_α_1$ and Ce $L_α_2$ emission lines with the excitation energies across the Ce $L_3$ edge on CeO$_2$ and Ce$_2$(CO$_3$)$_3$. The vertical axis of the RIXS map represents the energy difference between the incident and the emitted energies, referred to as the Energy Transfer. Variation of the colour in the plot related to the different scattering intensities. The HERFD-XANES spectrum corresponds to the diagonal cut through the RIXS plane, which can be taken at the maximum of the Ce $L_α_1$ or Ce $L_α_2$ emission lines. Interestingly the RIXS spectral features, excited above the Ce white lines are extended here along two diagonal directions, independent of the oxidation state, ground state, electron occupation or local Ce structure. However, the core-to-core RIXS over the Ce $L_3$ absorption pre-edge (shown at the bottom of the Figure 3) displays non-diagonal features, which can be used as an

indicator of the cerium ground state configuration. Experimental core-to-core RIXS over the pre-edge is compared here to the atomic multiplet calculations, which were done by considering the quadrupole transitions from the $2p^64f^N$ ground state to the $2p^54f^{N+1}$ intermediate state, and the dipole allowed transitions from the intermediate $2p^53d^{10}4f^{N+1}$ to the final $2p^63d^94f^{N+1}$ state. As seen here the pre-edge structure in RIXS and in HERFD-XANES is dependent on the number of the 4f electrons.[8]

Kotani and co-workers[9,10] employed both core-to-core and valence band RIXS techniques to investigate the influence of core-hole potential and ground state orbital mixing in CeO$_2$. Using Single Anderson Impurity Model (AIM) calculations, they demonstrated that CeO$_2$ cannot be adequately described by an ionic model, highlighting strong covalency or ground state mixing with nearly equal contributions from the $4f^2$ and $4f^1L$ configurations. Furthermore, the existence of the $4f^2L^2$ configuration must also be considered, particularly in the energy transfer range above 30 eV in valence band RIXS data. This finding confirms once again the previously reported results on the electronic structure of CeO$_2$.[4,5,39,40]

Figure 4 shows examples of valence band RIXS and HERFD-XANES data recorded at the Ce $L_3$ edge on CeO$_2$[9,10] and Ce$_2$(SO$_4$)$_3$. The RIXS process is based on the excitation of a core electron to an excited state, followed by the decay of the electron from the intermediate to the final state. This process involves two levels. The initial part of the RIXS process (both core-to-core and valence band RIXS) is identical to XANES, thus allowing for direct comparison of information obtained from RIXS data analysis to XANES interpretation. The final state is in

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Core-to-core RIXS data[8] recorded for CeO$_2$ and Ce$_2$(CO$_3$)$_3$, displayed as a contour map with axes corresponding to the incident and transferred energies over the Ce $L_3$ absorption edge and the Ce $L_α_1$ and Ce $L_α_2$ emission lines. Dashed lines indicate the maximum of the Ce $L_α_1$ and Ce $L_α_2$ at which HERFD-XANES spectra can be collected. The schematic representation of the core-to-core RIXS processes is given. Bottom: The experimental (a,c) and theoretical (b,d) core-to-core RIXS data, recorded over the pre-edge region of Ce $L_3$ absorption edge.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 4.** Valence band (or valence to core) RIXS data at the Ce L₃ edge recorded for CeO₂[⁹,¹⁰] and Ce₂(SO₄)₃. A schematic representation of the RIXS and HERFD-XANES processes from the ground to the intermediate and final states for CeO₂ is given.</figcaption></figure>

the range of sub-kilo-electron volts in core-to-core RIXS and in the range of just a few electron volts for valence band RIXS. Figure 4 shows that there is a distinct difference between valence band RIXS recorded on CeO₂ and Ce₂(SO₄)₃ systems. The RIXS excitations recorded on Ce₂(SO₄)₃ are situated along the diagonal direction, similar to core-to-core RIXS data (reported in Figure 3). Valence band RIXS data recorded on CeO₂ displays many non-diagonal features. Kotani and co-authors demonstrated that the same final state (energy transfer at ~10 eV) in valence band RIXS is reached by excitation from the A1 and B1 states, while the same RIXS final state (at ~15 eV) is reached by excitation from the A2 and B2 states. This indicates that the origin of the A1 and B1 states remains the same and is due to low-energy *e*₉ transitions, whereas the A2 and B2 transitions belong to higher-energy *t*₂g transitions in the Ce 5d level. A schematic representation of these processes is shown in Figure 4.

It is worth noting that theoretical calculations of the entire Ce L₃ XANES spectrum on CeO₂ have only been conducted by Bianconi,[⁴] Soldatov,[⁵] Kotani[⁹,¹⁰] and their co-workers. Reproducing multi-electron excitations in spectra using other theoretical approaches remains challenging. Recently, Sergentu and co-workers[⁴¹] attempted to calculate the CeO₂ XANES spectrum in standard mode using a relativistic ab-initio multiconfigurational wavefunction approach. Their agreement with experimental data is excellent. The authors discuss in detail the relationship between 4f electron occupation in the ground state versus the core-excited states. An example of the Ce L₃ data recorded on cerocene (Ce(C₈H₈)₂ system) is given, which has been considered as a case where the mixed ground state is

present.[⁴²⁻⁴⁵] However, the Ce XANES data at the Ce L₃ edge and relative intensities of the double XANES structure of both Ce compounds are different. The authors demonstrated that peak intensities differ from each other due to the 4f¹ versus 4f⁰ sub-configurations. Moreover, one of the cerocene peaks is associated with 4f² configuration. Both peaks in XANES provide information on the Ce 5d splitting into *e*₉ and *t*₂g transitions, which follow the same order and splitting as the Ce main edge.

The difference between Sergentu's and Kotani's approaches is in the description of the ground state. However, it is not necessarily different meaning that researchers are giving while studying CeO₂ electronic structure. Kotani and all other scientists who used AIM approximation have considered the complexity of the CeO₂ XANES data. The single electron approximation cannot be used and XANES data itself indicate mixed valent nature of the excited states in CeO₂. The introduction of the 4f⁰ and 4f¹L ground state configurations was done in order to acknowledge the covalent nature of the CeO₂ bond or strong hybridization between 4f localized state and ligand. The 4f⁰ and 4f¹L ground state configurations were never supposed to indicate the presence of the Ce(III) and Ce(IV) oxidation states in CeO₂. The relativistic ab-initio multiconfigurational wavefunction approach[⁴¹,⁴⁶] nowadays provides great possibilities to calculate multi-electron excitations starting from the single ground state. It will be beneficial to use novel molecular orbital theory and other methods[⁴¹,⁴³,⁴⁵⁻⁵⁰] and reproduce Ce HERFD-XANES and RIXS experimental data in both core-to-core and valence-to-core regimes through the entire range of the pre-edge and main edge excitations on CeO₂.
<figure><img src="image_11.png" /></figure>

As mentioned earlier, it is always challenging to identify or
understand the presence of multi-electron excitations in XANES
data. I believe that RIXS offers an excellent opportunity to
address this phenomenon. The RIXS results presented in
Figure 4 clearly indicate the differences between CeO₂ and
Ce₂(SO₄)₃, compounds where presence and absence of multi-
electron excitations in XANES data might take place. The
appearance of non-diagonal features in valence band RIXS can
be used as an indication of multi-electron excitations. More
experimental RIXS data should be collected on novel materials
where extra features are observed in XANES, not only in Ce, but
also in Pr, Tb, and other lanthanide systems.[51] Moreover, it
might be interesting to look not only at the Ce L₃ XANES
interpretation but at the Ce L₁, M₄,₅ edge XANES, ligand K-edge
XANES and electronic structure information available there.[51,52]

The pre-edge structure in HERFD data or in valence-to-core
RIXS can provide information about the ground state. In the
case of CeO₂, it is clear from pre-edge HERFD or from core-to-
core RIXS that the CeO₂ ground state has a sole 4f⁰ config-
uration. The excited states, probed by valence band RIXS, are
intense and contain a lot of information. It is interesting to
compare HERFD data on CeO₂ to the cerocene (Ce(C₈H₈)₂
system), which has a known mixed-valent ground state.[42–45]
Figure 5 shows that the pre-edge structure on cerocene
(marked as A) indeed indicates the mixed-valent ground state
with 4f⁰ and 4f¹ configurations. The excited states in the HERFD
process exhibit a detailed profile of the Ce 5d states. It is
evident that the spectral shape of the main peak (marked as B)
is quite different compared to CeO₂ or any other tetravalent or
trivalent cerium compounds (data for those reported in Fig-
ure 2). The shape of the multi-electron excitations (marked as C)
is also quite different. XANES recorded in TFY mode is in

agreement with previously reported data.[42,44] Figure 5 also
shows XANES spectra recorded in TFY and HERFD modes on
cerocene, reduced under the X-ray beam. The pre-edge
structure and main edge transitions are similar to the HERFD
and TFY recorded on trivalent cerium. However, the post-edge
features still have quite high intensity, indicating the presence
of the multi-electron excitations. The TFY spectrum recorded on
reduced cerocene is quite similar to the spectrum reported by
Walter an co-workers[44] on cerocene sample after it was heated
to 500 K. I find this case interesting and I hope that more
theoretical and experimental analysis can be conducted on
cerocene and other lanthanocene complexes in the future.

Overall, what is it known for the moment is that information
regarding the crystal-field splitting of the Ce 5d level can be
observed through multi-electron excitations. It can be valuable
in challenging cases when Ce L₃ XANES or XANES-HERFD data
analysis are done for compounds with mixed oxidation states.
As discussed earlier, the Ce L₃ main edge XANES transitions of
Ce(III) compounds are located at very similar incident energy
positions as features belonging to Ce(IV). Therefore, in cases of
uncertainty, an examination of multi-electron excitations is
necessary. If these transitions do not align with the trend of the
main excitation (as they should be mirrored in multi-electron
excitations), it suggests the possible reduction in electron
occupation takes place, and might be coupled with a presence
of Ce(III) oxidation state in the investigated compounds. It is
worth noting that the HERFD-XANES detection mode is much
more preferable in comparison to standard XANES in such
analysis. Figure 6 shows the Ce L₃ HERFD-XANES data recorded
on various tetravalent Ce systems. In most cases, the main edge
transitions exhibit a similar shape to the multi-electron
excitations. The Ce 2p-5d transition exhibits a narrow profile for
the Ce(IV) spectrum recorded in solution, produced in an

<figure><img src="image_12.png" /><figcaption>**Figure 5.** Ce L₃ HERFD – XANES and TFY spectra of cerocene (green curves) and cerocene reduced under X-ray beam (black curves), compared to the HERFD-XANES of Ce(IV) and Ce(III) reference compounds.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 6.** Full Ce L₃ HERFD spectra of Ce(IV) reference compounds, recorded with the X-ray emission spectrometer set to the maximum of the Ce Lα₁ emission line. All materials were measured in solid state, except Ce(IV) ion which was recorded in-situ during the electro-chemical reaction, reported by Estevenon et al.[18]</figcaption></figure>
<figure><img src="image_14.png" /></figure>

electrochemical cell.[18] Narrow features are also observed for the (NH₄)₂Ce(NO₃)₆ system. Other spectra exhibit a wide splitting of the Ce 5d states, which is reflected in the case of multi-electron excitations, except for the data recorded on the CeF₄ system, which was reduced under the beam. This particular case is interesting and will be discussed in detail later.

## What Information Does the Ce L₃ Edge in XAS/XANES or XANES-HERFD Contain?

For non-expert users of X-ray absorption spectroscopy, I summarize below the information available on the electronic transitions and spectral features of the Ce L₃ XANES, using the example of HERFD-XANES data recorded for CeO₂ and CePO₄ reference compounds with Ce(IV) and Ce(III) oxidation states, respectively (see Figure 1). I divide the HERFD-XANES spectra into three regions – pre-edge, main edge, and post-edge regions – and discuss their basis in further detail:

1. The pre-edge structure (in the energy region of 5712–5720 eV) originates from the dipole-forbidden but quadrupole allowed 2p<sub>3/2</sub>→4f transitions and directly probes the number of the 4f electrons at the ground state and the Ce valence state.[4,5,8,13,15] Generally, 4f states are considered to be the most localized states in the entire periodic table, where the hybridization between the 4f shell and ligand state has minimal impact. As a result, the pre-edge structure of all lanthanides at the L₃ edge can be calculated by the atomic multiplet theory and hybridization between different orbitals can be omitted.[8,14,53,54] Figure 1 shows the experimental Ce HERFD-XANES spectra over the pre-edge region of CeO₂ and CePO₄ with Ce(IV) and Ce(III) oxidation states. Ce(IV) contains one 4f electron in the absorption final state (excited state) and the CeO₂ spectrum shows a single pre-edge peak at ~5718 eV in the pre-edge region. When the number of 4f electrons in the final state is increased to two for Ce(III) the spectral shape becomes different. The transitions to excited states are split in two groups (at ~5715.5 eV and at ~5718.5 eV) due to the electron-electron interactions in the 4f valence level.[8,14,53,54] Therefore, the pre-edge region can be used to examine the ground state configuration, the number of the valence electrons and the reduction or oxidation process which might take place in cerium compounds.[8,14–16,18,53] The single pre-edge profile will always correspond to the 4f⁰ ground state or the Ce(IV) oxidation state and any intensity gain at the lower energy side from Ce(IV) pre-edge is a direct indication of the reduction or the formation of Ce(III) oxidation state with 4f¹ character.

2. The main edge transitions (in the energy region of 5720–5732 eV) correspond to the dipole allowed 2p<sub>3/2</sub>→5d transitions and are affected by the crystal structure of Ce compounds.[8–10,14–16,18,21,37,55–57] The main edge region (5720–5732) shown in Figure 1 reflects the distribution of the Ce 5d states, which was found to be very different for CeO₂ and CePO₄ compounds. Clear splitting of the 5d states in the cubic crystal structure is seen for the CeO₂. Contrary to that,

only a single peak due to the narrow distribution of the 5d states is seen for CePO₄. To better understand the origin of the main edge transitions, electronic structure calculations using the FEFF9.6 ab-initio code[58] were conducted and reported in Figure 7. The experimental results are very well reproduced by theoretical calculations which consider the corresponding crystal structures of the CePO₄ and CeO₂. The calculations have been done in a similar way to those reported before by Li and co-workers,[7] and Plakhova and co-workers.[16] The projected 5d density of states (DOS) is shown at the bottom of the figure for clarity. It has been previously shown that due to the cubic crystal field, the Ce(IV) 5d configuration in CeO₂ is split into the e₉ and t<sub>2g</sub> levels, as clearly seen and resolved in the Ce L₃ HERFD-XANES of CeO₂.[4,5,18,21] Moreover, the crystal field splitting parameter can be found from the energy difference between the e₉ and t<sub>2g</sub> levels, which is in order of ~4 eV for CeO₂. Recently, Estevenon and co-workers conducted an investigation of Ce clusters using Ce L₃ HERFD-XANES and demonstrated a gradual splitting of the Ce 5d states as the size of the Ce cluster increases.[18]

3. The last part of the HERFD spectra (in the energy range of 5732–5780 eV) typically corresponds to the post-edge region, involving transitions from the 2p<sub>3/2</sub> to the continuum. The shape of the post-edge features in the HERFD spectrum for CePO₄ is well reproduced by the electronic structure calculations (c.f. Figure 5). However, the Ce L₃ HERFD of CeO₂ shows extra features in the region of 5732–5745 eV,

<figure><img src="image_15.png" /><figcaption>**Figure 7.** Ce L₃ HERFD-XANES spectra of CeO₂ and CePO₄ reference compounds, recorded with the X-ray emission spectrometer set to the maximum of the Ce Lα₁ emission line and compared to the Ce L₃ HERFD spectra, calculated by ab-initio FEFF9.6 code. The projected density of states (DOS) are shown at the bottom of each spectrum for clarity. For CeO₂ the DOS is shown twice to indicate the presence of the Ce 5d states in the multi-electron excitations region.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

marked as B1 and B2 in Figure 1, which are due to the multi-electron excitations.[5,9,10] The main edge and post-edge features in CeO₂ HERFD-XANES spectrum are often named as screened and unscreened excited states.[9,10] Interestingly, the first two main peaks in Ce L₃ HERFD of CeO₂ (marked A1 and A2) and the two peaks in the post-edge regions (marked B1 and B2) show identical profiles (but with mirrored intensity variation) as both transitions represent 2p-5d excitations. It should be also mentioned here that the FEFF9.6 approach is based on the single-electron approximation, thus, the second part of the CeO₂ spectrum cannot be reproduced, as previously discussed.[7,16,21] The shape of the multi-electron excitations together with main dipole 2p-5d transitions will always depend on the crystal structure of various Ce(IV) compounds.[37] To add clarity to the nature of those transitions, the Ce 5d DOS is shown in both regions in Figure 7. Further HERFD and RIXS data on various Ce(IV) systems should be recorded and explored in this context.

## Several Strategies can be Employed to Detect the Oxidation or Reduction Mechanism of Cerium from the Ce L₃ Edge XAS/XANES or HERFD-XANES

**Main Edge Position and Intensity:** The classical way to approach the oxidation state identification at the Ce L₃ edge is to investigate the main edge transitions. The HERFD detection mode offers several advantages in this regard. The position of the white line or the main edge transitions in the incident energy direction indicates the Ce oxidation state.[59-61] As observed in Figure 1, there is a shift between the white line of Ce(III) (as seen in the case of CePO₄) and Ce(IV) (as seen in the case of CeO₂). During in-situ reactions, if oxidation or reduction occurs, the intensity of the white line starts to deviate.[15,26,62]

**Pre-edge Features:** A straightforward method involves examining the Ce L₃ pre-edge region. The HERFD data of the Ce(IV) systems will consistently show a single peak at an energy of 5718 eV (due to the 4f⁰ ground state configuration), while a double pre-edge structure indicates the presence of 4f¹ ground state configuration or Ce(III) oxidation state.[8,15,16,21] However, the position of the single pre-edge feature in Ce(IV) compounds can be variable for different cerium complexes. I will address these complexities in the following section.

**Multi-Electron (Post-edge) Excitations:** The presence of the multi-electron excitations in the Ce L₃ HERFD is a clear indication of the presence of the Ce(IV) oxidation state (and the 4f⁰ ground state configuration) in Ce compounds.[9,10,37] An increase in intensity in the post-edge region can be used to identify the presence of Ce(IV) from Ce(III). It should be noted here that my limited experience has never given me the opportunity to observe the presence of multi-electron excitations in pure Ce(III) systems. However, novel types of lanthanide(III) complexes with exotic ligands might exhibit very unusual electronic structures, where multiconfigurational interactions could play a role.

Overall, the best approach is to consider changes in all three XANES regions, which might take place during the reduction or

oxidation processes or while comparing the XANES shape on unknown cerium systems with references. Cafun and co-workers[15] recorded time-dependent Ce L₃ HERFD-XANES during the in-situ synthesis of CeO₂ nanoparticles from Ce(NO₃)₃·6H₂O. The data clearly show that the intensity of the Ce L₃ main edge decreases while CeO₂ nanoparticles are formed. The pre-edge structure indicates the presence of Ce(III) and Ce(IV) species during the reaction, and the intensity of the post-edge features (multi-electron excitations) is increasing, indicating a formation of Ce(IV) within the system. The final product of the reaction – CeO₂ nanoparticles – contains only Ce(IV) oxidation state. Nanoceria's versatile properties have led to a significant interest and exploration across multiple disciplines.[38,63-68]

Gasperi and co-workers[62] also reported Ce L₃ edge HERFD-XANES recorded in-situ on a Ce thin film with 2 ML thickness at different temperatures during thermal cycles in high vacuum and oxygen-rich atmospheres. The changes in the oxidation states from Ce(IV) to Ce(III) are observed in the pre-edge, main edge, and post-edge regions. Rueff and co-authors[34,69] conducted high-pressure in-situ studies on various Ce systems using RIXS and XANES in high-energy resolution mode. The region corresponding to multi-electron excitations was utilized to investigate the presence of the 4f⁰ configuration. It was one of the first ground-breaking in-situ experiments on Ce systems, which have enabled the recording of f-electron variations under the pressure. Lender and colleagues[70] recently conducted in-situ high-temperature HERFD-XANES measurements at the Ce L₃ edge on Ca₀.₅Ce₀.₅PO₄ to better understand the redox behavior of cerium during the incorporation of tetravalent Ce into the monazite structure. Changes were observed once again in the pre-edge, main edge, and post-edge regions.

Special attention has recently been given to the biogeochemical reactions involving cerium systems. Romanchuk and co-workers[22] reported evidence of oxidation and nanoparticle formation during Ce(III) sorption onto mineral birnessite surfaces. HERFD-XANES at the Ce L₃ edge was used to fingerprint the Ce oxidation state. Manceau and co-workers[25] employed HERFD-XANES to probe cerium in bioapatites from ocean-floor sediments. Additionally, the same group utilized HERFD detection mode to study fluorapatite minerals, demonstrating that EXAFS data[24] recorded in HERFD mode can elucidate the presence of other lanthanides in natural minerals, providing a straightforward approach to accessing crystal structure information of trace elements in complex natural materials.

It is important to mention, that in-situ reactions using X-rays can sometimes lead to radiation damage, especially when high-intensity X-rays are used for extended period. Radiation damage can result in structural changes, chemical transformations and even sample degradation. Figure 8 displays data recorded on CeF₄ under different X-ray exposure times, labelled 1, 2, and 3. This is an interesting example, where the formation of the Ce(III) takes place under the beam exposure, which can be seen in three regions of the HERFD-XANES Ce L₃ data. Firstly, the multi-electron excitations do not duplicate the Ce 5d splitting of the main edge transitions, indicating that CeF₄ has been reduced to Ce(III) after only a few seconds of exposure under the X-ray
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 8.** Ce L₃ HERFD - XANES spectra of CeF₄ recorded under different X-ray exposure times with the X-ray emission spectrometer set to the maximum of the Ce Lα₁ emission line and compared to the Ce L₃ HERFD spectra, calculated by ab-initio FEFF9.6 code.</figcaption></figure>

beam. There is a distinct peak on the low-energy side, which matches the position of the CeF₃ white line, depicted in Figure 8 as a Ce(III) reference. To investigate the potential Ce 5d splitting, the electronic structure calculations were conducted using the FEFF9.6 code. The results are presented at the bottom of Figure 8. Similar to CeO₂, the fresh CeF₄ system may exhibit a peak on the low-energy side (~5724 eV) due to Ce 5d crystal field splitting. However, the position of this peak coincides with the main edge of the Ce(III) reference. Data reported in Figure 8 indicates that CeF₄ has been reduced under the beam, as the intensity of this peak in the experimental data is much higher compared to theoretical predictions. Furthermore, the pre-edge structure provides clear fingerprint information regarding the mixed Ce(III)/Ce(IV) character of the damaged CeF₄ sample.

The mixed cerium systems have attracted considerable attention, and the exact quantitative estimation of the Ce(III)/ (IV) ratio remains one of the main tasks for many scientists. For many systems, this ratio can be determined through linear combinations analysis of known XANES or HERFD spectra from model or reference compounds. More sophisticated techniques, such as principal component analysis, can also be applied. However, such analyses must be conducted with special care, particularly when focusing on the main edge transitions.[67,68,71] As discussed earlier, the crystal field splits Ce 5d states differently depending on the local Ce environment. This means that the states belonging to Ce(III) and Ce(IV) may overlap, depends on the studied compounds. Moreover, the self-absorption effects in XANES data may affect the final interpretation.

The situation improves when the pre-edge structure is utilized in such quantitative analyses, as the shape of the pre-edge structure can be calculated by atomic multiplet theory, considering only the number of 4f electrons in the ground and excited states. However, it has been noticed that for the Ce(IV) systems, the pre-edge structure can shift towards the main edge depending on the local coordination near the Ce atom (see Figure 9). It should be also noted that the position of the HERFD pre-edge and main edge features strongly depends on the selected X-ray emission energy.[72] The data reported in Figure 8 were recorded at a fixed X-ray emission energy and a fixed X-ray spectrometer position.

This behaviour has been observed only in Ce(IV) compounds but has not been detected in Ce(III) systems up to now. I speculate that this observation may be directly linked to the empty 4f ground state of the Ce(IV) compounds. The pre-edge structure exhibits a single profile due to the 4f¹ configuration in the excited state; however, the promotion of the electron from the 2p to 5d levels causes a shake-up of the excited states, resulting in a detectable shift. The 4f¹ ground state, as in the case of Ce(III) systems, is less sensitive to such shake-up excitations. I find this experimental evidence quite intriguing, and it should be addressed in future studies, as there may be other phenomena that could explain the observed shifts.

Cafun and colleagues[15] were the first to report such an observation. The authors examined the oxidation state of colloidal nanoparticles using Ce L₃ HERFD-XANES and did not find any presence of Ce(III) in the systems. However, a pre-edge shift between bulk CeO₂ and CeO₂ nanoparticles was detected. This finding was later confirmed by Plakhova and co-workers[16] utilizing the HERFD-XANES approach, which showed that Ce(IV) is the sole oxidation state in colloidal nanoparticles. Simultaneously, they reported the observation of hydroxo-group formation at the surface of nanoparticles by analysing the Ce 2p-5d main transitions of CeO₂ nanoparticles under different

<figure><img src="image_19.png" /><figcaption>**Figure 9.** Ce L₃ HERFD - XANES spectra recorded in the pre-edge region on the number of Ce(III) and Ce(IV) references.</figcaption></figure>
<figure><img src="image_20.png" /></figure>

temperatures. Prieur and co-authors[21] reported an interesting observation by investigating *e*<sub>g</sub> and *t*<sub>2g</sub> transitions in CeO<sub>2</sub> nanoparticles of different size. They found that the *e*<sub>g</sub> feature intensity remains constant for both CeO<sub>2</sub> nanoparticles and bulk CeO<sub>2</sub>, while the *t*<sub>2g</sub> intensity is proportional to the particle size. This example demonstrates that the *t*<sub>2g</sub> orbital should be more sensitive to changes in the molecular environment or to distortions of the local structure and/or overlap with ligand orbitals. This phenomenon could be further expanded and investigated in the future through in-situ studies to better understand the electronic structure and spectroscopic properties of Ce-containing compounds.

Last but not least, the progress in theoretical simulations must be reviewed. Most theoretical codes, based on density functional theory, are capable of accurately reproducing XANES spectra in standard or HERFD modes for trivalent cerium compounds. HERFD-XANES reveals clear pre-edge structures, which can be modelled by codes based on atomic multiplet theory. The situation becomes more complicated for tetravalent cerium systems. All cerium systems with Ce(IV) oxidation state exhibit multi-electron excitations that standard codes struggle to reproduce. However, several groups have worked on code developments that provide users with the ability to reproduce XANES spectra for tetravalent cerium. Future directions in electronic structure calculations should focus on user-friendly codes that enable the reproduction of pre-edge, main edge, and multi-electron excitations in a single calculation.

Machine learning approaches have been heavily developed recently,[73-76] particularly for cases where quantitative XANES analysis is not straightforward. These approaches allow for the establishment of relationships between the edge position, white line intensity, and the shape and position of post-edge features, linking this information with the local and electronic structure of unknown compounds. While this methodology holds potential for application, it has not yet been applied to Ce L<sub>3</sub> XANES or HERFD-XANES.

## Conclusions

This article provides an overview of how Ce L<sub>3</sub> XANES spectroscopy can be utilized to investigate the electronic structure of cerium systems in a highly sophisticated manner. It addresses key questions, particularly regarding the oxidation state, ground state, electron occupation and local structure near the Ce atom, relevant to chemists working on the synthesis and application of cerium systems. I used the nominal term 'oxidation state' throughout the article, as this term is commonly used by chemists and material scientists. Understanding whether Ce(III) or Ce(IV) is present allows them to predict the chemical behaviour and reactivity of the investigated materials, understand the redox reactions and material properties. The oxidation state and electronic structure aspects are all accessible through experimental XANES data at the Ce L<sub>3</sub> edge. Furthermore, the HERFD mode offers additional advantages that need further exploration in combination with RIXS. Core-to-core and valence band RIXS methods offer great

potential to distinguish between mixed or single ground states, which are fascinating phenomena for physicists. The intriguing questions about the presence or absence of multi-electron excitations in the XANES data can be tackled with the help of RIXS. Given the high penetration depth of X-rays at the Ce L<sub>3</sub> edge, it is anticipated that many more in-situ reactions will be studied using these methods in the future. The advancements in electronic structure calculations, code developments, and the enhancement of user-friendly interfaces will facilitate data analysis.

## Methods

### Experimental Details

All XANES measurements in HERFD and TFY modes at the Ce L<sub>3</sub> edge were conducted either at the Rossendorf Beamline (BM20) of ESRF[77] or at the ID26 beamline of ESRF.[78,79] The incident energy was selected using the <111> reflection from a double Si crystal monochromator. Rejection of higher harmonics was achieved by two Rh mirrors working under total reflection at BM20 and by three Si mirrors at ID26. Johann-type X-ray emission spectrometers with five Ge(331) crystal analysers were used, either at BM20[11] or at ID26 beamlines.[12] Both instruments are very similar, with the only difference being beam size dimensions at the sample stage: ID26 has a smaller horizontal dimension of the beam (150 (v)×400 (h) µ²) and BM20 beam size is in order of 50 (v)×2000 (h) µ². The Ge <331> crystal analysers were chosen as one of the suitable reflections in the detection of the Lα<sub>r</sub> emission line of Ce (4839 eV). The sample, analyser crystal and photon detector (Ketek Detector) were arranged in a vertical scattering geometry. The spectra were recorded at a scattering angle of 90° in the horizontal plane with respect to the incident beam. A combined (incident convoluted with emitted) energy resolution of 0.8 eV was measured as half width at half maximum of the elastic scattering profile from the Kapton film at both beamlines. The total energy resolution is mainly defined by the resolution of the incident energy, the vertical beam size (in vertical geometry of X-ray emission spectrometer), and the quality of crystal analysers. Measurements were performed at room temperature. Ce-containing samples were sealed between two Kapton layers with 25 micron thickness. The initial reference materials were purchased from Sigma Aldrich and were used without dilution. Details about RIXS measurements can be found in previous publications[9,10].

### Theoretical Calculations

The XANES-HERFD spectra and the projected density of states were calculated with the ab-initio FEFF9.6 code,[58] based on the full multiple scattering theory. Scattering potentials are calculated by overlapping the free atom densities in the muffin tin approximation and then including the Hedin-Lundqvist self-energy for excited states. The Hedin-Lundqvist self-energy is used by default in the EXCHANGE card. The input file (feff.inp) was constructed by ATOMS program in Artemis software,[80] based on the structure of the CeO<sub>2</sub> (ICSD 88759), CePO<sub>4</sub> (ICSD 79748) and CeF<sub>4</sub> (ICSD 89621). The atomic potential is calculated self-consistently using a cluster of 8.0 Å radius. The theoretical HERFD-XANES spectra and projected density of states for all systems show a good agreement with experimental data. The reduction of the core-hole life time broadening was implemented to the EXCHANGE card in order to reproduce HERFD instead of XANES (EXCHANGE 0 0 -1). LDOS card was used when examining densities of states and for
<figure><img src="image_21.png" /></figure>

interpreting HERFD-XANES results. FEFF code will produce Idos00.-dat, Idos01.dat and other Idos0 N.dat files, which will correspond to the unique potential index, specified in POTENTIAL card. The absorbing Ce atom must be given unique potential index 0. Other atoms get further potential index. For example, the output of the CeO₂ calculations is written in 3 files: Idos00.dat for the central Ce atoms, calculated with a core hole, Idos01.dat for the other scattered Ce atoms and Idos02.dat for the O atoms. The effect of the core-hole can be studied by comparing the Idos00.dat and Idos01.dat outputs. Each Idos file generally contains several columns, named energy and *s*, *p*, *d*, *f* states. Figure 5 shows the Ce 5d states plotted at the bottom of calculations for clarity. The DOS for the central/absorbed Ce atom and scattered Ce atoms show different profiles, which indicate the importance of the core-hole effects in Ce L₃ XANES. The total 5d DOS corresponds to the sum of the Idos01.dat + 2*Idos02.dat and clearly reflects the shape of the HERFD calculations. The LDOS can be combined with any spectroscopy (not only XANES, HERFD, but EELS, XPS etc).

## Acknowledgements

The author would like to thank Pieter Glatzel, Sergei Butorin, Akio Kotani, Alexander Soldatov, Lucia Amidani for fruitful discussion on the electronic structure of CeO₂; David K. Shuh for providing cerocene sample; Tatiana Plakhova and Anna Roman-chuk for helpful discussion on chemistry, synthesis and reactivity of CeO₂ nanoparticles. Open Access funding enabled and organized by Projekt DEAL.

## Conflict of Interests

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

**Keywords:** Cerium · HERFD · XANES · Electronic structure calculations · RIXS

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Manuscript received: February 23, 2024

Accepted manuscript online: June 11, 2024

Version of record online: August 1, 2024