# Oxygen K-edge X-ray absorption spectra of ThO$_2$ and CeO$_2$: Experiment, interpretation, and structural effects

Lucia Amidani, Thomas Dumas, David Shuh, Sergei Butorin, Christoph Sahle, Alessandro Longo, Kristina Kvashnina

► To cite this version:

Lucia Amidani, Thomas Dumas, David Shuh, Sergei Butorin, Christoph Sahle, et al.. Oxygen K-edge X-ray absorption spectra of ThO$_2$ and CeO$_2$: Experiment, interpretation, and structural effects. Journal of Physical Chemistry C, 2023, 127 (6), pp.3077-3084. 10.1021/acs.jpcc.2c07771 .
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Lawrence Berkeley National Laboratory

**LBL Publications**

**Title**

Oxygen K-Edge X-ray Absorption Spectra of ThO2 and CeO2: Experiment, Interpretation, and Structural Effects

**Permalink**

https://escholarship.org/uc/item/461481t7

**Journal**

The Journal of Physical Chemistry C, 127(6)

**ISSN**

1932-7447

**Authors**

Amidani, Lucia
Dumas, Thomas
Shuh, David K
et al.

**Publication Date**

2023-02-16

**DOI**

10.1021/acs.jpcc.2c07771

**Copyright Information**

This work is made available under the terms of a Creative Commons Attribution-
NonCommercial License, available at https://creativecommons.org/licenses/by-nc/4.0/

Peer reviewed
Oxygen K-edge X-ray Absorption Spectra of ThO$_2$ and CeO$_2$: experiment, interpretation and structural effects.

Lucia Amidani,$^{1,2*}$ Thomas Dumas,$^3$ David K. Shuh,$^4$ Sergei M. Butorin,$^5$ Christoph J. Sahle,$^6$

Alessandro Longo,$^6$ Kristina O. Kvashnina$^{1,2*}$

$^1$The Rossendorf Beamline at ESRF – The European Synchrotron, 38043 Grenoble, France.

$^2$Helmholtz-Zentrum Dresden-Rossendorf, Institute of Resource Ecology, 01328 Dresden, Germany.

$^3$CEA, DES, ISEC, DMRC, Univ. Montpellier, 30207 Bagnols-sur-Cèze, France.

$^4$Lawrance Berkeley National Laboratory, Berkeley, California 94720, USA.

$^5$Condensed Matter Physics of Energy Materials, X-ray Photon Science, Department of Physics and Astronomy, Uppsala University, P.O. Box 516, SE-751 20 Uppsala, Sweden.

$^6$ESRF, The European Synchrotron, 71 Avenue des Martyrs, CS40220, 38043 Grenoble Cedex 9, France.

KEYWORDS. Actinides, XANES, thorium dioxide.
ABSTRACT. Experimental oxygen K-edge spectra of ThO₂ and CeO₂ are presented and interpreted based on density functional theory (DFT). The contribution of *d* and *f* orbitals to the O K-edge spectrum are identified as well distinguished peaks, the presence of which evidences the strong hybridization of Th and Ce metal centers with O orbitals. The sensitivity of the O K-edge to both *f*- and *d*-states in the absence of a core-hole on the metal ion results in an insightful overview of the electronic structure involved in the chemical bond. In particular, the large bandwidth of the Th 5f band as compared to the Ce 4f band is observed as a set of wider and more substantial set of peaks in the O K-edge, confirming the stronger hybridization of the former with O orbitals. The peak ascribed to the 5f band of ThO₂ is found at higher energy than the 6d band, as predicted from DFT calculations on actinide dioxides. To highlight the sensitivity and the potential use of the O K-edge for the characterization of ThO₂-based systems, the sensitivity of the spectrum to structural changes such as lattice expansion and size reduction are calculated and discussed.

INTRODUCTION. Understanding the physico-chemical properties of actinide materials will foster progresses in several fields of science. The quest for advanced nuclear fuel, the safe disposal of nuclear waste, preventing environmental contamination by radionuclides and promoting new applications of actinide materials are goals that require understanding the fundamentals of these materials.¹ One inherent characteristic that makes actinides unique is the presence of the 5f orbitals in the set of valence orbitals.²,³ From the accrued knowledge on actinides, we nowadays know that in the first half of the series, the 5f electrons participate to chemical bonding.³⁻⁷ Determining and
quantifying the involvement of 5f and 6d orbitals in actinide chemical bonds is currently of great
importance and interest,⁷⁻¹⁸ in particular for the enormous impact a rigorous understanding of the
chemical behavior of actinides could have on the field of separations chemistry. Few techniques
can access this information and a prominent role is played by XANES. In recent years, XANES at
the actinide M₄,₅ edges¹⁹⁻³² and at the ligand K-edge¹¹⁻¹⁴,³³⁻³⁹ has been largely used. While M₄,₅
edges probe directly the 5f orbitals, the ligand K-edge is sensitive to actinide 5f and 6d orbitals
only through their mixing with ligand p orbitals. XANES at the ligand K-edge involves transitions
of a 1s core electron, strongly localized on the ligand, to an unoccupied state of the allowed
symmetry. The presence at the K-edge of spectral features from the metal 5f/6d orbitals is only
possible if these states are involved in the unoccupied states probed by the photoelectron and
therefore it is a direct probe of orbital mixing.⁴⁰ Many ligand K-edges of interest are in the soft X-
ray regime and routine XANES measurements requires ultra-high vacuum (UHV). This represents
a difficult constraint for the safe manipulation of actinide materials and limits the access to soft X-
ray XANES for actinide research to a few high performance locations. The use of non-resonant
inelastic X-ray scattering (NIXS), which can access edges of a few tens to a few hundreds of eV
using hard X-rays, is a convenient possibility for ligand K-edge measurements on actinide
systems.⁴¹⁻⁴⁶ The similarity of K-edges in the soft X-rays measured with NIXS at low momentum
transfer and XANES is well assessed⁴⁷,⁴⁸ as also demonstrated by measurements at the O K-edge
of CeO₂ presented in this work.

To extract information on the electronic structure from XANES at the ligand K-edge, a correct
interpretation of the spectra is essential. DFT<sup>11-14,37-39,49</sup> and sophisticated quantum chemistry
approaches<sup>15</sup> were successfully used to interpret the ligand K-edge XANES on actinide molecular
systems and to quantify the mixing of 4f orbitals in lanthanide dioxides.<sup>49,50</sup> The projected density
of states (DOS) obtained with density functional theory (DFT) were used to identify the 5f
contribution to the O K-edge XANES of bulk UO₂, NpO₂ and PuO₂³⁵,³⁶. Surprisingly, the O K-
edge XANES of ThO₂ has never been the focus of accurate interpretation and is rarely encountered
in literature.⁵¹,⁵² This work fills this gap by reporting experimental O K-edge XANES of ThO₂ and
its interpretation based on theoretical calculations. The results on ThO₂ are compared with the
well-known case of CeO₂ and with literature data on light-actinide dioxides. To highlight the
sensitivity of O K-edge XANES to structural changes, we theoretically investigate the effects on
the spectra of lattice expansion and of size reduction. Our results i) confirm that the 5f band is
higher than the 6d band in ThO₂, as predicted by DFT calculations,⁵³,⁵⁴ ii) indicate that both 6d
and 5f Th orbitals are strongly involved in bonds with O, iii) predict a high sensitivity of the O K-
edge XANES to structural modifications.

METHODS.

SYNTHESIS AND MEASUREMENTS OF ThO₂. Thorium dioxide was synthesized using an oxalic conversion route. Thorium nitrate, Th(NO₃)₄·5H₂O, was used as precursor. The oxalate precipitate was synthesized in a vortex reactor (V = 20 mL) under ambient conditions by mixing a solution of Th(IV) ([Th(IV)] = 0.135 M) and a concentrated H₂C₂O₄ solution (with a slight excess of oxalic acid [H₂C₂O₄] = 0.05 M) in nitric medium ([HNO₃] = 2 mol.L⁻¹).⁵⁵⁻⁵⁷ The time of addition of the actinide solution and oxalic acid solution was fixed at 3 minutes. The resulting crystallized powders, Th(C₂O₄)₂·6H₂O, were filtered after 10 min of maturation and dried at room temperature. The oxide was formed by calcination under air. The temperature was raised at a rate of 5°C.min⁻¹ up to 600°C and the sample was left one hour at the maximum temperature.
The O K-edge XANES of ThO₂ was acquired at the Molecular Environmental Science (MES) Beamline 11.0.2 of the Advanced Light Source (Lawrence Berkeley National Laboratory, USA) equipped with a scanning transmission X-ray microscope (STXM).⁵⁸ The available energy range was approximately 100–2000 eV and the energy resolution of the measurements was less than 0.1 eV at the O K-edge. For the STXM measurements, the ThO₂ powder was sandwiched between two Si₃N₄ windows and the STXM chamber filled with He. Transmitted X-rays were measured as a function of the sample position (synchronized by an interferometer) to obtain X-ray images by optical density contrast. Image resolution was determined by the 25 nm zone plate and position steps. Elemental maps and NEXAFS spectra were obtained using image sequence scans over different photon energy ranges (520 eV to 600 eV for O K-edge) using the STAKS procedure implemented in the aXis2000 software.⁵⁹ Spectra at particular regions of interest in the sample were selected (regions allowing enough transmitted photons to be detected and excluding regions for which the optical density was too high to be in the Beer–Lambert’s law linear regime). The images extracted from the “stack”, which is a collection of images recorded at different photon energies close to the absorption edge, were then normalized with a virtual incident beam intensity measured through sample-free regions of the Si₃N₄ windows.

## MEASUREMENTS OF CeO₂
Cerium dioxide was acquired from Alfa Aesar and prepared as a sintered pellet for measurements. The O K-edge XANES was recorded at beamline 7.0.1 of the Advanced Light Source (ALS)⁶⁰ of Lawrence Berkeley National Laboratory in total electron yield (TEY) mode. The monochromator resolution was about 0.3 eV.

The O K-edge of CeO₂ measured with NIXS was acquired at the ID20 beamline of the ESRF, Grenoble. Photons from three U26 undulators were monochromatized by a high-heat-load Si(111) monochromator and a successive Si(311) channel-cut monochromator and focused to a spot size
of 20 x 20 µm² at the sample position using a Kirkpatrick-Baez mirror system. The large solid
angle spectrometer⁶¹ was used and 36 out of 72 spherically bent Si(660) crystal analyzers recorded
inelastically scattered photons with energy losses in the vicinity of the O K-edge. O K-edges were
measured at momentum transfers of 3.5 Å⁻¹ and 9.5 Å⁻¹. The overall energy resolution was 0.7 eV.
All data were extracted and treated as described in ⁴².

THEORETICAL CALCULATIONS. O K-edge XANES were calculated with the FDMNES⁶²⁻
⁶⁵ and FEFF9⁶⁶,⁶⁷ codes and very good agreement with the experimental data was obtained from
both codes. Because FDMNES allows analysis of the different components of the projected
densities of states (DOS) and provides crystal orbital overlap populations (COOP),⁶⁸ only
FDMNES results are reported in the main text while FEFF9 results are shown in the
Supplementary Information (SI) for completeness. FDMNES is a self-consistent *ab initio* code
based on the local-density approximation (LDA) DFT to calculate spectra related to the X-ray
absorption process. It accounts for relativistic and spin-orbit effects and the presence of a core-
hole. It implements two methods for calculations, the multiple-scattering theory (MS) and the finite
difference methods (FDM). All calculations shown here were obtained with the FDM, which gives
more precise results for the near-edge region. The potential was calculated self-consistently within
a radius of 7 Å around the absorber and the same radius was used for the FDM calculations.
Projected DOS are calculated with the atomic sphere approximation together with the XANES
spectra. We additionally calculated the COOP. Relativistic and spin-orbit effects were included.
The parameters for the convolution step were kept at the default value of the code. Only the core-
hole lifetime was increased to 0.5 eV from 0.3 eV⁶⁹ to have better agreement for the width of the
first sharp peak. To test the effect of the core-hole on the spectral shape, we ran calculations with
and without the core-hole. We found only slight changes induced by the core-hole and we therefore
report calculations obtained with a non-excited absorber. The negligible effect of the core-hole
derives probably by the dominance of Th DOS in the peaks at the O K absorption edge, as will be
explained in the results and discussion section. To evaluate the effect of lattice expansion, the
lattice constant was increased from 5.6032 Å to 5.6632 Å. To evaluate the effect of size reduction,
the atomic coordinates of a spherical nanoparticle of 2.1 nm diameter were isolated from a ThO₂
slab. The spectra of the non-equivalent O atoms in the nanoparticle were obtained within a single
calculation run to have the calculated spectra aligned to a common Fermi energy.

## RESULTS AND DISCUSSION.
ThO₂ and CeO₂ crystallize in the fluorite structure, with O surrounded by 4 metal ions in T_d local coordination and the metal ion surrounded by 8 O ions in cubic symmetry, i.e. arranged at the corner of the cube centered on the metal ion. In a cubic crystal field the *d* orbitals splits into a double-degenerate *e_g* and a triple-degenerate *t*₂g manifold, with the *e_g* states at lower energy than the *t*₂g states. The order is reversed compared to an octahedral crystal field, where the 6 ligands are along the axial directions.⁷⁰ A schematic of the splitting from cubic and octahedral crystal fields is shown in Figure S1. Figure 1 reports experimental data and calculation results for ThO₂ (panel a) and CeO₂ (panel b). The O K-edge XANES of ThO₂ was obtained in transmission mode from STXM. The two spectra of CeO₂ are from XANES collected in the TEY mode and a NIXS measurement. Theoretical calculations of spectra, projected DOS and COOP obtained with the FDMNES code are reported below the experimental data. The energy scale of experimental data is reported on the top axis while the bottom axis refers to the Fermi energy of calculations.

The O K-edge of both ThO₂ and CeO₂ are characterized by three prominent features, with the
former having an additional weak feature riding on the low-energy side of the second prominent
peak. For ThO₂ the first peak is extremely sharp and intense; the middle peak is weaker and more structured with the low-energy small feature; and the third is intense and broad. For CeO₂, NIXS and XANES measurements are similar and characterized by two sharp peaks and a broader third one. The agreement between the calculated XANES with the experimental spectral shapes is very good for both systems, with relative intensities and energy positions of the peaks well reproduced. Despite the similarities of the two spectra, the interpretation of peaks is different resulting from the differences in the relative ordering and energy spread of the *f* and *d* orbitals, as revealed by inspection of the projected DOS and COOP.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Experimental data (empty dots/squares) and O K-edge spectra calculated with FDMNES (thick black lines) of ThO₂ (panel a) and CeO₂ (panel b). For ThO₂, the experimental spectrum is a XANES obtained in transmission mode from STXM. For CeO₂, two spectra are shown, one obtained with NIXS (empty squares) and a XANES acquired in total electron yield (TEY). For both panels, below the calculated spectrum, the following results are reported: the O p DOS (black thin line); the COOP between O p and Th/Ce *d* and *f* orbitals (red thin line and blue thin line,</figcaption></figure>
respectively); the *e*<sub>*g*</sub> (yellow thin line) and *t*<sub>2g</sub> (light-blue thin line) components of Th/Ce d-DOS;
and the Th/Ce f-DOS (blue thin line).

As expected, all features of the calculated spectrum strongly correspond to structures found in
the calculated O *p* DOS, which is shown below the simulated spectra in Figure 1. For a more
detailed figure and labeling of the results, see Figure S2 in the Supplementary Information (SI). A
first indication of which Th (Ce) orbitals contribute to the O K-edge spectrum is given by the
position of the projected 5f (4f) and 6d (5d) bands of Th (Ce) with respect to the features of the
O *p* DOS. In Figure 1 the metal *f*-DOS is shown in blue and the *d*-DOS is reported as the sum of
the *e*<sub>*g*</sub>-*t*<sub>2g</sub> components (yellow and light-blue, respectively), resulting from the cubic crystal field
(see Fig. S1). The ThO<sub>2</sub> 5f DOS forms a broader band than that from the 4f DOS of CeO<sub>2</sub>. This
follows from the larger radial extent of the 5f allowing their participation in chemical bonds, and
are found correspondingly in the middle peak of the O K-edge spectrum. Contrasting to this
behavior, the sharper 4f band of CeO<sub>2</sub> corresponds to the first sharp peak in the O K-edge spectrum.
In both systems, the *d*-DOS splits into *e*<sub>*g*</sub> and *t*<sub>2g</sub> components in a similar manner. The *e*<sub>*g*</sub> band is
the sum of two identical contributions from the *d*<sub>z<sup>2</sup></sub> and the *d*<sub>x<sup>2</sup>-z<sup>2</sup></sub> components and the *t*<sub>2g</sub> band is
the sum of three identical contributions from *d*<sub>xz</sub>, *d*<sub>yz</sub> and *d*<sub>xy</sub>. The *e*<sub>*g*</sub> band is composed of three
sharp peaks at the low energy side of the broad *t*<sub>2g</sub> band, reflecting the stronger hybridization of
the *t*<sub>2g</sub> with the O ligands from the spatial orientation of the lobes, which gives stronger
superposition with the O orbitals. The main difference between the ThO<sub>2</sub> and CeO<sub>2</sub> spectra are the
larger separation of the *e*<sub>*g*</sub> peaks in ThO<sub>2</sub>. Comparison with the O *p* DOS reveals that in ThO<sub>2</sub> the
first peak of the *e*<sub>*g*</sub> DOS corresponds to the first very sharp peak of the O *p* DOS. Similarly, in
CeO<sub>2</sub> the same *e*<sub>*g*</sub> peak is found to correspond to the second sharp peak of the O *p* DOS. The broad
t<sub>2g</sub> band corresponds to the third broad feature of the O p DOS in both systems. Assignment of the peaks can be finalized by inspection of the hybridization as given by the COOP, also shown in Figure 1. The positive, negative and null COOP correspond to bonding, antibonding and non-bonding interactions, respectively. Inspection of the p-d COOP (red) indicates bonding character for the first sharp e<sub>g</sub> peak, non-bonding interaction with the other e<sub>g</sub> peaks and antibonding character for the broad t<sub>2g</sub> band in both CeO<sub>2</sub> and ThO<sub>2</sub>, with the distinction that the hybridization with the e<sub>g</sub> component of the d-DOS yields the first peak in ThO<sub>2</sub> spectrum and the second peak in the CeO<sub>2</sub> spectrum. The antibonding interaction with the t<sub>2g</sub> band gives rise to the third peak of the XANES spectra in both systems. Inspection of the *p*-*f* COOP (blue) reveals a predominant antibonding interaction corresponding to the *f*-DOS of both systems, from which the middle and first XANES peak in ThO<sub>2</sub> and CeO<sub>2</sub> originate, respectively. A *p*-*f* bonding interaction is also present in corresponding to the e<sub>g</sub> contribution, where the *f*-DOS is absent or very weak. This weak contribution may be due to the limits of the local-density approximation (LDA) DFT in treating localized orbitals like the *f*. The tendency is to overestimate their delocalization and as consequence their mixing with other orbitals.

The interpretation of the O K-edge XANES spectra of CeO₂ emerging from our calculations is in agreement with previous works⁵⁰,⁷¹,⁷² and the recent review by Frati et al.,⁶⁹ while the interpretation of ThO₂ O K-edge spectra based on spectral calculations is given here for the first time. The hybridization of O *p* orbitals with both Th (Ce) 6*d* (5*d*) and 5*f* (4*f*) orbitals makes the O K-edge a unique probe of the metal electronic structure, where all the orbitals relevant to the bonding are probed in a single energy regime without the perturbation of a core-hole localized on the metal center. Our calculations indicate that the O K-edge XANES of CeO₂ and ThO₂ reflect the ordering of *f* and *d* states expected for lanthanides and actinides.⁵³,⁵⁴ In CeO₂ and in all
lanthanide dioxides, the 4f orbitals are lower than the 5d and form sharp bands due to the strong
localization and weak interaction of the 4f. Differently, the ThO₂ 5f states are predicted to be
slightly higher than the 6d states.⁵³ The energy of the 5f states progressively decreases along the
actinide series, with the crossover at PaO₂, making ThO₂ the only actinide dioxide with 5f orbitals
higher than 6d. Indeed, this ordering is confirmed by the O K-edge spectra of UO₂, NpO₂, and
PuO₂ where the contribution of the 5f states is at the absorption edge, just before the peak of the
An 6d-e_g contribution.³⁶

The stronger involvement of Th 5f orbitals in chemical bonding compared to Ce 4f is also clearly
visible in the experimental O K-edge XANES spectra. The peak corresponding to the 4f orbitals
of CeO2 (first) is sharper than that due to the 5f orbitals of ThO2 (middle). The projected f-DOS
indicate that the Ce 4f forms a much sharper band than the Th 5f, because of the larger
delocalization of the latter. These assignments are compatible with FEFF⁶⁷ calculations, reported
in Figures S3 – S4 of the SI.

Lastly, the O *p* DOS hybridize with only part of the metal *d* DOS of *e*<sub>g</sub> and *t*<sub>2g</sub> nature as indicated
by comparison of the DOS shapes. For the *e*<sub>g</sub> contribution, this is clearly seen as only one peak of
the *e*<sub>g</sub> band appears in the O *p* DOS. Correspondingly in the *t*<sub>2g</sub>, the *p* DOS has a contribution only
at the higher energy part of the band. These details can be better observed in Figure S2.

Through the O K-edge XANES, the metal *d* and *f* contribution to chemical bonds can be probed
at once and in the absence of a core-hole localized on the metal ion. The O K-edge is therefore
expected to be quite sensitive to structural modifications. Theoretical calculations can help in
rationalizing how spectral features react to structural changes and guide the interpretation of data
on complex systems. With this scope, we investigated the effects of lattice expansion and size
reduction on ThO₂ by theoretical calculations. We focused on ThO₂ because of the stronger overlap of Th 5f and O 2p.

A variation of the lattice parameter is very frequently encountered in mixed metal oxide materials. In mixed actinide oxides, the lattice parameter varies linearly between that of the two end members<sup>73</sup> according to Vegard's Law while in ThO<sub>2</sub> nanoparticles of 2 nm size a 1% lattice expansion was recently reported.<sup>74,75</sup> Lattice variations are easily identified with X-ray diffraction (XRD). However, since XRD measures an average property of the system, the uniform variation of the lattice parameter does not correctly describe the local arrangement, as often evidenced when XRD and the results from extended X-ray absorption fine structure spectroscopy (EXAFS) are compared.<sup>73</sup> It is therefore interesting to see how the O K-edge XANES would be modified by lattice alterations. Figure 2 shows the calculated O K-edge XANES spectra for ThO<sub>2</sub> and for ThO<sub>2</sub> with 1% lattice expansion applied, corresponding to that observed for small nanoparticles.<sup>74</sup> The spectra have been aligned to the post-edge features, thus only relative energy positions are meaningful and comparable. The calculations predict that the three prominent peaks towards the edge threshold in the 1% expanded ThO<sub>2</sub> spectrum will get closer in energy. In particular, the third peak appears less affected since the relative distance from the post-edge features and the shape remain almost the same. On the other hand, the first and middle peaks get closer to each other. The first peak decreases significantly in intensity while the middle peak acquires intensity and sharpness. This behavior is consistent with the expected reaction of the electronic structure to a lattice expansion. The e<sub>g</sub> - t<sub>2g</sub> splitting of 6d orbitals will decrease due to the weakening of the crystal field. For the same reasons, the width of the 5f band manifold is reduced from the decreased interaction with ligand orbitals. This behavior is reflected in the reduced energy separation of the first and third peaks and in the sharpening of the middle peak. The corresponding DOS are reported
in Figure S5 in SI. This is the scenario expected in case of a uniform expansion like the one
described by the virtual crystal approximation. However, in the presence of pronounced local
distortions, a broadening of spectral features is anticipated due to the presence of absorbers with
different local configurations, which will yield different spectra.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Calculated O K-edge XANES spectra for ThO₂ (black empty dots) and ThO₂ with a 1% lattice expansion (red empty dots) obtained with FDMNES.</figcaption></figure>

The latter scenario can be partially considered by analyzing a nanoparticle, where the surface
breaks the symmetry of the bulk creating a set of non-equivalent O absorbers. We considered a 2.1
nm spherical nanoparticle of ThO₂ and, in analogy with our previous work on ThO₂ nanoparticles
at the Th L₃ edge,⁷⁶ we simulated the O K-edge XANES spectrum of the non-equivalent O
absorbers. The nanoparticle structure was isolated from a chunk of bulk ThO₂. Surface
reorganization and interaction with surfactants were neglected. The results reflect effects of the
surface and the reduced size as the consequences of symmetry break and lack of scatterers for a portion of absorbers. The results are shown in Figure 3, where 10 calculated spectra corresponding to the 10 non-equivalent O atoms in the nanoparticle are compared. The nanoparticle structure is shown in the inset together with absorbers near the surface identified. The local environment of all O atoms in the nanoparticle is schematically shown in Figure S6 of the SI. Absorbers 1 through 4 are inside the nanoparticle (first and second coordination shells as in bulk $ThO_2$); 5 and 6 are subsurface O atoms (second coordination shell different from bulk $ThO_2$); and 7 through 10 are surface atoms (first coordination shell different from bulk $ThO_2$). The three peaks characteristic of the O K-edge XANES spectra from bulk $ThO_2$ are well-distinguished for absorbers 1 through 6. Starting from the surface atoms, i.e. absorber 7, the first sharp peak is lost and the spectrum shows only two broad structures. The XANES spectra for all non-equivalent absorbers were obtained from a single calculation in order to have the spectra aligned to a common Fermi level. Because errors in the calculated Fermi energy of up to 1 eV are common in codes like FDMNES, the relative alignments have to be considered as qualitative. For absorbers 10 and 8, some low-energy peaks are observed well-below the main absorption edge. They appear because the calculated Fermi level is inside the occupied DOS. Both DOS and Fermi level are not accurately calculated because of the poor description of the structure at surface. Overall, the calculated spectra in Figure 3 indicate that O K-edge XANES spectra are very sensitive to changes in local coordination.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** O K-edge XANES calculated with FDMNES for the 10 non-equivalent absorbers from a 2.1 nm nanoparticle of ThO₂. The nanoparticle structure and the O absorbers close to the surface are shown in the inset.</figcaption></figure>

The O K-edge XANES spectra obtained by the weighted average of the non-equivalent absorbers is shown in Figure 4 together with the calculated XANES of bulk ThO₂ and of the oxygen at the center of the nanoparticle. The spectrum of the nanoparticle exhibits a much less intense first peak with broader features. As suggested by Figure 3, this is due to the contribution of surface atoms,
which represent 43% of all O atoms of the nanoparticle. This result is in agreement with the O K-edge data on ThO₂ nanoparticles embedded in a covalent organic framework by Moreau et al.,⁵¹ where the first sharp peak observed on bulk ThO₂ is not present on the spectrum of NPs.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** O K-edge XANES calculated with FDMNES for bulk ThO₂ (black), the central O atom of the 2.1 nm nanoparticle (blue) and the weighted average of all O absorber in the nanoparticle (red).</figcaption></figure>

As expected, calculations predict a high sensitivity of O K-edge XANES spectral features to structural changes of ThO₂. Real systems can be characterized by complex structural changes, with the simultaneous presence of local distortions, changes of local coordination and of the lattice parameter. It is therefore desirable to construct a structural model as close as possible to the real system to extract information from O K-edge XANES spectra with the help of calculations especially in the cases of reduced dimensionality.
CONCLUSIONS.

The O K-edge XANES spectra of ThO₂ and CeO₂ are presented and interpreted based on DFT spectral calculations and inspection of the electronic structure. Spectral features derived from metal *d* and *f* states are clearly visible and form well-separated peaks, a direct proof of their hybridization with O orbitals. In CeO₂ the 4f-band appears below the 5d, while in ThO₂ the 5f-band is found between the 6d *e*<sub>g</sub> and t<sub>2g</sub> states, in agreement with the expected ordering of 5f and 6d orbitals in actinide dioxides. Comparison with the O K-edge spectra of CeO₂ and other early actinide dioxides confirms the assignment of spectral features and agrees with the predicted electronic structure of these systems.

Calculated O K-edge XANES for a 1% expansion of the lattice parameter and for a ThO2
spherical nanoparticle of 2.1 nm diameter indicate a high sensitivity to structural changes. The
change in local coordination of surface atoms gives more drastic spectral change and results in
strong broadening and lowering of intensities from the main spectral features.

The insight given by O K-edge XANES spectra on the electronic structure of both ligand and metal is very promising for the study of lanthanide and actinide systems. The possibility to measure the O K-edge XANES spectrum with NIXS, which employs hard X-rays, is important for the actinide field as it avoids some difficulties that accompany and make soft X-ray XANES as well as electron-energy loss spectroscopy (EELS) complicated. Thus, NIXS presents a very promising avenue and means to measure O K-edge NIXS spectra on actinide compounds.

ASSOCIATED CONTENT

**Supporting Information.** Additional calculations performed with FEFF, scheme of the local environment of each O atom in the 2.1 nm nanoparticle. (PDF)
# AUTHOR INFORMATION

## Corresponding Author

*lucia.amidani@esrf.fr; kristina.kvashnina@esrf.fr

## Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

## ORCID

Lucia Amidani 0000-0003-2234-4173
Thomas Dumas 0000-0001-6425-6484
David K. Shuh 0000-0002-3104-3260
Sergei M. Butorin 0000-0003-3242-5305
Christop J. Sahle 0000-0001-8645-3163
Alessandro Longo 0000-0002-8819-2128
Krisitna O. Kvashnina 0000-0003-4447-4542

## Notes

Any additional relevant notes should be placed here.

## ACKNOWLEDGMENT

L. A. acknowledges Yves Joly for useful discussions. We acknowledge support from the European Research Council (ERC) under grant agreement No. 759696. This work was supported in part by the U.S. Department of Energy (DOE), Director, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences Heavy Element
Chemistry Program under Contract No. DE-AC02-05CH11231 at LBNL (DKS). This research
used resources of the Advanced Light Source, a U.S. DOE Office of Science User Facility under
contract no. DE-AC02-05CH11231. S.M.B acknowledges the support from the Swedish Research
Council (research grant 2017-06465).
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