
==== Front
J Am Chem Soc
J Am Chem Soc
ja
jacsat
Journal of the American Chemical Society
0002-7863
1520-5126
American Chemical Society

39241121
10.1021/jacs.4c07459
Article
The Counterintuitive Relationship between Orbital Energy, Orbital Overlap, and Bond Covalency in CeF62– and CeCl62–
https://orcid.org/0000-0002-3523-0303
Branson Jacob A. †‡
https://orcid.org/0000-0001-5575-4895
Smith Patrick W. ‡
https://orcid.org/0000-0001-6570-5245
Sergentu Dumitru-Claudiu §∥
https://orcid.org/0000-0003-4014-9216
Russo Dominic R. †‡
https://orcid.org/0000-0001-9843-3020
Gupta Himanshu #
Booth Corwin H. ‡
https://orcid.org/0000-0001-9671-227X
Arnold John †‡
https://orcid.org/0000-0002-8143-6206
Schelter Eric J. #
https://orcid.org/0000-0001-9392-877X
Autschbach Jochen *⊥
https://orcid.org/0000-0003-1346-7497
Minasian Stefan G. *‡
† Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
‡ Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
§ RA-03 (RECENT AIR) Laboratory, Alexandru Ioan Cuza University of Iaşi, Iaşi 700506, Romania
∥ Faculty of Chemistry, Alexandru Ioan Cuza University of Iaşi, Iaşi 700506, Romania
⊥ Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260, United States
# P. Roy and Diana T. Vagelos Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
* Email: jochena@buffalo.edu.
* Email: sgminasian@lbl.gov.
06 09 2024
18 09 2024
146 37 2564025655
01 06 2024
21 08 2024
20 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

The 4f orbitals of Ce(IV) have shown appreciably enhanced covalent mixing with ligand orbitals relative to those of Ce(III). Here, X-ray spectroscopy, magnetic susceptibility measurements, and theoretical methods are used to investigate 4f covalency in CeF62– and CeCl62–. These techniques show covalent mixing between Ce 4f and F 2p orbitals to be about 25% less than mixing between Ce 4f and Cl 3p orbitals, placing CeF62– among the most ionic Ce(IV) compounds to-date. However, ligand field analysis using the experimental data shows significantly higher 4f orbital overlap with the F 2p orbitals compared to the Cl 3p. This result is counterintuitive since the Ce–F bonds display less 4f covalency despite their higher orbital overlap, and greater overlap is traditionally associated with enhanced bond covalency. The weaker covalency is attributed to the large energy gap between Ce 4f and F 2p orbitals strongly counteracting the higher orbital overlap. These results highlight that only a concerted consideration of both atomic orbital overlap and energy matching in f-element systems leads to an accurate picture of their bonding.

Basic Energy Sciences 10.13039/100006151 DE-SC0020169 Universitatea Alexandru Ioan Cuza din Ia?i 10.13039/100021028 127324 SLAC National Accelerator Laboratory 10.13039/100011664 DE-AC0276SF00515 Lawrence Berkeley National Laboratory 10.13039/100006235 DE-SC0020169 Lawrence Berkeley National Laboratory 10.13039/100006235 DE-AC0205CH11231 document-id-old-9ja4c07459
document-id-new-14ja4c07459
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pmcIntroduction

Cerium holds a unique position among the other lanthanide elements because it can access the tetravalent (4f0) oxidation state in a wide range of chemical environments. In its trivalent state, spectroscopic and computational techniques have shown that the Ce 4f orbitals are core-like and only weakly involved in covalent bonding.1−4 Conversely, 4f covalency is frequently invoked in descriptions of chemical bonding for tetravalent Ce compounds.5−10 This versatility in accessible redox states and modes of chemical bonding has enabled a wide range of reactivity in Ce compounds including C–C bond activation, photocatalysis, and oxygen transfer.10−20 For Ce intermetallic compounds, strong electron correlations can have a significant impact on electronic structure and lead to properties such as heavy fermion behavior, Kondo magnetism, superconductivity, and intermediate Ce valency.21−25 Because of these unique electronic properties, Ce compounds have found technological applications in fields from catalysis and petroleum refinement to national security.26 Consequently, it is of increasing importance to develop improved models of Ce electronic structure that can provide a means to control its physical properties rationally.

A state-of-the-art approach to probing bond covalency applies X-ray spectroscopic techniques in tandem with electronic structure calculations. Cerium L3-edge (2p3/2 → 5d5/2) X-ray absorption spectroscopy (XAS) has been established as a versatile tool for probing the amount of 4f-electron density residing on a Ce(IV) ion.27−31 The L3-edge spectra exhibit features corresponding to a Ce(III)/Ce(IV) configuration interaction (CI) in the ground state and/or the probed core-excited states. Sergentu et al. have shown that both types of states have to be considered to evaluate the ground-state electronic structure correctly.32 From the relative intensities of the CI features, the effective number of Ce 4f electrons is determined as a value called nf. In addition to this metal-centered technique, measuring X-ray absorption spectra at the K-edge for ligand donor atoms, a technique known as ligand K-edge XAS, provides complementary insight into the metal–ligand covalency.33−35 Ligand K-edge XAS transitions occur from 1s orbitals localized on the ligand into molecular orbitals (MOs) formed by mixing of valence ligand np atomic orbitals (AOs) with metal AOs.36,37 This mixing is typically interpreted in terms of covalent bonding. The intensity of a pre-edge transition can be used to determine the amount of ligand p-orbital character in the acceptor MO, λ2. Specifically, λ2 represents the population of a ligand AO in the MO and is related to t′, the mixing coefficient, corresponding to the weight of the ligand AO in the MO. The value λ2 includes all the electron density associated with the ligand (t′2) and half that in the region of metal–ligand orbital overlap (t′SML). From perturbational MO theory, larger values of λ2 (and t′2) can be achieved both by increasing the amount of orbital overlap (SML = ∫φM*φL dV) and also by decreasing the energy difference between the AOs.38−41 It is important to note that t′2 alone cannot be evaluated with ligand K-edge XAS, as this value alone is not associated with total ligand electron density.

In the present study, fluorine K-edge XAS is used to evaluate orbital mixing and overlap in CeF62–. We chose CeF62– for comparison to the previously studied CeCl62–. Since the ligand orbital energies of these complexes can be associated with their known ionization potentials, the electronic structures can be evaluated confidently within a ligand field model. By comparing these isostructural species with analogous techniques, rigorous comparisons of bond covalency, bond stabilization, and orbital overlap can be made. Results from ligand K-edge XAS are corroborated by Ce L3-edge and M4,5-edge XAS, SQUID magnetometry, spectral simulations, and ground-state electronic structure calculations. We adopted this breadth of methodologies to form a very precise data set and in order to calibrate these measurements of covalency to one another. Together, these techniques reveal CeF62– as among the (if not the) most ionic Ce(IV) compounds. However, overlap analysis from the ligand K-edge XAS spectra of this CeF62– compared to the reported CeCl62– finds significantly greater 4f-ligand AO overlap in the Ce–F bond compared to the Ce–Cl bond, despite the less covalent nature of the Ce–F bond.

Results

Synthesis and Initial Characterization

For this spectroscopic study, well-isolated CeF62– units with noncoordinating countercations are desirable to ensure that the Ce–F bonds were probed directly. Though (Et4N)2CeF6·6H2O has been reported,42 the presence of water molecules could perturb with the Ce–F interactions via H-bonding. Therefore, a new anhydrous CeF62– salt with Ph4P+ countercations was prepared as a colorless crystalline solid in 79.5% yield from (Et4N)2CeF6·6H2O and two equivalents of Ph4PCl. X-ray quality crystals for a single crystal X-ray diffraction study were grown by vapor diffusion of diethyl ether into an acetonitrile (MeCN) solution (Figure 1). The structure of (Ph4P)2CeF6 has three unique Ce–F distances at 2.1599(14), 2.1456(12) and 2.1490(12) Å. The average Ce–F distance in (Ph4P)2CeF6 is 2.152(6) Å, which is similar to the average Ce–F distance of 2.148(10) Å reported for (Et4N)2CeF6·6H2O.42

Figure 1 Crystal structure of (Ph4P)2CeF6 (50% probability ellipsoids). Ph4P+ cations and co-crystallized MeCN are omitted for clarity.

The UV–vis spectrum of (Ph4P)2CeF6 in MeCN (Figure S3) shows multiple features resulting from coincident transitions associated with the CeF62– anion and Ph4P+ cations. However, the inflection point of the intense UV absorption band at 5.1 eV can be regarded as the lower bound of the LMCT energy, which agrees with the HOMO–LUMO gap determined from ground state electronic structure calculations, 5.99 eV (see Supporting Information). Vibrational spectroscopy shows an IR-active peak at 438.7 cm–1 (Figure S4) and a Raman-active peak at 528 cm–1 (Figure S5), which are assigned to the CeF62– octahedron. Previous studies on HfF62– and HfCl62– showed that the HfF62– vibrations are observed at higher energies relative to the HfCl62– vibrations owing to the higher mass of Cl.43−45 Hence, by comparison to vibrational data published for CeCl62– where ν1 and ν3 modes were identified at 295 and 268 cm–1,46 the peaks at 528 and 438.7 cm–1 in the vibrational spectra of CeF62– were assigned to ν1 and ν3 modes, respectively. A solution 19F NMR spectroscopy experiment on (Ph4P)2CeF6 recorded in CD3CN exhibited a peak at 180.7 ppm (externally referenced against CFCl3). Cyclic voltammetry (CV) of (Ph4P)2CeF6 in MeCN showed no reversible redox features (Figure S6), suggesting that it was redox inactive within the electrochemical window of MeCN.

Comparison of the UV–vis and CV data reported here for CeF62– versus those for CeCl62– provides an initial evaluation of the electronic structure of these complexes. For CeCl62–, the lowest energy LMCT from UV–vis is at 3.3 eV2 and a reversible CeCl62–/CeCl63– redox couple is observed at E1/2 = −0.03 V13 versus Fc/Fc+ (originally reported as the CeCl63–/CeCl62– couple). Compared to the >5.1 eV LMCT and unobservable redox couple for CeF62–, these data reveal a significantly higher energy separation between the HOMO and LUMO in CeF62– vs CeCl62–. However, this information alone is not sufficient for evaluating bond covalency.

SQUID Magnetometry

Magnetic susceptibility data were collected from 3 to 400 K for (Ph4P)2CeF6 and (Et4N)2CeCl6 (Figure 2, left). The samples were contained in quartz tubes for measurement as previously described.47−50 Diamagnetic corrections were applied for the quartz wool using Pascal’s constants,51 and a correction for ferromagnetic impurities was also applied as previously described.52 Due to the small magnetic moments of these compounds, the magnetometry data were collected in triplicate to ensure high data quality. The χ vs T data are fit to the Curie–Weiss Law to determine the Curie constant (C), the Curie–Weiss temperature (Θ), and the temperature-independent paramagnetism (TIP) (χ0).1

Figure 2 SQUID magnetometry data for CeF62– and CeCl62–. The Curie–Weiss parameters are determined from the fits of the χ vs T experimental data (left two windows). The χT vs T plot (right) emphasizes the difference in TIP between CeF62– and CeCl62–. Experimental data points between 35 and 55 K were removed from the fit due to oxygen contamination in the instrument.

For (Ph4P)2CeF6, the fit values are −4.3(2) K for Θ, 2.2(3) × 10–3 emu K mol–1 for C, and 0.81(4) × 10–4 emu mol–1 for χ0. For (Et4N)2CeCl6, the fit values are −1.5(1) K for Θ, 1.1(1) × 10–3 emu K mol–1 for C, and 1.6(2) × 10–4 emu mol–1 for χ0. A plot of χT vs T (Figure 2, right) shows this difference visually, where Θ is set to zero and the slope of the line is equal to χ0. The nonzero values of C indicate the presence of trace paramagnetic impurities in these samples. While the identity of these impurities is unknown, the magnitude of C in these samples may be assessed by assuming the impurity is Ce(III) (C = 0.807 emu K/mol). By making this assumption, the amount of Ce(III) impurity is 0.27(4)% for (Ph4P)2CeF6 and 0.14(1)% for (Et4N)2CeCl6.

Both complexes display TIP, as observed in many compounds with formal Ce(IV) ions.49,53−55 This behavior arises from the mixing of low lying magnetic excited states into the ground state, and the magnitude of χ0 is inversely proportional to the difference in energy between the ground state and the lowest lying excited states.56 The TIP for CeCl62– is comparable to the published values of 1.7(2) × 10–4 emu mol–1 reported for Ce(C8H8)2 and is of the same order of magnitude as many other molecular Ce(IV) compounds (Table 1).49 The TIP for CeF62–, however, is about half that of CeCl62–. Assuming a conserved state ordering, this finding can be rationalized by the greater spectral splitting of the metal orbitals by the fluoride ligand, increasing the energy gap between the ground and excited states.

Table 1 Summary of TIP for Selected Ce(IV) Compounds

compound	χ0 (emu mol–1)	references	
(Ph4P)2CeF6	0.81(4) × 10–4	this work	
(Et4N)2CeCl6	1.6(2) × 10–4	this work	
Ce(C8H8)2	1.7(2) × 10–4	(49)	
Ce(C8H4(SiiPr3-1,4)2)2	4.5(3) × 10–4	(57)	
Ce(trop)a	1.2(3) × 10–4	(55)	
Ce(acac)4b	2.1(2) × 10–4	(55)	
Ce(tmtaa)2c	2.33(6) × 10–4	(55)	
Ce–NHArF(TriNOx)d	1.10(6) × 10–4	(53)	
[K(dme)2][Ce = NArF(TriNOx)]d	2.2(2) × 10–4	(53)	
K4[Ce = O(TriNOx)]4d	4.2(5) × 10–4	(53)	
a trop = 2-hydroxy-2,4,6-cycloheptatrienone (tropolonate).

b acac = 2,4-pentanedione (acetylacetonate).

c tmtaa = tetramethyl-dibenzotetraaza[14]annulene.

d TriNOx = ([(2-tBuNO)C6H4CH2]3N)3–.

Ground State Electronic Structure Calculations

We begin with a discussion of the ground state electronic structure of CeF62– and CeCl62– based on expectations from MO theory and quantum chemical calculations. In an Oh ligand field, the Ce 5d orbitals transform as t2g + eg, and the 4f orbitals transform as a2u + t1u + t2u. These Ce AOs can mix with appropriate ligand-based symmetry-adapted ligand combinations (SALCs) of halide p AOs to form MOs featuring either σ interactions (eg), π interactions (t2g, t2u), or both σ and π interactions (t1u). The 4f orbital of a2u symmetry is nonbonding and represents the lowest unoccupied MO (LUMO). The remaining SALCs of t1g and t1u symmetry remain nonbonding with respect to the metal center, forming the highest occupied MOs (HOMO).

This qualitative picture of ground state electronic structure and metal–ligand bonding in CeF62– was examined computationally with three complementary approaches: density functional theory (DFT) with the B3LYP hybrid functional approximation, Hartree–Fock theory augmented by Møller–Plesset second-order perturbation theory (MP2) to treat the dynamic electron correlation, and coupled-cluster with doubles (OO-CCD). Calculations were performed on CeCl62– for comparison, which has also been the subject of in-depth computational investigations.2,58

Figure 3 shows quantitative MO diagrams for CeF62– and CeCl62– that were constructed based on DFT/B3LYP calculations using Oh symmetry and averaged experimental Ce–L (L = F, Cl) distances of 2.152 Å (Ce–F) and 2.599 Å (Ce–Cl). Relative MO energies are shown. The HOMO energy of each complex is negative, and no significant changes in the electronic structure are obtained when a continuum embedding model with infinite dielectric is used to represent the crystal environment. From the MO diagrams some similarities and differences are noted for the two complexes. Both complexes have large HOMO–LUMO gaps of 5.99 and 3.84 eV for CeF62– and CeCl62–, respectively. The HOMO–LUMO gap for CeF62– is similar to the band gap of ∼6 eV of CeO2 determined experimentally from X-ray photoelectron spectroscopy (XPS) and bremsstrahlung isochromat spectroscopy.59 The nonbonding a2u orbital is the LUMO for both systems, but the t1g orbitals are the HOMOs only for CeCl62–. For CeF62–, the HOMOs are derived from the F-based SALCs of t1u symmetry, with contributions from the Ce 5p (5.4%) and Ce 4f (3.2%) orbitals. We hypothesized that the different MO ordering for CeF62– is driven by the shorter Ce–F distance vs Ce–Cl, which allows the Ce 5p inner valence orbitals to interact with occupied F t1u SALCs and increases their energy relative to the t1g orbitals. As confirmation, test calculations on CeCl62– with shortened Ce–Cl distances had the same MO ordering observed for CeF62–.

Figure 3 Valence MO diagrams of CeL62– (L = F, Cl), obtained from DFT/B3LYP calculations with the ANO-RCC-QZP basis sets using symmetrized crystal structures. The diagrams are aligned to each other based on the energy of the Ce 4f orbital of a2u symmetry, which is rigorously nonbonding for each complex. The orbitals containing Ce 4f character are shown in red, and those containing Ce 5d character are shown in blue. Nonbonding ligand SALCs are shown in black.

Calculated electronic structure descriptors gathered in Table 2 show consistency among DFT calculations and the correlated wave function approaches, MP2 and CCSD. The OO-CCD metrics in Table 2 correspond to the “relaxed” coupled-cluster density including the desired correlation effects. Likewise, relaxed MP2 densities were used. The 4f and 5d electron populations, defined as nf and nd, extracted from the OO-CCD densities must be considered the most accurate among the present calculations. The nf and nd values are 0.66 and 0.93 for CeF62– and 0.85 and 1.48 for CeCl62–, indicating a larger ligand-to-metal donation with Cl, especially into the Ce 5d shell. The calculated metal charges, q(Ce) = +2.32 for CeF62– and +1.50 for CeCl62–, are quite low compared to the +4 formal charge for Ce(IV), which reflects mainly the ligand electron density donated into both the 4f and 5d shells combined. Assigning the 5d populations back to the ligands would result in metal charges of +3.25 (CeF62–) and +2.98 (CeCl62–), which are closer to the expected +4 charge, reflective of the 4f donation solely, and indicate a cerium oxidation state between Ce(III) and Ce(IV).

Table 2 Calculated Chemical Bonding Descriptors Using Various Computational Approachesa

 	computational method	
Bonding metric	B3LYP	MP2	OO-CCD	
CeF62–	
q(Ce)	2.09	2.21	2.32	
q(F)	–0.68	–0.70	–0.72	
nf	0.81	0.70	0.66	
nd	0.95	1.03	0.93	
MBO	0.53	0.47	0.44	
CeCl62–	
q(Ce)	1.45	1.35	1.50	
q(Cl)	–0.58	–0.56	–0.58	
nf	1.02	0.91	0.85	
nd	1.35	1.59	1.48	
MBO	0.75	0.71	0.67	
a Calculations were performed on Oh structures with averaged experimental Ce–L (L = F, Cl) distances and ANO-RCC-QZP basis sets.

Bonding metrics obtained from the calculations compare well (Table 2). However, the DFT/B3LYP calculations provide considerably larger nf values of 0.81 (CeF62–) and 1.02 (CeCl62–), and larger Mayer bond orders (MBOs) of 0.53 (CeF62–) and 0.75 (CeCl62–). This is attributed to the delocalization error associated with common density functional approximations.31 However, the trend of increasing ligand-to-metal donation for CeCl62– relative to CeF62– is the same. The comparison highlights the benefit of benchmarking DFT approaches to correlated wave function calculations when seeking insights into cerium electronic structure. Without the coupled-cluster reference data, it would be tempting to classify both CeF62– and CeCl62– as formally trivalent cerium complexes similar to the case of cerocene, Ce(C8H8)2.32,54,60 Further details are provided in the Supporting Information in the context of the dominantly single-configurational character of the ground states. It follows from the analysis that the bonding in CeF62– and CeCl62– is compatible with a description of the systems in terms of Ce(IV) accompanied by covalent bonding in the form of ligand-to-metal donation. Unlike systems such as Ce(C8H8)2 or Ce(η8-C8Me6)2,54,61 which require multiconfigurational treatments from the onset, the ground state electronic structure of CeF62– and CeCl62– can be safely explored with single-configurational approaches. However, the dynamic correlation is critical for a proper description of the donation and, therefore, the covalency.

Ce L3-Edge XAS

XAS measurements at the Ce L3-edge (2p3/2 → 5d5/2) were made on CeF62– to probe the amount of charge donation spectroscopically.27−29,54,62−64 A plot of the background subtracted, normalized, and curve fit Ce L3-edge XAS of CeF62– is shown in Figure 4. Charge transfer in the Ce L3-edge spectra of formally tetravalent Ce compounds is often reflected by the presence of two peaks, which are commonly described using a CI model where two configurations contribute to the ground state: the tetravalent, or ionic configuration (4f0L5d0) and the trivalent, charge transfer configuration (4f1L5d0), where L represents a ligand hole. At the Ce L3-edge, differences in the core-hole stabilization of the 4f0L5d1 and 4f1L5d1 final state configurations result in the two-peaked structure. However, inspection of the spectrum for CeF62– and its second derivative showed five main features. A low-intensity peak at 5723 eV precedes the intense, higher energy features starting with one at ca. 5730 eV, followed by a broader peak at ca. 5736 eV that is a composite of two closely spaced features, and a final high-energy peak at ca. 5741 eV. In analogy to CeCl62–, whose Ce L3-edge spectrum also deviated from the common two-peak structure, we attribute this structure to ligand field splitting of the 5d orbitals into t2g and eg components combined with the differing core-hole stabilizations. To quantify these two effects, a fitting model was developed based on 5 pseudo-Voigt functions and a step-like function. Within this model, the peak at ca. 5736 eV is a composite of the Ce(III) eg and Ce(IV) t2g components. To prevent unphysical fit results owing to these overlapping features, the widths of the crystal field components were constrained to be equal within each final state subconfiguration. This assignment of two features in the composite peak at ca. 5736 eV is supported by the presence of two minima in that energy region of the second derivative of the experimental spectrum.

Figure 4 Cerium L3-edge XAS spectrum of CeF62–. Ce L3-edge XAS features (black circles) are modeled using pseudo-Voigt functions (green and blue) and a step function (orange) to generate the total curve fit (red trace).

The relative amount of Ce(III) 4f1L5d0 character in the ground-state wave function is estimated by summing the areas of the peaks associated with Ce(III) and Ce(IV) components and taking the ratio of the Ce(III) area to the Ce(III) + Ce(IV) area, A3+/(A3+ + A4+). This ratio gives the nf value, representing the number of f electrons on the formally Ce(IV) center in the ground state. However, it is likely that this should be taken as the lower limit of nf due to a small Ce(II) component that cannot be resolved from the Ce(III) component.32,48,55 By this methodology, the extracted fraction of Ce(III) based on the fit was 0.46(3), with the error estimated by the profiling method (see Supporting Information). This nf is among the smallest reported to date for formal Ce(IV) compounds (Table 3). It is most notably smaller than those of Ce(C8H8)2 (nf = 0.89(3)),54 Ce(η8-C8Me6)2 (nf = 0.87(5)),61 CeO2 (nf = 0.56(4)),28,55,62 and CeCl62– (nf = 0.62(3)), and is comparable to that of Ce(NP(1,2-bis-tBu-diamidoethane)(NEt2))4 (“Ce(PN*)4”) (nf = 0.47(3)).6,65 The latter two comparisons were refit to a model equivalent to the present one in order to make accurate comparisons.

Table 3 Ce L3-Edge XAS Extracted nf Values

compound	nf	references	
(Ph4P)2CeF6	0.46(3)	this work	
(Et4N)2CeCl6	0.62(3)a	(2)	
Ce(PN*)4b	0.47(3)a	(6)	
CeO2	0.56(4)	(62)	
Ce(trop)4	0.50(3)	(55)	
Ce(acac)4	0.51(3)	(55)	
Ce(tmtaa)2	0.59(3)	(55)	
Ce–NHArF(TriNOx)	0.55(3c	(53)	
[K(dme)2][Ce = NArF(TriNOx)]	0.60(3)c	(53)	
K4[Ce = O(TriNOx)]4	0.59(3)c	(53)	
Ce(C8H8)2	0.89(3)	(54)	
Ce(η8-C8Me6)2	0.87(5)	(61)	
a To make accurate comparisons, the experimental data reported previously was curve-fit using a model similar to the one used for (Ph4P)2CeF6. See the Supporting Information for complete details.

b PN* = [NP(1,2-bis-tBu-diamidoethane)(NEt2)]−.

c These values were reported as nf0, and have been converted to nf by assuming nf = 1 – nf0.

Ab Initio Calculation of the Ce L3-Edge Spectra

CeF62– and CeCl62– were subjected to wave function theory (WFT) calculations for determining the Ce L3-edge structure. As for the previous calculations, octahedral structures with averaged experimental bond lengths were used. Following previous work on ab initio XAS,32,66,67 we performed a series of restricted active space self-consistent field (RAS-SCF) calculations for the valence and the core excited states targeted in the XAS experiments, followed by multireference second-order perturbation theory (PT2) calculations for the dynamic electron correlation.

The two-peak Ce L3-edge structure arises from 2p → 5d core excitations grouped into Ce(III) 4f1L5d1 and Ce(IV) 4f0L5d1 final-state subconfigurations. A recent ab initio analysis of such core excited states for the cases of CeO2 vs Ce(C8H8)2 can be found in ref (32). The transitions usually give two peak groups in the L3-edge, groups A (Ce(III)) and B (Ce(IV)), with transition types A at lower energy. The A/B intensity ratio relates to the Ce(III) vs Ce(IV) contributions to both the ground state wave function and the relevant wave functions of the core excited states. In the case of formally tetravalent compounds, these Ce(III) and Ce(IV) contributions are modulated by the ligand np to Ce 4f donation in the ground states, which typically shows up in calculations via ligand–metal orbital hybridization. In the present CeL62– (L = F, Cl) cases, Ce(III) vs Ce(IV) is modulated via the donation to the metal 4f AOs in the t1u and t2u species. Therefore, the Ce L3-edge spectra of CeF62– and CeCl62– were calculated separately for transitions involving the t1u and the t2u MO sets in order to overcome the computational complexity, and the total intensity from the two calculations was combined. With the chosen 2.0 eV Lorentzian broadening of the individual transitions, the calculated Ce L3-edge structures reproduce the experimental counterparts very well (Figure 5).

Figure 5 Calculated vs experimental Ce L3-edge XAS for CeF62– and CeCl62–. To avoid clutter, “stick” transitions are only shown for the RAS-PT2 spectra calculated with the ligand and the metal-centered t2u orbitals. The calculated spectral envelopes were generated with 2.0 eV Lorentzian broadening of the individual transitions.

The calculated L3-edge spectra depend mainly on the adequate description of the acceptor Ce(5d) MOs, the overall bonding involving the Ce(4f) shell, and the overall energy splitting of the orbitals. They depend less on the balance of the donation present in the t1u vs t2u MOs than the ligand K-edges (vide infra). The calculated spectra shown in Figure 5 clearly show that both the t1u and t2u bonding and antibonding MO pairs are needed to reproduce the experimental envelopes: they both generate Ce(III) and Ce(IV) (A vs B group) final-state configurations. Apart from this, the interpretation of these spectra follows closely that of CeO2:32 each peak group, A and B, is split by the ligand field splitting of the Ce(5d) orbitals, such that 3 or 4 peaks are resolved in the experimental spectrum. The larger the 5d t2g–eg splitting is, the closer is the high-energy peak in group A to the low-energy peak in group B. For CeF62–, which has the larger 5d splitting, the higher-energy A subpeak overlaps with the lower-energy B subpeak around 5736 eV. These peaks remain separated for CeCl62–, which has a smaller 5d t2g–eg splitting. Another conclusion from Figure 5 is that t1u contributes preferentially over t2u in peak group A. The opposite is the case for peak group B. To support the assignment of the Ce L3-edge peaks, we provide in Table 4 the natural orbital populations for the intense core excited states (involving the t2u MO set) shown as “sticks” in Figure 3. The natural populations were calculated from the configurations and their corresponding weights in the wave functions expressed in the state-averaged orbitals. Conveniently, for each case, these orbitals turned out to be localized in the t1u and t2u symmetry species (irreducible representations or “irreps”) such that they can be labeled straightforwardly as “L” for the ligand-based np combination and “f” for a Ce(4f) AO. It follows that for each state, the 4f population is indicative of the nf value of Ce, which in turn can be used to assign its oxidation number.

Table 4 Natural Configurations for the Ground State and the Four Core Excited State Transitions (Blue Sticks in Figure 3) Responsible for Intensities in the Ce L3-Edge Structures of the CeL62– Systems (L = F, Cl)a

system	param.	GS	A.1	A.2	B.1	B.2	
CeF62–	config.	L5.98f0.02	[L5.15f0.85]t2g1	[L5.19f0.81]eg1	[L5.74f0.26]t2g1	[L5.75f0.25]eg1	
 	ΔE, eV	 	0.00	4.47	4.94	9.59	
CeCl62–	config.	L5.88f0.12	[L5.04f0.96]t2g1	[L5.06f0.94]eg1	[L5.91f0.09]t2g1	[L5.91f0.09]eg1	
 	ΔE, eV	 	0.00	3.08	7.90	11.39	
a The Ce(III) 4f1L5d1 and Ce(IV) 4f0L5d1 configurations were generated with the t2u orbitals. A.1 & A.2 and B.1 & B.2 label the two transitions (“sticks”) under peak groups A and B shown in Figure 3. Note that the 4f populations extracted from the RAS calculations are uniformly smaller than those given in Table 2 because of a lack of dynamic correlation and differences in the way the populations were obtained. However, the spectral features are mainly indicative of the relative state assignments.

From the data in Table 4, we conclude that the ground states are best described as Ce(IV) because the 4f population is relatively small. The 4f population increases from 0.02 (F) to 0.12 (Cl), thus evidencing increasing ground state donation into the 4f orbitals in CeL62–. The same trend holds when analyzing the data obtained with the t1u MOs (not shown in Table 4). The excited states for transitions A.1 and A.2 (i.e., first and second transition under the first peak group A in Figure 3) have nearly one electron the Ce 4f shell, whereas the excited states of transitions B.1 and B.2 (first and second transition under the peak group B in Figure 3) have close to zero 4f population. In other words, to summarize this part of the study, the calculations confirm that peak group A is associated with Ce(III) core excited states, peak group B with Ce(IV) core excited states, both peaks are split by the 5d ligand field splitting but lead to overlapping bands in the fluoride complex, and the ground state of both complexes is described by Ce(IV) with some electron donation from the ligands.

Ce M5,4-Edge and F K-Edge XAS

A scanning transmission X-ray microscope (STXM) was utilized to obtain F K-edge and Ce M5,4-edge XAS from micron-scale crystals of (Ph4P)2CeF6. An X-ray image of representative crystallites of (Ph4P)2CeF6 alongside STXM elemental distribution maps of F and Ce is shown in Figure 6. Small droplets of (Ph4P)2CeF6 in MeCN were allowed to evaporate on Si3N4 windows, which formed a large number of small crystallites in a compact area that were suitable for STXM raster scans. By selecting thin crystals (ca. 0.5–1.0 μm) with a large surface area (ca. 50–100 μm2), this approach was effective at distributing the effect of radiation damage over a larger area. Radiation damage was not detected, and high-quality F K-edge and Ce M5,4-edge XAS were obtained by averaging data sets from multiple independent crystals.

Figure 6 STXM image and elemental distribution maps of F and Ce on representative crystallites of (Ph4P)2CeF6. The optical density in the Ce map is higher than that in the F map owing to the greater intrinsic intensity of the Ce M4,5-edge alongside the higher mass percent of Ce in the salt.

Ce M4,5-Edge XAS and Atomic Multiplet Simulation

Ce M4,5-edge XAS probes the electric-dipole-allowed transitions from core 3d orbitals into the valence 4f orbitals, providing a unique opportunity to directly probe the 4f shell. Typical Ln M4,5-edge spectra show well-defined M4- and M5-edges in addition to multiplet structure that is characteristic of the number of 4f-electrons.68−70 This technique has been used extensively to investigate partial 4f-orbital occupancies in lanthanide oxides, halides, and intermetallics, among other compounds.23,71−75 The Ce M4,5-edge spectrum for CeF62– is shown in Figure 7, and the associated peak energies and branching ratios are shown in Table 5. In comparison to CeCl62–, both the M5 and M4-edges are shifted to higher energy in CeF62–. In XAS, an edge shift to higher energy is often attributed to stabilized core orbitals due to an increase in positive charge on the absorbing atom.76

Figure 7 Comparison of the experimental (black) and CI calculated (red) Ce M4,5-edge spectrum for CeF62–.

Table 5 Comparison of Experimental Ce M4,5-Edge Peak Energies and Intensities

 	peak energies (eV)	peak splitting (eV)	branching ratio	
 	M5-edge	M4-edge	sat–main	M5–M4	A5/(A5 + A4)	
 	main	satellite	main	satellite	avg	main	 	
CeF62–	884.2	890.4	901.8	908.0	6.2	17.6	0.50(2)a	
CeCl62–b	883.7	888.6	901.6	906.4	4.9	17.9	0.48(2)	
a Peak areas were calculated by integrating the second derivative graph of the data above zero.77

b Chloride data from ref (2).

The M4,5-edge spectrum of 4f0 Ce(IV) compounds is expected to be qualitatively similar to that of 4f0 La(III) compounds, whose M4,5-edge spectra only have two intense features.68 The presence of satellite peaks like those observed for CeF62– has been attributed to excited state charge transfer enabled by metal–ligand orbital mixing.78 To relate these satellite features to the ground state electronic structure, a spectral simulation was performed using the Theo Thole multiplet code, with modifications by Ogasawara, as maintained and used by the CTM4XAS program.79 This code is based on the charge transfer multiplet (CTM) model and explicitly accounts for core-hole effects that are not considered in most DFT calculations. In particular, core-hole-induced charge transfer in the excited state is included, allowing us to simulate the satellite features described above. Input parameters used previously for CeCl62– were used for the atomic multiplet component of the calculation for CeF62–, except for the core-hole spin–orbit coupling, which was reduced to 98% (vs 99% for CeCl62–).2 For the charge transfer component, we are concerned with the following parameters:ΔEgs, the ground state charge transfer energy (4.6 eV)

Tgs, the ground state effective hopping integral (0.92 eV)

ΔEfs, the final state charge transfer energy (1.8 eV)

Tfs, the final state effective hopping integral (0.92 eV)

The values used in this calculation are given in parentheses. The result of this calculation for CeF62– is shown alongside the experimental spectrum in Figure 7. Starting from the values used for CeCl62–, ΔEgs was set by adding the difference in the HOMO–LUMO energy gap between CeF62– and CeCl62– (2.1 eV, from ground state computations) to the ΔEgs for CeCl62–. Then, ΔEfs was determined by incrementally increasing the value from CeCl62– until the spectral profiles of the main edges and satellite features were in good agreement with experiment. Finally, in order to confine the number of free variables, Tgs and Tfs were set equal to each other, and their value was varied until the energy splitting between the main edges and satellite features were also in good agreement with experiment. The complete input and output files may be found in the Supporting Information.

The charge transfer calculation produces the simulated spectrum by first computing a ground state wave function composed of Ce(III) 3d104f1L and Ce(IV) 3d104f0L components. The weight of the Ce(III) component, 0.19 is taken as the computed Ce nf. This value is lower than the value of 0.25 calculated previously based on the M5,4-edge spectrum of CeCl62–.2 Both nf are much lower than those found via L3-edge XAS, which likely reflects the limitations of the CTM model. However, the lowering of the nf value from CeCl62– to CeF62– based on M5,4-edge XAS and CTM calculations is consistent with the trend in nf values observed at the L3-edge, which indicates decreased ligand donation in CeF62–.

F K-Edge XAS and Spectral Simulation

The background-subtracted, normalized, and fit F K-edge spectrum of CeF62– obtained using a STXM is shown in Figure 8. The pre-edge region of the spectrum contains two features below 690 eV, which were modeled using two symmetrically constrained Gaussian functions at 683.4 and 686.7 eV (see Experimental Section).80−82 Based on the ground-state electronic structure model for CeF62– described above, and on the previously reported assignments of the Cl K-edge spectra for CeCl62– and UCl62–,2,81 we assigned the lowest energy feature at 683.4 eV to coincident transitions from the F 1s orbitals into the Ce–F antibonding orbitals of t1u and t2u symmetry. The individual transitions are not resolved by F K-edge XAS, presumably due to the weak ligand field splitting of 4f orbitals. Moving to higher energy, the feature at 686.7 eV represents the transition into the Ce–F antibonding orbitals of t2g symmetry. No single feature attributable to transitions into the eg orbitals were observed, which are presumably not resolved from other transitions in the rising edge region.

Figure 8 Normalized fluorine K-edge XAS spectrum of CeF62–. F K-edge XAS pre-edge features (black circles) are modeled using Gaussian functions (pink, blue, and purple) and a step function (orange) to generate the total curve fit (red trace). The spectral intensities (pink and blue numbers) are given by the areas under the Gaussian functions.

Figure 9 shows ligand K-edge spectra for CeF62– and CeCl62– that were calculated within the framework of WFT approaches, similar to the previously discussed L3-edge spectra calculations. For both systems, the relative intensities and energetic splitting of the two pre-edge features are in good agreement with experiment. The first pre-edge peak arises from core transitions into the Ce 4f antibonding orbitals of t1u and t2u symmetry, with the transition into the t2u being slightly more intense. The second and third peaks are assigned to transitions into the Ce 5d orbitals of t2g and eg symmetry, respectively. Based on these data, however, it is difficult to conclude whether the t2u MOs have more F 2p or Cl 3p character compared to the t1u MOs, as the orbital optimization in these calculations leads to rather strongly localized orbitals.

Figure 9 Calculated vs experimental ligand K-edge XAS for CeF62– and CeCl62–, from RAS-PT2 wave function calculations with quantitative assignments of the final state orbitals. The calculated spectra are obtained with a 0.5 eV Gaussian broadening of the individual transitions. The calculated spectra were shifted and scaled to match the experimental envelopes at the first pre-edge peak.

Evaluation of Orbital Mixing (Evaluation of f Covalency)

The F K-edge XAS results described above show that the F 2p orbitals engage in bonding with both the Ce 4f and 5d orbitals. Because the intensities of the F K-edge pre-edge transitions are weighted by the amount of F 2p orbital character in the acceptor orbitals, the orbital mixing can be determined experimentally and compared with expectations from the ground state calculations. Spectral intensities were determined by taking the area under the Gaussian functions that are fit to the experimental spectra, which provides a value of 1.2(1) for the function attributed to F 1s → t1u + t2u transitions and 2.4(2) for the function attributed to F 1s → t2g transitions.

For the t2g orbitals, the ligand p-orbital character (λt2g2) is calculated according to the general equation for ligand K-edge intensity2

where h is the number of holes in the acceptor orbital set (6 for t2g), N is the number of absorbing atoms bound to the metal (6 for CeL62–), n is the principal quantum number of the valence p-orbitals for a given ligand, and I1s→np is the intrinsic intensity for the 1s → np transition of the absorbing atom.36 For Cl K-edge measurements, the value of 7.0(2) for I1s→np has been well-established by Solomon and co-workers using CuCl42–.34,37 For these F K-edge measurements, the F K-edge spectrum of F2 gas was used to determine a value of 16.3(8) for I1s→np.83 With these values, we find λt2g2 = 0.15(1) for CeF62– and λt2g2 = 0.12(1) for CeCl62–. Since the lowest energy pre-edge feature gains intensity from two separate transitions involving the t1u and t2u orbitals that are not independently resolved in the F K-edge spectrum, the average ligand p-orbital character in these orbitals (λavg2) was calculated according to eq 33

A derivation of this equation starting from eq 2 is provided in the Supporting Information. Using eq 3, a λavg2 of 0.037(4) is calculated for CeF62–, which can be compared to the value of 0.050(5) determined using Cl K-edge data published previously for CeCl62– (reported originally as λt1u2 + λt2u2).2

The consequence of orbital mixing in the t1u and t2u MOs is donation of ligand electron density into the 4f orbitals. For the Ce M5,4 and L3-edge XAS measurements on CeF62– and CeCl62–, the electronic structure was described with localized orbitals using a CI model, and the extent of donation bonding was reflected by the value nf, or the weight of the Ce(III) configuration (vide infra).105 Comparison between the CI and MO models is achieved by nf = 12λavg2, where 12 reflects the number of bonding electrons in the t1u and t2u orbital sets. Results of this calculation and comparison with other measurements are provided in Table 6. The values of nf determined using λavg2 from F and Cl K-edge XAS were 0.44(4) for CeF62– and 0.60(6) for CeCl62–. These values are within error of those determined with Ce L3-edge XAS, 0.46(3) for CeF62– and 0.62(3) for CeCl62–. Moreover, this trend is consistent with that determined from OO-CCD ground state calculations (0.66 for CeF62– and 0.85 for CeCl62–). While the calculated values are higher than those determined experimentally, both approaches show CeCl62– to have an nf about 0.2 higher than CeF62–. Intermediate to the CeF62– and CeCl62– experimental nf values is that reported for CeO2, 0.56(4),62 and much higher is that of cerocene, 0.89(3).54 This comparison reveals a general trend between the electronegativity of the Ce(IV)-bound atom and the Ce(IV) nf value. However, this trend may not hold in the case of novel ligands or coordination geometries, as in the case of Ce(PN*)4 with an nf of 0.47(3).6,65

Table 6 Comparison of Experimental and Calculated Ce nf Values

 	CeF62–	CeCl62–	
exp. ligand K-edge	0.44(4)	0.60(6)	
exp. Ce L3-edge	0.46(3)	0.62(3)	
CTM Ce M4,5-edge	0.19	0.25	
OO-CCD ground state	0.66	0.85	

To a first approximation, the greater amount of donation bonding in CeCl62– can be rationalized simply by the fact that the Cl 3p orbitals are higher in energy, and thus closer in energy to the Ce 4f orbitals.84 However, the amount of orbital mixing is proportional not only to the inverse orbital energy difference, but also the orbital overlap.38 Using the second-order model applied by Burdett to transition metal complexes alongside the Wolfsberg–Helmholz approximation,40,85 λavg2 can be related to orbital overlap (Savg2) according to4

where EM and EX are the metal and ligand AO energies, respectively. EX is defined exactly as the negative of the first ionization potential of the halogen atom (−17.4 eV for F and −12.9 eV for Cl),86 as described by Koopmans’ theorem,87 and EM is estimated as the negative fourth ionization potential of Ce divided by four (−9.2 eV).86 With these energies and the λavg2 determined from ligand K-edge XAS, we find S4f,avg2 = 0.016(2) for CeF62– and S4f,avg2 = 0.0058(6) for CeCl62–. These values show that the Ce–F bonds in CeF62– are characterized by significantly more Ce 4f and F 2p overlap compared with the amount of Ce 4f and Cl 3p overlap in the Ce–Cl bonds of CeCl62–. We note that greater 5f-orbital overlap with the halide ligands in UF6n– compared with UCl6n– (n = 1, 2) has been observed previously by fitting 5f–5f transitions within a modified crystal field model.88 The λt2g2 values can be used to estimate St2g2 relative to S4f,avg2 as a function of the value of E(Ce 5d). While the Ce 5d orbitals are expected to be 1–2 eV higher in energy than the 4f,89 an experimental value corresponding to the energy of the 5d orbitals of the 4f05d0 Ce(IV) ion is not known. As shown in Figure S11, at values of E(Ce 5d) ≥ E(Ce 4f), overlap in the t2g MOs is greater than that in the 4f MOs for both CeF62– and CeCl62–. Using the energy of the Hf(IV) 5d orbitals (−8.3 eV) as a proxy for that of the Ce(IV) 5d orbitals, we estimate the value of St2g2 at 0.084(8) for CeF62– and 0.024(2) for CeCl62–.

The presence of greater ligand overlap with the 4f orbitals In CeF62– relative to CeCl62– may seem counterintuitive since the other metrics of bonding, λavg2 and nf, suggest that CeF62– has both less orbital mixing and less ligand-to-metal charge donation than CeCl62–. However, these concepts are not mutually exclusive. The λavg2 determined here account for the electron density on the ligand atoms plus half that in the region of metal–ligand orbital overlap. A large overlap can be accompanied by low internuclear charge buildup if the mixing coefficient is sufficiently low, as is the case here (see Supporting Information). While overlap in CeF62– does not lead to much greater orbital mixing, it plays an important role in the energetic stabilization of bonding (or destabilization of antibonding) orbitals, for which ΔEbonding ≈ S2EM2/(EL – EM).40,90 Therefore, it is likely that the greater overlap in the Ce–F bond of CeF62– enhances the contribution of orbital mixing to overall bond stabilization relative to the Ce–Cl bond of CeCl62–.

Conclusions

In summary, CeF62– was synthesized as (Ph4P)2CeF6 and initially characterized by optical and vibrational spectroscopy, which were not sufficient to evaluate the extent of metal–ligand orbital mixing. With SQUID magnetometry, we showed that CeF62– displays less TIP than CeCl62– and other representative coordination compounds of Ce(IV), hinting at a departure from typical Ce(IV) electronic structure. Then, a broad suite of X-ray spectroscopic and theoretical tools was used to show operative 4f orbital mixing in the Ce–F bonds in CeF62–. Excellent, quantitative agreement was observed between the experimental F K-edge and Ce L3-edge data and computational metrics of bonding, which provides confidence in the reliability of the results. Ground state electronic structure calculations and ab initio spectral simulations suggest the 4f orbitals engage in both σ and π-bonding interactions involving the t1u and t2u orbitals. F K-edge XAS was used to evaluate mixing of F 2p character into the t1u and t2u orbital sets, which represent F 2p → Ce 4f electron donation. The amount of F 2p → Ce 4f electron donation (nf) for CeF62– determined using F K-edge XAS (0.44(4)) was found to be equivalent to that determined from Ce L3-edge XAS (0.46(3)). Comparison with CeCl62– showed that CeF62– has less electron donation. In fact, CeF62– appears to be among the most ionic Ce(IV) compounds reported to-date.

The increased metal–ligand orbital mixing, λavg2, in CeCl62– versus CeF62– is rationalized by its inverse dependence on the difference between the Ce 4f and ligand AO energies (EM – EL), which is smaller for CeCl62– (∼3.7 eV) than in CeF62– (∼8.2 eV). Experimentally determined values for metal–ligand orbital overlap were calculated using these values, which showed greater orbital overlap in the Ce–F bonds compared to the Ce–Cl bonds. Such a result is, perhaps, counterintuitive since the other metrics of metal–ligand bonding show greater orbital mixing (λ2) and Cl 3p → Ce 4f charge donation (nf) in CeCl62–. Overlap in π interactions is known to be smaller for 3p versus 2p elements,91−93 and thus better overlap in CeF62– may be a consequence of the Oh symmetry (6 σ and 12 π interactions involving f-orbitals94) and better size match between Ce 4f and F 2p orbitals. Since the t2g orbital is solely π-bonding, the greater λt2g2 and estimated St2g2 in CeF62− vs CeCl62− support that enhanced π-bonding is enabled by the F 2p orbitals. Ultimately, the enhanced overlap in CeF62– is more than offset by the larger difference in orbital energies (EM – EL), such that CeCl62– has the most orbital mixing. However, the energetic stabilization due to 4f-orbital mixing is likely larger in CeF62– due to the extra dependence of MO energy on overlap, ΔEbonding ≈ S2EM2/(EL – EM).40,90 It is important to note that this behavior differs from the counterintuitive orbital mixing discussed by Whangbo and Hoffman, wherein an out-of-phase antibonding orbital is lower in energy than the corresponding in-phase bonding orbital.95 The relative influence of overlap vs energy matching remains strongly debated.96 Conceptually, a full understanding of the relative importance of overlap vs AO energy matching requires, among other aspects, unambiguous definitions of AOs and their energies for the purpose of the bond formation, alongside a careful comparison among them for free atoms, free ions, and the atoms in the complexes. Work along these lines is under way in our laboratories, and the availability of experimentally derived overlaps for the systems studied here will greatly assist these future analyses. Further future work will use the approach described herein to directly probe overlap in other d- and f-block fluorides, chlorides, and bromides.

Experimental Section

General Considerations

Unless otherwise noted, all manipulations were performed using standard Schlenk techniques or in an MBraun glovebox under an atmosphere of argon. All glassware was dried at 150 °C for at least 12 h. Propylene carbonate (99%, Thermo Scientific) was vacuum distilled and degassed by sparging with argon for 20 min. Acetonitrile (MeCN) (Fisher) was purified by passage through a column of activated alumina prior to use. Acetone (Sigma-Aldrich, ACS grade) was used as received. Cerium(IV) fluoride (Sigma-Aldrich) and Et4NF·xH2O (Thermo Scientific) were used as received. (Et4N)2CeCl6 was prepared as previously described.2 Samples for UV–vis spectroscopy were measured as solutions in MeCN on a Cary 5G Spectrophotometer from 200 to 2000 nm with 1 nm step sizes. Samples for IR spectroscopy were prepared as nujol mulls with KBr plates and measured with a Bruker Vertex 80v spectrometer. Raman data was collected on JASCO NRS-5500 Raman Spectrometer using a 532 nm laser. More details on the Raman sample preparation and collection parameters are found in the Supporting Information.

Single Crystal X-ray Crystallography

In a dry argon glovebox, single crystals of (Ph4P)2CeF6 were coated in Paratone-N oil. A suitable crystal was selected and mounted on a MiTeGen 100 μm Dual-Thickness MicroLoop for measurement on a Rigaku XtaLAB Synergy, Dualflex, HyPix diffractometer using Mo Kα radiation (λ = 0.71073 Å). The crystal was kept at 100.0(5) K during data collection. CrysAlisPro97 was used from data collections and processing, including multiscan absorption correction applied using the SCALE3 ABSPACK scaling algorithm within CrysAlisPro. With Olex2,98 the structure was solved with the SHELXT99 structure solution program using Intrinsic Phasing and refined with the SHELXL100 refinement package using least-squares minimization. Thermal parameters for all non-hydrogen atoms were refined anisotropically.

Synthesis of (Ph4P)2CeF6

The synthesis of the (Et4N)2CeF6·6H2O intermediate was adapted from that reported by Balasekaran et al.42 CeF4 (507.8 mg, 2.35 mmol) and Et4NF·xH2O (980.6 mg, 6.56 mmol anhydrous) were added to a flask with a stir bar propylene carbonate (1.0 mL). As Et4NF·xH2O cannot be dried without decomposition, the exact level of hydration is unknown and an excess is used. This mixture is heated to 80 °C and allowed to stir until complete dissolution of the CeF4 occurs. After cooling to room temperature, acetone (10 mL) followed by Et2O (20 mL) are added to precipitate (Et4N)2CeF6·6H2O. This colorless solid was redissolved in a solution of Ph4PCl (1865.9 mg, 4.99 mmol) in MeCN (15.0 mL). Et2O (20 mL) is added, and the solution is stirred for 5 min, during which a colorless precipitate formed. The solvent was decanted and the solid washed three times with acetone (20 mL). The resulting solids were dried overnight under vacuum to remove volatile materials before being brought into a glovebox. The solid was dissolved in MeCN (20 mL), and Et2O was allowed to vapor diffuse into the solution overnight. X-ray quality crystals were produced in 79.5% yield with respect to the starting CeF4. Higher yields may be obtained by allowing the vapor diffusion to run for a longer time, with a maximum yield after 1 week. This crystallization afforded off-white chunks of (Ph4P)2CeF6·MeCN (CCDC: 2359877). The solvent of crystallization can be removed by drying in vacuo. IR (KBr, cm–1): 438.7 (m), 529.2 (m), 615.0 (w), 691.7 (m), 723.7 (m), 763.0 (m), 801.0 (w), 996.2 (w), 1025.0 (w), 1106.6 (m), 1165.8 (w), 1189.6 (w), 1261.9 (w), 1312.1 (w), 1340.2 (w), 1377.5 (m), 1440.5 (m), 1463.6 (s), 1583.5 (w), 1632.6 (w), 1658.1 (w), 1680.1 (w), 2672.9 (w), 2725.8 (w), 2855.1 (s), 2924.7 (s), 2957.3 (s), 3198.4 (w), 3295.7 (w), 3429.6 (w), 3514.3 (w), 3661.3 (w). Raman (532 nm): 528 cm–1. 19F NMR (CD3CN): 180.7 ppm externally referenced against CFCl3. Anal. Calcd for C48H40P2CeF6: C, 61.80%; H, 4.32%. Found: C, 61.56%; H, 4.44%.

STXM Sample Preparation

Glassware and sample windows were stored in an oven at 160 °C for at least 12 h prior to use. Organic solvents were purified by passage through a column of activated alumina prior to use. A small amount (∼1 mg) of each sample was dissolved in 1 mL of MeCN, and a pipet was used to transfer a small aliquot of this solution onto a Si3N4 window (100 nm, Silson). The MeCN was allowed to evaporate and deposit crystallites of the sample onto the window. After drying for a few more minutes, a second window was placed over the sample, and the edges were sealed with Hardman Double/Bubble epoxy. This preparation results in the samples being sealed off from environmental oxygen and moisture while being transferred into the instrument chamber for measurement.

Fluorine K-Edge and Cerium M4,5-Edge XAS STXM Measurements

Fluorine K-edge spectra, Ce M4,5-edge spectra, and elemental maps were taken using the STXM instrument at the Canadian Light Source Spectromicroscopy (SM) beamline (10ID-1) in a vacuum chamber at ambient temperature. An energy calibration was performed at the F K-edge using SF6 gas (688.0 eV) for F and Ne gas (867.12 eV) for Ce. The X-ray beam was focused onto the sample with a zone plate, and the X-ray transmission was detected. The spot size and spectral resolution were determined from characteristics of the 35 nm zone plate. Single-energy images were collected by raster-scanning the sample with monochromatic light and recording the transmitted intensity as a function of sample position. A collection of these monochromatic images taken at multiple, closely spaced photon energies across the absorption edge form a “stack.” The transmittance data were converted to optical density using the Beer–Lambert law. Incident beam intensity was measured through the sample-free region of the Si3N4 window. Spectra were obtained by averaging over the signal of the sample deposited on the window. During the experiment, the samples showed no signs of radiation damage, and the spectra were reproducible with multiple independent crystallites.

Fluorine K-Edge XAS Data Reduction

The normalization was completed based on a previously described procedure. For each scan, the pre-edge region was fit to a Victoreen polynomial, and that polynomial was extrapolated across the energy range measured. This extrapolated polynomial curve is then subtracted from the experimental data. To normalize the spectral intensity, a third-order polynomial is fit to the postedge region in this background-subtracted spectrum. Then, this spectrum is divided by a constant so that the intensity at the postedge normalization energy (714 eV) in the fit is equal to one. Once this normalization process is complete for each scan, the normalized spectra are averaged to produce the final, normalized spectrum. The spectral intensities of the pre-edge transitions were determined by fitting the spectrum with symmetrically constrained Gaussian functions to represent pre-edge features and a step function with a 1:1 ratio of arctangent and error function contributions to represent the rising edge. Spectral curve fitting was performed using a modified version of the EDG_FIT procedure in IGOR Pro 8.0.101 The pre-edge peak intensities are determined from the area under the functions used to fit them. Uncertainty in the areas under the Gaussian functions due to background subtraction, normalization, and spectral curve fitting is estimated at 10% or less based on previous studies,34 curve fitting error, and STXM data reproducibility.

Ce L3-Edge XAS Sample Preparation and Measurement

X-ray absorption near edge structure data at the Ce L3 absorption edge were collected at the Stanford Synchrotron Radiation Lightsource (SSRL) beamline 11-2 using a Si(220) (φ = 0°) monochromator detuned to 50% and a Rh-coated harmonic rejection mirror with a cutoff energy set near 10 keV. The vertical slit height was sufficiently narrow that the energy resolution was core–hole lifetime limited. Data were collected in transmission geometry and the monochromator energy was calibrated by defining the energy of the first inflection point at the Ce L3-edge of the absorption from a CeO2 standard to be 5724.0 eV. Data were processed by subtracting a Chebychev spline pre-edge background and normalizing the edge step to one. Powder samples were prepared in an argon-filled glovebox for measurement by mixing with dry boron nitride and packed into a slotted aluminum holder with aluminized mylar windows, sealed with crushed indium wire. Since the samples are air sensitive, the sealed holders were kept under argon until measurement, and exposed to air for less than 1 min during transfer to vacuum. Samples were measured both at 50 and 300 K using a liquid-helium cooled cryostat to test for temperature dependence of the resulting spectra. An easily oxidizable “canary” sample, such as cerium tris(tetramethylcyclopentadienyl) (CeCp3tet), was measured along with the samples to ensure that no O2 had leaked into the sample holder during measurement.

Fitting of the spectra was performed using the FITEDGE utility, a component of the RSXAP software library.102 For each spectrum, 5 peaks comprised of 50% each equal-width Gaussian and Lorentzian components (commonly termed a pseudo-Voigt) were used to model resonant transitions in the edge. The edge step was modeled as a pure error function (i.e., integrated Gaussian) with a half-width (σ) of about twice the core-hole lifetime broadening (Γ) for the Ce L3-edge (Γ = 3.27 eV). This larger width models the chemical broadening of the continuum excitations, which XPS suggest should have a double structure similar to those of the bound resonances of the edge.103 Due to strong correlation between the crystal field subpeaks of the f1 and f0 multiplets, errors in the area have been estimated using a profiling method, rather than the typical treatment based on the diagonal elements of the covariance matrix implemented in FITEDGE. In order to make accurate comparisons to the present data, curve fits to the Ce L3-edge data reported previously for (Et4N)2CeCl62 and Ce(PN*)46 were modified with a broad edge step whose position and width are constrained by the edge features.

SQUID Magnetometry

Samples of (Ph4P)2CeF6 (8.6 mg) and (Et4N)2CeCl6 (11.8 mg) were loaded into 3 mm (O.D.) quartz tubes and sandwiched between two pieces of quartz wool (QW) by a modified literature procedure.47−49 Outside the glovebox, a preweighed amount of quartz wool ((Ph4P)2CeF6, QW = 3.6 mg; (Et4N)2CeCl6, QW = 4.2 mg), which had previously been leeched with oxalic and hydrochloric acid, was inserted and packed into a quartz tube with quartz rods. Afterward, the tubes were oven-dried for 24 h at 150 °C. Inside a glovebox, crystals of both complexes were ground in oven-dried agate mortars and pestles and two 0.075” (O.D.) polyimide liners were placed inside both ends of a quartz tube. A mild vacuum was applied to one end, such that no quartz wool was pushed out; the other end was used to vacuum sample into the tube landing onto the quartz wool without touching the sidewalls. The polyimide liners were removed, and a second piece of quartz wool was inserted into the tube on top of the compound. The sample was compressed into a pellet with two quartz rods. The ends of the tube were capped with two 5 mm NMR tube rubber septa. The center of the tube was wrapped with a piece of open-cell foam, saturated with liquid nitrogen, and the ends were flame-sealed with a propane/oxygen torch. Variable temperature magnetization data were recorded from 3 to 400 K at 1 and 5 T with a 7 T Quantum Design MPMS magnetometer utilizing a superconducting quantum interference device (SQUID). Molar susceptibility, χm, was calculated using the formula

In this formula, MW is the molecular weight of the sample, m is the mass of the sample, Mmeas is the measured magnetization, Mimp is the magnetization due to an assumed ferromagnetic impurity, H is the applied field, and χQW as well as χd are the diamagnetic corrections due to the quartz wool and the sample, respectively, calculated from Pascal’s constants.51 The different applied fields were chosen to saturate Mimp so that its field dependence could be treated as a constant. The value of Mimp was allowed to vary to minimize the least-squares difference of χmT between the measured fields from 100 to 300 K.

Ce M4,5-Edge CTM Calculation Parameters

The CTM calculations on the Ce M4,5-edge of CeF62– were performed using the Theo Thole multiplet code, with modifications by Ogasawara, as maintained and used by the CTM4XAS program.79 The CTM4XAS graphical user interface does not support charge transfer calculations for the lanthanide M4,5-edges, so the calculations must be run from the command line in the underlying CTM code. This calculation was performed in analogy to a previous calculation on CeCl62–.2 The atomic parameters were kept the same, except for the spin–orbit coupling, which was reduced to 98% (versus 99% with CeCl62–). For the charge transfer component of the calculation, the hopping integrals in the ground and final states, Tgs and Tfs, were both set to 0.92 eV. The ground state charge transfer energy, ΔEgs, was set to 4.6 eV, and the final state charge transfer energy, ΔEfs, was set to 1.8 eV. Lorentzian broadenings of 0.4 and 0.6 eV were applied to the M5 and M4-edges, respectively, and Gaussian broadening of 0.25 eV was applied to both edges. The calculated spectrum was shifted by −0.15 eV to match the experimental energies. The complete set of input and output files is given in the Supporting Information.

Ground State Electronic Structure Calculations

Starting from the crystal structures, equilibrium structures of octahedral CeL62– (L = F, Cl) complexes were optimized with Kohn–Sham DFT with the ORCA program (version 5.0.3).104,105 The popular B3LYP hybrid generalized gradient approximation106 was used, in conjunction with all-electron ANO-RCC-QZP basis sets107,108 for all atoms and the scalar-relativistic, second-order Douglas–Kroll–Hess (DKH2) Hamiltonian.109 Additional B3LYP single-point energy calculations were performed on Oh structures of the complexes with the metal–ligand bond lengths fixed to the averaged distances in the crystal structures. Geometry optimizations were additionally performed with coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)],110 within the domain-based local pair natural orbital (DLPNO) formalism,111,112 by varying the Ce–L bond lengths in the octahedral complexes in increments of 0.01 Å. The resolution of identity approximation for the Coulomb and exchange terms (RIJK) was applied, together with large automatically generated auxiliary basis sets (AUTOAUX).113 Single-point energy calculations with orbital-optimized coupled cluster doubles OO-CCD114,115 were additionally performed on the “averaged” crystal structures with Ce–F and Ce–Cl bond lengths of 2.152 and 2.599 Å, respectively. Heterolytic bond dissociation energies (BDEs) were also calculated to assess the polarity of the Ce–L bonds. Counterpoise corrections were not applied because of the high quality of the basis sets used. Reported atomic shell populations and atomic charges based on the Mulliken partitioning were checked against results from natural population analyses with the NBO program,116 showing similar trends. Comments on the optimized geometries, (localized) MOs and BDEs are given in the Supporting Information file.

Ab Initio Calculation of the Ce L3-Edge and F and Cl K-Edge XAS

The crystal structures (averaged bond lengths) of CeF62– and CeCl62– were subjected to WFT calculations for determining the ligand K-edge and Ce L3-edge X-ray absorption structure (XAS) spectra. These calculations were performed with OpenMolcas.117 Following previous work on ab initio XAS,32,66,67 we performed a series of RAS-SCF118 calculations for the valence and the core excited states targeted in the XAS experiments. For the ligand K edges, the 6 ligand 1s orbitals with 12 electrons comprised RAS1 and the unoccupied, antibonding MOs with Ce(5f)–L(np) and Ce(5d)–L(np) character (t1u, t2u, eg, and t2g) comprised RAS2. These K-edge calculations were started from B3LYP orbitals. A similar strategy was employed in ref (58) for calculating the Cl K-edge spectrum of CeCl62– using a relativistic, variational multireference configuration interaction approach (MRCI). Despite using a somewhat less demanding correlation method in the present study, PT2 vs MRCI in ref (58), the calculated spectra are in excellent agreement. Concerning the Ce L3-edges, since Ce(4f)–L(np) covalency appears to various extents in both the t1u and t2u irreps, two sets of calculations were performed to obtain the total intensity, both using the Ce 2p6 core for RAS1 and the unoccupied t2g and eg MOs with Ce(5d) character in RAS3. In a first set of calculations, the t1u Ce(4f)–L(np) bonding and antibonding MOs with six electrons comprised RAS2 whereas, in a second set of calculations, RAS2 corresponded to the t2u Ce(4f)–L(np) bonding and antibonding MOs and six electrons. Performing these two sets of calculations was necessary to allow Ce(III) and Ce(IV) configurations, generated via covalency in both the t1u and t2u irreps, to contribute to the initial and final states that generate intensity under the L3-edges. In all these calculations targeting the Ce L3-edge, the ground state wave function was obtained from a state-average calculation over the four lowest energy valence states of Ag symmetry (D2h point group). Concerning the core excited state wave functions, these were obtained in state-average calculations of all possible such states in the electric dipole-allowed irreps of D2h, i.e., b1u, b2u, and b3u. Using the RAS-SCF wave functions, dynamic correlation was introduced in the state energies via RAS perturbation theory at second-order (PT2).119,120 The oscillator strengths necessary for generating intensities between the ground state and the core excited states were calculated with the RAS-SCF wave functions and RAS-PT2 energies with the RAS state-interaction (RASSI) module of OpenMolcas. For the Ce L3-edge, the ratio of the scaling factors used for the chloride vs the fluoride complex was 1.78, reflecting that the calculations produced an overall stronger intensity at the Ce L3-edge for CeF62– compared to CeCl62–, in agreement with the experimental trend. All XAS calculations used a finite-volume Gaussian representation of the nuclear charges. Modified ANO-RCC-VTZP basis sets were used in these XAS calculations. Following a previous strategy,84 the two most diffuse Ce d-type functions (exponents of 0.080 and 0.032) and ligand p-type functions (exponents of 0.155 and 0.054 for F, 0.103 and 0.041 for Cl) were removed from the basis sets in order to obtain a better description of the virtual MOs, in particular those of eg symmetry.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c07459.Complete fit parameters, additional computational details, additional data interpretation details, crystallographic information, Raman, IR, UV–vis, CV, and tables of X-ray absorption data (PDF)

Supplementary Material

ja4c07459_si_001.pdf

The authors declare no competing financial interest.

Acknowledgments

This work was supported at Lawrence Berkeley National Laboratory by Director, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences Heavy Element Chemistry (HEC) program of the United States Department of Energy (DOE) under contract DE-AC02-05CH11231 and at U. Penn. and U. Buffalo by HEC grant DE-SC0020169. Specifically, E.J.S. acknowledges support from HEC grant DE-SC0020169 for support of H.G. for the Raman spectroscopy, 19F NMR spectroscopy, and electrochemistry studies performed in this work. E.J.S. also acknowledges the JASCO facility for Spectroscopic Excellence in the Chemistry Department at the University of Pennsylvania for support of the Raman spectroscopy. J.A.B. received funding from the US-DOE through the Office of Nuclear Energy, Integrated University Program Graduate Fellowship. D.C.S. acknowledges support provided by the RECENT AIR grant agreement MySIMS no. 127324 and the computing resources provided by RECENT AIR. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract no. DE-AC02-76SF00515. The F K-edge and Ce M4,5-edge XAS described in this paper was performed at the Canadian Light Source, a national research facility of the University of Saskatchewan, which is supported by the Canada Foundation for Innovation (CFI), the Natural Sciences and Engineering Research Council (NSERC), the National Research Council (NRC), the Canadian Institutes of Health Research (CIHR), the Government of Saskatchewan, and the University of Saskatchewan.
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References

Altman A. B. ; Pacold J. I. ; Wang J. ; Lukens W. W. ; Minasian S. G. Evidence for 5d-σ and 5d-π Covalency in Lanthanide Sesquioxides from Oxygen K-Edge X-Ray Absorption Spectroscopy. Dalton Trans. 2016, 45 (24 ), 9948–9961. 10.1039/C6DT00358C.26979662
Löble M. W. ; Keith J. M. ; Altman A. B. ; Stieber S. C. E. ; Batista E. R. ; Boland K. S. ; Conradson S. D. ; Clark D. L. ; Lezama Pacheco J. ; Kozimor S. A. ; Martin R. L. ; Minasian S. G. ; Olson A. C. ; Scott B. L. ; Shuh D. K. ; Tyliszczak T. ; Wilkerson M. P. ; Zehnder R. A. Covalency in Lanthanides. An X-Ray Absorption Spectroscopy and Density Functional Theory Study of LnCl6x – (x = 3, 2). J. Am. Chem. Soc. 2015, 137 (7 ), 2506–2523. 10.1021/ja510067v.25689484
Kaltsoyannis N. ; Scott P. The F-Elements; Oxford University Press: Oxford, 1999.
Burns C. J. ; Bursten B. E. Covalency in F-Element Organometallic Complexes: Theory and Experiment. Comments Inorg. Chem. 1989, 9 (2 ), 61–93. 10.1080/02603598908035804.
Qiao Y. ; Yin H. ; Moreau L. M. ; Feng R. ; Higgins R. F. ; Manor B. C. ; Carroll P. J. ; Booth C. H. ; Autschbach J. ; Schelter E. J. Cerium(IV) Complexes with Guanidinate Ligands: Intense Colors and Anomalous Electronic Structures. Chem. Sci. 2021, 12 (10 ), 3558–3567. 10.1039/D0SC05193D.
Rice N. T. ; Su J. ; Gompa T. P. ; Russo D. R. ; Telser J. ; Palatinus L. ; Bacsa J. ; Yang P. ; Batista E. R. ; La Pierre H. S. Homoleptic Imidophosphorane Stabilization of Tetravalent Cerium. Inorg. Chem. 2019, 58 (8 ), 5289–5304. 10.1021/acs.inorgchem.9b00368.30943020
Cheisson T. ; Kersey K. D. ; Mahieu N. ; McSkimming A. ; Gau M. R. ; Carroll P. J. ; Schelter E. J. Multiple Bonding in Lanthanides and Actinides: Direct Comparison of Covalency in Thorium(IV)- and Cerium(IV)-Imido Complexes. J. Am. Chem. Soc. 2019, 141 (23 ), 9185–9190. 10.1021/jacs.9b04061.31117665
Gregson M. ; Lu E. ; McMaster J. ; Lewis W. ; Blake A. J. ; Liddle S. T. A Cerium(IV)–Carbon Multiple Bond. Angew. Chem., Int. Ed. 2013, 52 (49 ), 13016–13019. 10.1002/anie.201306984.
So Y.-M. ; Wang G.-C. ; Li Y. ; Sung H. H.-Y. ; Williams I. D. ; Lin Z. ; Leung W.-H. A Tetravalent Cerium Complex Containing a Ce = O Bond. Angew. Chem., Int. Ed. 2014, 53 (6 ), 1626–1629. 10.1002/anie.201309764.
Solola L. A. ; Zabula A. V. ; Dorfner W. L. ; Manor B. C. ; Carroll P. J. ; Schelter E. J. Cerium(IV) Imido Complexes: Structural, Computational, and Reactivity Studies. J. Am. Chem. Soc. 2017, 139 (6 ), 2435–2442. 10.1021/jacs.6b12369.28076948
Kynman A. E. ; Elghanayan L. K. ; Desnoyer A. N. ; Yang Y. ; Sévery L. ; Di Giuseppe A. ; Tilley T. D. ; Maron L. ; Arnold P. L. Controlled Monodefluorination and Alkylation of C(Sp3)–F Bonds by Lanthanide Photocatalysts: Importance of Metal–Ligand Cooperativity. Chem. Sci. 2022, 13 (47 ), 14090–14100. 10.1039/D2SC04192H.36540817
Yang Q. ; Wang Y.-H. ; Qiao Y. ; Gau M. ; Carroll P. J. ; Walsh P. J. ; Schelter E. J. Photocatalytic C–H Activation and the Subtle Role of Chlorine Radical Complexation in Reactivity. Science 2021, 372 (6544 ), 847–852. 10.1126/science.abd8408.34016778
Yin H. ; Jin Y. ; Hertzog J. E. ; Mullane K. C. ; Carroll P. J. ; Manor B. C. ; Anna J. M. ; Schelter E. J. The Hexachlorocerate(III) Anion: A Potent, Benchtop Stable, and Readily Available Ultraviolet A Photosensitizer for Aryl Chlorides. J. Am. Chem. Soc. 2016, 138 (50 ), 16266–16273. 10.1021/jacs.6b05712.27936638
Yin H. ; Carroll P. J. ; Anna J. M. ; Schelter E. J. Luminescent Ce(III) Complexes as Stoichiometric and Catalytic Photoreductants for Halogen Atom Abstraction Reactions. J. Am. Chem. Soc. 2015, 137 (29 ), 9234–9237. 10.1021/jacs.5b05411.26151154
Qiao Y. ; Schelter E. J. Lanthanide Photocatalysis. Acc. Chem. Res. 2018, 51 (11 ), 2926–2936. 10.1021/acs.accounts.8b00336.30335356
Nagata T. ; Miyajima K. ; Hardy R. A. ; Metha G. F. ; Mafuné F. Reactivity of Oxygen Deficient Cerium Oxide Clusters with Small Gaseous Molecules. J. Phys. Chem. A 2015, 119 (22 ), 5545–5552. 10.1021/acs.jpca.5b02816.25965076
Fokin A. A. ; Peleshanko S. A. ; Gunchenko P. A. ; Gusev D. V. ; Schreiner P. R. Hydrocarbon Activation with Cerium(IV) Ammonium Nitrate: Free Radical versus Oxidative Pathways. Eur. J. Org Chem. 2000, 2000 (19 ), 3357–3362. 10.1002/1099-0690(200010)2000:19<3357::AID-EJOC3357>3.0.CO;2-R.
Pham H.-L. ; Rajeshkumar T. ; Wang L. U. ; Ng Y. H. ; Wong K.-H. ; So Y.-M. ; Sung H. H. Y. ; Lortz R. ; Williams I. D. ; Maron L. ; Leung W.-H. Synthesis and Reactivity of Redox-Active Cerium(IV) Aryloxide Complexes. Organometallics 2023, 42 , 1094–1105. 10.1021/acs.organomet.2c00569.
Wong W.-H. ; Wong K.-H. ; Au-Yeung K.-C. ; So Y.-M. ; Cheung W.-M. ; Sung H. H. Y. ; Williams I. D. ; Leung W.-H. Synthesis, Structure, and Reactivity of Tetravalent Cerium Complexes Containing Oxidizing Oxyanion Ligands. J. Organomet. Chem. 2019, 899 , 120902 10.1016/j.jorganchem.2019.120902.
Qasim H. M. ; Ayass W. W. ; Donfack P. ; Mougharbel A. S. ; Bhattacharya S. ; Nisar T. ; Balster T. ; Solé-Daura A. ; Römer I. ; Goura J. ; Materny A. ; Wagner V. ; Poblet J. M. ; Bassil B. S. ; Kortz U. Peroxo-Cerium(IV)-Containing Polyoxometalates: [CeIV6(O2)9(GeW10O37)3]24–, a Recyclable Homogeneous Oxidation Catalyst. Inorg. Chem. 2019, 58 (17 ), 11300–11307. 10.1021/acs.inorgchem.9b01164.31411859
Matthias B. T. ; Suhl H. ; Corenzwit E. Ferromagnetic Superconductors. Phys. Rev. Lett. 1958, 1 (12 ), 449–450. 10.1103/PhysRevLett.1.449.
Andres K. ; Graebner J. E. ; Ott H. R. 4f-Virtual-Bound-State Formation in CeAl3 at Low Temperatures. Phys. Rev. Lett. 1975, 35 (26 ), 1779–1782. 10.1103/PhysRevLett.35.1779.
Kaindl G. ; Kalkowski G. ; Brewer W. D. ; Sampathkumaran E. V. ; Holtzberg F. ; v Wittenau A. S. 4f Occupation and Hybridization from M-Shell Excitations in Rare-Earth Materials. J. Magn. Magn. Mater. 1985, 47–48 , 181–189. 10.1016/0304-8853(85)90390-7.
Amorese A. ; Hansmann P. ; Marino A. ; Körner P. ; Willers T. ; Walters A. ; Zhou K.-J. ; Kummer K. ; Brookes N. B. ; Lin H.-J. ; Chen C.-T. ; Lejay P. ; Haverkort M. W. ; Tjeng L. H. ; Severing A. Orbital Selective Coupling in CeRh3B2: Coexistence of High Curie and High Kondo Temperatures. Phys. Rev. B 2023, 107 (11 ), 115164 10.1103/PhysRevB.107.115164.
Matar S. F. Review on Cerium Intermetallic Compounds: A Bird’s Eye Outlook through DFT. Prog. Solid State Chem. 2013, 41 (3 ), 55–85. 10.1016/j.progsolidstchem.2013.03.001.
Humphries M. Rare Earth Elements: The Global Supply Chain; Congressional Research Service: Washington, D.C., 2013; p R41347.
Bianconi A. ; Marcelli A. ; Dexpert H. ; Karnatak R. ; Kotani A. ; Jo T. ; Petiau J. Specific Intermediate-Valence State of Insulating 4f Compounds Detected by L3 x-Ray Absorption. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 35 (2 ), 806–812. 10.1103/PhysRevB.35.806.
Dexpert H. ; Karnatak R. C. ; Esteva J.-M. ; Connerade J. P. ; Gasgnier M. ; Caro P. E. ; Albert L. X-Ray Absorption Studies of CeO2, PrO2, and TbO2. II. Rare-Earth Valence State by LIII Absorption Edges. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 36 (3 ), 1750–1753. 10.1103/PhysRevB.36.1750.
Kaindl G. ; Schmiester G. ; Sampathkumaran E. V. ; Wachter P. Pressure-Induced Changes in LIII x-Ray-Absorption near-Edge Structure of CeO2 and CeF4: Relevance to 4f-Electronic Structure. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 38 (14 ), 10174–10177. 10.1103/PhysRevB.38.10174.
Kotani A. ; Kvashnina K. O. ; Butorin S. M. ; Glatzel P. A New Method of Directly Determining the Core–Hole Effect in the Ce L3 XAS of Mixed Valence Ce Compounds—An Application of Resonant X-Ray Emission Spectroscopy. J. Electron Spectrosc. Relat. Phenom. 2011, 184 (3–6 ), 210–215. 10.1016/j.elspec.2010.12.028.
Duignan T. J. ; Autschbach J. Impact of the Kohn–Sham Delocalization Error on the 4f Shell Localization and Population in Lanthanide Complexes. J. Chem. Theory Comput. 2016, 12 (7 ), 3109–3121. 10.1021/acs.jctc.6b00238.27224494
Sergentu D. ; Booth C. H. ; Autschbach J. Probing Multiconfigurational States by Spectroscopy: The Cerium XAS L3-edge Puzzle. Chem.—Eur. J. 2021, 27 (25 ), 7239–7251. 10.1002/chem.202100145.33566372
Glaser T. ; Hedman B. ; Hodgson K. O. ; Solomon E. I. Ligand K-Edge X-Ray Absorption Spectroscopy: A Direct Probe of Ligand–Metal Covalency. Acc. Chem. Res. 2000, 33 (12 ), 859–868. 10.1021/ar990125c.11123885
Solomon E. I. ; Hedman B. ; Hodgson K. O. ; Dey A. ; Szilagyi R. K. Ligand K-Edge X-Ray Absorption Spectroscopy: Covalency of Ligand–Metal Bonds. Coord. Chem. Rev. 2005, 249 (1–2 ), 97–129. 10.1016/j.ccr.2004.03.020.
Hedman B. ; Hodgson K. O. ; Solomon E. I. X-Ray Absorption Edge Spectroscopy of Ligands Bound to Open-Shell Metal Ions: Chlorine K-Edge Studies of Covalency in CuCl42–. J. Am. Chem. Soc. 1990, 112 (4 ), 1643–1645. 10.1021/ja00160a062.
Neese F. ; Hedman B. ; Hodgson K. O. ; Solomon E. I. Relationship between the Dipole Strength of Ligand Pre-Edge Transitions and Metal–Ligand Covalency. Inorg. Chem. 1999, 38 (21 ), 4854–4860. 10.1021/ic990461p.11671216
Shadle S. E. ; Hedman B. ; Hodgson K. O. ; Solomon E. I. Ligand K-Edge x-Ray Absorption Spectroscopic Studies: Metal-Ligand Covalency in a Series of Transition Metal Tetrachlorides. J. Am. Chem. Soc. 1995, 117 (8 ), 2259–2272. 10.1021/ja00113a015.
Albright T. ; Burdett J. ; Whangbo M.-H. Orbital Interactions in Chemistry; John Wiley & Sons, 2013.
Whangbo M.-H. ; Schlegel H. B. ; Wolfe S. Molecular Orbitals from Group Orbitals. 3. Quantitative Perturbational Molecular Orbital Analysis of Ab Initio SCF-MO Wave Functions. J. Am. Chem. Soc. 1977, 99 (5 ), 1296–1304. 10.1021/ja00447a002.
Burdett J. K. The .sigma. strength of ligands coordinated to transition metal ions. J. Am. Chem. Soc. 1979, 101 (3 ), 580–583. 10.1021/ja00497a015.
Hoffmann R. Interaction of Orbitals through Space and through Bonds. Acc. Chem. Res. 1971, 4 (1 ), 1–9. 10.1021/ar50037a001.
Balasekaran S. M. ; Hagenbach A. ; Lentz D. ; Poineau F. Tetraethylammonium Hexafluoro Uranate(IV), Hafnate(IV), and Cerate(IV) Salts: Preparation and Solid-state Structure. Z. Anorg. Allg. Chem. 2019, 645 (16 ), 1052–1056. 10.1002/zaac.201900135.
Forrest I. W. ; Lane A. P. Single-Crystal Polarized Infrared and Raman Spectra and Normal-Coordinate Analysis of Some Group 4 Complex Hexafluorometalates. Inorg. Chem. 1976, 15 (2 ), 265–269. 10.1021/ic50156a004.
Brown T. L. ; McDugle W. G. ; Kent L. G. Vibrational and Pure Nuclear Quadrupole Resonance Spectra of Hexahalometalates. J. Am. Chem. Soc. 1970, 92 (12 ), 3645–3653. 10.1021/ja00715a017.
Nakamoto K. Infrared and Raman Spectra of Inorganic and Coordination Compounds: Part A: Theory and Applications in Inorganic Chemistry; John Wiley & Sons, Inc., 2009.
Adams D. M. ; Morris D. M. Vibrational Spectra of Halides and Complex Halides. Part IV. Some Tetrahalogenothallates and the Effects of d-Electronic Structure on the Frequencies of Hexachlorometallates. J. Chem. Soc. A 1968, 694–695. 10.1039/j19680000694.
Booth C. H. ; Kazhdan D. ; Werkema E. L. ; Walter M. D. ; Lukens W. W. ; Bauer E. D. ; Hu Y.-J. ; Maron L. ; Eisenstein O. ; Head-Gordon M. ; Andersen R. A. Intermediate-Valence Tautomerism in Decamethylytterbocene Complexes of Methyl-Substituted Bipyridines. J. Am. Chem. Soc. 2010, 132 (49 ), 17537–17549. 10.1021/ja106902s.21090709
Booth C. H. ; Walter M. D. ; Kazhdan D. ; Hu Y.-J. ; Lukens W. W. ; Bauer E. D. ; Maron L. ; Eisenstein O. ; Andersen R. A. Decamethylytterbocene Complexes of Bipyridines and Diazabutadienes: Multiconfigurational Ground States and Open-Shell Singlet Formation. J. Am. Chem. Soc. 2009, 131 (18 ), 6480–6491. 10.1021/ja809624w.19385617
Walter M. D. ; Booth C. H. ; Lukens W. W. ; Andersen R. A. Cerocene Revisited: The Electronic Structure of and Interconversion Between Ce2(C8H8)3 and Ce(C8H8)2. Organometallics 2009, 28 (3 ), 698–707. 10.1021/om7012327.
Walter M. D. ; Schultz M. ; Andersen R. A. Weak Paramagnetism in Compounds of the Type Cp′2Yb(Bipy). New J. Chem. 2006, 30 (2 ), 238–246. 10.1039/b512865j.
Bain G. A. ; Berry J. F. Diamagnetic Corrections and Pascal’s Constants. J. Chem. Educ. 2008, 85 (4 ), 532 10.1021/ed085p532.
Myers A. J. ; Tarlton M. L. ; Kelley S. P. ; Lukens W. W. ; Walensky J. R. Synthesis and Utility of Neptunium(III) Hydrocarbyl Complex. Angew. Chem., Int. Ed. 2019, 58 (42 ), 14891–14895. 10.1002/anie.201906324.
Moreau L. M. ; Lapsheva E. ; Amaro-Estrada J. I. ; Gau M. R. ; Carroll P. J. ; Manor B. C. ; Qiao Y. ; Yang Q. ; Lukens W. W. ; Sokaras D. ; Schelter E. J. ; Maron L. ; Booth C. H. Electronic Structure Studies Reveal 4f/5d Mixing and Its Effect on Bonding Characteristics in Ce-Imido and -Oxo Complexes. Chem. Sci. 2022, 13 (6 ), 1759–1773. 10.1039/D1SC06623D.35282640
Booth C. H. ; Walter M. D. ; Daniel M. ; Lukens W. W. ; Andersen R. A. Self-Contained Kondo Effect in Single Molecules. Phys. Rev. Lett. 2005, 95 (26 ), 267202 10.1103/PhysRevLett.95.267202.16486392
Halbach R. L. ; Nocton G. ; Booth C. H. ; Maron L. ; Andersen R. A. Cerium Tetrakis(Tropolonate) and Cerium Tetrakis(Acetylacetonate) Are Not Diamagnetic but Temperature-Independent Paramagnets. Inorg. Chem. 2018, 57 (12 ), 7290–7298. 10.1021/acs.inorgchem.8b00928.29863340
Van Vleck J. H. The Theory of Electric and Magnetic Susceptibilities; Clarendon Press, 1932.
Balazs G. ; Cloke F. G. N. ; Green J. C. ; Harker R. M. ; Harrison A. ; Hitchcock P. B. ; Jardine C. N. ; Walton R. Cerium(III) and Cerium(IV) Bis(η8-Pentalene) Sandwich Complexes: Synthetic, Structural, Spectroscopic, and Theoretical Studies. Organometallics 2007, 26 (13 ), 3111–3119. 10.1021/om7002738.
Shumilov K. D. ; Jenkins A. J. ; La Pierre H. S. ; Vlaisavljevich B. ; Li X. Overdestabilization vs Overstabilization in the Theoretical Analysis of F-Orbital Covalency. J. Am. Chem. Soc. 2024, 146 (17 ), 12030–12039. 10.1021/jacs.4c01665.38648269
Wuilloud E. ; Delley B. ; Schneider W.-D. ; Baer Y. Spectroscopic Evidence for Localized and Extended f-Symmetry States in CeO2. Phys. Rev. Lett. 1984, 53 (2 ), 202–205. 10.1103/PhysRevLett.53.202.
Mooßen O. ; Dolg M. Two Interpretations of the Cerocene Electronic Ground State. Chem. Phys. Lett. 2014, 594 , 47–50. 10.1016/j.cplett.2014.01.022.
Ashley A. ; Balazs G. ; Cowley A. ; Green J. ; Booth C. H. ; O’Hare D. Bis(Permethylpentalene)Cerium – Another Ambiguity in Lanthanide Oxidation State. Chem. Commun. 2007, 1515–1517. 10.1039/b700303j.
Minasian S. G. ; Batista E. R. ; Booth C. H. ; Clark D. L. ; Keith J. M. ; Kozimor S. A. ; Lukens W. W. ; Martin R. L. ; Shuh D. K. ; Stieber S. C. E. ; Tylisczcak T. ; Wen X. Quantitative Evidence for Lanthanide-Oxygen Orbital Mixing in CeO2, PrO2, and TbO2. J. Am. Chem. Soc. 2017, 139 (49 ), 18052–18064. 10.1021/jacs.7b10361.29182343
Kotani A. Core-hole Effect in the Ce L3 X-ray Absorption Spectra of CeO2 and CeFe2: New Examination by Using Resonant X-ray Emission Spectroscopy. Mod. Phys. Lett. B 2013, 27 (16 ), 1330012 10.1142/S0217984913300123.
Sham T. K. ; Gordon R. A. ; Heald S. M. Resonant Inelastic X-Ray Scattering at the Ce L3 Edge of CePO4 and CeO2: Implications for the Valence of CeO2 and Related Phenomena. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72 (3 ), 035113 10.1103/PhysRevB.72.035113.
Rice N. T. ; Popov I. A. ; Russo D. R. ; Gompa T. P. ; Ramanathan A. ; Bacsa J. ; Batista E. R. ; Yang P. ; La Pierre H. S. Comparison of Tetravalent Cerium and Terbium Ions in a Conserved, Homoleptic Imidophosphorane Ligand Field. Chem. Sci. 2020, 11 (24 ), 6149–6159. 10.1039/D0SC01414A.32832060
Sergentu D.-C. ; Autschbach J. X-Ray Absorption Spectra of f-Element Complexes: Insight from Relativistic Multiconfigurational Wavefunction Theory. Dalton Trans. 2022, 51 (5 ), 1754–1764. 10.1039/D1DT04075H.35022645
Sergentu D.-C. ; Duignan T. J. ; Autschbach J. Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-Ray Absorption Spectra of Actinide Complexes. J. Phys. Chem. Lett. 2018, 9 (18 ), 5583–5591. 10.1021/acs.jpclett.8b02412.30180572
Kaindl G. ; Kalkowski G. ; Brewer W. D. ; Perscheid B. ; Holtzberg F. M-edge X-ray Absorption Spectroscopy of 4f Instabilities in Rare-earth Systems (Invited). J. Appl. Phys. 1984, 55 (6 ), 1910–1915. 10.1063/1.333517.
Jo T. ; Kotani A. Effect of Valence Mixing on Multiplet Structure in Core Photoabsorption Spectra for Ce Compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 38 (1 ), 830–833. 10.1103/PhysRevB.38.830.
Thole B. T. ; van der Laan G. ; Fuggle J. C. ; Sawatzky G. A. ; Karnatak R. C. ; Esteva J.-M. 3d x-Ray-Absorption Lines and the 3d94fn+1 Multiplets of the Lanthanides. Phys. Rev. B: Condens. Matter Mater. Phys. 1985, 32 (8 ), 5107–5118. 10.1103/PhysRevB.32.5107.
Hu Z. ; Kaindl G. ; Müller B. G. Core-Level Spectroscopy of the Tetravalent Lanthanide Compounds M3LnF7 (with M = Cs, Rb; Ln = Ce, Pr, Nd, Tb, Dy). J. Alloys Compd. 1997, 246 (1 ), 177–185. 10.1016/S0925-8388(96)02474-7.
Kaindl G. ; Brewer W. D. ; Kalkowski G. ; Holtzberg F. M-Edge X-Ray Absorption Spectroscopy: A New Tool for Dilute Mixed-Valent Materials. Phys. Rev. Lett. 1983, 51 (22 ), 2056–2059. 10.1103/PhysRevLett.51.2056.
Kalkowski G. ; Kaindl G. ; Wortmann G. ; Lentz D. ; Krause S. 4 f-Ligand Hybridization in CeF4 and TbF4 Probed by Core-Level Spectroscopies. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37 (3 ), 1376–1382. 10.1103/PhysRevB.37.1376.
Manoubi T. ; Colliex C. ; Rez P. Quantitative Electron Energy Loss Spectroscopy on M45 Edges in Rare Earth Oxides. J. Electron Spectrosc. Relat. Phenom. 1990, 50 (1 ), 1–18. 10.1016/0368-2048(90)80001-Q.
Meihaus K. R. ; Minasian S. G. ; Lukens W. W. ; Kozimor S. A. ; Shuh D. K. ; Tyliszczak T. ; Long J. R. Influence of Pyrazolate vs N-Heterocyclic Carbene Ligands on the Slow Magnetic Relaxation of Homoleptic Trischelate Lanthanide(III) and Uranium(III) Complexes. J. Am. Chem. Soc. 2014, 136 (16 ), 6056–6068. 10.1021/ja501569t.24650296
de Groot F. ; Kotani A. Core Level Spectroscopy of Solids, 1st ed.; CRC Press: Boca Raton, 2008.
Moore K. T. ; van der Laan G. ; Haire R. G. ; Wall M. A. ; Schwartz A. J. Oxidation and Aging in U and Pu Probed by Spin-Orbit Sum Rule Analysis: Indications for Covalent Metal-Oxide Bonds. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73 (3 ), 033109 10.1103/PhysRevB.73.033109.
Kotani A. ; Ogasawara H. Theory of Core-Level Spectroscopy of Rare-Earth Oxides. J. Electron Spectrosc. Relat. Phenom. 1992, 60 (4 ), 257–299. 10.1016/0368-2048(92)80024-3.
Stavitski E. ; de Groot F. M. F. The CTM4XAS Program for EELS and XAS Spectral Shape Analysis of Transition Metal L Edges. Micron 2010, 41 (7 ), 687–694. 10.1016/j.micron.2010.06.005.20637641
Minasian S. G. ; Keith J. M. ; Batista E. R. ; Boland K. S. ; Kozimor S. A. ; Martin R. L. ; Shuh D. K. ; Tyliszczak T. ; Vernon L. J. Carbon K-Edge X-Ray Absorption Spectroscopy and Time-Dependent Density Functional Theory Examination of Metal–Carbon Bonding in Metallocene Dichlorides. J. Am. Chem. Soc. 2013, 135 (39 ), 14731–14740. 10.1021/ja405844j.24047199
Minasian S. G. ; Keith J. M. ; Batista E. R. ; Boland K. S. ; Clark D. L. ; Conradson S. D. ; Kozimor S. A. ; Martin R. L. ; Schwarz D. E. ; Shuh D. K. ; Wagner G. L. ; Wilkerson M. P. ; Wolfsberg L. E. ; Yang P. Determining Relative f and d Orbital Contributions to M–Cl Covalency in MCl62–(M = Ti, Zr, Hf, U) and UOCl5– Using Cl K-Edge X-Ray Absorption Spectroscopy and Time-Dependent Density Functional Theory. J. Am. Chem. Soc. 2012, 134 (12 ), 5586–5597. 10.1021/ja2105015.22404133
Minasian S. G. ; Keith J. M. ; Batista E. R. ; Boland K. S. ; Bradley J. A. ; Daly S. R. ; Kozimor S. A. ; Lukens W. W. ; Martin R. L. ; Nordlund D. ; Seidler G. T. ; Shuh D. K. ; Sokaras D. ; Tyliszczak T. ; Wagner G. L. ; Weng T.-C. ; Yang P. Covalency in Metal–Oxygen Multiple Bonds Evaluated Using Oxygen K-Edge Spectroscopy and Electronic Structure Theory. J. Am. Chem. Soc. 2013, 135 (5 ), 1864–1871. 10.1021/ja310223b.23351138
Branson J. A. ; Smith P. W. ; Arnold J. ; Minasian S. G. Analyzing the Intensities of K-Edge Transitions in X2 Molecules (X = F, Cl, Br) for Use in Ligand K-Edge XAS. Inorg. Chem. 2024, 63 (34 ), 15557–15562. 10.1021/acs.inorgchem.4c01666.39112430
Su J. ; Batista E. R. ; Boland K. S. ; Bone S. E. ; Bradley J. A. ; Cary S. K. ; Clark D. L. ; Conradson S. D. ; Ditter A. S. ; Kaltsoyannis N. ; Keith J. M. ; Kerridge A. ; Kozimor S. A. ; Löble M. W. ; Martin R. L. ; Minasian S. G. ; Mocko V. ; La Pierre H. S. ; Seidler G. T. ; Shuh D. K. ; Wilkerson M. P. ; Wolfsberg L. E. ; Yang P. Energy-Degeneracy-Driven Covalency in Actinide Bonding. J. Am. Chem. Soc. 2018, 140 (51 ), 17977–17984. 10.1021/jacs.8b09436.30540455
Wolfsberg M. ; Helmholz L. The Spectra and Electronic Structure of the Tetrahedral Ions MnO4–, CrO4––, and ClO4–. J. Chem. Phys. 1952, 20 (5 ), 837–843. 10.1063/1.1700580.
Ionization Potentials of Atoms and Atomic Ions–Section 10. Atomic, Molecular, and Optical Physics. In CRC Handbook of Chemistry and Physics; Lide D. R. , Ed.; CRC Press, 2004; pp 10-178–10-180.
Koopmans T. Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms. Physica 1934, 1 (1–6 ), 104–113. 10.1016/S0031-8914(34)90011-2.
Edelstein N. M. ; Lukens W. W. F.-O. Mixing in the Octahedral f2 Compounds UX62– [X = F, Br, Cl, I] and PrCl63–. J. Phys. Chem. A 2020, 124 (21 ), 4253–4262. 10.1021/acs.jpca.0c02022.32354208
Brewer L. Energies of the Electronic Configurations of the Singly, Doubly, and Triply Ionized Lanthanides and Actinides. J. Opt. Soc. Am. 1971, 61 (12 ), 1666–1682. 10.1364/JOSA.61.001666.
Lukens W. W. ; Edelstein N. M. ; Magnani N. ; Hayton T. W. ; Fortier S. ; Seaman L. A. Quantifying the σ and π Interactions between U(V) f Orbitals and Halide, Alkyl, Alkoxide, Amide and Ketimide Ligands. J. Am. Chem. Soc. 2013, 135 (29 ), 10742–10754. 10.1021/ja403815h.23837946
Kutzelnigg W. Chemical Bonding in Higher Main Group Elements. Angew. Chem., Int. Ed. 1984, 23 (4 ), 272–295. 10.1002/anie.198402721.
Kaupp M. The Role of Radial Nodes of Atomic Orbitals for Chemical Bonding and the Periodic Table. J. Comput. Chem. 2007, 28 (1 ), 320–325. 10.1002/jcc.20522.17143872
Pyykkö P. Dirac-Fock One-Centre Calculations Part 8. The 1Σ States of ScH, YH, LaH, AcH, TmH, LuH and LrH. Phys. Scr. 1979, 20 (5–6 ), 647–651. 10.1088/0031-8949/20/5-6/016.
Burns G. ; Axe J. D. In Optical Properties of Ions in Crystals; Chrosswhite H. M. , Moos H. W. , Eds.; Interscience: New York, 1967.
Whangbo M. ; Hoffmann R. Counterintuitive Orbital Mixing. J. Chem. Phys. 1978, 68 (12 ), 5498–5500. 10.1063/1.435677.
Pereiro F. A. ; Galley S. S. ; Jackson J. A. ; Shafer J. C. Contemporary Assessment of Energy Degeneracy in Orbital Mixing with Tetravalent F-Block Compounds. Inorg. Chem. 2024, 63 (21 ), 9687–9700. 10.1021/acs.inorgchem.3c03828.38743642
CrysAlis PRO; Agilent Technologies Ltd: Yarnton, Oxfordshire, England, 2013.
Dolomanov O. V. ; Bourhis L. J. ; Gildea R. J. ; Howard J. a. K. ; Puschmann H. OLEX2: A Complete Structure Solution, Refinement and Analysis Program. J. Appl. Crystallogr. 2009, 42 (2 ), 339–341. 10.1107/S0021889808042726.
Sheldrick G. M. SHELXT – Integrated Space-Group and Crystal-Structure Determination. Acta Crystallogr., Sect. A: Found. Adv. 2015, 71 (1 ), 3–8. 10.1107/S2053273314026370.25537383
Sheldrick G. M. Crystal Structure Refinement with SHELXL. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2015, 71 (1 ), 3–8. 10.1107/S2053229614024218.
George G. N. EDG_FIT; Stanford Synchrotron Radiation Laboratory: Stanford Linear Accelerator Center: Stanford, CA, 2023.
Booth C. H. ; Bridges F. Real-Space X-Ray Absorption Package (RSXAP); Wiley, 2021.
Paparazzo E. ; Ingo G. M. ; Zacchetti N. X-ray Induced Reduction Effects at CeO2 Surfaces: An X-ray Photoelectron Spectroscopy Study. J. Vac. Sci. Technol., A 1991, 9 (3 ), 1416–1420. 10.1116/1.577638.
Neese F. Software Update: The ORCA Program System—Version 5.0. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2022, 12 (5 ), e1606 10.1002/wcms.1606.
Neese F. The ORCA Program System. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2 (1 ), 73–78. 10.1002/wcms.81.
Stephens P. J. ; Devlin F. J. ; Chabalowski C. F. ; Frisch M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98 (45 ), 11623–11627. 10.1021/j100096a001.
Roos B. O. ; Lindh R. ; Malmqvist P.-Å. ; Veryazov V. ; Widmark P.-O. ; Borin A. C. New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3. J. Phys. Chem. A 2008, 112 (45 ), 11431–11435. 10.1021/jp803213j.18928264
Roos B. O. ; Lindh R. ; Malmqvist P.-Å. ; Veryazov V. ; Widmark P.-O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set. J. Phys. Chem. A 2004, 108 (15 ), 2851–2858. 10.1021/jp031064+.
Reiher M. Douglas–Kroll–Hess Theory: A Relativistic Electrons-Only Theory for Chemistry. Theor. Chem. Acc. 2006, 116 (1–3 ), 241–252. 10.1007/s00214-005-0003-2.
Raghavachari K. ; Trucks G. W. ; Pople J. A. ; Head-Gordon M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157 (6 ), 479–483. 10.1016/S0009-2614(89)87395-6.
Riplinger C. ; Neese F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138 (3 ), 034106 10.1063/1.4773581.23343267
Guo Y. ; Riplinger C. ; Becker U. ; Liakos D. G. ; Minenkov Y. ; Cavallo L. ; Neese F. Communication: An Improved Linear Scaling Perturbative Triples Correction for the Domain Based Local Pair-Natural Orbital Based Singles and Doubles Coupled Cluster Method [DLPNO-CCSD(T)]. J. Chem. Phys. 2018, 148 (1 ), 011101 10.1063/1.5011798.29306283
Stoychev G. L. ; Auer A. A. ; Neese F. Automatic Generation of Auxiliary Basis Sets. J. Chem. Theory Comput. 2017, 13 (2 ), 554–562. 10.1021/acs.jctc.6b01041.28005364
Purvis G. D. ; Bartlett R. J. A Full Coupled-cluster Singles and Doubles Model: The Inclusion of Disconnected Triples. J. Chem. Phys. 1982, 76 (4 ), 1910–1918. 10.1063/1.443164.
Bozkaya U. ; Turney J. M. ; Yamaguchi Y. ; Schaefer H. F. ; Sherrill C. D. Quadratically Convergent Algorithm for Orbital Optimization in the Orbital-Optimized Coupled-Cluster Doubles Method and in Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory. J. Chem. Phys. 2011, 135 (10 ), 104103 10.1063/1.3631129.21932872
Glendening E. D. ; Landis C. R. ; Weinhold F. NBO 6.0: Natural Bond Orbital Analysis Program. J. Comput. Chem. 2013, 34 (16 ), 1429–1437. 10.1002/jcc.23266.23483590
Li Manni G. ; Fdez Galván I. ; Alavi A. ; Aleotti F. ; Aquilante F. ; Autschbach J. ; Avagliano D. ; Baiardi A. ; Bao J. J. ; Battaglia S. ; Birnoschi L. ; Blanco-González A. ; Bokarev S. I. ; Broer R. ; Cacciari R. ; Calio P. B. ; Carlson R. K. ; Carvalho Couto R. ; Cerdán L. ; Chibotaru L. F. ; Chilton N. F. ; Church J. R. ; Conti I. ; Coriani S. ; Cuéllar-Zuquin J. ; Daoud R. E. ; Dattani N. ; Decleva P. ; de Graaf C. ; Delcey M. G. ; De Vico L. ; Dobrautz W. ; Dong S. S. ; Feng R. ; Ferré N. ; FilatovGulak M. ; Gagliardi L. ; Garavelli M. ; González L. ; Guan Y. ; Guo M. ; Hennefarth M. R. ; Hermes M. R. ; Hoyer C. E. ; Huix-Rotllant M. ; Jaiswal V. K. ; Kaiser A. ; Kaliakin D. S. ; Khamesian M. ; King D. S. ; Kochetov V. ; Krośnicki M. ; Kumaar A. A. ; Larsson E. D. ; Lehtola S. ; Lepetit M. B. ; Lischka H. ; López Ríos P. ; Lundberg M. ; Ma D. ; Mai S. ; Marquetand P. ; Merritt I. C. D. ; Montorsi F. ; Mörchen M. ; Nenov A. ; Nguyen V. H. A. ; Nishimoto Y. ; Oakley M. S. ; Olivucci M. ; Oppel M. ; Padula D. ; Pandharkar R. ; Phung Q. M. ; Plasser F. ; Raggi G. ; Rebolini E. ; Reiher M. ; Rivalta I. ; Roca-Sanjuán D. ; Romig T. ; Safari A. A. ; Sánchez-Mansilla A. ; Sand A. M. ; Schapiro I. ; Scott T. R. ; Segarra-Martí J. ; Segatta F. ; Sergentu D. C. ; Sharma P. ; Shepard R. ; Shu Y. ; Staab J. K. ; Straatsma T. P. ; Sørensen L. K. ; Tenorio B. N. C. ; Truhlar D. G. ; Ungur L. ; Vacher M. ; Veryazov V. ; Voß T. A. ; Weser O. ; Wu D. ; Yang X. ; Yarkony D. ; Zhou C. ; Zobel J. P. ; Lindh R. ; Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry. J. Chem. Theory Comput. 2023, 19 (20 ), 6933–6991. 10.1021/acs.jctc.3c00182.37216210
Roos B. O. ; Taylor P. R. ; Sigbahn P. E. M. A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48 (2 ), 157–173. 10.1016/0301-0104(80)80045-0.
Andersson K. ; Malmqvist P. ; Roos B. O. Second-order Perturbation Theory with a Complete Active Space Self-consistent Field Reference Function. J. Chem. Phys. 1992, 96 (2 ), 1218–1226. 10.1063/1.462209.
Malmqvist P. Å. ; Pierloot K. ; Shahi A. R. M. ; Cramer C. J. ; Gagliardi L. The Restricted Active Space Followed by Second-Order Perturbation Theory Method: Theory and Application to the Study of CuO2 and Cu2O2 Systems. J. Chem. Phys. 2008, 128 (20 ), 204109 10.1063/1.2920188.18513012
