Electronic structure studies reveal 4f/5d mixing and its effect on bonding characteristics in Ce-imido and -oxo complexes

This study presents the role of 5d orbitals in the bonding, and electronic and magnetic structure of Ce imido and oxo complexes synthesized with a tris(hydroxylaminato) [((2-tBuNO)C6H4CH2)3N]3− (TriNOx3−) ligand framework, including the reported synthesis and characterization of two new alkali metal-capped Ce oxo species. X-ray spectroscopy measurements reveal that the imido and oxo materials exhibit an intermediate valent ground state of the Ce, displaying hallmark features in the Ce LIII absorption of partial f-orbital occupancy that are relatively constant for all measured compounds. These spectra feature a double peak consistent with other formal Ce(iv) compounds. Magnetic susceptibility measurements reveal enhanced levels of temperature-independent paramagnetism (TIP). In contrast to systems with direct bonding to an aromatic ligand, no clear correlation between the level of TIP and f-orbital occupancy is observed. CASSCF calculations defy a conventional van Vleck explanation of the TIP, indicating a single-reference ground state with no low-lying triplet excited state, despite accurately predicting the measured values of f-orbital occupancy. The calculations do, however, predict strong 4f/5d hybridization. In fact, within these complexes, despite having similar f-orbital occupancies and therefore levels of 4f/5d hybridization, the d-state distributions vary depending on the bonding motif (Ce 
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 O vs. CeN) of the complex, and can also be fine-tuned based on varying alkali metal cation capping species. This system therefore provides a platform for understanding the characteristic nature of Ce multiple bonds and potential impact that the associated d-state distribution may have on resulting reactivity.


XANES Sample Holder Integrity
Figure S12. Standard XANES spectra. CeCp tet 3 (Ce(III)) and CeO 2 (Ce(IV)) standards are shown to demonstrate the features expected for formal Ce(III) vs. formal Ce(IV) compounds. CeCp tet

Temperature-dependent XANES spectra
From the plots below in Figures S9 and S10, no temperature dependence in the XANES or HERFD spectra was observed, suggesting no changes in electronic structure of the Ce TriNOx complexes as a function of temperature. XANES data were available for all samples except for (2-Cs) 4 , so the HERFD data are instead displayed here. Figure S13. L III edge XANES spectra of TriNO x complexes at varying temperatures. None of the complexes exhibit temperature dependent spectral differences at 50 K (dotted lines) versus 300 K (solid lines in 1-H, 1-Li, 1-Rb, 1, (2-K) 4 , and (2-Rb) 4 ) or 200 K (solid lines in 1-K and 1-Cs). Figure S14. HERFD spectra of (2-Cs) 4 show no temperature-dependent differences between 50 K and 200 K. HERFD data were shown instead of XANES, as temperature-dependent XANES data on this sample was not collected.

XANES fitting methods
XANES data were fit in order to extract n(f 0 ) according to previously described methods. 1-3 The fits consisted of a sum of a step-like function to model the absorption edge and two Gaussians to fit peaks associated with f 1,2 and f 0 configurations, in addition to a third Gaussian fit to a shoulder in the EXAFS region. The step-like function (integrated Gaussian) models excitations into the continuum whose position is given by a weighted average of the f 1,2 and f 0 peak energies, rather than using two step-like functions, in order to reduce the number of parameters in the fit and to control correlations between the fit parameters. This edge step is defined according to the expression: ', and the Gaussians defined according to the expression: where E is the incident energy, e i is the peak energy, σ i is the half-width of the Gaussian and I i is the intensity of peak i. E 0 is constrained to be the average of the peak energies of f 1,2 and f 0 weighted by the area under each associated Gaussian, A i . The Gaussian widths of the f 1,2 and f 0 peaks were held equal. The calculation of error bars for fitting parameters was achieved using a covariance matrix assuming normal distributions for variances in the data. Normally, the f-occupancy n f is calculated via: where A III and A IV are the areas for the so-called Ce(III) and Ce(IV) features in the spectra, as described below. However it is possible that any f 2 contribution will affect the area of the A(III) peak. This issue has been noted for Yb edges. 2 To avoid this issue, we instead report here the f 0 contribution: Error bars on calculated n(f 0 ) values determined from the f 1,2 and f 0 peak areas are estimated to be about 0.03 normalized units. Parameters reported without error bars were held fixed or constrained during the fit.

Results from XANES fitting used to determine n(f 0 )
The following figures and tables show representative results from XANES fitting. In some cases, more than one data set per sample was collected, in which case the numbers in Table 1 of the manuscript represent average n(f 0 ) values, where the error bars encompass any variation from data set to data set, which was small. Note that the fit quality, especially for the (2-M) 4 samples, is not as high as has previously been reported in other formal Ce(IV) complexes. 3,4 This is due to increased splitting of the 5d manifold. Despite this difference in the model, the 4f/5d feature was not used in determining n(f 0 ), given the correlation with other parameters in the fitting procedure. A 3-peak fit was also attempted that uses a third peak fit to the 4f/5d feature and is shown in figure  10 and described below. We demonstrate, however, that the overall integrated intensity ratios between f 1,2 and f 0 are conserved regardless of using a 3 vs. 2-peak fitting model, and therefore the n(f 0 ) results are deemed reliable to within the estimated errors. The pre-edge feature at ~5715 eV which is thought to arise from either 2p-4f quadrupole excitation 5 or from mixed d-and f-states 6 was not included in the fit due to its small contribution and high correlation with other parameters.    Table S1. Fit parameter results for f 1,2 and f 0 integrated peak areas. Error estimates are determined from the covariance matrix and data errors determined by assuming the fitted  2 parameter equals the degrees of freedom in the fit.

XANES fitting using a 3-peak vs. 2-peak model
In order to estimate the error introduced into the n(f 0 ) fits as a result of using a 2-peak model that cannot account for the "middle peak" which results from d-state broadening, a 3-peak simulation was used. Figure 10a shows a 3 peak simulation to the (2-K) 4 XANES spectrum. As with the 2-peak fits, an EXAFS shoulder at higher energy is also included. The position of the middle peak was fixed to the weighted average of the energies of the f 1,2 and f 0 peaks. The simulation appears to match the experimental spectrum well, with an n(f 0 ) value of 0.395. Through fitting the standard 2-peak model introduced earlier to this 3-peak simulation, the n(f 0 ) value from the fit could be compared to a "known" n(f 0 ) value from the simulation. The 2-peak model fit to the 3-peak simulation from Figure 10a is shown in Figure 10b. Interestingly, the n(f 0 ) result from the 2-peak fit was nearly identical to that from the 3-peak simulation 0.4 (3). Therefore, the error bar reported for the n(f 0 ) values extracted from the 2-peak fits presented above should accurately encompass any error that would result from using a 2-peak vs. 3-peak model. Figure S16. a) A simulation of (2-K) 4 using 3 peaks (f 1,2 , f 0 and an additional middle peak (red)) with a known n(f 0 ) value of 0.395 matched well with the (2-K) 4 experimental XANES data in comparison to the 2-peak fits to the (2-M) 4 sample spectra. When the simulation was fit with a 2-peak model (b) the resulting n(f 0 ) value extracted was 0.4 (3). Therefore, the 2-peak model was shown to still result in a representative value for n(f 0 ) and legitimizes its use.  4 5725.7 5735.7 (2-Rb) 4 5725.8 5735.9 (2-Cs) 4 5725.9 5735.7

Magnetic susceptibility curves
Magnetic susceptibility curves for all samples are shown. In cases where more than one data set was collected, average χ 0 values have been reported in Table 1 of the manuscript, with error bars included to represent variation in results. Here, only one representative data set per sample has been shown, with the exception of 1, given the especially wide variation compared with the other samples, whose results varied minimally between data sets.         4 .

Evans Method Analysis
Evans measurement of (2-K) 4 susceptibility: 1.9 mM solution of (2-K) 4 in THF-d8 was used. Δ ppm = 0.025 ppm was observed. χ m = 0.0033 emu/mol. Evans measurement of (2-Cs) 4 susceptibility: 2.85 mM solution of (2-Cs) 4 in THF-d8 was used. Peak splitting was not observable by 1 H NMR. Figure S22. Restricted Open-Shell Hartree-Fock molecular orbitals used to build the Complete Active Space (CAS) for each Ce imido and oxo complex. Spin-multiplicity values are shown in brackets.