The role of the 5f valence orbitals of early actinides in chemical bonding

One of the long standing debates in actinide chemistry is the level of localization and participation of the actinide 5f valence orbitals in covalent bonds across the actinide series. Here we illuminate the role of the 5f valence orbitals of uranium, neptunium and plutonium in chemical bonding using advanced spectroscopies: actinide M4,5 HR-XANES and 3d4f RIXS. Results reveal that the 5f orbitals are active in the chemical bonding for uranium and neptunium, shown by significant variations in the level of their localization evidenced in the spectra. In contrast, the 5f orbitals of plutonium appear localized and surprisingly insensitive to different bonding environments. We envisage that this report of using relative energy differences between the 5fδ/ϕ and 5fπ*/5fσ* orbitals as a qualitative measure of overlap-driven actinyl bond covalency will spark activity, and extend to numerous applications of RIXS and HR-XANES to gain new insights into the electronic structures of the actinide elements.

and (b) Pu 5f density of states (DOS) spectra with and without spin-orbit coupling included in the finite difference method (FDM) calculations. The Fermi energy position is at +1.41 eV and it divides the occupied from the unoccupied molecular orbitals (MO). The unoccupied MO are marked in (b) for the calculation "with spin orbit".

UO 2 in spent nuclear fuel (SNF, U(IV)_1) and high burn-up structure (HBS, U(IV)_2).
The studied SNF samples were taken from the SBS1108 N0204 fuel rod segment, which was irradiated in the pressurized water reactor Gösgen nuclear power plant in Switzerland. The irradiation was carried out in four cycles for a period of time of 1226 days with an average linear power rate of 260 W/cm and achieving an average burn-up of 50.4 GWd/t HM . The fuel rod segment was discharged the 27 th of May 1989 that implies a cooling time of 24 years before characterization and cutting of the segment. Characteristic data of the studied SBS1108 N0204 fuel rod segment are given in. 5,6 A pellet size sample (about 10 mm length) was cut in the gap between two adjacent pellet of the fuel rod segment. The pellet was mechanically decladded and fractured. The high burn-up structure 7 sample (HBS, U(IV)_2) was prepared by fixing the SNF dust stuck on the cladding wall of the emptied pellet on a Kapton tape strip. The dust particles size well below 300 µm and belong to the outer region of the SNF pellet, where the HBS is formed. The second SNF sample (U(IV)_1) has been prepared by bringing a particle of several mm size, which was obtained from the centre region of a the fractured SNF pellet, in contact with a Kapton tape. The on the glue caught SNF footprint particles size about 1 mm. Both samples have then be covered with 13 µm thick Kapton foil and mounted in a Plexiglas cell with an additional 8 µm Kapton foil containment for measurement. The HBS U(IV)_2 sample is partially oxidized to U 4 O 9 , which contains U(IV) and U(V), due to the small particle size.

Electrochemical preparation of [UO 2 (CO 3 ) 3 ] 5-(U(V)) and [UO 2 (CO 3 ) 3 ] 4-(U(VI)_3) in 1M
Na 2 CO 3. The electrochemical preparation and the recording of the UV-Vis spectra and the cyclic voltamogramms of the samples were first performed in an Ar glove box following the description of Ikeda et al. 8 The same cell was used for the in-situ spectroelectrochemical experiments at the INE-Beamline. This cell enables coupling of UV-Vis spectroscopy with electrochemistry and X-ray absorption/emission spectroscopy. 9 A Pt-mesh (80 μm, 25×35 mm) was used as a working electrode, a Pt-spiral (0.5 mm Ø, 23 cm length) as a counter electrode and Hg/HgO as a reference electrode (ALS Co., Ltd). The negative potential of -775 mV determined from cyclic voltammetry measurements was applied to reduce U(VI) to U(V). 8 UV-Vis spectra were continuously recorded during the electrochemical reaction. The intensity of the U(VI)-yl characteristic UV-VIS peaks diminished after 120 minutes of electrolysis changing the color of the solution from yellow to colorless. These were clear evidences for complete reduction of U(VI) to U(V). The U(V) species remained stable for at least 800 minutes under anoxic conditions (flushed with He continuously. The RIXS/HR-XANES spectra were measured prior and after the U(VI) reduction was completed. with Kapton windows with 8 µm thickness, which has an adapted design of the standard INE-Beamline inert-gas cell, 11 including larger windows and inner volume. Yellow crystals having the composition UO 2 (ClO 4 ) 2 ·5H 2 O were obtained from this solution. These crystals were found to be very hygroscopic.

Supplementary Note 2. Modeling and computational details.
Modeling of HR-XANES. Linear combination least-squares (LCLS) fit analyses of the M 4,5 edge HR-XANES spectra were performed with the WINXAS program (www.winxas.de) using five pseudo-Voigt (PV) [f(x) = αGaussian + (1 − α)Lorentzian] and one arctangent functions. The Levenberg−Marquardt least-squares algorithm is used in the fit. The results are reported in Supplementary Figure 3 and Supplementary Table 3.

Multiplet calculations.
We briefly describe the essential features of our approach. The wavefunctions are built from 4 component spinors, described in a non-relativistic nomenclature as orbitals. These orbitals are solutions of the Dirac Hartree-Fock, DHF, selfconsistent field equations. The orbitals are optimized for two separate configurations. First for the ground state configuration, where the M 5 shell is filled and the 5f shell contains 2 electrons. For this configuration, the orbitals are optimized for the average of configurations 15 where the 2 electrons are distributed in all possible ways over the 14 5f orbitals. Second for the excited state configuration, where the M 5 shell contains only 5 electrons and the 5f shell contains 3 electrons; here also the orbitals are optimized for the average of configurations. It is necessary to use two sets of orbitals in order to take into account the screening of the core, M 5 , hole by the other electrons, especially those in the shells spatially more extended than the M 5 shell. A special advantage of this approach is that a single set of orbitals can be used to describe the multiplets that arise for these open shell configurations. The angular momentum coupling is determined by mixing the determinants where the open shell electrons are distributed in all possible ways over the 3d 5/2 and 5f shells. The only constraint is that the number of electrons in each shell is fixed as for the configuration used to optimize the orbitals. These are described as configuration interaction, CI, wavefunctions 16 and give reasonably accurate descriptions of the multiplet WF's and energies. It is appropriate to stress that it is not possible to correctly describe multiplets, except in very special cases, with only one determinant; a many determinantly description is essential. In order to compute the intensities to the different M 5 edge multiplets, we compute the many electron dipole matrix elements between each pair of initial state and final state wavefunctions. Because it is necessary to use different sets of orbitals for the initial and final states, these many electron matrix elements cannot be written in terms of a single reduced matrix element. Rather it is necessary to take suitable sums over products of orbital overlap integrals with orbital dipole moment integrals. The relative intensity, I rel , is taken as proportional to the square of the dipole matrix element where the term in the transition energy, E 3 , is neglected since this term is essentially constant over the ~50 eV range of energies of interest given the 3800 eV excitation energy from M 5 to 5f. The transitions are summed over all degenerate intial states of the J=4 ground state level of Pu 6+ and averaged over all directions, x, y, and z. Our calculated I rel to the discrete states are broadened with a Voigt convolution of a Gaussian, to represent resolution, with an FWHM of 1.2 eV and a Lorentzian, to represent lifetime, of 0.5 eV. These choices are based on the experimental parameters for the HR-XANES measurements. In Figure S4, we show the broadened calculated XANES intensity for the M 5 edge of Pu 6+ . The black solid line shows the sum over all transitions to excited states while the individual blue solid lines show the largest contributions from the excitations to the individual final multiplets. Clearly, the individual multiplets cannot be resolved.