Hanna Oher
email: hannaoher@gmail.com

Geoffroy Ferru

Laurent Couston

Laurence Berthon

Dominique Guillaumont

Florent Réal

Thomas Vercouter

Valérie Vallet
email: valerie.vallet@univ-lille.fr

Influence of the first coordination of uranyl on its luminescence properties: study of uranyl binitrate with N,N-dialkyl amide DEHiBA and water

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The production of electricity from nuclear energy has been developed in several countries. Some countries among which the U.S.A., France, the United Kingdom, chose to reprocess the spent nuclear fuel for an economic reuse of the uranium and plutonium, and a reduction of the radioactivity and volume of the wastes. [START_REF] Taylor | Reprocessing and recycling of spent nuclear fuel[END_REF] The recovery of uranium and plutonium, and effective separation from fission products and minor actinides has been achieved at both laboratory and industrial scales by solvent extraction techniques using an aqueous phase and an immiscible organic phase. The transfer of actinide metal cations occurs from an acidic aqueous phase resulting from the dissolution of the fuel in nitric acid into an organic phase by complexation with liposoluble extracting molecules. [START_REF] Moyer | Ion Exchange and Solvent Extraction: A Series of Advances[END_REF] Nowadays, the main industrial solvent extraction process is Plutonium Uranium Refining by Extraction (PUREX) in which the trin-butyl phosphate (TBP) extracting agent is used to separate U(VI) and Pu(IV) from minor actinides and fission products in highly concentrated nitric acid solution. [START_REF] Boullis | Facing the challenge of predicting the standard formation enthalpies of n-butyl-phosphate species with ab initio methods[END_REF] Though efficient the PUREX process requires a reduction of plutonium for the U/Pu partitioning by addition of U(IV) and anti-nitrous reagents. Moreover, the washing and recycling of the solvent has to account for the degradation of TBP by radiolysis. 4 Thus, several processes have been developed to modify or replace the PUREX process, and meet new requirements such as the development of a one-cycle process without redox chemistry. Following the principle of interaction of O-or N-donor organic molecules with uranium or plutonium, [START_REF] Madic | Separation of long-lived radionuclides from high active nuclear waste[END_REF][START_REF] Dinh | In Le traitement-recyclage du combustible nucléaire usé[END_REF] new types of complexing agents have been studied.

In France, the Group ActiNide EXtraction (GANEX) process has been developed for the industrial reprocessing of spent nuclear fuel and the homogeneous recycling of actinides. [START_REF] Adnet | Development of new hydrometallurgical processes for actinide recovery: GANEX concept[END_REF][START_REF] Miguirditchian | HA demonstration in the Atalante facility of the Ganex 1st cycle for the selective extraction of Uranium from HLW[END_REF] In this process, the selective separation is operated by solvent extraction using a new group of the N,N-dialkyl amides (further monoamides) first appeared in the 1960s. [START_REF] Siddall | Effects of structure of N, N-disubstituted amides on their extraction of (17) Prabhu, D.; Mahajan, G.; Nair, G. Di (2-ethyl hexyl) butyramide and di (2-ethyl hexyl) isobutyramide as extractants for uranium (VI) and plutonium (IV)[END_REF][10][11] It has been demonstrated that monoamides have a strong affinity with both the uranyl or plutonium cations. [12][13][14][15] Their selectivity can be adjusted by varying either the length or the ramification of monoamide alkyl chain. [START_REF] Siddall | Effects of structure of N, N-disubstituted amides on their extraction of (17) Prabhu, D.; Mahajan, G.; Nair, G. Di (2-ethyl hexyl) butyramide and di (2-ethyl hexyl) isobutyramide as extractants for uranium (VI) and plutonium (IV)[END_REF]16,17 The use of N,N-di-(ethyl-2-hexyl)isobutyramide (DEHiBA) has been proposed for U(VI) recovery and U(VI)/Pu(IV) or U(VI)/Th(IV). The knowledge of the stoichiometries and coordination of the actinide cations in aqueous and organic media are of high importance not only to better understand the extraction mechanism but also to optimize the extraction efficiency and selectivity. In the case of uranyl extraction, it has been shown that the neutral complex UO 2 (NO 3 ) 2 (L) 2 forms in the organic phase. [START_REF] Condamines | The extraction by NN-dialkylamides. II. Extraction of actinide cations[END_REF][START_REF] Vasudevan | Extraction of U (VI) from nitrate and thiocyanate media with monoamides[END_REF][START_REF] Rodrigues | New insights into the extraction of uranium(VI) by an N,N-dialkylamide[END_REF] It has a hexagonal bipyramidal geometry corresponding to the uranyl center to which two nitrates and two amide groups are linked as it has been confirmed by X-ray Diffraction (XRD), Raman, and IR spectroscopies. 12, [START_REF] Wahu | Structural versatility of uranyl (VI) nitrate complexes that involve the diamide ligand Et 2 N (C --O)(CH 2 ) n (C --O) NEt 2 (0 -n -6)[END_REF] One should point out that the nitrates can be located either in cis-or trans-positions. Although they are cases reported in the literature involving a cis-conformation around the uranyl moiety, 12,13,[START_REF] Kannan | Synthesis, structural and emission studies of a bis (carbamoyl methyl) sulfone complex of uranyl nitrate[END_REF] it is far less common than the trans conformation. As the two conformations exist in crystals, they might both be present in nitric acid solution and in organic phases.

The existence of different species could induce a change in the electronic structure of uranyl binitrate complexes. In order to reveal a difference in the coordination sphere of uranyl in terms of position of the nitrates and monoamides, the organic phase after extraction can be characterized by UV-Vis or time-resolved laser-induced fluorescence spectroscopy (TRLFS).

The latter method has some advantageous features allowing to measure luminescence spectra at low total uranium concentration and discriminate side emitting compounds by temporal resolution. Moreover, the positions of the luminescence bands, band spacings, bandwidths, and intensities are features that can be interpreted to determine the nature and the number of ligands in the first coordination layer of UO 2 2+ , as well as the local symmetry of the complex. For this, the spectroscopic characteristics should be well analyzed and interpreted.

However, the determination of an electronic structure information from the luminescence spectra is either still unresolved or it requires additional experimental data. For instance, to study an electronic structure of UO 2 Cl 4 2complex, Görller-Warland et al. [START_REF] Görller-Walrand | Spectroscopic properties of uranyl chloride complexes in non-aqueous solvents[END_REF] used UV-Vis and magnetic circular dichroism spectroscopies. Another way is based on the Franck-Condon principle, where the overlapped region between the absorption and luminescence spectra gives an idea about the position of the electronic transitions on the energy scale, but not the exact value, since several transitions may appear in that region.

As it has already been described previously, [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF][START_REF] Oher | Influence of alkaline earth metal ions on structures and luminescent properties of Na m Me n UO 2 (CO 3 ) 3 (4 -m -2n) -(Me = Mg, Ca; m, n = 0-2): time-resolved fluorescence spectroscopy and ab initio studies[END_REF] to study the uranium-based complexes and interpret the experimental spectra, the quantum chemical modeling is an insightful tool as it provides an accurate description of the electronic structure. Using the methodology described in our recent publications, [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF][START_REF] Oher | Influence of alkaline earth metal ions on structures and luminescent properties of Na m Me n UO 2 (CO 3 ) 3 (4 -m -2n) -(Me = Mg, Ca; m, n = 0-2): time-resolved fluorescence spectroscopy and ab initio studies[END_REF] the luminescence spectra, as well as spectroscopic characteristics can be computed and used for the assignment of the experimental spectra.

In our previous studies, the methodology has been proven to give an accurate description of the uranyl complexes electronic structures allowing to elucidate and quantify the influence of the first and second coordination spheres on the luminescence features. The structural parameters, emission energies and simulated luminescence spectra were found to be in good accordance with experimental data giving a significant level of confidence in the chosen theoretical methodology.

Here, we aim at studying the uranyl binitrate complexes and the influence of water and monoamide molecules in the first coordination sphere using quantum chemical simulations and the comparison to available and newly acquired experimental data. Theoretical models were created based on previous studies on the uranyl binitrate compounds [START_REF] Gal | Mid-, far-infrared and raman spectra of uranyl complexes in aqueous solutions[END_REF][START_REF] Acher | Structures of plutonium (IV) and uranium (VI) with N, N-dialkyl amides from crystallography, X-ray absorption spectra, and theoretical calculations[END_REF] and will be described in details further. The structural parameters of uranyl binitrate models will be discussed at the relativistic PBE0 level of theory in their cis and trans configurations. In the sake of guiding future experimental studies on uranyl binitrate compounds, the conformers stabilities and probabilities have been computed. As the spin-orbit CAM-B3LYP method has been found to accurately place electron transition energies of actinide complexes, [START_REF] Tecmer | Electronic spectroscopy of UO 2 2+ , NUO + and NUN: an evaluation of time-dependent density functional theory for actinides[END_REF] it is used to determine the "hot band" position in experimental luminescence spectra, since it is not easily identified experimentally. Moreover, we expect that this study is not only useful in illustrating the broad applicability of quantum modeling, but may also guide scientists in spectral data processing, i.e., identification of the bands and importance of their intensities.

Experimental details

Materials

DEHiBA was purchased from Pharmasynthese (purity ≥ 99%) and used as received. Hydrogenated tetrapropylene (TPH) used as a diluent was purchased from Novasep. The organic phases were prepared by dissolving weighed amounts of monoamide in TPH.

The U(VI) aqueous phase was prepared by dissolution of solid uranium (VI) nitrate hexahydrate (UO 2 (NO 3 ) 2 • 6 H 2 O) obtained from Prolabo (purity ≥ 99 %) into a solution of 2 mol L -1 lithium nitrate (reagent grade) with deionized water produced by the Milli-Q Plus apparatus (Millipore). The pH was adjusted to pH=2 by adding a suitable volume of 1 mol L -1 nitric acid.

Liquid-liquid extraction

Suitable volumes of DEHiBA at a concentration of 1.5 mol L -1 in n-TPH were contacted with aqueous phases (V org /V aq ). Extraction was performed at room temperature (≈ 25 °C) with 30 min stirring. Then, the solution was centrifugated and separated for titration and analytical procedures.

Uranyl concentrations were determined using X-ray fluorescence technique (Thermo Scientific -ARL QUANT'X -EDRXRF Analyser). Samples were diluted in 1 mol L -1 DEHiBA in TPH. The calibration range, performed with references solutions of uranyl nitrate in the same matrix is 100-2000 mg L -1 .

UV-Vis absorption spectroscopy UV-Vis measurements were performed on a Varian Cary 50 Scan spectrophotometer between 350 and 500 nm in quartz cells.

TRLFS analysis

A narrow-band Nd-YAG/OPO/Fx1 laser line (tripled Surelite 8010 and doubled sunlite EX from Continuum) was used as the excitation source. This solid-state laser is ideal for selecting any wavelength between 220 and 1800 nm (energies from 1 to 20 mJ). In this work, the excitation source was tuned 420 nm to avoid the decomposition of the organic ligand by UV radiation. The laser pulse energy was decreased until the intensity of the fluorescence remained stable with excitation times, i.e. 0.6 mJ and the laser beam was defocused into the cell by a quartz lens. A double chamber cell was used to attenuate the energy. The first chamber contained a reference aqueous solution of uranyl nitrate 0.1 mol L -1 in 2 mol L -1 LiNO 3 pH=2 used for normalization of the spectra while the sample was in the second chamber.

The samples were excited with a 10 Hz repetition rate. The recording of spectra was performed by integration of the pulse light signal given by the intensifier with a time delay of 150 ns and during a determined aperture time of 1 µs. Accumulation of 5 laser shots were averaged for each spectrum.

Computational Details

The choice of the used QM methods is justified in previous works. [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF][START_REF] Oher | Influence of alkaline earth metal ions on structures and luminescent properties of Na m Me n UO 2 (CO 3 ) 3 (4 -m -2n) -(Me = Mg, Ca; m, n = 0-2): time-resolved fluorescence spectroscopy and ab initio studies[END_REF][START_REF] Tecmer | Charge-Transfer Excitations in Uranyl Tetrachloride ([UO 2 Cl 4 ] 2 -): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?[END_REF] The ground and excited-state molecular geometries were optimized with Gaussian 16 30 software including scalar relativistic effects and using the PBE0 functional of the density. [START_REF] Ernzerhof | Assessment of the Perdew-Burke-Ernzerhof exchangecorrelation functional[END_REF] For the UO

2 (NO 3 ) 2 (H 2 O)
and cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complexes, the water solvent was accounted for using the continuum polarizable conductor model (CPCM) [START_REF] Tomasi | Quantum mechanical continuum solvation models[END_REF] (ε r = 78.36). The experimentally studied N,N-di(2-ethylhexyl)-iso-butanamide (DEHiBA) molecule was transformed to the N,N-diethyl-iso-butanamide (DEiBA) molecule with a shorter alkyl chain, to keep the computational costs reasonable, as the original alkyl chain is located beyond the first coordination sphere of U(VI) and is expected not to affect the uranyl-core electronic structure. [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF] The experimental luminescence spectrum of the UO 2 (NO 3 ) 2 (DEHiBA) 2 complex was recorded in hydrogenated tetrapropylen (TPH), which is an industrial solvent that is often described as a branched dodecane; thus one can assume that it has similar properties to that of n-dodecane, namely a low polarity. Therefore, the structures of cis-/trans -UO 2 (NO 3 ) 2 (DEiBA) 2 complexes were optimized in the gas phase, as the solvent is expected not to induce sizable changes of the complex geometries because of its low permittivity value (ε r = 2.00 taken for n-dodecane). [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF] The geometries of the luminescent states (first triplet excited states) were optimized using the time-dependent (TD)-DFT/PBE0 approach as implemented in Gaussian 16 code [START_REF] Frisch | Gaussian 16 Revision B.01[END_REF] with equilibrium solvation where it was necessary. The vibrational harmonic frequencies of the ground and luminescent states were computed analytically. All optimized geometries considered for the vibronic spectra calculations represent real minima as they have no imaginary frequencies. In these calculations, the def2-TZVP basis sets [START_REF] Weigend | RI-MP2: optimized auxiliary basis sets and demonstration of efficiency[END_REF][START_REF] Weigend | Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy[END_REF] were used for the H, C, N and O elements. A small-core Relativistic Effective Core Potential (RECP), that accounts for scalar relativistic effects of the 60 core electrons [START_REF] Küchle | Energy-adjusted pseudopotentials for the actinides. Parameter sets and test calculations for thorium and thorium monoxide[END_REF][START_REF] Cao | Valence basis sets for relativistic energy-consistent small-core actinide pseudopotentials[END_REF] was used for the uranium atom, while the valence electrons were described by the def-TZVP basis set. [START_REF] Eichkorn | Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials[END_REF] To speed up the TD-DFT calculations within the Gaussian 16 package, the inner U(5s, 5p, 5d), O(1s), C(1s), N(1s) orbitals were frozen.

In order to compute accurate absolute energies of the electronic transitions involved in the luminescence spectra of uranyl nitrate complexes, we have performed CAM-B3LYP with the conductor-like screening model COSMO. [START_REF] Klamt | a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient[END_REF][START_REF] Klamt | Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena[END_REF][START_REF] Klamt | Treatment of the outlying charge in continuum solvation models[END_REF] These calculations were carried out with the Amsterdam Density Functional package (ADF 2018.01). 43 All atoms were described by TZ2P Slater-type basis sets [START_REF] Van Lenthe | Optimized Slater-type basis sets for the elements 1-118[END_REF] without freezing the atomic cores.

The theoretical luminescence spectra of uranium (VI) complexes have been computed

with the ezSpectrum 3.0 45 software. The Franck-Condon factors (FCFs) were computed analytically including Duschinsky transformations of the normal modes between the ground and excited states. The number of vibrational quanta in the luminescent and ground state were selected to be one and five, respectively, to match the recorded experimental vibronic transitions. All the vibronic progressions were computed at 300 K to include contributions from the thermally active vibrational modes. As the proposed quantum chemical methods cannot compute absolute intensities, the intensity of the "hot band" peak was manually adjusted to match the experimental intensity distributions. The spectral shapes were estimated by convoluting the discrete stick spectra with Lorentzian broadening functions adjusting the width to match the experimental one.

The free energy calculations were performed using a composite method. While all the entropic and vibrational contributions are obtained from teh DFT calculations, the electronic energies are estimated either at DFT/PBE0 or at the MP2 levels of theory using the Turbomole 7.3 46 and the Gaussian 16. [START_REF] Frisch | Gaussian 16 Revision B.01[END_REF]

Choice of the model systems

In general, the coordination number of the uranyl unit varies from four to six depending on the ligands nature and media. [START_REF] Grenthe | The Chemistry of the Actinide and Transactinide Elements[END_REF] In nitric acid solutions the uranium(VI) speciation may be composed of several species like uranyl UO 2 2+ and uranyl nitrate complexes

(UO 2 (NO 3 ) n (2 -n) , n = 1, 2)
that can be detected by TRLFS. [START_REF] Moulin | Direct uranium (VI) and nitrate determinations in nuclear reprocessing by time-resolved laser-induced fluorescence[END_REF] In organic media the uranyl nitrate complex is soluble as a neutral compound UO 2 (NO 3 ) 2 (L) 2 . [START_REF] Acher | Structures of plutonium (IV) and uranium (VI) with N, N-dialkyl amides from crystallography, X-ray absorption spectra, and theoretical calculations[END_REF] As one of the main goals of this study is to elucidate the influence of organic ligands present in the first coordination sphere, the chemical model systems should have the same coordination number and molecular charge. In the present work, the majority of the model systems are sixfold coordinated and are neutral. The structures are shown in Figure 1. In the crystal phase, the uranyl nitrate complex hydration shell contains six water molecules, but there are at most two water molecules in the first coordination sphere, [UO [START_REF] Field | Inorganic nitrates and nitrato-compounds[END_REF] As the UO 2 (NO 3 ) 2 molecule has a coordination of four, with the two bidentate nitrate groups coordinated to uranyl, we have added one or two water molecules in the uranyl equatorial plane 1 to check the influence of the amount of water molecules on the UO 2 (NO 3 ) 2 (H 2 O) n

2 (NO 3 ) 2 (H 2 O) 2 ] • 4 H 2 O.
(n = 1, 2) complexes spectra and emission energies, and 2) to quantify the relative stabil- S1 of the ESI). Hereafter, the two water molecules were substituted by two N,N-dialkyl amides. As already mentionned, in order to keep reasonable computational costs, the N,N-di(2-ethylhexyl)-iso-butanamide (DEHiBA) ligand was substituted with the N,N-diethyl-iso-butanamide (DEiBA), which has shorter alkyl chains.

ity of cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) 2 conformers (see Table

Results

Theoretical ground and excited-state structures

cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) n (n=1, 2)
Uranyl nitrate is a water-soluble uranium salt. It exists in the form of the crystal uranyl binitrate hexahydrate

[UO 2 (NO 3 ) 2 ] • 6 H 2 O.
The structural studies performed on a crystal compound showed that there are two bidentate nitrates and two water molecules bounded to uranyl unit in a trans-configuration. [START_REF] Pauling | The crystal structure of uranyl nitrate hexahydrate[END_REF][START_REF] Taylor | A neutron diffraction study of uranyl nitrate hexahydrate[END_REF][START_REF] Hall | The crystal structure of bisnitratodiaquodioxo-uranium (VI) tetrahydrate (uranyl nitrate hexahydrate)[END_REF] Unluckily, the speciation of uranyl nitrate compounds in aqueous phase is less documented as there are other solvated and nitrate species present. [START_REF] Moulin | Direct uranium (VI) and nitrate determinations in nuclear reprocessing by time-resolved laser-induced fluorescence[END_REF][START_REF] Couston | Speciation of uranyl species in nitric acid medium by time-resolved laser-induced fluorescence[END_REF] The dissolution of crystallohydrates in water may be accompanied by the destruction of the crystal lattice, as well as (de-)hydration process. Thus, we have made an assumption that either one or two water molecules may fill the UO 2 (NO 3 ) 2 first coordination sphere.

All the distances for the UO [START_REF] Bühl | Effect of hydration on coordination prop-erties of uranyl (VI) complexes. A first-principles molecular dynamics study[END_REF] The results obtained by these two methods overestimate the bond lengths found in the crystal structures by neutron diffraction measurements, 51 whereas our DFT/PBE0 ground-state structures are in better agreement with the experimental structural data. These compiled results indicate that the choices of both the functional and the basis sets have a significant impact on the accuracy of the computed U(VI)-based complexes structures, and since we are aiming at capturing the changes between the ground and luminescent-state geometries, we can postulate that any functional should be benchmarked to be able to provide a reasonable picture.

Comparing the computed geometries of cis-and trans -UO 2 (NO 3 ) 2 (H 2 O) 2 conformers, we did not observe any change in the structures except for the U -O H 2 O bond which was found to be 0.014 Å longer in the cis conformer than in the trans. This is probably related to the greater energetic stability of the trans complex as shown in Table S1 of the ESI.

The geometrical parameters of the lowest triplet excited states are also reported in Table 1. As a result of the electronic excitation, we observe an elongation of the U -O ax bond length by 0.038 Å for the uranyl binitrate complex with one water molecule and 0.037 Å for both cis-and trans -UO 2 (NO 3 ) 2 (H 2 O) 2 conformers. For the equatorial ligands, the structural changes are found to be very minor; the greatest bond-length change is 0.006 Å, suggesting that there are no significant contributions of the water ligands to the orbitals participating to the excitation.

Insofar as vibrational frequencies contribute to the luminescence spectra to some extent, it is of high importance to characterize them. There are three main vibrational modes that may appear in the vibronic progressions: uranyl bending ν b , symmetrical stretching ν s and asymmetrical stretching ν a modes. The values of these frequencies are reported in Table 2 together with the experimental IR and Raman data obtained for solid [START_REF] Mcglynn | Electronic structure, spectra, and magnetic properties of oxycations. III. Ligation effects on the infrared spectrum of the uranyl ion[END_REF] Moreover, our calculations showed that the ν b mode is coupled with the motions of ligands, an information that cannot be deduced from the IR spectra of UO 2 (NO 3 ) 2 in solution. [START_REF] Gal | Mid-, far-infrared and raman spectra of uranyl complexes in aqueous solutions[END_REF] It is thus inappropriate to describe this vibrational frequency as a pure uranyl bending mode.

Experimentally, it was measured at 254 cm -1 , matching the range of our computed values 217-276 cm -1 . To probe the electronic structure of U(VI) surrounded by inorganic and organic ligands, two molecules of the DEiBA monoamide were placed in the first coordination sphere instead of the water molecules forming UO 2 (NO 3 ) 2 (DEiBA) 2 cis-and trans-conformers (Fig. 2). The optimized bond distances are shown in Table 1. The ground-state geometries of the cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complexes have very similar distances in the equatorial plane, and the free energy difference of two conformers is small. Nevertheless, the trans conformer is found to be more stable as compared to cis, by about 23 kJ mol -1 and 15 kJ mol -1 at the DFT/PBE0 and MP2 levels of theory, respectively (see Table S1 of the ESI). The computed geometry of the trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complex agrees well with the experimental EXAFS results obtained by Acher et al. [START_REF] Acher | Structures of plutonium (IV) and uranium (VI) with N, N-dialkyl amides from crystallography, X-ray absorption spectra, and theoretical calculations[END_REF] In the same way, the computed bond lengths within UO 2 (NO 3 ) 2 (DEiBA) 2 conformers also agree with the single-crystal X-ray structures of similar amide compounds like cis -UO 2 (NO 3 ) 2 (dam) 2 (dam -N',N-diethylacetamide) and trans -UO 2 (NO 3 ) 2 (eam) 2 (eam -N-ethylacetamide). 12

The changes in the geometries when switching from the ground to the luminescent state in cis-/ trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complexes is of the same order as that reported for the cis- The changes between the ground and the luminescent states vibrational frequencies in the cis-/trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complexes are equal in average to 90 cm -1 and 138 cm -1

/
for the symmetrical and asymmetrical uranyl stretching modes, respectively, while the ν b frequency is similar to that in the ground state.

Emission energies

For the uranyl-based complexes, the nature of the luminescent emission was previously discussed in several experimental [START_REF] Denning | The electronic structure of the uranyl ion: Part I. The electronic spectrum of Cs 2 UO 2 Cl 4[END_REF][START_REF] Flint | Luminescence spectrum of Cs 2 UO 2 Cl 4[END_REF][START_REF] Dau | Photoelectron spectroscopy and the electronic structure of the uranyl tetrachloride dianion: UO 2 Cl 4 2[END_REF] to an orbital that has a uranyl σ character possibly mixed with orbitals of the equatorial ligands. In the present UO 2 (NO 3 ) 3 (L) 2 complexes, the plots of the molecular orbitals involved in the luminescent process shown in Figure 3 reveal that the emission corresponds to a metal-to-ligand charge transfer de-excitation from non-bonding uranium(VI) orbitals to orbitals delocalized over the uranyl unit, the nitrate ligands and the monoamide linking groups.

Since the luminescence spectra of uranyl-based complexes have similar shapes (with some exceptions like UO 2 Cl 4 2 -), the nature of the equatorial ligands can be deduced from the position of the spectral envelope in the energy scale. In the luminescence spectra, the origin is usually defined by the position of the "hot band." For instance, luminescence blue shifts of the uranyl triscarbonate complexes are observed as compared to most other uranyl species, while hydrated uranyl exhibits a red shift. [START_REF] Wang | A cryogenic fluorescence spectroscopic study of uranyl carbonate, phosphate and oxyhydroxide minerals[END_REF][START_REF] Bernhard | Uranyl(VI) carbonate complex formation: Validation of the Ca 2 UO 2 (CO 3 )(3) (aq • ) species. Radiochim[END_REF][START_REF] Geipel | Mixed complexes of alkaline earth uranyl carbonates: A laser-induced time-resolved fluorescence spectroscopic study[END_REF] It has been proposed by Wang et al. [START_REF] Wang | A cryogenic fluorescence spectroscopic study of uranyl carbonate, phosphate and oxyhydroxide minerals[END_REF] that the position of the "hot band" in uranyl minerals depends on the basicity of the equatorial ligand. The ionic interactions between uranyl ion and ligands with higher pKa lead to a larger decrease of the ν s frequency, and a larger red shift of the luminescence spectra.

Here, we have used the SOC CAM-B3LYP calculations to predict the "hot band" positions by the averaging of first four vertical emission energies computed out of the first low-lying excited state geometry and corrected by the zero-point energies of the ground and luminescent states of the UO 2 (NO 3 ) 2 (H 2 O) and cis-/ trans-UO 2 (NO 3 ) 2 (L) 2 (L=H 2 O, DEiBA). The computed "hot band" energies E are listed in Table 3. The comparison of theoretical data with experimental results is not relevant at this stage, because to our knowledge, the position of the "hot band" was never discussed before for the uranyl binitrate complexes. -is placed at 20 978 cm -1 (477 nm), while the averaged value of the uranyl binitrate "hot band" is 20 425 cm -1 (490 nm), showing 553 cm -1 (13 nm) red shift which is in consistency with Wang's assumption. et al. [START_REF] Wang | A cryogenic fluorescence spectroscopic study of uranyl carbonate, phosphate and oxyhydroxide minerals[END_REF] For the cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 (for which the basicity is not known yet)

in n-dodecane, we have computed the "hot band" energies at 20 116 cm -1 (497 nm) and 20 171 cm -1 (496 nm), respectively. They are somewhat red shifted with respect to that of the water complexes of uranyl binitrate. As compared to the "hot band" value of the [A336] 2 [UO 2 Cl 4 ] complex, 20 001 cm -1 (500 nm), the uranyl binitrates with monoamides "hot band" energy exhibit a blue shift.

One can notice that the cis-and trans-conformers of uranyl binitrate complexes may hardly be discriminated solely by the "hot band" energy.

Vibronic progressions

In the luminescent emission of U(VI) complexes, the principal vibronic progression is a result of an electronic transition coupled to the symmetrical stretching mode of the uranyl unit. Secondary progressions may also appear to some extent because of the coupling to other symmetrical motions of the molecular complex. The quantum chemical simulations of the vibronic spectra allow to quantify the contributions of the vibronic modes. To guide the discussion and the comparison to experimental data, the computed stick spectra of all binitrate uranyl complexes are convoluted and drawn on Figure 4.

The structural and vibrational parameters directly reflect in the shape of the luminescence spectra. The most evident and easily detectable fingerprint is the ground state symmetrical stretching mode of the uranyl moiety, as it is equal to the spacing between the main peaks of the vibronically resolved envelope. Some other vibrational frequencies (symmetrical mostly) appear in the vibronic progression to a smaller extent and might hardly be detectable in the broad spectral envelope. The vibrational frequencies contributions, their natures and intensities are listed in Table 4 for the UO

2 (NO 3 ) 2 (H 2 O) and cis-/ trans-UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEiBA) complexes.
One can note that the excited state uranyl symmetrical stretching mode can be detected in these luminescence spectra as discussed further.

The ground-state symmetrical stretching uranyl frequency has been discussed previously.

From the comparison of the spectra displayed in Figure 4 and the symmetric stretching frequencies listed in Table 4, we can infer that the vibronic band spacings are very similar, thus the spectra of aqueous and organic uranyl binitrate complexes are difficult to separate trans-UO 2 (NO 3 ) 2 (DEiBA) 2 cis-UO 2 (NO 3 ) 2 (DEiBA) 2

Intensity / a.u.

Wavenumber / cm 1 Figure 4: Theoretical vibronic progressions of the UO 2 (NO 3 ) 2 (H 2 O) and cis-/ trans-UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEiBA) complexes.
The position of the first peak is adjusted to the computed "hot band" value of the trans -complexes and corrected by the ν s of the excited state. The spectral shapes were estimated by convoluting the stick spectra with Lorentzian functions with a FWHM of 400 cm -1 . solely by the main vibronic band spacings. The detailed analysis of the vibronic bands (See Table 4) reveals that some other modes build up a secondary vibronic progression. In the case of the UO 2 (NO 3 ) 2 (H 2 O) complex, the uranyl rocking appears at 156 cm -1 after the 0 → 0 band. In the cis-and trans-UO 2 (NO 3 ) 2 (H 2 O) 2 spectra, we observe contributions from the U -H 2 O stretching mode coupled to uranyl bending motions at 249 cm -1 and 315 cm -1 for the cis-and trans-conformers, respectively. A symmetrical U -NO 3 stretching mode coupled with the weak uranyl bending motion contributes to the spectra of the cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complexes at 234 cm -1 and 212 cm -1 , respectively.

The theoretical luminescence intensities distributions are mainly linked to the U -O ax bond elongations between the ground to the luminescent state, 69 but this relationship is not defined yet. We have performed a comparison of the vibronic progressions to elucidate the influence of the nature of the ligands and of their orientations on theoretical intensities. On the top panel of Figure 4 we observe that the absolute intensity of the trans-UO 2 (NO 3 ) 2 (H 2 O) 2 complex is higher than that of UO 2 (NO 3 ) 2 (H 2 O) by 0.184 au for the 0 → 0 band. The middle panel of Figure 4 reveals that the trans-conformer of uranyl binitrate with two water molecules exhibits higher intensities than the cis conformer by 0.107 au. In the bottom panel of Figure 4, the spectra of cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 have been compared and, unlike in the uranyl binitrate water complexes, the spectrum of the cis conformer is more intense by 0.216 au than the trans-one. From the analysis of the geometries and the shifts from the ground to the luminescent state, we did not find any significant difference, especially in the U -O ax bond. It means that intensities change is not related here to the geometrical changes discussed earlier, but rather to some other factors. As the vibronic intensities arise from the Franck-Condon overlaps between the ground and excited-state normal modes, if they are not parallel, Duschinsky rotations need to be accounted for, and may contribute to the intensity changes.

Table 4: Assignments of the UO 2 (NO 3 ) 2 (H 2 O) and cis-/ trans-UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEiBA) theoretical luminescence spectra computed in the gas phase and in the CPCM water solvent for complexes with organic and inorganic ligands respectively. The energy of the spectrum was adjusted to the theoretical "hot band" value and corrected by ν s of the excited state.

E [cm -1 ] ∆E [cm -1 ] I [au] E [cm -1 ] ∆E [cm -1 ] I [au] Identification UO 2 (NO 3 ) 2 (H 2 O) 0.

Discussions

As for most of the U(VI) compounds, the luminescence spectra of the uranyl nitrate complexes show well-resolved vibronic progressions that overlap with the pure electronic transition from the luminescent state to the ground state. We have collected TRLFS experimental data for UO 2 (NO 3 ) 2 in nitric acid (plain line), [START_REF] Moulin | Direct uranium (VI) and nitrate determinations in nuclear reprocessing by time-resolved laser-induced fluorescence[END_REF] UO 2 (NO 3 ) 2 (DEHiBA) 2 in TPH solvent (dotted line) and UO 2 (NO 3 ) 2 (TBP) 2 in supercritical CO 2 (dashed line). [START_REF] Addleman | Luminescence quenching of UO 2 (NO 3 ) 2 • 2 TBP in supercritical fluid CO 2[END_REF] The normalized experimental time-resolved luminescence spectra are shown in Figure 5. It has been assumed that in uranium(VI) sample with 0.2-4.0 M nitric acid concentration, three species are present: UO 2 2+ (aq), UO 2 (NO 3 ) + (aq) and UO 2 (NO 3 ) 2 (aq). [START_REF] Moulin | Direct uranium (VI) and nitrate determinations in nuclear reprocessing by time-resolved laser-induced fluorescence[END_REF] First, the UO 2 2+ (aq) species was measured in highly acidic conditions. Then, using the assumption of a bathochromic shift upon nitrate complexation, stepwise least square fittings were applied iteratively to a set of experimental and numerical data gathered over the nitric acid concentration range. Accordingly, the spectrum of UO 2 (NO 3 ) 2 in nitric acid was extracted by the deconvolution procedure detailed by Couston et al. [START_REF] Couston | Speciation of uranyl species in nitric acid medium by time-resolved laser-induced fluorescence[END_REF] The spectral shape and characteristics compare well with the ones measured earlier in similar conditions [START_REF] Pant | The absorption and fluorescence spectra of uranyl nitrate solutions at room temperature[END_REF] and in the solid state. [START_REF] Nichols | Fluorescence of the uranyl salts[END_REF] The picture becomes less complicated in the presence of organic extracting agent (like TBP or monoamides), when the uranyl binitrate complexes can be present as a single species, and only potentially conformers.

To the best of our knowledge, there is no information in the literature about the nature of observed transitions in the uranyl binitrate complexes. The general observation that the vibronic progression overlaps with the electronic transition can be interpreted in different ways. In the example of the emission spectrum of the UO 2 (NO 3 ) 2 (DEHiBA) 2 complex (Fig. 5 and Fig. 6) we observe two peaks in the low energy region at 480-495 nm with different intensities. It is known that the intensity of luminescence depends on the quantum yield -the ratio of the rate of de-excitation by photons emission and the rate of de-excitation by both radiative and non-radiative processes. [START_REF] Su | Uranyl-glycine-water complexes in solution: Comprehensive computational modeling of coordination geometries, stabilization energies, and luminescence properties[END_REF] For this particular case, it is difficult not only to determine the origin of the relaxation but also to predict the temporal evolution of the electronic intensity; thus both transitions could correspond to the electronic one. From another viewpoint, in most of the uranium(VI)-based complexes the absorption spectrum is a mirror image of the emission spectrum. [START_REF] Görller-Walrand | Spectroscopic properties of uranyl chloride complexes in non-aqueous solvents[END_REF] This phenomenon is known as the mirror image rule and is related to the Franck-Condon principle which states that electronic transitions are vertical, that is the energy changes without any geometry change. This means that the vibration levels of the excited state resemble that of the ground state. Usually, when the absorption and emission spectra are built on the same energy scale, they overlap at the electronic transition region as shown on Figure 6. Here we notice the overlay of the same two peaks around 480 and 495 nm. Using the analogy adverted by Görller-Warland et al. [START_REF] Görller-Walrand | Spectroscopic properties of uranyl chloride complexes in non-aqueous solvents[END_REF] on the example of uranyl chloride complexes, the first small peak at 480 nm could be assigned to a "hot band," while the second at 495 nm should correspond to the 0 → 0 band (dashed line on Figure 6). Another way to attribute the position of the "hot band" in UO 2 (NO 3 ) 2 (L) 2 is to use the band spacing value and results obtained by the ab initio calculations. In the luminescence spectrum, the vibronic progression starts at the 0 → 0 transition with a spacing equal to the ground state uranyl stretching frequency ν gs s . The "hot band" appears at an energy shifted by the excited state uranyl stretching frequency ν es s above the 0 → 0 transition. A multi-peaks Lorentzian fitting was applied to the experimental spectra to determine the band spacing values. The results of this fitting and the ν gs s , ν es s frequencies computed by (TD)-DFT/PBE0 methods are shown in Table 5.

It has been observed that for UO 2 (NO 3 ) 2 (L) 2 complexes, the experimental ground and excited-state symmetrical stretching frequencies of the uranyl reproduced the theoretical trend that the ν gs s frequency is larger than the ν es s . Moreover, the ν gs s extracted from the luminescence spectra agreed within 11 cm -1 with Raman data for UO 2 (NO 3 ) 2 (H 2 O) 2 in liquid. [START_REF] Gal | Mid-, far-infrared and raman spectra of uranyl complexes in aqueous solutions[END_REF] The shifts between the ground and excited state stretching frequencies ∆ν s are 65 and 49 cm -1 for the UO 2 (NO 3 ) 2 and UO 2 (NO 3 ) 2 (DEHiBA) 2 , respectively, while the theoretical shifts equal to 90 cm -1 in average. As it has been explained in previous works, [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF][START_REF] Oher | Influence of alkaline earth metal ions on structures and luminescent properties of Na m Me n UO 2 (CO 3 ) 3 (4 -m -2n) -(Me = Mg, Ca; m, n = 0-2): time-resolved fluorescence spectroscopy and ab initio studies[END_REF] our theoretical methodology tends to overestimate the vibrational frequencies values; thus we can consider that the agreement between theoretical and experimental data is satisfactory. Moreover, it is difficult to estimate the degree of anharmonicity effects in experimental spectra, which might obviously decrease the band spacings in the higher energy region. Based on the discussions above we have tried to attribute the electronic and vibronic transitions of experimental spectra being guided by the theoretical results. The direct comparisons of our theoretical spectra with the experimental ones can be visualized on Figure 7, the spectral characteristics and attribution of bands are listed in Table 5. To simplify the discussion, we have shifted the theoretical spectra to match the experimental energy range and normalized the intensities of both sets to the maximum value. First of all, the differ-ence between the ν gs s and ν es s experimental values lead us to propose that the 1 → 0 band pops up at 507 and 495 nm for UO 2 (NO 3 ) 2 (H 2 O) 2 and UO 2 (NO 3 ) 2 (DEHiBA) 2 , respectively.

L 1 → 0 0 → 0 0 → 1 0 → 2 0 → 3 [cm -1 ] [cm -
Another remarkable result is that the theoretical vibronic progression intensities distributions beautifully match the experimental ones when placing them next to the proposed "hot band." Moreover, it has been confirmed previously that the 0 → 0 bands in uranium(VI)based complexes are usually more intense compared to the "hot band" intensity at room temperature. [START_REF] Oher | Investigation of the Luminescence of [UO 2 X 4 ] 2 -(X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations[END_REF][START_REF] Wang | A cryogenic fluorescence spectroscopic study of uranyl carbonate, phosphate and oxyhydroxide minerals[END_REF][START_REF] Su | Uranyl-glycine-water complexes in solution: Comprehensive computational modeling of coordination geometries, stabilization energies, and luminescence properties[END_REF] The nature of the bands at 495 and 480 nm in UO 2 (NO 3 ) 2 (H 2 O) 2 and UO 2 (NO 3 ) 2 (DEHiBA) 2 , respectively, remains an open question. Thus we can just suggest that these bands are related to the sample reabsorption, since the luminescence intensity of the band at 480 nm changes depending on the uranium(VI) concentration. Also this band could correspond to an emission from another excited state.

One last point that was not yet discussed in details is the detection probability of the cisand trans-conformers of uranyl binitrate complexes to confirm it from the experimental luminescence data. When we discussed the differences in the structures (Table 1) and harmonic frequencies (Table 2) of both conformers, the same as predicted luminescence spectra (Table 5), it was difficult to distinguish the more probable configuration of the UO 2 (NO 3 ) 2 (H 2 O) 2 and UO 2 (NO 3 ) 2 (DEiBA) 2 . Furthermore, the relative free energies between the two conformers (see Table S1 of ESI) are found to be very small to give an exact picture. Nevertheless, the cis-trans energetic difference data predicted the cis-and trans-isomers to be probable by about 30 % and 70% respectively for the uranyl binitrate complexes with water, and trans -UO 2 (NO 3 ) 2 (DEiBA) 2 complex to be 100% probable. This kind of analysis represents a static picture only, while in the experimental conditions, the systems are dynamics, with possible rapid exchanges between conformers.

  Fluorescence was observed at right angle to the excitation by an alignment of 8 Si/Si optical fibers illuminating the entrance slit of a flat-field spectrometer (300i from Princeton Instrument) equipped with a pulsed intensified CCD camera (IMAX, 1024×256 pixels, Princeton Instrument, USA) synchronized on the laser shot. The multichannel detection of eight local fluorescence channels along the laser beam in the quartz cell enables real-time correction in case of prefilter effect.

Figure 1 :

 1 Figure 1: The structures of UO 2 (NO 3 ) 2 (H 2 O) and UO 2 (NO 3 ) 2 (L) 2 (L=H 2 O, DEiBA) model systems in their trans-and cis-configurations. The view is made along the z axis defined by the uranuyl unit.

  The substitution of water molecules by the DEiBA monoamide ligands induces a lengthening of the U -O ax , U -O NO 3 and U -N NO 3 bonds in the range of 0.007-0.031 Å for trans-and 0.006-0.015 Å for cis-conformer, while the distance between uranium and the oxygen atom of the monoamide is shorter than that with the oxygens of the water molecules, by 0.108 Å and 0.071 Å for the trans and cis configurations, respectively. This is simply a result of the larger electron donation to uranium by the DEiBA monoamide as compared to water.[START_REF] Acher | Structures of plutonium (IV) and uranium (VI) with N, N-dialkyl amides from crystallography, X-ray absorption spectra, and theoretical calculations[END_REF]

Figure 2 :

 2 Figure 2: The optimized at R-ECP DFT/PBE0 ground state geometries of the cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 conformers.

Figure 3 :

 3 Figure 3: The highest occupied (right panel) and lowest unoccupied (left panel) molecular orbitals of trans-UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEiBA) involved in the triplet-singlet electronic transitions, responsible of uranyl luminescence. The molecular orbitals were obtained at the RECP DFT/PBE0 level of theory.

  NO 3 ) 2 UO 2 (NO 3 ) 2 (DEHiBA) 2 UO 2 (NO 3 ) 2 (TBP) 2

Figure 5 :

 5 Figure5: Experimental time-resolved luminescence spectra of UO 2 (NO 3 ) 2 in nitric acid[START_REF] Moulin | Direct uranium (VI) and nitrate determinations in nuclear reprocessing by time-resolved laser-induced fluorescence[END_REF] (plain lines), UO 2 (NO 3 ) 2 (DEHiBA) 2 in TPH solvent, ε=2.0 (dotted line) and UO 2 (NO 3 ) 2 (TBP) 2 in a supercritical CO 2 , ε=1.6 70 (dashed line). The spectra were rebuilt from the data of the quoted references.

Figure 6 :

 6 Figure 6: Superposition of the emission (TRLFS) and absorption (UV-vis) spectra of UO 2 (NO 3 ) 2 (DEHiBA) 2 in TPH solvent of the same sample.

Figure 7 :

 7 Figure 7: Comparison of experimental emission spectra (TRLFS) with theoretical spectra of (a) UO 2 (NO 3 ) 2 (H 2 O) 2 and (b) UO 2 (NO 3 ) 2 (DEiBA) 2 .

( 16 )

 16 Nair, G.; Prabhu, D.; Mahajan, G. Extraction of uranium (VI) and plutonium (IV) with dihexylbutyramide and dihexylisobutyramide from nitric acid medium. J. Rad. Nucl. Chem. 1994, 182, 393-399, DOI: 10.1007/bf02037516.

  We suspect the experimental bond length difference to be related to the fit uncertainty, because most of the uranyl complexes have almost equivalent U -O ax bond lengths.[START_REF] Watkin | Structure of dicaesium tetrachlorodioxouranium (VI)[END_REF][START_REF] Wilson | Structural studies coupling X-ray diffraction and high-energy X-ray scattering in the UO 2 2+ -HBr aq system[END_REF] The trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complex structure has been studied previously by theoretical DFT/SVWN 56 and Car-Parrinello (CP/BLYP) calculations.

2 (NO 3 ) 2 (H 2 O) and cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complexes are reported in Table

1

along with experimental data available in the literature. The groundstate structures of these two complexes are found to be almost identical with a maximum deviation of 0.003 Å for U -O ax , U -O NO 3 and U -N NO 3 bond lengths. The U -O H 2 O bond is 0.024 Å longer in the trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complex than in the UO 2 (NO 3 ) 2 (H 2 O) complex, as there are more electrostatic repulsions in the former than in the latter. One interesting observation is that Taylor et al.

[START_REF] Taylor | A neutron diffraction study of uranyl nitrate hexahydrate[END_REF]

obtained non-equivalent U -O ax bond distances (1.770(7) and 1.749(7) Å), while in our calculations these distances are strictly equal (1.749 Å).

Table 1 :

 1 and liquid[START_REF] Gal | Mid-, far-infrared and raman spectra of uranyl complexes in aqueous solutions[END_REF] uranyl binitrate. The experimental ν s and ν a are found to be almost identical for UO 2 (NO 3 ) 2 in solid and in solution, the largest difference being 16 cm -1 for the uranyl asymmetrical stretching mode. The analysis of the theoretical harmonic frequencies of UO 2 (NO 3 ) 2 (H 2 O) and cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complexes shows that they are nearly the same, but they Ground and excited state geometries (in Å) of UO theoretical frequency values are found to be 9 cm -1 and 11 cm -1 for ν s and ν a modes, respectively, values that are in line with the magnitudes of the structural changes.

	O, DEiBA)
	(L=H
	(L)
	)
	(NO
	-UO
	O) and cis-/trans
	(H
	)
	(NO

are found to be overestimated by at most 62 cm -1 for the uranyl symmetrical stretching mode as compared to experimental data. In the series of the chemical models, the largest

Table 2 :

 2 Ground and excited state vibrational frequencies (in cm -1 ) of the UO 2 (NO 3 ) 2 (H 2 O) and cis-/trans -UO 2 (NO 3 ) 2 (L) 2 (L=H 2 O, DEiBA) compared to selected results from the literature (dam -N',N-diethylacetamide; eam -N-ethylacetamide). (NO 3 ) 2 (H 2 O) 217-276 934 989 PBE0/CPCM this study trans -UO 2 (NO 3 ) 2 (H 2 O) 2 230-264 925 978 PBE0/CPCM this study cis -UO 2 (NO 3 ) 2 (H 2 O) 2 217-265 928 980 PBE0/CPCM this study trans -UO 2 (NO 3 ) 2 (DEiBA) 2 (NO 3 ) 2 (H 2 O) 210-267 833 856 PBE0/CPCM this study trans -UO 2 (NO 3 ) 2 (H 2 O) 2 220-257 833 857 PBE0/CPCM this study cis -UO 2 (NO 3 ) 2 (H 2 O) 2223-261 834 857 PBE0/CPCM this study trans -UO 2 (NO 3 ) 2 (DEiBA) 2 ax bond elongation from the ground to the luminescence state, the ν s and ν a vibrational frequencies are lowered by 101 cm -1 and 133 cm -1 , respectively in the trans -UO 2 (NO 3 ) 2 (H 2 O) complex. A similar behavior, within 12 cm -1 difference, is observed -/trans -UO 2 (NO 3 ) 2 (DEiBA) 2

	ν b	ν s	ν a Method	Ref.
			Ground state

for cis-/trans -UO 2 (NO 3 ) 2 (H 2 O) 2 complexes. One can, however, note that the coupled ν b frequency range is not significantly affected by the excitation process. cis

  trans-UO 2 (NO 3 ) 2 (H 2 O) 2 complexes. The minor differences are the variations of U -O NO 3 and U -N NO 3 bonds of monoamide complexes upon excitation which is a little larger than in complexes with water molecules, and the U -O L bonds are shortened by about 0.014 Å, while in case of the complexes with water, they remained almost unchanged. These structural changes will be reflected in the theoretical luminescence intensities distribution as discussed further.

The theoretical vibrational frequencies of cis-and trans-UO 2 (NO 3 ) 2 (DEiBA) 2 complexes are listed in the Table

2

. As in UO 2 (NO 3 ) 2 (H 2 O) 2 complexes, there is almost no difference for the ν b , ν s and ν a frequencies values between the cis and trans conformers. Moreover, the ν b frequency corresponds to a pure uranyl bending motion, uncoupled from the equatorial ligands, ν s is smaller and ν a remains almost unchanged. The changes are most probably related to the weakening of the U -O ax bond paired with the decrease in uranyl stretching force constant. The calculated ν a frequency can be compared with experimental data measured by IR spectroscopy for various crystals and liquid samples of cis-/ trans-UO 2 (NO 3 ) 2 (L) 2 complexes. 12,27 As observed for the UO 2 (NO 3 ) 2 (H 2 O) 2 complexes, our theoretical vibrational frequencies for the UO 2 (NO 3 ) 2 (DEiBA) 2 complexes are overall larger than the experimental values by 65 cm -1 . Thus this systematic difference might be related to choice of the computational methodology (DFT functional, basis sets, and/or solvation model).

  and theoretical[START_REF] Matsika | Electronic structure and spectra of actinyl ions[END_REF][START_REF] Van Besien | Electronic spectra of uranyl chloride complexes in acetone: a CASSCF/CASPT2 investigation[END_REF][START_REF] Pierloot | Electronic structure and spectrum of UO 2 2+ and UO 2 Cl 4 2[END_REF] studies. It was deduced from the

	examples of uranyl tetrachloride UO 2 Cl 4	2 -24 and uranyl triscarbonate UO 2 (CO 3 ) 3	4 -25 com-
	plexes that the luminescence state has a triplet character and that the emission occurs as a
	result of an electron transition from one of the four non-bonding 5f orbitals of uranium(VI)

Table 3 :

 3 The "hot band" energies E of uranyl binitrate complexes (in cm -1 and nm) compared to Na 3 UO 2 (CO 3 ) 3-and [A336] 2 [UO 2 Cl 4 ] results. The computed values are obtained at the all-electron SOC CAM-B3LYP level of theory, and corrected with the spin-free Zero-Point Energy correction of the ground and luminescent states. It is known from the study by Parr and Pearson et al.[START_REF] Parr | Absolute hardness: companion parameter to absolute electronegativity[END_REF] that nitrates and water molecules are less basic than the carbonate anions. From our calculations, the "hot band" of Na 3 UO 2 (CO 3 ) 3

	E [cm -1 ] E [nm]

The theoretical "hot band" energies of the UO 2 (NO 3 ) 2 (H 2 O) and cis-/trans-UO 2 (NO 3 ) 2 (H 2 O) 2 complexes in water come out close, within 413 cm -1 (10 nm). These differences are within the expected accuracy of our quantum chemical methodology. Notwithstanding, we restrict ourselves to making a comparison with the results obtained for compounds with different basicity of equatorial ligands. Within the uranyl binitrate water complexes with one or two coordinated water molecules, since the equatorial plane does not differ by the nature of the ligands (it means that basicity remains unchanged), we can take an average "hot band" value of UO 2 (NO 3 ) 2 (H 2 O), cis-/trans-UO 2 (NO 3 ) 2 (H 2 O) 2 and compare it to the Na 3 UO 2 (CO 3 ) 3 complex value.

  (NO 3 ) 2 (H 2 O) 2 cis -UO 2 (NO 3 ) 2 (H 2 O) 2 is uranyl rocking, ν 2 is U -H 2 O stretching + weak ν b , ν 3 is U -NO 3 stretching + weak ν b

		347			0(0)→1(0)
	156	0.061			0(0)→1(1ν 1 )
	934	0.138			0(0)→1(1ν s )
	156	0.018			0(0)→1(1ν 1 ,1ν s )
	934	0.037			0(0)→1(2ν s )
	156	0.004			0(0)→1(1ν 1 ,2ν s )
	935	0.008			0(0)→1(3ν s )
	934	0.001			0(0)→1(4ν s )
	trans -UO 2 0.531	20344		0.424 0(0)→1(0)
	315	0.005	20095	249	0.014 0(0)→1(1ν 2 )
	925	0.291	19417	927	0.236 0(0)→1(1ν s )
	315	0.003	19167	249	0.008 0(0)→1(1ν 2 ,1ν s )
	924	0.096	18489	927	0.080 0(0)→1(2ν s )
	315	0.000	18240	249	0.003 0(0)→1(1ν 2 ,2ν s )
	925	0.024	17562	927	0.021 0(0)→1(3ν s )
	925	0.005	16634	927	0.005 0(0)→1(4ν s )
	trans -UO 2 (NO 3 ) 2 (DEiBA) 2	cis -UO 2 (NO 3 ) 2 (DEiBA) 2
		0.097	19850		0.313 0(0)→1(0)
	212	0.007	19616	234	0.011 0(0)→1(1ν 3 )
	911	0.047	18937	913	0.158 0(0)→1(1ν s )
	212	0.003	18703	234	0.007 0(0)→1(1ν 3 ,1ν s )
	911	0.014	18024	913	0.049 0(0)→1(2ν s )
	212	0.000	17790	234	0.002 0(0)→1(1ν 3 ,2ν s )
	911	0.003	17111	913	0.012 0(0)→1(3ν s )
	ν 1

Table 5 :

 5 Experimental and theoretical spectral characteristics of uranyl binitrate complexes. The peak maxima are reported in nm. Experimental ν gs s and ν es s values were obtained by a Lorentzian fitting procedure. The ν gs s corresponds to the averaged band-spacing values between the vibronic transitions, the ν es s corresponds to spacing between the 1 → 0 and 0 → 0 transitions. ν gs s and ν es s are given in cm -1 .

	UO 2 (NO 3 ) 2 (L) 2	Spectral maxima (nm)	ν gs s	ν es s

  , b the 1 → 0 was taken from experimental UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEHiBA) emission spectra to match position of theoretical peaks with experimental ones

								1 ]
				Experimental
	H 2 O 48	507	529	554			864	799
	DEHiBA	495	516	540	566	593	844	795
				Theoretical
	trans-H 2 O a	507	529	557	587	621	925	833
	cis-H 2 O a	507	529	557	587	621	928	834
	trans-DEiBA b	495	516	542	570	601	911	822
	cis-DEiBA b	495	516	542	570	601	913	823
	a

trans-UO 2 (NO 3 ) 2 (H 2 O) 2 cis-UO 2 (NO 3 ) 2 (H 2 O) 2

Acknowledgements

We acknowledge support by the French government through the Program "Investissement d'avenir" (LABEX CaPPA / ANR-11-LABX-0005-01 and I-SITE ULNE / ANR-16-IDEX-0004 ULNE), as well as by the Ministry of Higher Education and Research, Hauts de France council and European Regional Development Fund (ERDF) through the Contrat de Projets État-Région (CPER CLIMIBIO). Furthermore, this work was granted access to the HPC resources of [CINES/IDRIS/TGCC] under the allocation 2020-2021 [A0090801859] made by GENCI. We also acknowledge the CEA for the PhD grant attributed to H.O.

Conclusions

The speciation of uranyl in solution can be investigated by TRLFS to determine the species that may dominate or coexist. This requires an accurate decomposition scheme and experimental data of high quality. In the context of spent fuel reprocessing, monoamide molecules are developed to selectively extract uranium(VI) from the aqueous to the organic phase. The present work by TRLFS and ab initio based methodology shows that no significant change is to be expected in the electronic structure of the uranium binitrate moiety. PBE0 (TD)-DFT approach accurately captured the ground and excited state structures with minor discrepancies which can probably be attributed to the choice of the functional of the density, the basis set and the solvation model. The proposed theoretical methodology allowed to calculate the main vibronic progression of the complexes with the corresponding assignment of the electronic transitions and vibrational modes involved, showing that PBE0 (TD)-DFT is an effective tool for prediction and assignment of luminescent spectra of U(VI)-based complexes.

In this work, we have used a stepwise growth of the chemical models to assess the sensitivity to the amount of water molecules in the coordination sphere of uranyl, and by substituting the water molecules with monoamide DEiBA. Using the chemical models in a form of UO 2 (NO 3 ) 2 (H 2 O) and cis-/trans-UO 2 (NO 3 ) 2 (L) 2 (L = H 2 O, DEiBA) it has been confirmed that the structural and spectroscopic parameters exhibit similar and hardly distinguishable features. Structural isomers for a given stoichiometry are indeed energetically very close and have almost identical TRLFS spectra. Calculations of luminescence bands intensities were found to be in excellent agreement with experimental TRLFS spectra, giving confidence in the validity of our methodology. This approach could be emphasized for a deeper interpretation of the data from time-resolved laser-induced fluorescent spectroscopy which is often efficiently used to track changes in the first coordination sphere of uranyl unit.

Graphical TOC Entry

By comparing available experimental spectra of uranyl complexes and a newly recorded one, in which the latter is in interaction with large organic ligands, with extensive ab initio simulations, we rationalize to which extent the inorganic and organic uranyl coordination spheres, as well as the solvent polarity, influence the spectral shapes and vibrational progressions. Relativistic DFT calculations of the luminescence spectra based on the Franck-Condon principle allow us to reproduce and assign the peak positions.


Jean-Charles Roger

Pierre Dissaux

Jérôme Legrand

Mourad Dridi

Stéphane Rubini

Frank Singhoff

Timing analysis of TASTE models for reconfigurable software Model-Based Systems and Software Engineering (MBSE

INTRODUCTION

Model Based Software Engineering aims at mastering the complexity of software development processes while ensuring a high level of performance, safety and security that can be estimated early in the life cycle by appropriate verification techniques. Dedicated to the space domain, the TASTE [START_REF] Perrotin | TASTE: a real-time software engineering tool-chain overview, status, and future[END_REF][START_REF]TASTE project[END_REF] approach brings an integrated solution to build embedded real-time software running on a list of predefined execution platforms. The TASTE package comes with a graphical editor, various libraries, tools and Ada/C code generators. The underlying modelling paradigms are based on international standards such as ASN.1 and AADL [START_REF] Feiler | Model-based engineering with AADL: an introduction to the SAE architecture analysis & design language[END_REF].

MOSAR (MOdular Spacecraft Assembly and Reconfiguration), is a project developed by a consortium of European organizations [START_REF]MOSAR project[END_REF]. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 821966. The goal of the MOSAR project is to demonstrate several scenarios of modular satellite reconfiguration during operation. This includes adding or removing standardized hardware modules of a client spacecraft by a servicer spacecraft. The impact of spacecraft reconfiguration during operation on the on-board software has been studied using the TASTE toolchain that has been enhanced with proper support of operational modes and an early verification approach based on timing simulation.

TASTE FOR RECONFIGURABLE SOFTWARE TASTE Life Cycle

The TASTE development process is briefly summarized in Figure 1. During step 1, the software architect can build the model through three main views:

-The Data View formalizes all data types that may be used for communication messages.

-The Interface View shows the logical architecture of the software composed of interacting modules.

-The Deployment View describes the physical architecture in terms of computational nodes and networks.

A fourth view, the Concurrency View, is automatically derived from the three above mentioned modelling views. It contains a consistent AADL model including all the required real-time artifacts to capture the software behavior at architectural level. This model is the baseline for source code generation, identified by step 3 in Figure 1. The Concurrency View model can also be efficiently used for early timing analysis to assess timing aspects of the software architecture before code generation. Time aspect verification can be made with the Marzhin AADL simulator [START_REF] Dissaux | The SMART Project: Multi-Agent Scheduling Simulation of Real-time Architectures[END_REF] and with the Cheddar tool [START_REF] Singhoff | Cheddar: a Flexible Real-time Scheduling Framework[END_REF]. This is represented by step 2 in Figure 1.

Figure 1: TASTE development life cycle TASTE Enhancements for Dynamic Software Reconfiguration

A requirement of the MOSAR project is to support software reconfiguration during operation. This can be typically supported by the management of operational modes, which may be expressed within the TASTE model at an applicative level. In order to ease the use of this feature by the software architect and make it more robust and consistent all along the development life cycle, operational modes management has been added to the list of artifacts natively supported by TASTE models and tools.

These enhancements have impacted the following components of the TASTE package:

-Extension of the TASTE meta-model to support modes and modal elements; -Add-ons in the TASTE editor to capture modal information; -Update of the Concurrency View generator to reflect the intended mode change behavior; -Update of the timing analysis tools included in the TASTE toolchain.

CASE STUDY

To illustrate the improvement made in the TASTE toolset, we introduce a case study shown in Figure 2. The case study is based on a simplified model of the MOSAR satellite including reconfigurable payloads. The OBC (On Board Computer) is a fixed subsystem that handles the communication with the ground and all general satellite management tasks. The R-ICU (Reduced Instrument Control Unit) is also fixed and controls the internal communication network. Communications use the R-MAP protocol through SpaceWire connections. The SMs (Spacecraft Modules) are payloads of the satellite than can be removed and replaced during flight operation thanks to a standardized mechanical, electrical and thermal interface. Three of them have been selected for the purpose of our case study: a battery payload (BAT), an optical sensor (OSP1) and a second optical sensor (OSP2).

Marzhin Simulation

This MOSAR model mainly focuses on specific scenarios and transitional regimes between modes to analyze the timing dynamics of software reconfiguration using the Marzhin AADL run-time simulator. The demonstration scenario aims at showing the behavior of the various software tasks that are distributed over the internal satellite network during a reconfiguration operation. Each task in the model has its own behavior defined using the AADL Behavioral Annex leveraged by Marzhin for the simulation. Data exchanged between the tasks through the busses are encoded as integer messages.

Figure 2 presents the TASTE Interface View for the case study. It is a preliminary architecture of a client satellite subject to receipt or disposal of hardware modules during operation. We use such model to run timing simulation with Marzhin. The model contains 3 payloads: BAT (battery), OSP1 (optical sensor 1) and OSP2 (optical sensor 2). The simulation is running with a scenario that reconfigures the system several times and exchange telemetry in the meantime. Figure 3 presents the timelines produced by the Marzhin simulation.

Figure 3 Marzhin simulation chronogram

Worst case timing analysis with the Cheddar tool

The TASTE model shown in Figure 2 can also be used to drive worst case analysis of the timing properties. For such a purpose, we use the Cheddar tool. It focuses on steady regimes, one mode at a time.

Cheddar allows to assess schedulability of a real-time system either by simulation or by mathematical feasibility tests. Contrary to Marzhin which runs online and interactive simulations, Cheddar computes the worst case timing behavior to verify that the timing requirements of the MOSAR case study are never jeopardized. Computing the worst case time behavior requires to specify the worst case behavior of each entity of the TASTE model, which is not required with Marzhin. Furthermore, Cheddar analysis is not run interactively but is made off-line.

For each modal configuration of the MOSAR case study, we generate a Cheddar model on which the schedulability is assessed. This allows us to verify that timing requirements are met on any modal state the MOSAR system can reach. This analysis covers both tasks run on the MOSAR nodes and the SpaceWire communications between those nodes. To both analyze tasks and communications, we apply SCM (SpaceWire Communication Model) which combines task and communications interference specification on the same DAG model for schedulability computation.

CONCLUSION

The full article will start by presenting the TASTE toolset developed at ESA and the extensions added to support dynamic system reconfiguration. It will then describe the MOSAR project and its context. A description of the MOSAR client satellite use case will follow together with the early timing analysis objectives. The first analysis, using the Marzhin simulator will focus on specific scenarios and transitional regimes between modes. The second analysis, using Cheddar will use formal computation and focus on steady states (one mode at a time). We will conclude the article with a comparison between these two approaches and their respective strengths and weaknesses.

Figure 2 :

 2 Figure 2: MOSAR Case Study