Article pubs.acs.org/JPCB
Linking Solution Structures and Energetics: Thorium Nitrate Complexes S. Skanthakumar,† Geng Bang Jin,† Jian Lin,† Valérie Vallet,‡ and L. Soderholm*,† †
Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439, United States ‡ Université de Lille, CNRS, UMR 8523−PhLAM−Physique des Lasers Atomes et Molécules, F-59000 Lille, France S Supporting Information *
ABSTRACT: Seeking predictive insights into how metal-ion speciation impacts solution chemistry as well as the composition and structure of solid-precipitates, thorium correlations, with both solvent and other solute ions, were quantitatively probed in a series of acidic, nitrate/perchlorate solutions held at constant ionic strength. Difference pairdistribution functions (dPDF), obtained from high-energy Xray scattering (HEXS) data, provide unprecedented structural information on the number of Th ligating ions in solution and how they change with increasing nitrate concentration. A fit of the end member solution, Th (4 m perchloric acid and no nitrate), reveals a homoleptic Th aqua ion with 10 waters in its first coordination shell. Analyses of the acidic solutions containing nitrate reveal exclusively bidentate NO3− complexation with Th, consistent with published solid-state MIV nitrate structures, where MIV = Ce, Th, U, Np, Pu. Metrical fits of Th coordination as a function of nitrate concentration are used to calculate Th−NO3 stability constants, information important to a molecular-scale description of reaction energetics. The coordination environments of Th in solution were compared with single-crystal structures obtained from their precipitates, Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2. Relative stabilities of the solid-state compounds, assessed based on the results of molecular quantum chemical calculations, reveal the importance of including an accurate description of complexed waters when predicting relative energetics of dissolved ions in aqueous solution.
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INTRODUCTION Quantifying the speciation of dissolved metal ions is a critical first step to developing a predictive understanding of their solution chemistries and how to use this information for the targeted synthesis of new materials.1−4 The presence of other dissolved ions sets up a competition with the solvent for metal complexation, the result of which determines constituent chemistry while directing precipitate composition and structure.5 The availability of competing solution equilibria for metal−ligand complex formation has been recognized through a myriad of studies devoted to quantifying thermodynamic stability constants in a wide variety of aqueous systems.6−11 Such statistical-based studies often lack specific molecular-level details supporting claims of the underlying metal-complex structure(s) or composition(s) included in modeling equilibria, particularly with respect to correlated solvent molecules. The lack of molecular specificity renders the thermodynamic information of limited value to theorists and modelers who strive to predict solution speciation and likely reaction products based on the relative free energies of these putative solution species. What is missing is a link between the energetics reported for the formation of solution species, from bulk thermodynamic studies, and the molecular-scale speciation © 2017 American Chemical Society
metrics required by theorists seeking to model and predict solution behavior. Herein we use a novel approach to quantitatively measure atomic-scale metal coordination in a series of solutions, from which bulk thermodynamic free energies are extracted. Using difference pair distribution functions (dPDF), obtained from high energy X-ray scattering (HEXS),12−14 we obtain detailed structural information for the formation of Th(NO3)x solution complexes and tie them directly to their thermodynamic stability constants and formation energies. The findings are put into context with solid-state structural studies of Th-nitrate-hydrates that precipitate from the solutions under study, quantum chemical calculations on their relative stabilities and by comparison with previously reported stability constants.10 Aqueous Th nitrate solutions were chosen as model systems because of their relevance to chemical refining and reprocessing systems.15,16 ThIV is a redox-inactive, soft, spherically symmetric, cation that can be easily modeled. Nitrate forms relatively weak complexes that often permit competition with Received: July 4, 2017 Revised: August 15, 2017 Published: August 17, 2017 8577
DOI: 10.1021/acs.jpcb.7b06567 J. Phys. Chem. B 2017, 121, 8577−8584
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The Journal of Physical Chemistry B solvent and OH− ligation in aqueous solution. A previous study of the Th-NO3−H2O pseudo phase diagram at room temperature revealed simple solution chemistry, with only two precipitating binary phases, Th(NO3)4(H2O)4 and Th(NO3)4(H2O)5.17 There are few reports for any other neutral complexes including any polymeric hydrolyzed Th species,18,19 in contrast to reports for the precipitates from ThIV-sulfate solutions, where the sulfate serves to bridge adjacent Th centers.20−23 Critical to the described approach is the availability of quantitative information about correlations in solution systems.24−28 Herein we employ high-energy X-ray scattering (HEXS) in conjunction with a data-reduction procedure that produces difference pair-distribution functions (dPDFs), from which all correlations not directly involving the target ion have been removed.12,13 The resulting dPDF provides peaks at distances representing those from Th to coordinating ligands, with their intensities quantitatively related to coordination numbers to about 2% accuracies. When applied to a series of samples the obtained structural metrics enable a determination of stability constants, thereby supplying the sought-after, and heretofore unavailable, direct experimental link between atomic-scale structure and thermodynamic free energies14,29,30 This information will allow computational chemists to verify against a real system the robustness of their theory and predictive modeling of metal-ion speciation in solution.
water by varying HNO3 and HClO4 concentrations such that the final solutions were approximately constant ionic strength and constant acidity. Backgrounds were prepared for each sample by omitting the metal ion while matching nitrate and perchlorate concentrations. All concentrations were targeted to accuracies of greater than 99% of calculated values. Unless otherwise noted, all solution concentrations are reported as molal (m, mol/kg H2O). Theory and Modeling. The structures and relative stabilities of Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2 were investigated with quantum chemical models treating the aqueous solvent as a dielectric continuum medium (COSMO)34 with permittivity 80.1. Hybrid density functional theory (DFT) calculations with the PBE0 functional35−37 were carried out to optimize the geometries and compute the Gibbs free energies from the molecular partition functions at 298.15 K and 0.1 MPa based on unscaled harmonic vibrational frequencies. Single-point electronic calculations are carried out at the MP2 level. Thorium is described by the (14s13p10d8f5g)/[10s9p5d4f3g] segmented valence basis sets with Stuttgart−Bonn variety relativistic pseudopotentials were used thorium38,39 and the aug-cc-pVTZ basis sets for all other elements.40,41 All calculations were performed with the Turbomole quantum chemistry package with the Resolution of the Identity approach for computational savings.42 HEXS Studies. Samples were packaged for X-ray scattering measurement in Kapton capillaries (0.0571″ ID) sealed with a quick drying epoxy. As previously described,12,13 room temperature high-energy X-ray scattering data were collected at the Advanced Photon Source (APS), Argonne National Laboratory, beamline 11-ID-B. Using an incident-beam energy of 86.7 keV, corresponding to a wavelength of 0.143 Å, the experiment was performed in transmission geometry. The scattered intensity was measured using an amorphous silicon flat panel X-ray detector mounted in a static position (2θ = 0°) at two different distances, providing detection in momentum transfer space across a Q range from 0.26 to 31 Å−1. Unusual to our data treatment is the use of background solutions to remove all correlations not involving the metal ion, in this case Th. The reduced, partial SΔ(Q) were subsequently Fourier transformed to yield difference pair distribution functions (dPDF)s, presented as gΔ(r) vs r, which include only correlations involving the Th ion. Because the data have been background subtracted, all the peaks in the gΔ(r) vs r plots represent distances between thorium and its correlated atoms. Peak intensities are quantitatively related to the relative concentrations of the correlated pairs. Examples of this approach to data reduction are provided elsewhere12,13,30 with a specific Th-nitrate case, relevant to the work presented in the Supporting Information (Figure S1).
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EXPERIMENTS Crystal Syntheses. Caution! Natural thorium contains primarily 232Th, an α-emitting radioisotope. As such, standard precautions for handling radioactive materials should be followed when working with the quantities used in the syntheses that follow. Colorless crystals of Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2 were isolated by evaporating, at room temperature, aqueous nitric acid (2−10 M) solutions of thorium nitrate (0.1−0.2 M). Synthetic conditions were taken from a previous report that detailed requirements for isolating the two, related, crystalline products.17 Crystallographic Studies. Single-crystal X-ray diffraction data for both compounds were collected using graphitemonochromatized Mo Kα radiation (λ = 0.71073 Å) at 100 K on a Bruker APEXII diffractometer.31 The collection of intensity data as well as cell refinement and data reduction were carried out with the use of the program APEX2.31 Absorption corrections as well as incident beam and decay corrections were performed with the use of the program SADABS.32 The structures were solved with the direct-methods program SHELXS and refined with the least-squares program SHELXL.33 Satisfactory initial refinement results were obtained using the previous reported atomic coordinates of nonhydrogen atoms for Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2. For the noncentrosymmetric structure of the pentahydrate, the refined structure was inverted to obtain the correct absolute structure with an approximately 4% of another twin component. All H atoms of the water molecules in both structures were located in the difference Fourier maps except those for OW3 (W stands for water) in the pentahydrate. H positions were refined using direct O−H and H−H distance restraints of 0.82 and 1.40 Å within a water molecule, respectively. Solution Preparation. Aqueous solutions containing 0.4 m ThIV were prepared as a function of variable nitrate concentration. They were prepared using 18 MΩ distilled
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RESULTS Structure Refinement. To provide a basis for assigning dPDF correlation peaks from solution samples to specific Thligating species, single-crystal structural analyses were performed on X-ray diffraction data obtained from precipitates. Two compounds were isolated, Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2, the structures of which further refine previously published work.43−45 In addition, all the hydrogen positions in the tetrahydrate were determined, which informs the importance of the hydrogen bonding network in structure formation. Details of the structural refinements, together with selected bond distances, are reported in Supporting Informa8578
DOI: 10.1021/acs.jpcb.7b06567 J. Phys. Chem. B 2017, 121, 8577−8584
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The Journal of Physical Chemistry B tion. As depicted in Figure 1, the Th4+ complexes form as isolated monomers in Th(NO3)4(H2O)4, each with 12
modeled using their obtained structures as starting points. Both Th−nitrate−hydrate complexes were optimized in a water continuum solvent. In order to directly compare the energies of the 12 (tetrahydrate) and 11 (trihydrate) coordinated isomers, a water molecule was added in the second-sphere of the tetrahydrate. As quantified in Table 1, the trihydrate compound, Th(NO3)4(H2O)3·(H2O)2, is more stable than the tetrahydrate (with 4 waters in the first coordination sphere and one in the second) by 4.5 kJ mol−1. This result is consistent with the previous report,17 and our current findings, that both compounds crystallize from aqueous solutions under very similar conditions. It should be noted that there was no evidence, when modeling either structure, of a stable monodentate-nitrate coordination configuration. HEXS Solution Data Analysis. The dPDF patterns (Figure 2) were obtained from the series of 0.4 m Th solutions made by a 1:1 replacement of HClO4 by HNO3 such that the solutions are held near constant ionic strength and almost constant pH. Changes in scattering with increasing nitrate concentration were quantified by representing the correlation peaks with four Gaussians. The first two, centered at 2.46(1) and 2.93(3) Å, were obtained from a fit of the end-member HClO4 solution (see full description in SI) and are assigned to correlations involving Th−OW and Th−HW, respectively. This result, which includes a determination of 10 waters in the Th firstcoordination shell, supports the previous finding of 10 coordinating waters determined in HBr solutions46 and is relevant to ongoing interest in modeling the ThIV homoleptic aqua ion.47−52 The nitrate-containing solutions require two additional Gaussians to represent their dPDFs, the first at 2.58(2) Å and the second at 3.00(1) Å. The peak centered at 2.45(1) Å at the lowest nitrate concentration, shifts slightly to lower r as the nitrate concentration is increased. All other peak parameters, except their intensities, were held constant during the fits, the results of which are provided in Table 2. Based on comparison with the distances refined from the single-crystal data as discussed above, the fitted peaks are assigned to the oxygens and the nitrogen of bidentate-coordinating nitrate ions. Consistent with the calculations, there is no evidence of monodentate-nitrate coordination to Th, limiting its presence in solution to less than about 4%.53,54 The fits to the solution dPDFs provide direct information about the nitrate binding mode and total Th coordination. Even at the smallest nitrate concentration studied, the anion enters the cation’s first coordination sphere, displacing some but not all of the coordinating waters present in the perchlorate solution. With increasing nitrate concentration the Th totalinner-sphere oxygen coordination is seen to increase, consistent with expectation based upon steric factors−bidentate nitrate is smaller than two waters. At the highest concentration, the coordination saturates to about 11 O, consistent with the value seen in the trihydrate solid-state structure shown in Figure 1.
Figure 1. (Left) The coordination environment of Th in the binary tetrahydrate Th(NO3)4(H2O)4. (Right) The coordination environment of Th in the binary trihydrate Th(NO3)4(H2O)3·(H2O)2. Th (black), Onitrate (red), OW (magenta), N (blue), H (beige).
coordinating oxygens, eight coming from four bidentate NO3− anions and four from bound H2O molecules. The neutral [Th(NO3)4(H2O)4] moieties are interconnected to 12 identical neighbors via relatively weak intermolecular, water− nitrate, hydrogen bonds. The other isolated phase, Th(NO3)4(H2O)3·(H2O)2, has 11 coordinating oxygens, one less than observed for the tetrahydrate. There are eight oxygens contributed by four bidentate NO3− anions and three others by H2O molecules. The other two H2O molecules included in the chemical formula are not directly bound to the metal, but rather connect to the neutral [Th(NO3)4(H2O)3] complexes via hydrogen bonds. For the purposes of this study we present the structural formula for the putative pentahydrate as Th(NO3)4(H2O)3·(H2O)2 and describe the molecular Th complex as the trihydrate. Th(NO3)4(H2O)3 complexes in the structure of trihydrate are mostly connected by solvent water molecules through stronger intermolecular water−water and weak water−nitrate hydrogen bonds. The Th−O distances are a little bit shorter than the corresponding values found for the [Th(NO3)4(H2O)4], reflecting the larger coordination number of Th in the tetrahydrate. For example, the average Th−OW and Th−ONitrate distances in the trihydrate are 2.44(2) Å and 2.58(2) Å whereas the same distances in the tetrahydrate are, 2.52(2) Å and 2.60(2) Å. Selected Th-ligand distances and coordination numbers for the two structures, together with a detailed description of the hydrogen bonding is provided as Table S2b. Structure Modeling. The relative energetics of the solid phases Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2 were
Table 1. Comparison of the First Sphere Th-Ligand Distances for the Tetrahydrate [Th(NO3)4(H2O)4],(H2O) and Trihydrate Th(NO3)4(H2O)3·(H2O)2 Isomers Obtained from the PBE0/COSMO Geometry Optimization Refined from the Crystal Structures (cf. Table S2)a d(Th−OH2) [Å]
a
−1
d(Th-NO3) [Å]
molecule
ΔG [kJ mol ]
PBE0
Exp.
PBE0
Exp.
[Th(NO3)4(H2O)4]·(H2O) [Th(NO3)4(H2O)3]·(H2O)2
4.5 0.0
2.56(5) 2.48(3)
2.52(5) 2.44(3)
2.58(1) 2.55(2)
2.60(3) 2.58(4)
Relative free energies between both isomers computed at the MP2/COSMO level. 8579
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Figure 2. (Left) dPDFs of the correlations associated with the Th first coordination sphere as a function of solution nitrate concentration. (Right) Running integration for the intensities of the gΔ(r) vs r patterns, which provide the electron count for all correlating ions. The peak positions, together with the electron count provide insights into the nature and number of ions in thorium’s first coordination shell.
Table 2. Analyses of dPDF Patterns Shown in Figure 2a [NO3−]
integr. intensityb 2.0−3.6 Å
no. O waterc
peak centerd (Å)
no. O nitratec
peak centerd (Å)
no. elect.e H+N
Th−O coord numberf
sum fitted intensitiesb
0 0.5 1.0 1.5 2.0
99(3) 106 110 112 113
9.8 7.7 6.3 5.8 5.3
2.46 2.45 2.44 2.43 2.43
2.2 4.2 5.0 5.4
2.58 2.58 2.58 2.57
18 24 25 26 25
9.8 9.9 10.5 10.8 10.7
97 104 110 112 111
a Fitting the data with a series of four Gaussians yields the number of electrons involved in the ThIV ligand−ion correlation. Changes in intensity with changing nitrate concentration, together with a comparison of the peak center with bond distances in the solid-state structures (Table S2) are used to assign the peaks and obtain the number of atoms involved in the correlation. bError ±3. cError ±0.3. dError ±0.02. eError ±4. fError ±0.3.
This result adds to the findings of earlier studies to define a ternary “phase diagram”, undertaken to search for new Th-NO3 phases.17 The absence of evidence for the hexanitrato anion reflects the absence of a countercation, other than a proton, in solution to provide charge balance.
interfacial and extractant behaviors. Further work to explore this chemistry may prove fruitful. In contrast to nitrate, other multidentate anions including phosphate,68 sulfate,19,22,23,69 selenate,70,71 and carboxylate72−74 are known to coordinate with Th(IV) in a bridging bidentate mode, the latter of which has been shown to influence and direct cluster assembly.74−77 The bidentate binding mode of nitrate thus appears to prevent it from acting, by way of a bridging group, to enable polynuclear Th complex formation. This perspective is used to argue that nitrates will not produce the rich MIV oligomer formation and structural chemistry seen for other polydentate anions. As described, the fits of the dPDF patterns provide quantitative information on the average number of nitrate ions bound to Th as a function of nitrate concentration, which can be used to directly estimate stability constants, βn. A detailed description of this approach to the analyses of dPDF patterns has been previously published14,29,30 and is reproduced in the SI. Assuming solution equilibria of the form:
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DISCUSSION There is no evidence, in any of the solutions measured, for the presence of monodentate-coordinated nitrate. An analysis of previous studies of nitrate coordination modes and stereochemistry in inorganic compounds, both in solids and solutions, reveals terminal bidentate or monodentate ligation account for 47% and 6% of all nitrate coordination modes, respectively.55−57 Bridging nitrate groups occur less frequently (20%) and the rest are NO3− anions not considered bound to the metal ion. Studies specific to Th find the nitrate anion chelates exclusively in a terminal bidentate mode. This observation is consistent with our observations of solution behavior and also our calculations that show no evidence of monodentate nitrate coordination. Further extension to other reported tetravalent-metal (U,58,59 Np,60−62 Pu,63−65 and Ce66) nitrate complexes shows that these cations exhibit the same behavior as Th with respect to nitrate coordination. The observation of such limited metal speciation in nitric acid solutions is interesting in light of the its widespread use in the aqueous phase of solvent extraction processes used to refine a wide variety of metal ions.67 Although its favored employment is based upon its dissolution capabilities, coupled with its ease of use at the process level, the low dispersity of metal-complex speciation may also play a role in controlling and optimizing
Th(NO3)n(4 − n) + + NO3− ⇄ Th(NO3)n + 1(3 − n) + ; n=0−3
(1)
the best fit to the Th-nitrate complex concentrations as a function of solution nitrate yield stability constants of log10[β1] = 1.53, log10[β2] = 2.79, and log10[β3] = 3.21. These values are compared with results (Figure 3) calculated using results from a comparative review of various published stability constants, 78−83 with each numbered curve in the figure representing a different study. The compilation favors the 8580
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Figure 4. First coordination sphere of Th, comprised of water and bidentate nitrate (two O per nitrate). The overall coordination is seen to increase slightly with increasing solution nitrate concentration.
Figure 3. A comparison between predicted Th−NO3 complexes as a function of free nitrate concentrations (solid lines) and those determined from quantitative analyses of HEXS data as described in the text (red circles). Th−(NO3)n solution complex concentrations are calculated, following the procedure described by Rossati and Rossati,84 for the equilibria ThIV + nNO3− ↔ Th(NO3)n(4−n)+. The stability constants, log10β0n, used in generating the numbered curves, can be found in the literature, with specific values referenced for 1,78 2,79 3,80 4,81 5,82 and 6.83
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CONCLUSIONS Quantifying, at a molecular-level, the speciation of Th in nitrate solutions provides insights important to the prediction of aqueous chemistry in similar systems as well as an understanding of the mechanisms underlying precipitate composition and structure. The analysis of dPDF patterns obtained from HEXS data on a series of Th nitrate solutions reveals nitrate to form bidentate coordinated complexes with Th, a result consistent with the simple monomeric metal moieties seen to form as precipitates from acidic, aqueous MIV nitrate solutions, regardless of whether MIV is a transition metal, a lanthanide, or an actinide. Our results highlight a fundamental difficulty encountered with molecular-scale approaches to predicting solution behavior. Even for simple cases, such as Th-nitrate solutions, there are competing equilibria not just from the metal−ligand perspective but also as pertains to solvent molecules, an aspect that is neglected in a thermodynamic approach but important from a molecular-scale approach. Current DFT modeling is often used to extract one, lowest-energy structure, ignoring the dynamics often imparted on metal-ion speciation in solution. The resolution to the complication of how to treat competing species in dynamic equilibrium may lie in a re-evaluation of models we use to represent solution chemistry from a molecular perspective. Understanding this aspect of solution behavior is critical to efforts to synthesize targeted species using solution precipitation approaches.
results of Neck et al.82 Our results are consistent with those predicting that the Th solution speciation saturates at a Th:NO3 ratio of slightly less than three, leaving the solution complex as a monovalent cation.80−82 The free energies for the formation of Th(NO3)n complexes are slightly larger than seen for other coordinating monovalent anions such as perchlorate, Cl− or Br−, and may reflect the bidentate nature of its coordination to Th. All of the monovalent anions, including nitrate, have smaller stability constants for their complexes than do those for the divalent anion sulfate, which has log10[β1] = 6.1710 or the trivalent anion phosphate, which has a reported log10[β1] = 10.6.85 These trends indicate that denticity, in addition to anion charge, are expected to play a role in the strength of the complex formed. Whereas the βs extracted from dPDFs of a series of Th solutions as a function of free-nitrate concentration agree well with those obtained previously, our interpretation of the underlying equilibria represented by the stability constants is not well represented by eq 1.10 As is customary when evaluating thermodynamic equilibria, information is neglected concerning coordinated solvent ions. In the case under study herein, each bidentate-coordinating nitrate displaces slightly less than two water molecules (Table 2 and Figure 4) as evidenced by the change from 10-coordinating waters for the homoleptic complex in the absence of nitrate to 5.3 waters when 2.7 nitrate coordinate, for a total Th coordination number of 10.7. The contribution to the difference in free energy originating from ligating waters, estimated to be approximately 4.5 kJ/mol based on the molecular quantum chemical calculations. Because the complexing equilibria determining solution species are similar in energies, even a small error in determining their values can have a significant impact on predicted chemistries. Therefore, it is important, when assessing solution speciation based on small energetic differences between competing, that in addition to the anion the ligating solvent molecules are also accurately taken into account.51,52
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b06567. Crystal data, structure refinements, crystallographic files in cif format, and description of hydrogen bonding for Th(NO3)4(H2O)4 and Th(NO3)4(H2O)3·(H2O)2; example of HEXS data reduction to dPDF pattern; extended dPDF patterns for all solutions; description of Th speciation in perchlorate solution; and description of methodology for determining stability constants from dPDF fitting (PDF) 8581
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AUTHOR INFORMATION
Corresponding Author
*
[email protected]. ORCID
Geng Bang Jin: 0000-0002-6125-208X Valérie Vallet: 0000-0002-2202-3858 L. Soderholm: 0000-0003-4435-2721 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the U.S. DOE, BES, CSGB, Heavy Element Chemistry under contract DE-AC02-06CH11357. The Advanced Photon Source, which was used to obtain the HEXS data used in this study, is supported by the U.S. DOE, BES, Materials Sciences under the same contract number. The computations were performed on the PhLAM cluster financed by the CaPPA project (Chemical and Physical Properties of the Atmosphere) that is funded by the French National Research Agency (ANR) through the PIA (Programme d’Investissement d’Avenir) under contract “ANR-11-LABX-0005-01” and by the Regional Council “Nord-Pas de Calais” and the “European Funds for Regional Economic Development” (FEDER).
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