Theoretical Study of Plutonium(IV) Complexes Formed within the

Article pubs.acs.org/JPCA

Theoretical Study of Plutonium(IV) Complexes Formed within the PUREX Process: A Proposal of a Plutonium Surrogate in Fire Conditions Martin Šulka,†,‡ Laurent Cantrel,† and Valérie Vallet*,§ †

PSN-RES, SAG, LETR, Institut de Radioprotection et de Sûreté Nucléaire (IRSN), St Paul Lez Durance 13115, France Research Centre of Progressive Technologies, Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdóczyho 1, 917 24 Trnava, Slovakia § Laboratoire PhLAM, CNRS UMR 8523, CNRS FR 2416, Université de Lille, Bât P5, F-59655 Villeneuve d’Ascq Cedex, France ‡

S Supporting Information *

ABSTRACT: We present a relativistic quantum chemical study to determine the best surrogate for plutonium(IV) to be used in experimental investigations of the behavior of plutonium-nitrate-TBP in fire conditions that might occur in the nuclear fuel refining process known as PUREX. In this study geometries and stabilities of Pu(NO3 )62− and Pu(NO3)4(TBP)2 complexes were compared to that of equivalent complexes of selected elements from the lanthanide and actinide series (Ce, Th, U) chosen on the basis of similar ionic radii and stability as tetravalent species. PBE and PBE0 DFT functionals have proven to be sufficient and affordable for qualitative studies, performing as good as the wave function based correlated method MP2. On the basis of our results, cerium(IV) appears to be a good surrogate for plutonium(IV).

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INTRODUCTION

consistent with the values measured elsewhere for TPH-TBP solvents.8 To quantify the risk of radioactive material resuspension from a TBP solvent set on fire, some experiments have been carried out7−14 but, with the exception of Mishima et al.13 who studied fractional release from heating plutonium nitrate solution without TBP, no other experiment with plutonium was conducted due to the critical safety constraints. The main experimental results are gathered in Table 1, leaving out the tests involving ruthenium, because the possible formation of RuO4(g) may significantly alter the measured fractional release with respect to other radioactive materials. Jordan and Lindner7 have shown that the uranium release is proportional to its concentration in solvent and can reach several percent for a uranium concentration of 84 g/L. Mishima et al.13 performed some boiling tests involving plutonium nitrate and showed that the release fraction exponentially depends on the evaporation rate of the solvent. Later, they conducted experiments9 with contaminated 30% TBP−kerosene solvent, for U, Ce, and Cs and determined release values ranging from 0.1% to 1% with respect to the initial solvent content. Malet et al.10 carried out experiments with Cs, Th, and Ce and measured the release values either at the source of the fire or at the downstream filter. In the first data set, values ranged from 10% to 90%, whereas in the second one (not reported in Table 1) the values are significantly smaller, between 0.01% and 0.1%; the gap may

The 30 vol % tri-n-butyl phosphate (TBP) diluted in odorless kerosene (OK) or tetrapropylene hydrogenated (TPH) is used as the major actinide extraction agent in the liquid−liquid extraction involved in the nuclear reprocessing process known as PUREX in the presence of HNO3. In terms of risk analysis, the TBP/HNO3 biphasic solution is well-known to be an inflammable liquid.1 The flash point and fire points are low, respectively, 88.3 and 92.4 °C for fresh solutions, whereas for irradiated solvents, these values are lowered to 72.0 and 76.8 °C.1 Therefore, the in-cell solvent fire is considered to be an important postulated accident at a reprocessing plant even if its probability is low.2,3 A solvent fire containing plutonium is critical in terms of safety because of its high chemical toxicity and its ionizing radiation.4 The main threat to humans comes from inhalation, as plutonium remains in the lungs or migrates to the bones or organs. The 239-Pu and 238-Pu isotopes are αemitters, the median lethal dose (LD50) by inhalation of 239plutonium oxide is around 1 mg.5 For instance, the IAEA agency recommends a maximum permissible occupation in air of 8.7 × 10−11 g.m−3,6 which represents trace levels. The TBP− HNO3 complex decomposes around 130−135 °C, leading to an increase of the temperature solution up to 200 °C.7 During the fire, soot particles are formed in large amounts including up to 20% of the burned kerosene−TBP solvents. Unburned TBP was identified as the main soot substance formed with mass median diameters (MMD) ranging from 0.2 to 0.5 μm with a standard deviation of 2,7 depending on the fire conditions (free atmosphere or closed vessel). These AMMD values are © 2014 American Chemical Society

Received: July 30, 2014 Revised: October 2, 2014 Published: October 7, 2014 10073

dx.doi.org/10.1021/jp507684f | J. Phys. Chem. A 2014, 118, 10073−10080

Nishio and Hasimoto12

be due to the rapid deposition occurring between the two measurement locations. Ballinger et al.8,11 measured the uranium release rate from HNO3−paraffin−TBP solution but it is worth noting that the burning rate was probably too low, yielding an underestimation of the fraction released. Indeed, the nitric acid boiling causes the extinction of the combustion of the solvent, whereas water bubbles formed at the fire pool surface enhance U release. Some other tests were performed in the presence of some FPs (Ru, Cs, and Sr) in the acid phase with quite low concentrations (total smaller than 2.5 g/L) and suggest a release of uranium but without any convincing supporting arguments. Nishio and Hashimoto12 conducted some tests with uranium and some FPs and measured a low fractional release, smaller than 0.1% for U. In addition, they have analyzed their experimental data on the basis of a physical modeling of the phenomena involved but it appears that the phenomenology is complex and many model parameters are either fitted to experiments or calculated from empirical relationships. From this brief literature review, we conclude that experimental data concerning airborne release of radioactive materials are scarce and difficult to compare due to large discrepancies in either the boundary conditions and experimental configurations (heating conditions, gas flow, geometrical design, etc.), all the more that plutonium is absent from experiments. To be able to extrapolate with confidence the Pu fractional release to relevant conditions, additional tests are needed but, knowing that the use of Pu is complicated, the open question is to determine which surrogate could be used. Some authors have selected thorium,4 uranium,15 or cerium16 in place of plutonium on the basis of physical and chemical similarities, but without any deep justifications. In this paper, we will rely on quantum chemical methods to quantitatively compare the properties of plutonium nitrate TBP complexes to that of possible simulants taken in either the lanthanide or actinide series. The objective is to propose the best surrogate to simulate the plutonium release in case of solvent fire. The main difficulty is that for lanthanides and actinides, one has to choose the quantum chemical methods with care, as highlighted by several review papers.17−20 First of all, one has to account for relativistic effects as these elements are heavy. Spin−orbit splitting comes into play once the open-shell molecules are to be studied, even though it is supposed to have a small effect on geometries or reaction energies.21 The next problem is the large number of electrons to be correlated, which makes wave function based correlated calculations very computationally demanding. However, by replacing the core electrons by relativistic effective core potentials (RECP)22,23 mimicking their influence on the valence electrons, one can avoid using large all-electron basis sets and thus significantly reduce the computational effort. In general, actinide/lanthanide elements have very complicated electronic structure due to multiply occupied valence forbitals, together with relatively small gaps between the valence s, p, d, and f orbitals. This fact makes accurate predictions very sensitive to the selection of the quantum chemical methods. When orbital degeneracies occur, the wave function of the system may not be well-described by a single electronic configuration, causing the failure of single-reference methods. In such cases, it is necessary to switch to multireference methods, with the constraints that they are essentially applicable for relatively small molecules.17,18,24 Thus, for sizable molecular systems, the only remaining option is to use DFT

0.7−1.4% depending on U concentration up to 11% for max U concentration and same volume ratio between aqueous and organic phase still lower than 0.1% except for Ru; no great difference between small and large scale

Jordan et al.7 Ballinger et al.11

Article

Kerosene-like diluent. a

H2O or HNO3/70% ndodecane/30% TBP

cesium, cerium, strontium, and ruthenium + uranium UO2(NO3)2

high burning rate; 10−90 L, same volume for water and organics 150 mL

small area (33 cm2) large area, free atmosphere and closed containment large area (0.1−0.7 m2), free atmosphere small area (14 cm2), free atmosphere high burning rate; 50 mL of solvent + addition of a nitric solution

high burning rate

100 mL of organics + 100 mL of acid Low burning rate

HNO3 3 M + 70% normal paraffin hydrocarbona/30% TBP 70% kerosene/30% TBP HNO3/70% kerosene/30% TBP

uranium, 1−84 g/L

Ballinger et al.8

Malet et al.10

10−50% 20−90% 0.4−0.6%; 2.6% with fission products present in HNO3

Mishima et al.9 70% kerosene/30% TBP

uranium 270 g/L + traces of cesium, cerium and zirconium cesium, thorium cerium uranium at 100 g/L

25 mL of organics

duration 30−40 min/small area (13 cm2) small area (64 cm2) large area (1−3 m2) 30−40 min; 50% of unburned organic layer, free atmosphere

0.1−1.0%

contaminant released combustion details conditions contaminants solvent

Table 1. Main Experimental Results Available in Literature To Estimate Fraction of Radioactive Releases from Fire TBP Solvent

references

The Journal of Physical Chemistry A

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methods, bearing in mind that it might not best treat correlation in an intrinsically multireference system. Numerous studies have been conducted to evaluate the accuracy of DFT methods by systematic comparisons to high-level wave function correlated single-reference and multireference methods,19,25−27 together with the discussions of the performance of various density functionals.28−34 Although some of these works came to contradictory conclusions, a common statement is that if one is only interested in the structural behavior of the ground state, single-determinant DFT methods are accurate enough.27 For energetics, however, wave function correlated methods such as MP2 or its multireference counterpart (MR-PT2) must be used.18 In this work the plutonium(IV) coordination complexes were examined and compared with potential tetravalent surrogates from the lanthanide and actinide series, chosen for their similarities in ionic radii with Pu(IV) (0.96 Å), such as Ce(IV) (0.97 Å), Pr(IV) (0.96 Å), Th(IV) (1.05 Å), or U(IV) (1.00 Å). In addition Nd(IV) was also considered because it bears the same f2 electronic configuration. Sm(IV) was chosen as it lies right above Pu(IV) in the periodic table. It is important to bear in mind that in this list of elements, Ce(IV), Th(IV), and U(IV) are chemically relevant as they might exist in the tetravalent oxidation state, whereas Pr(IV), Nd(IV), and Sm(IV) have only been considered from a theoretical viewpoint to check for trends across the lanthanide series. The results for the latter three elements are in the Supporting Information. The choice of the optimal quantum chemical methodology to compare these elements was driven by the study of the hexanitrate systems M(NO3)62−, for which comparisons to data reported by Odoh and Schreckenbach is possible.35 We then discuss the structures, bonding, and thermodynamic stabilities of M(NO3)62− and [M(NO3)4(TBP)2] complexes (M = Ce, Th, U, Pu). These various criteria should help us proposing a suitable surrogate for Pu(IV).

Figure 1. Perspective view of the Pu(NO3)62− complex.

Table 2. Comparison of Several DFT Functionals for the Pu−O Distances (Å) of Pu(NO3)62− and Their Convergence with Respect to Basis Set Size basis set:

defSV(P)

defTZVP

def2TZVP

aug-ccpVDZ

aug-ccpVTZ

COSMO/ def-TZVPa

no. of basis functions:

435

555

843

651

1203

555

2.427

2.442

2.446

2.444

2.447

2.434

2.513 2.495

2.531 2.510

2.534 2.513

2.531 2.509

2.534 2.514

2.520 2.500

2.479

2.489

2.492

2.491

2.493

2.481

2.484

2.497

2.499

2.496

2.501

2.487

2.510

2.525

2.527

2.527

2.527

2.515

S-VWN (LDA) PBE (GGA) TPSS (MGGA) PBE0 (Hybrid) TPSSH (Hybrid) B3-LYP (Hybrid) experimentb

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COMPUTATIONAL METHODS Methodology for Geometry Optimizations. The geometries of all complexes were optimized without symmetry constraints in the gaseous phase (or in solution either TBP or water). Scalar relativistic effective core potentials (RECP) were used for central actinide and lanthanide atoms. The Stuttgart small-core22,23 RECPs (28 core electrons (lanthanides) or 60 core electrons (actinides) represented by RECP) were used associated with def-TZVP valence basis sets. Two series of basis sets, the def-SV(P)−def-TZVP−def2-TZVP and the aug-ccpVDZ−aug-cc-pVTZ, were employed on all other atoms. To assess the convergence with the basis set size and to propose the best approach with respect to price/performance considerations, six different DFT functionals covering various types of exchange correlation approximations (LDA, the GGA PBE, the meta-GGA TPSS, and three hybrids PBE0, TPSSH, and B3LYP) were tested on the geometry optimization of the Pu(NO3)62− complex. All calculations have been performed with the TURBOMOLE36 software package using the efficient resolution of the identity (RI) approach.37−39 The structure of Pu(NO3)62− is displayed in Figure 1 and the structural parameters obtained at various levels of theory are summarized in Table 2. The geometries obtained with the “def-” basis set series are virtually converged at the def-TZVP level; the def2TZVP basis (on light atoms) contributes to a slight improvement but with a significantly larger computational cost. The “def-” series also performs as well as the aug-cc-pVXZ

a

2.490

Optimization in aqueous phase, εr = 80.1. bReference 40.

basis sets that comprise more atomic basis functions. As a result we chose the def-TZVP basis sets for all calculations on the larger TBP-nitrate molecular complexes. The comparison of the various functionals indicates that the LDA functional S-VWN gives shorter bond distances than experiment, whereas GGA and M-GGA functionals give longer distances. All hybrid functionals yield very good agreement with experimental values, yet the widely used B3-LYP functional gives very similar results to that obtained with PBE, as noticed earlier by Odoh and Schreckenbach.35 Outer-sphere solvent effects were evaluated with the conductor-like screening model (COSMO)41 implemented in TURBOMOLE adopting the default settings, using a permittivity of 80.1 for water and 8.0 for TBP. To quantify spin−orbit (SO) effects on geometries, we have compared the optimized structures obtained from calculations in which the spin−orbit part of the relativistic ZORA Hamiltonian42 is either omitted (scalar-relativistic calculation) or included (two-component calculation) in the SCF procedure. These calculations were done at the PBE/TZ2P level of theory with the ADF software.43 The effect of spin− orbit coupling on the Pu−ONO3 distances in Pu(NO3)62− was 10075



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approaches such as MP2 or coupled clusters methods. The spin contamination was not larger than ≈2% in any of the U(IV) or Pu(IV) open-shell complexes. The spin contamination of the wave functions of Pr, Nd, Sm lanthanide complexes is discussed in Supporting Information. To quantify the degree of the multiconfiguration character into the ground-state wave function, the D1 diagnostic as proposed by Janssen and Nielsen45 was evaluated in all MP2 calculations. Large values (≥0.040) of D1 reveal that the multireference character builds up from strong orbital relaxation contributions. On the basis of this diagnostic, all studied systems show a multireference character, including closed-shell NO3− anion with D1 = 0.063. Thus, for NO3−, we performed full-valence (24/16) CASSCF/CASPT2 calculation together with inspection of CCSD excitation amplitudes. These calculations were performed with the MOLCAS 7.5 software package.46 The singlet closed-shell determinant used as reference in the MP2 calculation dominated the CASSCF wave function with a weight of 88%, whereas the weights of excited determinants were negligible (∼1%). Although the T1 diagnostic47 of CCSD amplitudes was 0.0206, just on the edge of the multireference limit, none of the T1 or T2 amplitudes (largest values 0.056) exceeded the generally accepted threshold of ∼0.2. Merging all diagnostic tools, we concluded that a single-reference approach can be applied to the molecular systems.

found to be small, 0.014 Å (the distances obtained with SO coupling being slightly shorter 2.534 Å, than those without SO, 2.548 Å). Methodology for Energetics. The formation energies of the various complexes have been evaluated by performing single-point calculations at the PBE/def-TZVP optimized geometries, either at the MP2 correlated level or at the DFT level using the PBE and PBE0 functionals in def-TZVPP basis set employing RECPs on heavy atoms. The inner core electrons C(1s), N(1s), O(1s), P(1s2s2p), and Pu(5s5p5d) were kept frozen in the MP2 correlated calculations. The performance of the def-TZVPP basis sets was assessed against Dunning’s correlation consistent basis sets, cc-pVXZ and aug-cc-pVXZ (X = 2, 3, 4), by monitoring the convergence of the Pu(NO3)62− formation energy (Figure 2) for reaction 1: Pu 4 + + 6(NO3)− → Pu(NO3)6 2 −

(1)

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RESULTS AND DISCUSSION Structures of M(NO3)62− and M(NO3)4(TBP)2 Complexes. In a recent paper, Odoh and Schreckenbach35 optimized the structure of Pu(NO3)62− at PBE and B3LYP levels using a small-core effective core pseudopotential for Pu. Their results show that both functionals yield very similar geometries, in good agreement with the EXAFS data recorded by Allen et al.40 The nitrate ligands are coordinated to the Pu(IV) central atom in a bidentate fashion as shown in Figure 1. Den Auwer et al.48 have recorded the EXAFS spectrum of M(NO3)4(TBP)2 complexes, for neptunium and plutonium, not for uranium as it was not stable in the (IV) oxidation state. The analysis of the EXAFS data unambiguously confirms our structural model shown in Figure 3, where the central atom is coordinated by two oxygen-bridged TBP ligands and four bidentate nitrate groups. In this work we report analogous structures considering possible surrogates of plutonium from the lanthanide and actinide series, namely Ce, Th, and U. The structural parameters obtained by optimization in the gas phase and solution for both M(NO3)62− and M(NO3)4(TBP)2 complexes are summarized in Table 3. The results show that the PBE optimized M−O(NO3) distance decreases with the increasing atomic number in the actinide series. The shortening of the metal−ligand bond distances is of the same magnitude in both types of complexes. The M−OTBP distance remains nearly constant within each series, a result that is in line with the experimental data of Den Auwer et al.48 Solvent effects have a minor impact on the bond distances: the M−O(NO3) distances get slightly shorter, by 0.01−0.02 Å in the hexanitrate complexes, whereas these distances get longer in the M(NO3)4(TBP)2 complexes. On the contrary, the M−OTBP bond distances are significantly more affected by solvent effects, as they are shortened by as much as 0.076 Å in the case of the cerium complex. The comparison of the structures optimized in

Figure 2. Basis set convergence of the binding energy (BE) in kcal mol−1 of the Pu(NO3)62− complex per Pu−O bond at various levels of theory, Hartree−Fock in blue, MP2 in red, PBE in gray, and PBE0 in green. The binding energy was calculated as the energy balance of eq 1. The full lines, dashed lines, and dotted lines represent def-, ccpVXZ, and aug-cc-pVXZ series, respectively, X = 2, 3, 4. The defseries consisted of def-SV(P), def-TZVP, and def-TZVPP basis.

Among the three basis sets, the def series offers an excellent compromise between energetic accuracy and basis set size, as it provides binding energies in very good agreement to the most extended aug-cc-pVXZ basis sets, with a reduced number of basis functions. All systems with unpaired electrons were treated in the spinunrestricted formalism; the lowest electronic configuration and the ground-state spin multiplicity were determined by allowing the orbital occupation to be smeared over various nearly degenerate orbitals44 with a temperature of 300 K, and then lowering the temperature at every SCF cycle until reaching 10 K. In all systems the high-spin states corresponding to the formal number of unpaired electron on the heavy metal center were found to be the ground states, i.e., singlet states for Ce(IV) and Th(IV) complexes, triplets for U(IV), and quintets for Pu(IV) complexes. However, in the spin-unrestricted framework, spin contaminations may appear in the wave function when the resulting eigenstates are not eigenfunctions of the S2 operator. The level of spin contamination reflects the appearance of a multireference character of the wave function, which might alter the accuracy of post-Hartree−Fock 10076



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methods used. We can say that all of them are able at least to reproduce the trends mentioned above and that all considered methods are suitable for relative comparison of binding energies within the two series. The computed values (Table 4 and Table S3 of the Supporting Information) reveal that the lanthanide elements form more stable complexes than their actinide counterparts. Zooming on the binding energies of individual elements with respect to plutonium, the best agreement is achieved for the elements at the beginning of the lanthanides series, in particular with cerium(IV). Although the similarities between cerium and plutonium may change with the correlation method used, when we consider the average difference, denoted as Δ̅ BE in Table 4, cerium appears to be the element most similar to plutonium. For example, thorium, which was used in some experiments, forms significantly less stable complexes than plutonium and at the same time has the largest Δ̅ BE among all elements considered. This suggests that Th(IV) is by far not the ideal surrogate for plutonium. To evaluate the effect of solvent on the binding energies, we have performed single-point calculations treating the solvent as a polarizable continuum media (COSMO). The results are compiled in Table 4. Solvent effects destabilize energetically the M−O bonds but do not alter the trends observed in the gas phase. In particular the difference in binding energies with respect to plutonium, ΔBE confirms that cerium nitrate is a surrogate for plutonium nitrate. QTAIM Analysis of the Metal−Ligand Chemical Bonds. To probe further the nature of the metal−ligand chemical bonds, we have investigated the topological analysis of the electron densities of the metal−nitrate and metal−TBP bond linkages using Bader’s quantum theory of atoms in molecules (QTAIM). To perform the QTAIM analysis, we have generated the densities at the PBE0 level with the basis sets used in the geometry optimization, with the Gaussian 09 (Revision C01) quantum chemistry package,50 which provides the appropriate wave function extended files (wfx) to be used by the AIMAll package.51 The QTAIM provides insight into the nature of a chemical bond by characterizing the topology of the density at the bond critical points (BCP). Key properties to monitor are the electron density ρb, its Laplacian ∇2ρb, and the energy density Hb. In addition, the delocalization index DI(M,L) which integrates the electron density in the bonding region between atoms M and L, can be used as a measure of the bond order. All these quantities are collected in Table 5. For all complexes the metal−TBP and metal−nitrate bonds the values of ρb range from 0.051 to 0.060 e−/bohr3, below the value 0.08 e−/bohr3 calculated for the ionic LiF molecule, suggesting only minor

Figure 3. Structure of Pu(NO3)4(TBP)2 complex.

a water solvent to the fitted parameters of the EXAFS data shows a fair agreement for the Pu−O(NO3) distances, whereas the computed Pu−OTBP distances are about 0.05 Å shorter than the experimental ones. Binding Energies. To propose a suitable surrogate of plutonium, we have compared the binding energies of the M(NO3)62− and M(NO3)4(TBP)2 complexes calculated as the energy balance of reactions given by eqs 1 and 2, respectively. A similar investigation was carried out by Gagliardi et al.49 on plutonium diketone complexes. M 4 + + 4(NO3)− + 2(TBP) → M(NO3)4 (TBP)2

(2)

The binding energies were evaluated both at the MP2 correlated level and DFT level using the PBE and PBE0 functionals. The results for M(NO3)62− complexes are given in Table 4 and Figure 4a. The binding energies of the M(NO3)4(TBP)2 complexes (Figure 4b) show the very same trends; therefore, we have built our discussion on the results for the M(NO3)62− complexes. As the central atom is coordinated to six nitrate groups accounting for 12 M−O bonds, the binding energy can be quantified per M−O bond. We first examine the energetics calculated in the gas phase, and will address the effect of the solvent later. For both lanthanide and actinide complexes, the binding energies steadily increase with the atomic number. This can be attributed to the increase of the effective charge on the central atom that is paired with the lanthanide/actinide contraction. Figure 4 displays the comparison of the binding energies for all

Table 3. Calculated Interatomic M−ONO3 and M−OTBP Distances (Å) in M(NO3)62− and M(NO3)4(TBP)2 Complexes Obtained at the PBE/def-TZVP Level in Gaseous and Liquid (TBP or Water) Phases M(NO3)62−

M(NO3)4(TBP)2

M−O(NO3)

a

M

f-occ

gas

waterb

Ce Th U Pu

f0 f0 f2 f4

2.572 2.596 2.539 2.531

2.559 2.586 2.529 2.520

M−O(NO3) exptc

gas

TBPa

waterb

2.49

2.518 2.553 2.490 2.481

2.516 2.565 2.503 2.494

2.520 2.569 2.507 2.497

M−OTBP exptc

gas

TBPa

waterb

exptc

2.48

2.402 2.399 2.383 2.377

2.339 2.370 2.343 2.334

2.326 2.359 2.332 2.326

2.38

Optimization in TBP, εr = 8.0. bOptimization in aqueous phase, εr = 80.1. cReferences 40 and 48. 10077



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Table 4. Binding Energies per M−O Bond (kcal mol−1) in M(NO3)62− Complexes

Ce Th U Pu

HF

MP2

gas phase

gas phase

PBE gas phase

PBE0 aqueous phase

gas phase

BE

ΔBEa

BE

ΔBEa

BE

ΔBEa

BE

ΔBEa

BE

ΔBEa

Δ̅ BEb

−143.60 −137.87 −141.31 −144.07

0.47 6.19 2.75

−152.75 −146.09 −150.99 −154.29

1.53 8.19 3.30

−158.35 −146.28 −151.92 −156.85

−1.50 10.57 4.92

−38.78 −26.70 −32.32 −37.34

−1.44 10.64 5.02

−154.16 −145.12 −149.91 −153.77

−0.39 8.66 3.86

0.03 8.40 3.71

(ΔBE) is the difference in the binding energy of (M) complex with respect to complex of plutonium Δ(M−Pu). b(Δ̅ ) is an average ΔBE for all methods (HF, MP2, PBE, PBE0). a

electron accumulations between the metal and the ligands. The metrics are all larger in absolute sense for the bonds to the TBP ligands than to the nitrate groups, reflecting the significantly shorter bonds. The bonds in the actinide complexes with Th(IV), U(IV), and Pu(IV) are as ionic as in the Ce(IV) complexes. The magnitude of the ionicity resembles that observed for An−N bonds in tetravalent actinide complexes with bis-phenyl β-ketoiminate N,O donor ligand studied by Schnaars et al.52 From an electron density viewpoint there is a strong similarity between the electronic densities in the Pu(IV) and Ce(IV) complexes, as there is between the metal−ligand bond distances and metal−ligand binding energies, suggesting that Ce(IV) can be used as a potential surrogate for Pu(IV).

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CONCLUSIONS A comparative theoretical study of structures and stabilities of M(NO3)62− and M(NO3)4(TBP)2 complexes (M = Ce, Th, U, Pu) is presented to propose a suitable surrogate of plutonium for experimental studies. PBE/def-TZVP method was chosen for structure optimizations followed by PBE, PBE0, and MP2 single-point calculations with def-TZVPP basis sets to evaluate the stability of complexes. The influence of solvent effects on structures and energetics was investigated using the COSMO solvation model, showing that solvent effects do not alter the trends observed in the gas phase. A fair agreement between the DFT and MP2 complex formation energies was observed. Overall, the DFT methods in conjunction with relativistic effective core potentials appear to be a strong tool for the purpose of qualitative comparison of bonding trends in lanthanide and actinide complexes. Ce(IV) seems to be a good surrogate for Pu(IV) in HNO3/ TBP solution in fire conditions due to similarities for the comparative parameters studied in terms of geometrical structures of TBP complexes, charge distribution, and binding energies, all the more that in terms of handling its use is quite easy. One main difficulty is that in nitric solution, cerium(IV) does not exist because it is reduced to Ce(III), as indicated by

Figure 4. Binding energies in (a) M(NO3)62− per M−O bond and (b) M(NO3)4(TBP)2. Colored horizontal lines represent the binding energy of plutonium complex at corresponding level of theory.

Table 5. Characteristics of the M−TBP and M−NO3 Bond Critical Points (BCP) for the Various M(NO3)4(TBP)2 Complexesa M−TBP

M−NO3

M

DI(M,TBP)

ρb

∇ ρb

Hb

DI(M,NO3)

ρb

∇2ρb

Hb

Ce Th U Pu

0.334 0.350 0.349 0.340

0.057 0.063 0.064 0.060

0.192 0.205 0.219 0.228

−0.007 −0.010 −0.010 −0.008

0.320 0.276 0.315 0.327

0.051 0.053 0.057 0.057

0.135 0.134 0.166 0.162

−0.007 −0.009 −0.010 −0.009

2

ρb and ∇2ρb are the electron density and the Laplacian at the bond critical point (BCP) given in e−/bohr3 and e−/bohr5. DI(M,L) is the delocalization index. Hb (au) is the energy density at the critical point.

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the redox potential listed in Table 6. For all surrogates examined, only thorium is very stable in oxidation state +4 in Table 6. Comparison of the M(IV)/M(III) Redox Potentials ox/red HNO3/HNO2 HNO3/NO Th(IV)/Th(III) U(IV)/U(III) Pu(IV)/Pu(III) Ce(IV)/Ce(III) Pr(IV)/Pr(III) Nd(IV)/Nd(III) Sm(IV)/Sm(III)

E°(V/ ENH) 0.94 0.96 −3.80 −0.63 1.01 1.72 3.20 4.90

reaction NO3− + 3H+ + 2e− ⇌ HNO2 + H2O NO3− + 4H+ + 3e− ⇌ NO(g) + 2H2O Th4+ + e− ⇌ Th3+ U4+ + e− ⇌ U3+ Pu4+ + e− ⇌ Pu3+ Ce4+ + e− ⇌ Ce3+ Pr4+ + e− ⇌ Pr3+ Nd4+ + e− ⇌ Nd3+ Sm4+ + e− ⇌ Sm3+

nitric solutions but does not chemically resemble Pu(IV) close enough. To use Ce as surrogate for Pu, it is necessary to add oxidative agents like hydrogen peroxide, to stabilize cerium in the +4 oxidized form, knowing that preliminary experiments are needed not only to define the accurate conditions of such an oxidative addition but also to ensure that the solvent fire conditions (heat of combustion, etc.) will not be too much altered.

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ASSOCIATED CONTENT

S Supporting Information *

Additional results (bond distances, binding energies, bond critical points, spin contamination) including other elements from the lanthanide series, namely, Pr, Nd, and Sm, and discussion of spin-contamination issues in these complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*V. Vallet. E-mail: [email protected] Phone: +33 3 2033 5985. Fax: +33 3 2033 7020. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by AREVA company. Additional support has been provided by the Slovak Grant Agency VEGA under the contract 1/0770/13, and by the French National Research Agency under contract ANR-11-LABX-0005 Chemical and Physical Properties of the Atmosphere (CaPPA). The authors thank also P. Neogrády, F. Réal, F. Virot, and S. Souvi for fruitful discussions.

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REFERENCES

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