A coupled EXAFS-molecular dynamics study on PuO

A coupled EXAFS–Molecular Dynamics study on the PuO2+and NpO2+hydration: the importance of the electron correlation in the force field building Gema Raposo-Hernández,†José M. Martínez,†Rafael R. Pappalardo,†Christophe Den Auwer,‡and Enrique Sánchez Marcos∗,† †Department of Physical Chemistry, University of Seville, 41012 Seville, Seville, Spain ‡Université Côte d’Azur, CNRS, ICN, 06108 Nice, France E-mail: [email protected] Phone: +34 955421005 Abstract The physicochemical properties of the monovalent actinyl cations, PuO2+and NpO2+, in water have been studied by means of classical Molecular Dynamic simulations. A specific set of cation-water intermolecular potentials based on ab initio potential energy surfaces has been built on the basis of the hydrated ion concept. The TIP4P water model was adopted. Given the paramagnetic character of these actinyls, the cationwater interaction energies were computed from highly correlated wavefunctions using the NEVPT2 method. It is shown that the multi-determinantal character of the wavefunction has a relevant effect on the main distances of the hydrated molecular cations. Several structural, dynamical and energetic properties of the aqueous solutions have been obtained and analyzed. Structural RDF analysis gives an An-Oyl distance of 1.82 1 and 1.84 Å and an An-O(water) distance of 2.51 and 2.53 Å for PuO2+and NpO2+in water, respectively. Experimental EXAFS spectra from dilute aqueous solutions of PuO2+and NpO2+are revisited and analyzed, assuming tetra- and penta-hydration of the actinyl cations. Simulated EXAFS spectra have been computed from the snapshots of the MD simulations. A good agreement with the experimental information available is found. The global analysis leads us to conclude that both PuO2+and NpO2+cations in water are stable pentahydrated aqua ions. Introduction The actinyl forms of actinoids are their trans-dioxo molecular cations, AnO2+/2+ , present in the high oxidation states V and VI.1They exhibit high solubilities in water what leads to a rich solution chemistry in a wide set of scenarios where their chemical behavior may be quite different: ligand complexation, hydrolysis processes coupled to acidity or basicity of the medium, adsorption on surfaces, polymerization and others.2–7 It is of primary interest the proper structural characterization of the hydration of such actinyls in order to further understand their physicochemical properties in the different environments that they may face. It has been shown that these actinyls in water are surrounded by water molecules defining stable aqua ions, [AnO2(H2O)n]+/2+ being generally accepted a hydration number of five,3,8–13 although four has also been proposed in some cases.14–16 The actinyl aqua ion chemistry is intimately joined to nuclear technology due to its role in spent nuclear fuel, reprocessing, temporary and permanent storage and environmental speciation.6,17 The structural characterization of these cations has been performed by both experimental and theoretical techniques. Among the experimental ones, the technique giving a more direct information is the X-ray absorption spectroscopy (XAS), in particular the extended X-ray absorption fine structure (EXAFS).4,17–20 The great advantage of this technique is its ability to supply short-range structural information around an specific atom, the absorbing atom, with a structural precision of one hundredth of angstrom for the first coordination shell 2 distance and one unit in the coordination number.10,12,19,21,22 Given that no long-range order is needed and submillimolar concentrations of the absorbing atom can be detected, EXAFS is a really powerful and very suitable tool for the study of solutions containing actinoid cations.4,17,20,23 Among the theoretical techniques, quantum-mechanical methods and computer simulations have also provided valuable information. In the first case, the studies usually combine the molecular cation with a small number of water molecules forming the hydrated ion and add solvent boundary conditions by means of a continuum solvation model.24–29 A general solvent molecular description can be reached by using statistical techniques, either assuming ab initio Molecular Dynamics (AIMD) at reliable QM levels or classical MD simulations employing in this case reliable force fields. The combination of XAS spectroscopy and MD simulations has been revealed as an useful strategy30–33 to refine the structural properties of solutions when the standard fitting of the experimental spectra are clouded by different factors as complexity of the system, low concentrations, spectroscopical phenomena as multi-excitations, low signal/noise ratio and others.34 The good reproduction of an experimental spectrum by means of the use of the structural information derived from a statistical simulation has a double consequence.23 On one hand, it allows the access to a direct EXAFS-structure assignment provided by the atomistic picture of the statistical trajectory. On the other hand, the agreement shows the ability of the interaction potentials employed in the statistical simulation when using classical force fields, or the quantum-mechanical level in AIMD simulations to describe properly the system. Within the actinyl series, PuO2+has been scarcely studied due to its trend to disproportionation to lower, e.g. Pu4+, and higher, PuO2+ 2oxidation states. EXAFS studies have dealt with PuO2+acidic aqueous solutions.14,15,20 The main distances, Pu-Oyl and Pu-OI, and the hydration number are collected in Table 1. The EXAFS fitting supplies a reduced range for the main distances, Pu-Oyl and Pu-OI, but coordination numbers proposed varies 3 from 3.3 to 5.3. Bearing in mind the typical uncertainty in the coordination number determination from an EXAFS fitting due to multi-parameter correlation, additional information must be included to elucidate this issue. Some QM calculations had concluded that coordination number is five with distances quite different from those obtained by EXAFS, as collected in Table 1.35 Dalodière et al.,20 in a recent study on the PuO2+aqua ion, showed an interesting synthesis method of this species based on sonochemistry which allowed them to reach millimolar PuO2+solutions free of other Pu oxidation states. They recorded the EXAFS spectrum of this species and compared it with simulated spectra obtained from the QM [PuO2(H2O)5]+(H2O)10 and [PuO2(H2O)4]+(H2O)8clusters, obtained by B3LYP optimizations and Debye-Waller factors computed from the QM frequencies of these clusters. They concluded that the best theoretical-experimental agreement corresponds to the PuO2+tetrahydrate. In previous works,36–38 we have performed classical MD simulations of actinyls, AnO2+/2+ , in water using interaction potentials based on first-principles QM calculations. EXAFS and XANES spectra have been simulated using the structural information and the theoretical scattering phases and amplitude functions computed by the ab initio FEFF code (v.9.6).39 Whereas the theoretical-experimental agreement was quite satisfactory for UO22+, NpO22+ and PuO22+ using force fields derived from B3LYP potential energy surfaces, the NpO2+case was not satisfactory.38 This fact compelled us to develop for NpO2+a new force field based on QM wavefunctions with explicit inclusion of the dynamic and non-dynamic electron correlation, as NEVPT2 method does.40,41 The simulated EXAFS spectrum gave a fair comparison with the experimental spectra. As far as authors know, there is not simulated spectra based on statistical computations for PuO2+, the coordination number and geometrical parameter remaining controversial. The aim of this work is to confirm the importance of the use of multi-determinantal wavefunctions as reference QM computations to provide accurate enough force fields when dealing with a higher multiplet open-shell system, as it is that of the PuO2+cation. Like- 4 wise, we envisage to develop and test a simpler formulation of the actinyl potential model. For these reasons, we have built a new NpO2+–H2O interaction potential to double check the validity of this new formulation. A revisited analysis of former experimental EXAFS spectra of PuO2+and NpO2+aqueous solutions15 has also been carried out on the light of the theoretical results. Methods Quantum Chemical Calculations A main motivation of this study is to get insight into the impact that static and dynamic electron correlation may have on the structure and the dynamical and structural disorder of the close environment of the actinyls. Multireference NEVPT240–42calculations, which incorporate both types of electron correlation, were performed using the ORCA43 program. The chosen active space was the set of atomic-like f-orbitals in addition to the molecular orbitals resulting from combining actinide f-orbitals and Oyl p-orbitals. The active space involves 10 molecular orbitals, 2πu, 3σu, 1φu, 1δu, 4σ∗ uand 3π∗ u, as shown by Denning in Figure 1 of his study.44 The main atomic orbital composition of these molecular orbitals is given in Table S1 of SI. A similar selection was adopted by Gendron et al.45 for neptunyl(VI) complexes. This resulted in CASSCF(8,10) configurations for NpO+ 2and CASSCF(9,10) configurations for PuO+ 2. A more complete active space would include non bonding, bonding and antibonding molecular orbitals resulting of the inclusion of 6d actinide orbitals and their combination with Oyl 2s- and 2p-orbitals. However this would lead up to a 16 orbitals active space what increased dramatically the number of configurations, e.g. for the PuO2+case the number of configurations for the (9,10) one is ∼7·103, whereas for the (15,16) is ∼4.9·106. Bearing in mind that we have to deal with the hydrated actinyl aqua ions, both optimizing their geometries and producing a significant numbers of single points to build the interaction potentials, we have adopted the 10 orbitals active space also used in precedent studies of 5 complexes of similar sizes.28,45 Since the triplet and quartet ground states for NpO2+and PuO2+, respectively, are degenerate, calculations were carried out using a state average over the degenerate states excluding excited states. The perturbational step of the calculation was done using quasi-degenerate perturbation theory. The basis sets used were ma-def2-TZVP for O, def2-SVP for H46,47 and SD(60,MWB)//def-TZVP for actinoids.48 The calculations were accelerated using the RI and RIJK pseudospectral methods with “autoaux” auxiliary basis sets. Due to the lack of analytical gradients, geometry optimizations were performed numerically by evenly changing the M-Oyl and M-OIdistances in a 2D grid with a step of ∼0.005Å. The structure was assumed to be optimized when the energy of the predicted optimized structure within the grid differs from the QM value obtained for such optimized geometry in less than 10−5Eh, otherwise a reduced 2D grid, with a smaller step, around this point is computed to estimate the minimum. Interaction Potentials for AnO+ 2in water To describe the interactions of PuO2+and NpO2+in aqueous solution we have developed a procedure based on our statistical implementation of the hydrated ion concept,49,50 particularly adapted for the case of monovalent molecular cations.36,51 Figure 1 displays a sketch of the interaction potentials involved in the system definition. The basic idea is that the Hydrated Ion53 is the representative species interacting with the bulk water, ([AnO2(H2O)n]+–H2O) by means of a hydrated ion-bulk water potential (HIW). For this aim, the QM interaction energy, EQM int , is described by two potentials, one of them is the TIP4P potential,52 which describes the interaction among the first-shell and bulk water molecules, and the other one collects the interactions between the bulk water molecules and the actinyl cation. The functional form is: 6 Figure 1: Interaction Potentials defined in the system: IMC (Intramolecular cation interaction), IW1 (Molecular cation-water first-shell interactions, HIW (hydrated ion-bulk water interactions). The water-water interactions are described by the TIP4P model.52 EQM int =EHIW = AnO+ 2 sites X i Bulk water sites X j Cij 4 r4 ij +Cij 6 r6 ij +Cij 8 r8 ij +Cij 12 r12 ij +qiqj rij + H2OI sites X i Bulk water X j ETIP4P ij (1) The interaction of the molecular cation with its first hydration shell (IW1) was parameterized by a series of r−nterms with n= 4,6,8,12 plus the Coulombic term. EIW1 = AnO2 sites X i CiO 4 r4 iO +CiO 6 r6 iO +CiO 8 r8 iO +CiO 12 r12 iO + AnO2 sites X i Water sites X j qiqj rij (2) At this point it should be noted that the first-shell water molecules are ruled by an interaction potential with the actinyl cation (IW1) different from that of bulk water molecules (HIW). This supplies a refined definition of the interaction within the aqua ion and with the bulk water which allows classical optimized geometries of the aqua ion, as those shown in Table 1, very close to the QM ones, but requiring computational times of seconds instead 7 of tens of hours. The shortcoming associated to this methodological advantage is the fact that no exchange of water molecules between the first-shell and the bulk must occur. Along the MD simulations no water molecule release from the aqua ions to the bulk was observed. Finally, to describe the intrinsic dynamics of the actinyl cation we have adopted for the intramolecular cation (IMC) potential a new functional form with respect to our previous development.36–38,51 We have replaced an interatomic potential based on a power series, as in the EHIW or EIW1 functional forms, by an anharmonic potential to describe the An-Oyl bonds and a harmonic potential for the bending. EIMC = Oyl sites X i [kAn-Oyl,i(ri−r0)2+k0 An-Oyl,i(ri−r0)3] + k00 Oyl-An-Oyl(θ−θ0)2(3) Figure 2 displays some representative structures used to build the intermolecular potentials. 64 structures were used for the HIW potential, 220 structures for the IW1 and 87 ones for the IMC. For this development it has been assumed that the aqua ions are pentahydrates. Figures S1 and S2 show the fitting of the set of PuO2+and NpO2+potentials. Potential coefficients are given in the SI (Tables S2-S5) including their corresponding standard deviations. To check the fitted potentials, we have examined the interaction energy of a bulk water molecule approaching the hydrated actinyl from different regions. Figure S3 of SI shows the good correlation between the QM interaction energy and the value predicted by the force field. It must be stressed that these structures were taken from 50 snapshots of an MD simulation where the closest water molecule to the actinyl aqua ion in each angular region was taken. Given that for the PuO2+aqueous solution, several authors14,15,20 have pointed out that its aqua ion is a tetrahydrate instead of a pentahydrate, a specific force field assuming that the hydrated ion is [PuO2(H2O)4]+was also developed. A fitting procedure similar to that explained for the pentahydrate plutonyl was applied to define the new IMC potential, and the new PuO2+polarization on the tetrahydrate was reflected in the Pu and Oyl effective 8 Figure 2: Representative type of structures employed to fit the potentials defined in the system: IMC (Intramolecular cation interaction), IW1 (Molecular cation-water first-shell interactions) and HIW (hydrated ion-bulk water interactions) 9 Figure 3: An-O (top) and An-H (bottom) radial distribution functions and their coordination numbers for Np(V) (red) and Pu(V) (black) in aqueous solution as obtained from the MD simulations 16 light on the relative orientation of water molecules. Thus, in the equatorial region, hydration shells take an ion-dipole orientation, because the An-H peak is shifted ∼0.7 Å from the An- O peak. In the intermediate zones (30◦-60◦and 120◦-150◦), the running integration number is ∼9 centered far from the actinyl, ∼4.5 Å, and the An-O and An-H peaks overlap, what means that water molecules orientation is rather a compromise of their interactions among the molecular cation and the hydration water molecules. In the axial regions ∼3.4 molecules are associated to the main peak which is centered at ∼4.5 Å from the actinide. This rather depopulated axial region shows that hydrogen atoms are closer to the metal cation than to the oxygen atoms due to the presence of Oyl atoms. Bearing in mind that the An-Oyl distance is ∼1.8 Å, the mean distance of one water hydrogen atom to the Oyl atom is ∼ 2.2 Å. This weak hydrogen bond pattern was not found in the previous cases studied of divalent actinyl.51 The last two regions can be envisaged as hydration structures that build the condensed medium around the aqua ion as well as they solvate slightly the actinyl cation. Table 3 collects a set of energetic and dynamical properties of the monovalent aqueous solutions. The hydration enthalpies agree well with the estimated experimental values given by Gibson et al.59 It must be indicated that the sensitivity of PuO2+electron wavefunction to its close environment have caused a large uncertainty in the hydration energy among different authors29 as indicated by Ryzhkov et al.35 in their recent study on Pu complexes in water. Taking into account the uncertainties, one can conclude that the hydration enthalpy of both cations is almost the same. Regarding the aqua ion dynamics, their size-corrected diffusion coefficient values for neptunyl and plutonyl are also quite similar. The calculated ion mobility is affected by the water mobility, which depends on the water model employed, in our case TIP4P. This model overestimates the water diffusion coefficient, 3.3·10−5cm2 s−1,60 as the experimental value is 2.3·10−5cm2s−1. For this reason a better test is to compare the values normalized by the water self-diffusion coefficient. Then DAn/Dware 0.44 and 0.43 for NpO2+, and PuO2+, respectively. Tiwari et al.61 have computed the diffusion coefficient for the monovalent actinyls using the SPC/E water model, their normalized 17 Figure 4: An-O and An-H angle-solved RDFs Np(V) (red) and Pu(V) (black) in aqueous solution as obtained from the MD simulations. 18 values of the size-corrected DAn/Dware 0.46 and 0.45 for NpO2+and PuO2+, respectively. Their corresponding values for the divalent actinyls, NpO22+ and PuO22+, computed in our previous work38 with the same methodology but using a B3LYP-based force field are 0.38, that represents a low limit of diffusion for PuO2+and NpO2+as they are singly-charged. Simonin et al.62 have determined experimentally for UO22+ at infinite dilute aqueous solution a normalized value of 0.30. Our theoretical normalized value for the divalent uranyl, which was also computed in our previous work38 was 0.37. Table 3: Energetic and dynamical properties calculated from the MD simulations. Property NpO2+PuO2+ ∆Hhyd (kcal mol−1)-166 ±3 -165 ±3 ∆Hexp hyd 59 (kcal mol−1)-180 ±20 -178 ±20 DAn(10−5cm2s−1)1.1 ±0.2 1.1 ±0.2 Dcorr An (10−5cm2s−1)1.4 ±0.2 1.4 ±0.2 DAn/DW0.44 ±0.04 0.43 ±0.04 Another illustrative test of the actinyl dynamics in aqueous solutions is the analysis of the most representative vibrational normal modes. Table 4 shows the symmetric (1A1) and asymmetric (A2) An-Oyl stretching normal modes, the Oyl-An-Oyl bending (E1) and the water breathing stretching (2A1). To account for the solvent effects, the gas phase frequencies of the two pentahydrates have been included in the table. Interestingly, one can observe that for the two actinyl stretching modes the solvation induces red-shifts of their frequencies of about 15-20 cm−1. This is a consequence of the interactions with secondshell water molecules in the intermediate and axial regions. On the contrary, solvent effects induce a blue-shift of ∼50 cm−1in the water breathing mode. This is due to the strong aqua ion-water interactions in the equatorial region, where second-shell water molecules causes a compactness of the first-shell water molecules, then increasing the corresponding frequency of the water breathing vibrational mode. Only three experimental frequencies have been reported in the literature,63–65 the error of our estimation is smaller than 4% and the sequence predicted by our potentials is the same than the experimental one. 19 Table 4: Experimental and MD normal mode frecuencies in cm−1. Frecuencies Method E12A11A1A2 [NpO2(H2O)5]+MD (gas phase) 393 251 819 870 MD (solution) 227 305 798 853 Exp63,64 767 824 [PuO2(H2O)5]+MD (gas phase) 441 250 780 828 MD (solution) 276 296 764 811 Exp65 748 Figures 5 and 6 display the comparison of the experimental EXAFS spectrum reported in the literature from several authors for NpO2+and PuO2+in dilute aqueous solutions, together with the revisited spectra previously reported by Giandomenico et al.15 In the NpO2+case, we can see the reasonable agreement of our simulated spectrum with the three experimental ones.9,12,15 Because the experimental difficulties for the x-ray absorption spectrum recording, the difference among the experimental spectra is similar to that observed for the experimental-theoretical comparison. In the bottom of Figure 5 we have included the simulated EXAFS spectrum obtained using our previous NEVPT2-based intermolecular potential.38 This spectrum almost matches the spectrum obtained in this work which employs a simplified version of the intramolecular actinyl potential (IMC). Regarding the PuO2+EXAFS spectra, Figure 6 also shows that the differences among them are similar to the relative discrepancy of our simulated spectrum with the three experimental spectra. From the set of EXAFS measurements carried out by one of us on the actinyls in a previous work,15 the revisited PuO2+spectrum recorded in transmision mode has been analyzed and included in Figure 6. The spectrum is similar to the spectrum published in that article, although signal/noise is higher as well as global intensity. (cf.“revisited spectrum” in Figure 6 with Pu(V)/HClO4in Figure 4 of Ref.[15]). The complicated shape of the EXAFS spectrum is well reproduced by the simulated one in the five oscillations experimentally recorded. The striking question is the fact that the S2 0values needed to match the main oscillations 20 Figure 5: Top: Simulated (dashed black line) vs. experimental (solid line green (ref.[12]), blue (ref.[9]), red (re-analyzed from ref.[15])) LIII-edge k3-weighted EXAFS spectra for NpO2+in water. Bottom: Comparison between the two simulated EXAFS spectra computed by means of the new NEVPT2 force field developed in this work (black) and the force field developed in a previous work (magenta).38 21 (maximum at k= 5 Å−1) are small, 0.7 for the transmision mode spectrum,15 0.6 for that of Dalodière et al.20 and 0.45 for the Panak et al.’s one.14 In the case of the NpO2+, the values needed are in the range of 0.7-0.9. This fact might be related to the reduction of the coordination number from 5 water molecules in NpO2+aqueous solution to 4 in the PuO2+case. Figure 6: Simulated (dashed black line) vs. experimental (solid line blue (ref.[20]), green (ref.[14]) and red (re-analyzed from ref.[15])) LIII-edge k3-weighted EXAFS spectra for PuO2+in water. To find out on this issue we have undertaken three additional analysis: (i) The quantum-mechanical computation of the relative stability of the two hydrates in 22 water at the same level of calculation employed to develop the force field. (ii) The experimental fitting of the previously recorded plutonyl EXAFS spectrum assuming the constraint of a hydration number: four or five. (iii) The development a force field for PuO2+in water based on a tetrahydrate cation and the analysis of results derived from the corresponding MD simulation at 300 K. A direct procedure to estimate quantum-mechanically the relative stability of [PuO2(H2O)4]+and [PuO2(H2O)5]+in water is the computation of the equilibrium [PuO2(H2O)4]+(aq) + H2O(aq) * )[PuO2(H2O)5]+(aq) (4) This equation can be envisaged as the difference between the PuO2+hydration free energy corresponding to the formation of the tetrahydrate and pentahydrate aqua ions in water PuO2 +(g) + 4 H2O (g) ∆G0 g −−→ [PuO2(H2O)4]+(g) ∆G∗ solv −−−−→ [PuO2(H2O)4]+(aq) (5) PuO2 +(g) + 5 H2O (g) ∆G0 g −−→ [PuO2(H2O)5]+(g) ∆G∗ solv −−−−→ [PuO2(H2O)5]+(aq) (6) nH2O(g) ∆G∗ solv −−−−→ nH2O(aq) (7) The hydration free energy of PuO2+is then computed by the addition of the gas phase hydrate formation, ∆G0 (g), its solvation in water, ∆G∗ solv, computed by means of the continuum polarizable model,66 CPCM,67 as implemented in the ORCA program,43 the vaporization free energy of nwater and the standard state correction associated to the gas phase-solution transfer, as given by Goddard and col.68 The values of the hydration energy are -124 kcal/mol and -128 kcal/mol for the tetra- and penta-hydrate, respectively. Table S6 in SI collects the different contributions to these estimations. From these data, the free energy of equation (4) is -4 kcal/mol what indicates the preference for the pentahydration of PuO2+in water from 23 a quantum-mechanical semicontinuum model of solvation.69 Figure 7 shows the revisited experimental L3-edge k3-weighted EXAFS spectra of NpO2+and PuO2+15 and their fits obtained when the first hydration shell is constraint to be 4 (cyan dashed line) or 5 (black dashed line). It is observed that the two fits are very similar, conclusion that is verified by examining Table 5 that collects the main parameters of the fits. This leads to the fact that the assumption of a given coordination number does not change the values of the fitted parameters, being the quality of the fits almost the same. As already indicated, the sensitivity of the EXAFS for these spectra with such a low signal/noise ratio, due to the high experimental complexity of the measurements, blurs the subtle discrimination of one unit coordination number. Regarding the main An-O distances, one can compare the sequence of distances derived from our MD simulations (MD_POT5 (300K) rows in Table 1) with the EXAFS fit of Table 5. The trend with the change of actinoid is the same, i.e. R(NpOyl) > R(PuOyl) and R(NpOI) > R(PuOI). Even more, the distance changes when going from Np to Pu given by MD simulations and the EXAFS fittings are close: ∆RAnOyl is -0.02 Å(MD) and -0.03 Å(EXAFS fit); and ∆RAnOI is -0.02 Å(MD) and -0.04 Å(EXAFS fit). Table 5: EXAFS best fit parameters of NpO2+and PuO2+in HClO4, this work Fit Parameters NpO2+(CN=4) NpO2+(CN=5) PuO2+(CN=4) PuO2+(CN=5) R(An-Oyl) (Å) 1.83(1) 1.83(1) 1.80(1) 1.80(1) σ2(An-Oyl)(Å2) 0.0003 0.0000 0.0019 0.0015 R(An-OI) (Å) 2.51(1) 2.51(1) 2.47(1) 2.47(1) σ2(An-OI)(Å2) 0.0034 0.0044 0.0061 0.0074 S2 00.9 0.8 0.8 0.7 E0(eV) 6.0 5.6 6.4 6.1 Rfactor(%) 2.5 2.6 4.9 6.5 The final analysis deals with the use of a force field developped on the basis of the intramolecular and intermolecular interactions of [PuO2(H2O)4]+. When running free a MD simulation at 300 K, the plutonyl cation hydration evolves always to a pentahydrate. 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