Hydrolysis and Dimerization of Th4+ Ion

energy of Th(OH2)n. 4+ clusters having different hydration numbers n at the B3LYP level and concluded that the hydration number of the Th4+ aquo ion i...
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J. Phys. Chem. B 2008, 112, 7080–7085

Hydrolysis and Dimerization of Th4+ Ion Satoru Tsushima* Institut für Radiochemie, Forschungszentrum Dresden-Rossendorf (FZD), P.O. Box 510119, Dresden D-01314, Germany ReceiVed: March 4, 2008; ReVised Manuscript ReceiVed: March 31, 2008

Hydrolysis of Th4+ in aqueous solution was studied by density functional theory (DFT) calculations. First, stable coordination numbers (CNs) of Th4+ hydrolysis products were studied systematically, and it was found that the CN significantly decreases as a stepwise hydrolysis reaction proceeds. The fourth hydrolysis product Th(OH)40 has CN 6 with an octahedron coordination. Th(OH)4(OH2)20 can readily form a dimer complex Th2(OH)80 via a Th-OH-Th bridging through an exergonic reaction with a Gibbs energy change of -24.0 kJ/mol. Consequently, dimerization inhibits Th(OH)40 to stay as stable aqueous species. The calculated result is in agreement with the fact that there is no direct evidence to confirm the presence of Th(OH)40 while oligomeric species such as Th4(OH)160 are presumably present. Similar calculations on the Th4+ disulfato complex reveal that the CN and the average Th-O distance of Th(SO4)20 remain almost the same as those in the Th4+ aquo ion, which is also in agreement with experimental data. 1. Introduction Th4+

ion has been a subject of Hydration and hydrolysis of a number of theoretical studies.1–6 The formal electronic configuration of Th4+ is 6d05f0 and allows restricted B3LYP calculations to be applied on the Th4+ aquo ion and its hydrolysis products. Tsushima et al.6 compared the binding energy of Th(OH2)n4+ clusters having different hydration numbers n at the B3LYP level and concluded that the hydration number of the Th4+ aquo ion is 9 or 10. In the same article, the authors compared the average Th-OH2 distances obtained by B3LYP calculations (2.47 Å for Th(H2O)94+ and 2.51 Å for Th(H2O)104+) with those obtained by extended X-ray absorption fine structure (EXAFS) spectroscopy7,8 (2.45 Å) and concluded that in point of bond distances the 9-fold is more likely than the 10-fold. The energy difference between the 9-fold and the 10-fold aquo ions was, however, found to be very small. It has been demonstrated recently by Wilson et al.9 that Th(H2O)104+ can also stay as a dominant species in aqueous solution when Br- is chosen as the counteranion. Th4+ ion has a strong tendency to go through hydrolysis reactions.10–16 The hydrolysis reactions start already at a pH around 1. The presence of monomeric hydroxo species such as Th(OH)3+, Th(OH)22+, Th(OH)3+, Th(OH)40, and Th(OH)5- has been assumed, and their thermodynamic properties have been summarized.17–20 Currently, the Nuclear Energy Agency (NEA) of the Organization for Economic Co-operation and Development (OECD) is making a peer review over existing Th thermodynamic data and this will soon be published. One of the questions concerning Th4+ hydrolysis is whether or not the fourth and fifth hydrolysis products Th(OH)40 and Th(OH)5exist in water. There is no a priori reason to inhibit further hydrolysis reaction to proceed beyond Th(OH)3+; however, Moulin et al.15 were able to confirm the presence of only three monomeric species by electron-spray ionization mass spectrometry, which are Th(OH)3+, Th(OH)22+, and Th(OH)3+. Therefore, despite the fact that a number of publications refer to the thermodynamics data of Th(OH)40 and Th(OH)5-, one may * E-mail: [email protected].

doubt if these species really exist, because in potentiometric titration it is not possible to distinguish Th(OH)40 from Th2(OH)80 or from Th4(OH)160. Another factor that complicates the study of the higher hydrolyzed species is that the solubility of amorphous ThIVO2 · xH2O significantly decreases around the neutral pH region; it is in the order of 10-8-10-9 M, and also, there are formations of various polymeric species (e.g., Th4(OH)88+ and Th6(OH)159+)14 and colloidal species.21 Tsushima et al.6 studied the hydrolysis reaction of Th4+ ion with B3LYP level calculations and concluded that the coordination number slightly decreases as hydrolysis reactions proceed. The coordination number of the Th4+ aquo ion was found to be 9 or 10, and that of the tetrahydroxo complex Th(OH)40 was found to be 8. However, geometry optimizations of the hydroxo complexes in their study were performed in the gas phase, although the final energy includes both the thermal correction and the solvation energy. Ayala22 has recently demonstrated for Po4+ ion that there is a drastic decrease in the coordination number as hydrolysis reaction proceeds; the coordination number of the Po4+ aquo ion was found to be 9, while that of the tetrahydroxo complex Po(OH)40 was found to be 5. Generally, it is very important to make geometry optimization in the solvent when discussing geometry and energy of aqueous species because some complexes rather prefer to be either dissociative or unstable when geometry optimizations are performed in the gas phase. It is especially important for nonhomoleptic complexes like in the case of hydroxo complexes where both OHand OH2 ligands are sharing the same coordination sphere and therefore the coordination geometry is significantly affected by the presence/absence of surrounding solvent molecules. In the present study, the hydrolysis of Th4+ ion was studied (again) in the aqueous phase in order to check the validity of the previous study6 that was performed in the gas phase. Unlike the previous study that was performed in the gas phase, Th4+ was found to have significantly low coordination number (CN) as hydrolysis reaction proceeds. Interestingly, the species Th(OH)40 with reduced CN was found to readily form a dimer complex. The present calculations

10.1021/jp8018974 CCC: $40.75  2008 American Chemical Society Published on Web 05/17/2008

Hydrolysis and Dimerization of Th4+ Ion

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TABLE 1: Calculated Bond Distances and Relative Gibbs Energies of Various Complexes of Th(OH)3+, Th(OH)40, and Th(OH)5- a complex +

Th(OH)3

N 4 5 6

Th(OH)40

7 2 3 4

Th(OH)5-

5 0 1 2

model clusterb +

[Th(OH)3(OH2)3](OH2) [Th(OH)3(OH2)4]+ [Th(OH)3(OH2)4](OH2)+ [Th(OH)3(OH2)5]+ [Th(OH)3(OH2)5](OH2)+ [Th(OH)3(OH2)6]+ [Th(OH)3(OH2)6](OH2)+ [Th(OH)4(OH2)](OH2)0 [Th(OH)4(OH2)2]0 [Th(OH)4(OH2)2](OH2)0 [Th(OH)4(OH2)3]0 [Th(OH)4(OH2)3](OH2)0 [Th(OH)4(OH2)4]0 [Th(OH)4(OH2)4](OH2)0 [Th(OH)5][Th(OH)5](OH2)[Th(OH)5(OH2)][Th(OH)5(OH2)](OH2)[Th(OH)5(OH2)2]-

CN

Th-OH, Th-OH2(1st shell) (Å)

∆G (kJ/mol)

6 7 7 8 8 9 9 5 6 6 7 7 8 8 5 5 6 6 7

2.157, 2.152, 2.216, 2.561, 2.536, 2.520 2.183, 2.181, 2.182, 2.617, 2.624, 2.566, 2.568 2.194, 2.186, 2.182, 2.571, 2.606, 2.537, 2.641 2.215, 2.204, 2.215, 2.631, 2.654, 2.605, 2.674, 2.666 2.219, 2.210, 2.218, 2.621, 2.617, 2.620, 2.672, 2.657 2.227, 2.241, 2.220, 2.731, 2.710, 2.652, 2.730, 2.677, 2.682 2.237, 2.254, 2.222, 2.685, 2.665, 2.734, 2.711, 2.671, 2.682 2.288, 2.209, 2.223, 2.197, 2.540 2.229, 2.238, 2.225, 2.218, 2.575, 2.571 2.218, 2.227, 2.208, 2.285, 2.564, 2.564 2.252, 2.246, 2.231, 2.264, 2.605, 2.690, 2.665 2.284, 2.250, 2.242, 2.247, 2.565, 2.684, 2.685 2.266, 2.325, 2.266, 2.255, 2.664, 2.682, 2.696, 2.785 2.298, 2.327, 2.273, 2.232, 2.610, 2.665, 2.742, 2.775 2.285, 2.277, 2.247, 2.281, 2.267 2.335, 2.252, 2.245, 2.271, 2.249 2.288, 2.286, 2.276, 2.284, 2.272, 2.667 2.263, 2.270, 2.285, 2.254, 2.341, 2.666 2.389, 2.282, 2.281, 2.293, 2.314, 2.740, 2.700

+27.1 0.0 0.0 +17.9 +25.1 0.0 +12.5 0.0 0.0 +0.4 0.0 +14.8 +0.6 0.0 0.0 +32.3

a N denotes the total number of water molecules in the first and second coordination spheres. CN denotes the coordination number (OH + OH2) of the first coordination sphere. b OH2 outside the bracket denotes the water molecule in the second coordination sphere.

provide a possible explanation for the fact that the presence of Th(OH)40 has not been experimentally confirmed. 2. Computational Methods All calculations were performed using the Gaussian 03 package of programs.23 Geometry optimization and successive vibrational frequency calculations were performed at the restricted B3LYP level in the aqueous phase through the use of the conductor-like polarizable continuum model (CPCM)24 using UAHF radii25 as implemented in Gaussian 03. Effective core potential (ECP) was used on thorium,26 sulfur,27 and oxygen,27 comprising 60, 10, and 2 electrons in the core, respectively, with corresponding basis sets. The most diffuse basis functions on thorium with the exponent 0.005 were omitted, and the d-function on oxygen basis was included. For hydrogen, a 5s contracted to 3s basis set was used.28 Gibbs energy was calculated the same way as in various recent studies,29 through vibrational frequency calculations in the aqueous phase and by using the pressure and temperature parameters p ) 1 atm and T ) 298.15 K. Presumably, due to a very flat potential energy surface for a geometry optimization in solvent, it was not possible to remove a single and small imaginary vibrational frequency in some of the calculations. Such a small imaginary frequency is often a computational artifact, therefore considered to be unimportant.30 The presence of an imaginary frequency, however, affects the accuracy of the Gibbs energy calculations because imaginary vibrational modes are simply neglected when the partition function is calculated from the vibrational frequencies. 3. Results and Discussion 3.1. Stable Coordination Numbers of Th(OH)3+, Th(OH)40, Th(OH)5-, and Th(SO4)20. Stable coordination numbers (CNs) of the three hydrolysis products Th(OH)3+, Th(OH)40, and Th(OH)5- were studied first. This was done by comparing the Gibbs energy of two complexes, one having CN n and the other having CN n + 1. To make the number of atoms consistent in the two models, one water molecule was added in the second coordination sphere of the model with smaller CN n.

In Table 1, Th-O atomic distances and relative Gibbs energies of all molecular models that have been considered are provided. By comparing the energy of the first two model clusters in Table 1, [Th(OH)3(OH2)3](OH2)+ and [Th(OH)3(OH2)4]+, it can be found that Th(OH)3+ with CN 7 is 27.1 kJ/mol more stable than that with CN 6. Similar comparisons of other molecular clusters of Th(OH)3+ lead to a conclusion that the most stable CN of Th(OH)3+ is 7. Similarly, it can be concluded from Table 1 that Th(OH)40 has a coordination number of 6 or 7. The energy difference between CN 6 and CN 7 is only 0.4 kJ/mol and is comparable to the kinetic energy at room temperature, which is 2-3 kJ/ mol. Th(OH)5- has a coordination number of 5 or 6. The energy difference between CN 5 and CN 6 is also very small; it is only 0.6 kJ/mol. When the CN of Th(OH)5- is 5, that means there is no more water molecules in the first coordination sphere; hence, the sixth hydrolysis product Th(OH)62- cannot be formed through a deprotonation of Th(OH)5-. A significant decrease in the coordination number was found for Th4+ ion as a stepwise hydrolysis reaction proceeds. Previously, my co-workers and I have performed similar calculations to study the CN of Th4+ hydrolysis products, but we performed geometry optimization only in the gas phase. In the previous study, we found that the CN slightly decreases as the hydrolysis reaction proceeds; i.e., Th4+ has CN 9-10 and Th(OH)40 has CN 8. The present study shows that the decrease in CN is more prominent when geometry optimizations are performed in the aqueous phase. It demonstrates that geometry optimization in the aqueous phase is mandatory for this type of study. It is not easy to confirm the results of the present calculations experimentally because the higher hydrolysis products become dominant species only in the neutral pH region, but in such a pH region, the total Th(IV) concentration is limited to the order of 10-8 M by the solubility. Such a low concentration is beyond the limit of EXAFS measurements. Hennig et al.31 have recently shown that ThIV(SO4)20, which is also a charge-neutral complex like Th(OH)40, has almost the same coordination number as the Th4+ aquo ion, and also the average Th-O distance remains the same as that in the aquo ion. To check whether the small

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Figure 1. The structures of Th(SO4)20 with CN 9 (a), CN 8 + 1 (b), CN 8 (c), CN 7 + 1 (d), and CN 7 (e) obtained at the B3LYP level.

CN of Th(OH)40 obtained here is a computational artifact or not, the CN of Th(SO4)20 was also studied by B3LYP calculations. Figure 1 shows five Th(SO4)20 complexes, one with CN 9, two with CN 8, and two with CN 7. The Gibbs energy of the complex with CN 9 was found to be 12.2 kJ/mol lower than that with CN 8, and the Gibbs energy of the complex with CN 8 was found to be 8.3 kJ/mol lower than that with CN 7, which implies that CN basically remains unchanged in Th(SO4)20 and in Th4+(aq). This is the same finding as that experimentally

obtained by Hennig et al. The average Th-O and Th-S interatomic distances in Th(SO4)20 obtained by B3LYP calculations with CN 9 (and those obtained by EXAFS by Hennig et al.31) are 2.483 Å (2.43Å) and 3.728 Å (3.80Å), respectively. The deviation between B3LYP calculations and EXAFS spectroscopy is in the same level as in the uranium(VI) sulfate case31 and is at an acceptable level. In Table 2, the Mulliken populations of Th(OH2)94+, Th(SO4)2(OH2)70, and Th(OH)4(OH2)20 are provided. It can be

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TABLE 2: The Mulliken Population of Th Atom in Th(OH2)94+, Th(SO4)2(OH2)70, and Th(OH)4(OH2)20 s p d f net

Th4+

Th(OH2)94+

Th(SO4)2(OH2)70

Th(OH)4(OH2)20

4.00 12.00 10.00 0.00 +4.00

4.16 12.07 10.80 0.41 (σ 0.07, π 0.08, δ 0.14, φ 0.12) +2.55

4.15 12.06 10.83 0.46 (σ 0.05, π 0.13, δ 0.11, φ 0.16) +2.49

4.09 12.02 10.99 0.59 (σ 0.06, π 0.18, δ 0.24, φ 0.11) +2.31

seen that there is a significant outflow of electrons from the OH- ligand to the metal in Th(OH)4(OH2)20 when compared to Th(OH2)94+. Some of the electrons are localized on the metal but to some extent contribute to the π-type interaction between OH- and Th. The Th-OH distances are rather short (2.22-2.23 Å); hence, the steric effect limits the number of water molecules that can freely coordinate to Th. This effect is partially relaxed due to the prolongation of the Th-OH2 distances which takes place because of the decrease in the net charge of Th from +2.55 in Th(OH2)94+ to +2.31 in Th(OH)4(OH2)20. Finally, the CN of Th(OH)40 gets much lower than the Th4+ aquo ion. By contrast, SO42- binds exclusively in unidentate fashion to Th4+,31 which is a substitution process of a water molecule by SO42ligand. The Th population remains essentially the same as that in Th(OH2)94+ (Table 2), and there is no change in the CN. Recently, Brendebach characterized the structure and thermodynamic properties of Ca4[ThIV(OH)8]4+.32 Their study clearly demonstrated that a highly negatively charged Th(OH)84can be stabilized by incorporating countercations while the CN of the corresponding complex, Ca4[ThIV(OH)8]4+, remains essentially the same as that in the Th4+ aquo ion. The effect of counterions on the hydrolysis reaction is an interesting subject in its own right; however, it was not pursued in the present theoretical study because where to put counterions remains ambiguous and searching the global energy minimum is hence too complicated. Perhaps, we need to perform molecular dynamics (MD) simulations to study such a large molecule; however, MD simulations of a tetravalent cation are not at all straightforward.1 3.2. Activation Energy of the Hydrolysis Reactions. From the discussions in the previous section, it was concluded that the CN of Th4+ ion decreases significantly as the stepwise hydrolysis reaction proceeds. However, no evidence has been uncovered to exclude the presence of Th(OH)40 and Th(OH)5-. Here, I focus on the activation barrier of the hydrolysis reactions. An attempt to identify the transition state between Th(OH)40 and Th(OH)5- failed presumably due to a very low activation barrier of the reaction. Okamoto et al.4 studied the activation energy of the hydrolysis reactions of Th4+ ion. They have found that the activation energy decreases as hydrolysis reaction proceeds. They have also found that the activation energy increases as the CN of Th decreases. Accordingly, Okamoto et al. were led to propose a pseudolinear correlation between the net charge of the Th atom versus the activation energy of the hydrolysis reaction; the activation energy decreases as the net charge on Th decreases. Such an assumption is sensible because when the net charge on the Th atom decreases, the Th-OH2 bond distance(s) get lengthened, and the activation energy for the hydrolysis reaction (deprotonation) should decrease. In the present case, according to the Mulliken population analysis, the net charge of Th ion is +2.55 in Th(OH2)94+, +2.41 in Th(OH)3(OH2)4+, and +2.31 in Th(OH)4(OH2)20. The average Th-OH2 distance increases from 2.48 Å in Th(OH2)94+ to 2.59 Å in Th(OH)3(OH2)40. Hence, it is natural to assume that the activation energy of the hydrolysis reaction of Th(OH)3+ is much

lower than that of Th4+. Therefore, the activation energy cannot be considered as an inhibiting factor to prohibit the formation of Th(OH)40 from Th(OH)3-. 3.3. Dimerization of Th(OH)40. Previous discussions (sections 3.1 and 3.2) show that Th(OH)40 can indeed be formed through hydrolysis of Th(OH)3-. The lack of the evidence to prove that Th(OH)40 truly exists might be an indication that it can readily go through the oligomerization process. Now, I focus on the oligomerization reaction of Th(OH)40. Oligomeric species of Th4+ having OH bridging are known to exist both in solid and in aqueous solution, and their structures have been characterized.33–35 According to the discussions in section 3.1, the CN of Th(OH)40 is 6 or 7, slightly favoring the former. Figure 2a shows the optimized structure of Th(OH)40 having CN 6. The starting model of the dimer complex was assumed to have CN 6 with two Th(OH)40 connected via hydrogen bonds. The structure of the hydrogen-bonded dimer complex Th2(OH)80 is given in Figure 2b. The complex may be further stabilized by the formation of an OH bridge.

Th2(OH)80(H-bond-bridge) T Th2(OH)80(OH-bridge) (1) The structure of the OH-bridged product is given in Figure 2c. Reaction 1 is an exergonic reaction with a Gibbs energy change of -24.0 kJ/mol. The complex on the left-hand side of reaction 1 is favored in terms of the solvation energy (9.6 kJ/ mol) and the entropy term -ST (2.8 kJ/mol), while the orbital energy is much lower in the right-hand-side complex, and the total Gibbs energy in solution favors the complex on the righthand side. Thus, Th(OH)40 is energetically more stable to stay as OH-bridged dimeric Th2(OH)80 rather than to stay as two independent Th(OH)40. The Th-Th distance in the OH-bridged complex obtained by the density functional theory (DFT) calculations is 4.074 Å. This value is close to the Th-Th distance of ∼4.0 Å obtained by Wilson et al.33 by high energy X-ray scattering (HEXS) for the Th(IV) hydroxo dimer sample, although the details of the sample and the stoichiometry of the species present is not reported by Wilson et al. The peaks at around 8-9 Å in Figure 4 (red line) of ref 33 may be an indication of the presence of higher oligomerized species or the colloidal species as claimed by Wilson et al. themselves. The XAFS investigation of the solution containing Th(IV) polymeric and colloidal species was carried out elsewhere,21 and a Th-Th distance of 3.99 Å has been found. Generally, it is not easy to distinguish Th(IV) hydroxo dimer and higher oligomeric species purely from the EXAFS spectra because the Th-Th distance is more or less similar among these oligomers and also the CN is not a reliable number to conclude whether it is a dimer or a higher oligomeric species. In only special cases such a distinction is possible, as in the case of U(VI) hydroxo dimer (UO2)2(OH)22+ and trimer (UO2)3(µ3-O)(OH)3+, where the latter complex has an oxo bridge and hence the U-U distances are clearly different between the dimer and the trimer.36

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Figure 2. The structures of Th(OH)4(OH2)20 (a) and Th2(OH)8(OH2)40 with hydrogen-bond bridging (b) and OH bridging (c).

The OH-bridged Th2(OH)80 may go through higher oligomerization or further to colloidal formation. Unfortunately, it is difficult to study higher oligomerized species by the DFT calculation because the calculations of such a large molecule are computationally too demanding, and also searching the global energy minimum is not trivial. To summarize, hydrolysis reactions and dimerization of Th4+ ion was studied by DFT calculations. It was found that the CN of Th significantly decreases as a stepwise hydrolysis reaction proceeds. The fourth hydrolysis product Th(OH)40 has a CN of 6 or 7 and can readily form a dimeric complex Th2(OH)80 which has two OH bridges. The present calculations demonstrate that the oligomerization process can inhibit Th(OH)40 from being a stable aqueous species. Acknowledgment. The author was supported by the Alexander von Humboldt foundation, Germany. Generous allocation of computation time on supercomputers at Zentrum fu¨r Informationsdienste and Hochleistungsrechnen (ZIH), Technische Universita¨t Dresden, Germany, is gratefully acknowledged. Supporting Information Available: Coordinates of all complexes. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Yang, T. X.; Tsushima, S.; Suzuki, A. J. Phys. Chem. A 2001, 105, 10439–10445. (2) Yang, T. X.; Tsushima, S.; Suzuki, A. Chem. Phys. Lett. 2002, 360, 534–542. (3) Mochizuki, Y.; Tsushima, S. Chem. Phys. Lett. 2003, 372, 114– 120. (4) Okamoto, Y.; Mochizuki, Y.; Tsushima, S. Chem. Phys. Lett. 2003, 373, 213–217.

(5) Yang, T. X.; Tsushima, S.; Suzuki, A. J. Solid State Chem. 2003, 171, 235–241. (6) Tsushima, S.; Yang, T. X.; Mochizuki, Y.; Okamoto, Y. Chem. Phys. Lett. 2003, 375, 204–212. (7) Moll, H.; Denecke, M. A.; Jalilehvand, F.; Sandstro¨m, M.; Grenthe, I. Inorg. Chem. 1999, 38, 1795–1799. (8) Sandstro¨m, M.; Persson, I.; Jalilehvand, F.; Lindquist-Reis, P.; Spa˚ngberg, D.; Hermansson, K. J. Synchrotron Radiat. 2001, 8, 657–659. (9) Wilson, R. E.; Skanthakumar, S.; Burns, P. C.; Soderholm, L. Angew. Chem., Int. Ed. 2007, 46, 8043–8045. (10) Hietanen, S. Acta Chem. Scand. 1954, 8, 1626–1642. (11) Baes, C. F.; Meyer, N. J.; Roberts, C. E. Inorg. Chem. 1965, 4, 518–527. (12) Brown, P. L.; Ellis, J.; Sylva, R. N. J. Chem. Soc., Dalton Trans. 1983, 31. (13) Grenthe, I.; Lagermann, B. Acta Chem. Scand. 1991, 45, 231–238. (14) Ekberg, C.; Albinsson, Y.; Comarmond, M. J.; Brown, P. L. J. Solution Chem. 2000, 29, 63–86. (15) Moulin, C.; Amekraz, B.; Hubert, S.; Moulin, V. Anal. Chim. Acta 2001, 441, 269–279. (16) Bentouhami, E.; Bouet, G. M.; Meullemeestre, J.; Vierling, F.; Khan, M. A. C. R. Chim. 2004, 7, 537–545. (17) Neck, V.; Kim, J. I. Radiochim. Acta 2001, 89, 1–16. (18) Neck, V.; Mu¨ller, R.; Bouby, M.; Altmaier, M.; Rothe, J.; Denecke, M. A.; Kim, J. I. Radiochim. Acta 2002, 90, 485–494. (19) Szabo´, Z.; Toraishi, T.; Vallet, V.; Grenthe, I. Coord. Chem. ReV. 2006, 250, 784–815. (20) Moriyama, H.; Sasaki, T.; Kobayashi, T.; Takagi, I. J. Nucl. Sci. Technol. 2005, 42, 626–635. (21) Rothe, J.; Denecke, M. A.; Neck, V.; Mu¨ller, R.; Kim, J. I. Inorg. Chem. 2002, 41, 249–258. (22) Ayala, R. “Po (IV) hydration by QM and MD calculations”, ACTINET Workshop on Actinide Speciation using XAFS: How can we improve coupling theoretical chemistry with X-ray absorption spectroscopy?, October 11-12, 2007, Avignon, France (http://www.actinet-network.org/ joint_projects/education_training/jrp_07_07). (23) Frisch, M. J.; et al. Gaussian 03, revision D.01; Gaussian, Inc.: Pittsburgh, PA, 2003. (24) Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995–2001. (25) Bondi, A. J. Phys. Chem. 1964, 68, 441–451. (26) Ku¨chle, W.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1994, 100, 7535–7542.

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