2.1 Equilibrium constants

For consistency, we used reaction data – i.e. Δ_rG° (equivalently standard equilibrium constants and potentials of redox couples) – they were preferred to formation data (Δ_fG°) [2].

logK1° values were plotted as a function of pKa°, for example when K1° is the formation constant of AmCO32+, 1/Ka° is the protonation constant of CO32−. We observed

Since b_x did not seem to strongly depend on X, we finally used the same b_x (=b) value for all the oxidation states; in that case, for comparing An(X) complexes with An(VI) ones, we used:

2.2 Activity coefficients

For ionic strength corrections, we used γ_i, the molal activity coefficient of ion i calculated with the “Specific Interaction Theory”, the SIT formula [2,4]. The corresponding ɛ_ij empirical (pair interaction) coefficients are taken from the NEA-TDB reviews [4]:

Unknown ɛ_ij numerical values can be estimated by analogy with ions of same charge and similar sizes [3,4]. In that case it was proposed to increase the ɛ_ij uncertainties by ±0.05 kg mol⁻¹ [4]. Moreover, we observed a reasonable linear correlation between interaction coefficients and the charge/radius ratios (Fig. 2(a)). For this correlation we used the formal charge of the cation (or the complex), which is indeed the charge seen by the (ClO₄⁻) counter-anion at large distance. Unfortunately this assumption does not hold for high ionic strengths, the only conditions where the ɛ_ij m_j term cannot be neglected. Indeed some data for AnO2X−4 cations are not in the middle of the correlation cloud, indicating that the relevant phenomenological charge might be higher (than the formal one). Conversely, the corresponding points are moved to the other side of this correlation plot (not represented on the figure), when using the atomic charge (Section 2.3) of An (in AnO2X−4, for this reason, we also plotted other correlations without using the charges (Fig. 2(b) and (c))).

2.3 Quantum calculations

In our hydrolysis correlation study, we used the formal charges of An³⁺ (3) and An⁴⁺ (4), while we used the atomic charge of An(X) in AnO2X−4 (X = 5 or 6). This latter was deduced from quantum (DFT) calculations performed at the same calculation levels (ECP and basis sets) as in our recent previous works [17,20], from which we extracted NPA atomic charges [21,22]. Note that in Gaussian98 and 03, these NPA charges are calculated with the NBO software, which is known to consider the UO22+ 6d orbitals as Rydberg orbitals, despite the final result gives the 7s5f6d electronic configuration. This overestimates the U atomic charge by 0.50 electron. For this reason we recalculated the NPA charge assuming the 6d to be valence orbitals for all the oxy actinide cations.

For the ligands (alone) closed-shell ab initio calculations were performed at the MP2/6-311+g(2df,2p) level; open-shell calculations are not needed, as checked at the B3LYP/6-31+g(d,p) level. All the quantum calculations were done with the Gaussian98 and 03 suites of programs [23,24].

Δ_rE, the ab initio energy, was calculated for the protonation reaction corresponding to the pK_a equilibrium (Fig. 3). pK_a represents pH_1/2; similarly, when adding the entropic contribution to Δ_rE, it represents PH1/2+, the H⁺ partial pressure: the hydration energy of H⁺ is related to the slope in the Δ_rE plot as a function of pK_a (Fig. 3), while the intercept rather reflects the hydration energy change between the reactants and products. Since the slope is much greater than 1, the E scale had to be contracted, which means that the final correlation is quite poor. Slope ≠ 1 also means it is not equivalent to use pK_a or Δ_rE for our estimates of complexing constants: pK_a appeared to be better correlated with measured complexing constants. Furthermore pK_a represents a marginal value of Δ_rE, which already is a marginal part of the DFT calculated electronic energy: the experimental pK_a values are more reliable for our purpose and more accurate than the Δ_rE ones obtained from quantum calculations in the gas phase.

3.1 Comparing the affinities of hard anions for H⁺ and AnO22+

We first examined U(VI) aqueous complexation and hydrolysis data, since a sufficiently large set of complexing constants is available. Positive logK1°vspKa° correlations are observed, and even linear correlations appear to fit the data reasonably well. The plot appeared to be less scattered when restricted to the consistent set of data selected by the NEA-TDB reviews (Fig. 4): we finally used these (NEA-TDB) consistent sets of data for the figures and numerical correlations given in the present paper with the following exceptions. For An(VI) we did not use the NEA-TDB PuO₂CO₃(aq) formation constant based on only (logK1°=13.8−0.6+0.8 [26] and 9.3 ± 0.5 [27]) two experimental determinations that are not consistent (within uncertainties). The latter value (that we published ourselves) is closer to the U(VI) and Np(VI) ones (Table 1) [2,4], but it is rather a maximum possible value corresponding to the detection limit of our solubility measurements. For this reason, we also do not rely on the 9.5 ± 0.5 similar value more recently updated by the NEA-TDB review [16].

The PO43− tri-anion is out of the correlation, while the F⁻ mono anion could probably be included into the correlation, but HO⁻ cannot (Fig. 4). When restricting the correlations to LzL=RO22− potentially bidentate oxygen-donor ligands, virtually the same logK1° value is observed for a given ligand with AnO22+ for An = U, Np, Pu or Am: the variations along this series are only slightly higher than experimental uncertainties. logK1,VI°=((2.0±0.3)+(0.665±0.085)pKa°) is obtained for these (AnO22+) cations. Adding not critically reviewed (logK1,VI°) values gives similar regression coefficients with increased uncertainties, namely (2.6 ± 0.8) instead of (2.0 ± 0.3), and (0.58 ± 0.08) instead of (0.66₅ ± 0.08₅).

3.2 AnO₂RO₂/MRO2zM−2 exchanges for MzM = An³⁺, An⁴⁺ or AnO2+

Similar logK1°vspKa° correlations and observations (as for AnO22+, Section 3.1) are made for the An³⁺ and AnO2+, cations, while there are too few data for M⁴⁺. For the M³⁺/CO32− systems, we used our own complexing constants (Table 1) [28], AmHCO3+ is an outlier, in part due to the stabilisation of H₂CO₃ as CO₂(aq): the measured pK_a (of the HCO3−/CO2(aq) couple) is not the relevant parameter for our correlations. For LzL=RO22− we found K1° values in the order An4+>AnO22+≈An3+>AnO2+, a classical order for the reactivity of actinide cations toward hard anions. However, AnO22+≥An3+ is often written (instead of AnO22+≈An3+). Here the available data for An³⁺ appear to be within the correlation lines of AnO22+. The atomic charge of U in UO22+ is 2.8 electron, which compares with the charge of Am³⁺. Nevertheless, using atomic charges in the correlations gave poorer results (see below and Fig. 4(c)). We obtained logK1,III°≈2.2+0.55pKa° for An³⁺ and logK1,v°≈−0.7+0.54pKa° for AnO22+.

There are too few data for a statistical evaluation of all the uncertainties. Nevertheless, it seems that b_x, the slopes (of every logK1°vs pKa° correlations) are the same within uncertainties. Indeed a reasonable fit is obtained when fixing b_x = b_VI (=0.66₅), namely logK1,X°=(aX+0.665pKa°) for all the oxidation states. We finally fitted the slope (and a_x) on all the data, and obtained logK1,X°=(aX+(0.616±0.055)pKa°) with a_III = 2.25₃ ± 0.07₅, a_IV = 5.44₄ ± 0.24₉, a_V = −1.23₆ ± 0.48₉ and a_VI = 2.40₈ ± 0.45₃ fitted values, where uncertainties are 1.96σ (the maximum errors on logK1,X° was +0.9 for UO₂CO₃ and −0.8 for AnCO3+). Since there are not enough data for a meaningful statistical analysis, we finally increased the uncertainties: logK1,X°−aX=(0.62±0.16)pKa° (Fig. 4(b)). The standard deviation of the fit is 0.5 (it represents less than 3 kJ mol⁻¹), a value only a little higher than that of many direct experimental determinations in aqueous solutions, and of the order of magnitude of the variations of the logK1° values among the series of the analogous cations considered here. However, when a slope is fitted for each oxidation state, a small systematic deviation can be inferred, namely the slopes seem slightly different for each type of central cation (AnO22+, An³⁺ and AnO2+). On the other hand, this difference is small as compared to the scatter in the available data, and it is not specially correlated with the charge of the cation.

Since the (0.62 ± 0.16) slope does not depend on X, (aX−aVI)=logKX,VI° (Eq. (5)), the shift between the lines in Fig. 4(a) is related to the following equation:

We also attempted to force b = 1 in the fits, but without success: the correlations cannot simply be interpreted with Eq. (4).

Similarly, hydrolysis equilibria were compared using KX/VI°∗ (Eq. (8)), the constant of a hydrolysis competition equilibrium (Eq. (7)) between actinide ions at oxidation states X and +6: log∗KIII/VI°=−1.7, log∗KIV/VI°=4.81 and log∗KV/VI°=−6.2 for Np [4]. These results give nearly the same An4+>>AnO22+>An3+>>AnO2+ qualitative scale (Fig. 4(c)), and the log∗KX/VI°=(0.36+0.60)log∗KX/VI° linear correlation.

3.3 Estimating the stabilities of An(IV)RO22+ complexes

We now want to estimate missing complexing constants for U(IV), namely with the SO32− and S2O32− anions. For this we could not use the same type of correlations as those observed for UO22+ and the other cations (Section 3.2), because reliable formation constant has been published for only one type of 1:1 An(IV) complexes, namely for the MSO42+ complexes: logK1,IV°=6.58(USO42+) [2], 6.85 (NpSO42+) [4], 6.89 (PuSO42+) [4] and 7.04 (ZrSO42+) [15]. When using this single datum and the (0.62 ± 0.16) slope value estimated above, the (logK1,IV°=((5.6±0.2)+(0.62±0.16)pKa°) line is drawn, from which logK1,IV°=(12.0±1.9), (10.1 ± 1.4), (6.8 ± 0.5) and (6.6 ± 0.5) are calculated for the An(IV) complexes of CO32−, SO32−,SO42− and S2O32−, respectively. The value of a_IV = 5.6 ± 0.2 was chosen to fit the 6.58 (USO42+), 6.85 (NpSO42+) and 6.89 (PuSO42+) data by giving less weight to USO42+, because the +4 oxidation state is more difficult to stabilise for uranium, even if more experimental studies of U(IV) are available. However, the logK1,IV° (=6.6 ± 0.5) MS2O32+ value is close to the MSO42+ fixed point (of the correlation). Therefore it does not depend sensitively on the value estimated for the slope (of the logK1,IV°vspKa° linear correlation). Consequently the uncertainties are relatively small for (the logK1,IV° estimate of) MS2O32+. Conversely the biggest uncertainty is for MCO32+ the most stable complex, since CO32− appeared to be the most reactive RO22− ligand we studied: it is one of the endpoints of the correlation lines. For this reason, we estimated an upper bound for the value of logK1,IV° from experimental data: we re-interpreted available published experimental solubilities of actinides(IV) by using the same methodology as in Refs. [4,5,29]. We obtained formation constants consistent with the original interpretation (by the authors of Ref. [9]). However, for consistency we added the known stabilities of An(CO₃)_i⁴⁻²ⁱ (i = 4 and 5), and we tested many possible complexes for which we also estimated maximum possible stabilities (Table 2) for sensibility analysis; our purpose was essentially to estimate a value for AnCO32+. As expected from pH vs log[CO32−] predominance diagrams [7,26,28], the most restrictive conditions were found for published solubilities of An(IV) measured at low pH and high CO₂ partial pressure, namely in Refs. [9,30]. In both cases we obtained virtually the same values: logK1,IV°≤11.1or11.5 for the ThCO32+ complex. Using this value (and the sulfate data), logK1,IV°=(5.8+0.51pKa°) is calculated, from which logK1,IV°=11.1, 9.5, 6.8 and 6.6 are calculated for the An(IV) complexes CO32−, SO32−, SO42− and S2O32−, respectively. These values are within the uncertainties of the previous estimates above. The AnCO32+ value of 11.1 is identical as, or slightly smaller (by 0.9 ± 1.9) than the central value (12.0 ± 1.9) of the above estimate, and the same trend was observed for AmCO3+: it was overestimated by 0.8 log₁₀ unit when using the same slope (0.62) for all oxidation states. This correlation predicts under-stabilisation of the AnCO3X−2 complexes (X = 3 or 4) as compared to the AnO2CO3X−6 systems (X = 5 or 6): it might be attributed to the planar structure of CO32−, which offers a better fit to the geometry of the coordinating equatorial plane of the AnO2X−4 actinyl cations. Unfortunately, such an explanation would also hold for the SO32− (quasi-) planar ligand (Fig. 5), which is not specially confirmed (Fig. 4). For consistency with our estimate, logK1,IV°≤11.1, we prefer the last correlation logK1,IV°=(5.8+0.51pKa°), where we increased the uncertainties to encompass the previous logK1,IV°=((5.6±0.2)+(0.62±0.16)pKa°) correlation: logK1,IV°=((5.8±0.4)+(0.51±0.27)pKa°) from which we obtain logK1,IV°≤11.1±3.2 for AnCO32+,=9.5±2.3 for AnSO32+, 9.₅ ± 2.₃ for AnHPO42+ and 6.6 ± 0.8 for AnS2O32+, where uncertainties are increased take into account the lack of experimental data.

logK1,IV°=6.6±0.8, the value estimated for AnS2O32+ is quite similar to those for the AnSO42+ complexes: 6.58 (USO42+), 6.85 (NpSO42+) and 6.89 (PuSO42+). This is consistent with the molecular structures of these ligands: SO42− and S2O32− both have a tetrahedral structure (Fig. 5) – an O atom (of SO42−) being replaced by an S atom (in S2O32−) and similar pK_a values. SO32− has a different structure, a higher pK_a, and a higher estimated value of the complexation constant. Unfortunately, it does not seem easy to draw any simple explanation just from z_O, the atomic charge of the free ligand in vacuum (Fig. 4(d)).

3.4 Uranium geochemistry

In non-complexing aqueous solutions, the solubility of uranium is controlled by uraninite (UO₂(s)) in reducing conditions, and by schoepite (UO₃(s)) in oxidizing and neutral conditions, as illustrated in Fig. 6(a) for 1 μM [U]_t. Besides those minerals, aqueous U(VI) species are predominant in a large E–pH domain, while aqueous U(IV) is stable only in reducing conditions, and is mostly hydrolysed.

On adding carbonate ions at a typical concentration of underground waters, aqueous U(VI) carbonate complexes prevail between pH 4 and 12 (Fig. 6(b)), UO₃(s) is totally dissolved, and the UO₂(s) stability domain is reduced. We have ignored the reduction of the carbonate ions, since this reaction is usually very slow. Nevertheless, no carbonate complex of U(IV) appears on the Pourbaix diagrams. These complexes would predominate only at higher carbonate concentrations than those studied here. Rai and Ryan have already proposed that carbonate complexation of actinide(IV) ions in environmental conditions can be neglected [8].

Among the main sulfur species, SO42− prevails over a large (E–pH) domain in oxidizing to slightly reducing equilibrium conditions. For high pH values, this domain even extends to reducing conditions (Fig. 1). H₂S, HS⁻ and S²⁻ prevail in reducing conditions, but their complexing properties are not significant for the (hard) cations of the f-block elements. UO₂SO₄(aq) is the only predominating sulfur species in our typical underground water conditions (Fig. 6(c)), even when introducing the 1:1 complexing constants estimated above (Section 3.3, Table 1) for US2O32+ and USO32+. The RO22− ligands are protonated in acidic conditions, which decreases their concentrations: the corresponding 1:1 complexing equilibria are actually the

In a first simulation we assumed that the major S species are in the +6 oxidation state (namely HiSO4i−2), and that [HiSO4i−2]/[HiS2O3i−2]≈20, which corresponds to much higher HiS2O3i−2 concentrations than in equilibrium conditions (for kinetic reasons). The USO42+ and U(SO₄)₂ sulfate complexes still appear to be U(IV) major species in acidic conditions (pH < 3.2), while nearly 1% of US2O32+ can be formed (Fig. 7(a)). Yet US2O32+ might be a kinetic intermediate, since uraninite is often associated with pyrite (FeS₂); indeed S2O32− is an intermediary product of its oxidative dissolution [14]. S2O32− and SO42− have similar reactivities (Fig. 4), but (in our hypothesis) the SO42− concentration is higher (than the S2O32− one), which explains why the sulfate complexes dominate. Although the SO32− ions are more reactive, the USO32− complex is negligible in that simulation, since the reduction of SO32− (Fig. 1) decreases its concentration and consequently its complexing ability.

In a second simulation we assumed that SO42− is not formed at all (still for kinetic reasons). Therefore S2O32− is now the dominating S aqueous species (Fig. 1). US2O32+ is the major U(IV) species, and up to a few percent of USO32+ is formed at pH less than 3.0 (Fig. 7(b)).

Even if sulfoxy-anions complexes of U(IV) are certainly not stable in equilibrium conditions, these simulations indicate that they might be formed as kinetic intermediates typically in the course of uraninite and pyrite oxidative dissolutions, or the interaction of aqueous uranium (including U(VI)) with pyrite surfaces [31,32]. Of course, this statement needs experimental confirmation, specially in less acidic to basic conditions, where higher and mixed An(RO2)i(OH)j4-2i-j complexes may form. Furthermore, at pH > 3, U(OH)₄(aq) is the dominant species in equilibrium reducing conditions, and the formation of S-containing complexes is less favourable, specially in the usual pH conditions of equilibrated natural under-ground-waters.

3.5 Hydrolysis of actinide ions

We now consider where protactinium should be placed in the above correlations. There is little experimental published information on Pa aqueous chemistry. We first used the available information on its aqueous species in non-complexing (acidic) solutions and its hydrolysis. Although Pa is known to be an f-block element [17], Pa(V) aqueous chemistry is closer to that of d elements (in the same – the 5th- column of the periodic table) than to the chemistry of AnO2+ trans-protactinian actinide cations. Here is a strong indication that PaO2+ is not the dominating aqueous Pa species.

Jaussaud et al. recently reviewed previous measurements of the Pa(V) hydrolysis constants [33–35]. They are essentially based on liquid–liquid extraction measurements, for which they pointed out many experimental difficulties: side reactions of the organic chemicals, sorption of Pa(V) on vessels and unwanted side reactions. Surprisingly most of the published studies are only based on measurements at trace concentrations of Pa(V), while sorption reactions are classically made negligible by using (non-radioactive) chemical analogues at macro-concentrations. The hydrolysis behaviour of Nb(V) seems similar to that proposed for Pa(V): we calculated the hydrolysis constants of Nb(V) by interpreting the aqueous solubility of Nb₂O₅ (Table 3) [25]. We re-interpreted the (Pa) experimental measurements at 25 °C by giving more weight to the data for which systematic errors seemed the lowest according to Jaussaud's observations and comments: the measurements at high ionic strength and low (TTA = thenoyltrifluoroacetone) extractant concentrations. This essentially confirmed the original interpretation given by the authors, but increased uncertainties and suppressed an inconsistency (Table 3). Namely, classical slope analyses of the raw experimental data imply a Pa species of charge +1 in 0.1 M NaClO₄ aqueous solutions, and +2 at higher I (3 M), consistent with the PaOOH(OH)⁺ and PaOOH²⁺ stoichiometries [17] in nearly the whole pH range studied (0 < pH < 4). Indeed, high I usually stabilizes the species of higher charges. There is no clear evidence for neutral and tri-cationic species, due to the scattering of the data (Fig. 8). A neutral Pa species is certainly formed, but it is clearly stabilized by increasing [TTA]_t, the total TTA concentration (results not reproduced in Fig. 8 for clarity), which suggests the corresponding aqueous Pa(V) species might include ionised deprotonated TTA ligands, which would hide the formation of PaOOH(OH)₂ (equivalently written PaO(OH)₃ or Pa(OH)₅). The formation of PaO³⁺ is not proposed in the original interpretation of the authors, and indeed needs confirmation. Finally, the most reliable published Pa(V) standard hydrolysis constant is certainly log∗K2°=−(1.26±0.15) [34], a value consistent with our re-interpretation (−1.44 ± 0.71) (Fig. 8 and Table 3), and with the Nb(V) value of −(1.65 ± 0.2). We also propose log∗K1°=−(0.04±0.36) and log∗K3°≪−3.6, giving no credit to the (−(7.15 ± 0.4) [34] and −(7.03 ± 0.15) [33,35]) published interpretations from the same experimental data, because the corresponding hydrolysis species could not be detected in the experimental conditions used in this work (pH ≤ 4 corresponding to a maximum value of about 10⁻⁷⁺⁴ = 0.1% for the concentration of the hydrolysis species to be compared with the 10^0.71 uncertainty in the measurements of log∗K2°), even though they might provide a reasonable value: the Nb(V) value of −4.95 ± 0.2 might also be used as a rough estimate. These Ki°∗ constants are actually the hydrolysis constant of PaO³⁺, but the existence of this species has not clearly been demonstrated, and for this reason only the second stepwise experimental determination (K2°∗) seems reliable, while the first one (K1°∗) needs confirmation. The −log∗K2° value is only a little larger than that of −log∗K1°: the two first hydrolyses of Pa(V) would be nearly simultaneous. This is also observed for the other actinide aqueous species.

A linear regression correlates reasonably well log∗K1°, the logarithm of the hydrolysis constant and z, the charge of the M^z+ cation for M^z+ = Ra²⁺, Am³⁺, Pu⁴⁺ (brown dotted line in Fig. 9(a)): −log∗Ki°≈(25.24−6.16z). Adding other An³⁺ and An⁴⁺ cations gives virtually the same correlation (brown dotted line in Fig. 9(b)): −log∗Ki°≈(25.67−6.28z). The actinyl ions such as UO22+, and NpO2+ are below this correlation line. This stabilisation of their hydrolysed species might be originated in an An–O_yl (intramolecular) charge transfer induced on approaching equatorial water molecules to UO22+ [21], an inductive effects of O_water, which is expected to be more important for HO⁻ equatorial ligands (where O_yl is an O atom of an AnO2(X−4)+ actinyl cation, while O_water is an O atom of a water equatorial ligand of the actinyl). Nevertheless, the actinyl cations are not far from the correlation lines: including UO22+ and NpO2+ but excluding Ra²⁺ (black lines in Fig. 9); −logKi°∗≈(24.43−6.01z), and adding other AnO22+ and AnO2+: −logKi°∗≈(22.73−5.62z), while extrapolating (blue dashed lines in Fig. 9) the AnO22+ and AnO2+ data give (blue dashed) lines (in Fig. 9) that are between the PaO³⁺ and PaOOH²⁺ data. Namely, PaO³⁺(aq) would be intermediate between the bare actinide hard cations (An^x+, X = 3 or 4), and the usual actinyl cations (AnO₂^(x−4)+, X = 5 or 6, An = U, Np, Pu or Am), whose polarization by equatorial ligands essentially results in the intramolecular charge transfer between An and O_yl. Note that despite this polarization AnO2(X−4)+ is still a hard cation for the equatorial ligands – i.e. negligible charge transfer from the equatorial ligands – we may wonder whether assuming this concept of (equatorial) hardness/(intra-actinyl) softness is still relevant for such a behaviour. However, the AnO2+/AnO22+/PaO3+ set can as well be considered as a series of actinide oxo-cations on their own line (approximately the blue dashed one in Fig. 9). As a result of their polarizability, these oxo-cations are below the (brown dotted) line of the bare M^z+ cations. This polarizibility probably decreases z_An, the An atomic charge (in the oxo-cation) by inductive effect. This inductive effect would increase with z_An: this can explain the quite surprisingly low calculated atomic charges of U (in UO2+) and Pa (in PaO³⁺), which would therefore be at the origin of the more negative slope for the actinide oxo-cation line (as compared to that of the bare cations). However, this proposition needs confirmation, since the Pa(V) experimental results are neither very accurate, nor validated, and since physical explanations cannot be proven by only such empirical correlations: it is a limit of such correlations, rather than problems in the (very few) experimental data. According to this interpretation, two correlation lines are expected, one for the bare An^x+ cations, and the other one for the AnO2(X−4)+ di-oxo-cations, while the PaO³⁺ mono-oxo-cation would fall between these lines, as we actually observed.

The experimental hydrolysis data already indicated that PaOOH²⁺ should be only a little less reactive than Pu⁴⁺. Finally, it can still be under debate whether it is better to consider PaO³⁺ or PaOOH²⁺, or both, as the Pa(V) aqueous species. Using atomic charges here gave unexpected correlations, as compared to the other chemical studies reviewed in the present paper. Nevertheless, it is not a convincing proof that PaO³⁺ can be an important aqueous species (i.e. it is not a confirmation of the above estimate of its −log∗K1° value).

Our DFT calculations give pictures confirming that PaOOH²⁺(aq) is a logical species, similar to UO22+(aq), while PaO2+(aq) is easily protonated. PaOOH²⁺ is merely protonated PaO2+ [17]. However, our continuing DFT calculations for interpreting published EXAFS measurements clearly indicate that the PaO³⁺ geometry exists in the Pa(V) species formed in concentrated H₂SO₄ aqueous solutions, since none of the other tested model geometries reproduced the shortest experimental distance, including PaOOH²⁺: it thus dissociates in complexing media, to give aqueous sulfate complexes of PaO³⁺.