Stability of the Protactinium(V) Mono-Oxo Cation Probed by First-Principle Calculations
Graphical Abstract
Protactinium (Z=91) deviates from the neighboring actinides by forming PaO3+ in solution instead of PaO2+. Complex stability, evaluated through Gibbs free energy, favors PaO(OH)2(X)(H2O) with Cl−, Br−, I−, NCS−, NO3− and SO42−, but not with OH−, F− and C2O42−. QTAIM and NBO analyses reveal a triple bond in Pa mono-oxo bond, with increased covalency Cl−, Br−, I−, NCS−, NO3− providing insights into protactinium's unique chemical behavior.
Abstract
This study explores the distinctive behavior of protactinium (Z=91) within the actinide series. In contrast to neighboring elements like uranium or plutonium, protactinium in the pentavalent state diverges by not forming the typical dioxo protactinyl moiety PaO2+ in aqueous phase. Instead, it manifests as a monooxo PaO3+ cation or a Pa5+. Employing first-principle calculations with implicit and explicit solvation, we investigate two stoichiometrically equivalent neutral complexes: PaO(OH)2(X)(H2O) and Pa(OH)4(X), where X represents various monodentate and bidentate ligands. Calculating the Gibbs free energy for the reaction PaO(OH)2(X)(H2O)→Pa(OH)4(X), we find that the PaO(OH)2(X)(H2O) complex is stabilized with Cl−, Br−, I−, NCS−, NO3−, and SO42− ligands, while it is not favored with OH−, F−, and C2O42− ligands. Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) methods reveal the Pa mono-oxo bond as a triple bond, with significant contributions from the 5f and 6d shells. Covalency of the Pa mono-oxo bond increases with certain ligands, such as Cl−, Br−, I−, NCS−, and NO3−. These findings elucidate protactinium's unique chemical attributes and provide insights into the conditions supporting the stability of relevant complexes.
Introduction
Understanding and predicting the physico-chemical properties of radionuclides, in particular actinides, is at the heart of the challenges posed by multiple applications related to environment, energy or health. Questions related to the management of the nuclear fuels used are at the heart of the concerns of our Western societies, and the integrated radioactivity of these nuclei makes them interesting for nuclear medicine. Better understanding of the physical and chemical properties of actinide (An) complexes in the solvated phase, that is to say, their speciation, the nature of the chemical bonds between actinides and their environment partners, their thermodynamic properties, can have direct contributions in societal and industrial applications.
Protactinium (Z=91) stands out as the first actinide element to possess actual 5f electrons in its free-atom ground state ([Rn]5f26d17s2). This unique electronic configuration allows for an interplay between the valence 6d and 5f orbitals, making it an intriguing element.1 However, it also presents challenges in our understanding of its chemistry, as it is one of the most complex and less studied radioactive elements.2 Protactinium can exist in both the pentavalent and tetravalent oxidation states, similarly to the transition metals niobium and tantalum within the same chemical group. In solution, PaV is predominant because PaIV is unstable and readily oxidizes to PaV unless strong reducing conditions are at play.3
In this paper, our focus centers on PaV. Like its heavier counterparts, uranium, neptunium and plutonium, PaO2+ is stable in the gas phase.4, 5 Both high-level electronic structure calculations and experimental data suggest the monohydrate PaO2+(H2O) and the PaO(OH)2+ dihydroxyl complex are isoenergetic.6-9 However, in solution, the dioxo moiety PaO2+ has not yet been identified.10-12 Indeed the protactinyl(V) ion is a much stronger acid than its successors in the actinide series and, in fact, the least hydrolyzed species of Pa(V) appears to be PaO(OH)2+.10 PaV may exist as a mono-oxo ion PaO3+, in highly acidic media, rendering it a truly unique actinide12, 13 or a sole-cation Pa5+.14 However, studying PaV presents formidable challenges due to its strong tendency towards hydrolysis, polymerization, precipitation and sorption on any solid.12 To mitigate these competitive reactions, careful control of Pa concentrations and complexing media is essential. PaV displays high solubility in hydrofluoric and sulfuric acids, as well as in oxalic acids. Depending on the concentrations and the medium, it can either form oxo complexes or hydroxocomplexes. For instance, PaV mono-oxo ion complexes, such as [PaOF]2+, [PaOF2]+, PaOF3, have been postulated in fluoride media under specific hydrofluoric acid concentrations.15 In concentrated sulfuric acid16 and oxalic acid,17 [PaOLn]3−2n (where L=SO42− and C2O42−) with stoichiometries ranging from 1 : 1 to 1 : 3 have been observed.11 In cases of higher stoichiometry, X-ray absorption spectroscopy at the PaLIII edge has proven useful for confirming the presence or absence of the mono-oxo bond.13, 16-18
To date, only one crystal structure [NEt4]2[PaOCl5]19 provides evidence of a short Pa−O bond of 1.74 Å. The apparent strength of the Pa−O bond, however, is highly dependent on the concentration and medium, prompting questions about how coordinated ligands and solvent media influence its stability. This issue can be addressed through state-of-the-art quantum calculations. In a study conducted by Toraishi et al., it was concluded that, in the presence of water molecules, PaV mono-oxo ionic complexes are the preferable species and that PaO2+ does not exist.20 In our research, we also employ quantum chemical methods to compare the relative stability of the two possible basic units of PaV, namely the bare Pa5+ and the Pa mono-oxo cation PaO3+. Given that the mono-oxo PaO3+ moiety can be regarded as half of an actinyl dioxo cation, it is chemically relevant to discuss the nature of the Pa−O bond in the context of known uranyl complexes for the isoelectronic hexavalent uranium.
Since, PaV exhibits a closed-shell electronic ground state in most chemical complexes, we will apply single-reference approaches of the density functional theory (DFT) and wave-function Theory (WFT) based approaches, namely the coupled-cluster with single, double and perturbative triple excitations (CCSD(T)), within a relativistic framework. Although relativistic effects, i. e. scalar and spin-orbit ones, are typically considered relevant for open-shell systems, we will also quantify the impact of the spin-orbit coupling on properties of these closed-shell systems, as Vasiliu et al.21 pointed out can amount to about 10 kJ in PaV hydrates and hydroxide species.
Choice of Systems
(1)
Perspectives of PaO(OH)2(F)(H2O) (a) and Pa(OH)4(F) (b) complexes in water. Color code: navy blue (Pa), dark green (F), red (O), white (H).
(2)
(3)where the variable n can take on the value 1, 2 or 3, representing different water coordinations, and making the first-sphere coordination number rise formally from 5 to 8. As discussed later, complexes with three water molecules in the first coordination sphere turned out to be not stable, as one of the water molecules is pushed out to the second coordination sphere, resulting in a maximum coordination number of 7, as found by Oher et al.24
Results and discussion
Solvent effect on geometries with implicit solvation models
The optimization of complex geometries in a solvent like water is essential because it accounts for the influence of the solvent on the molecular structures. In this work, the complexes PaO(OH)3(H2O) and Pa(OH)5 (Figure 2) have demonstrated significant structural changes when transitioning from the gas phase to a solvent environment like water. The relaxation effect, quantified by the energy difference between the gas phase and solvent phase structures, is substantial. In the case of PaO(OH)3(H2O), the complex is stabilized by −76.3 kJ when subjected to geometry optimization in the solvent. Similarly, for Pa(OH)5, it experiences a stabilization of −28.0 kJ in a solvent environment. This emphasizes the importance of considering solvent effects in studying these complexes, as the solvent can significantly impact their stability and geometry.
Pa(OH)5 structures in gas phase (a) and in water (COSMO model) (b). Color code: navy blue (Pa), red (O), white (H).
The comparison of bond lengths between the gas phase and solvent phase structures of Pa(OH)4(X) and PaO(OH)2(X)(H2O) complexes provides valuable insights into the influence of the solvent on these complexes. In the case of Pa(OH)4(X) complexes, we observe that the Pa−X distance increases by approximately 0.1 Å with various ligands when transitioning from gas phase structures (see Table S6 of the SI) to solvent phase structures (Table 1). Similarly, the Pa−OH distances generally increase by up to 0.1 Å with all ligands, except when using the SO42− and C2O42− ligands. This suggests that the solvent environment has a slight elongating effect on these bond distances. However, there does not seem to be a clear trend regarding the Pa−OH distance. On the other hand, for the PaO(OH)2(X)(H2O) complexes, the Pa−O distance increases by a maximum of 0.02 Å, and the Pa−X distance increases by up to 0.1 Å with different ligands when transitioning from gas phase (see Table S7 of the SI) to solvent phase structures (Table 2). Interestingly, the Pa−OH2 distance decreases by 0.2 Å in water, favoring closer interaction with the central atom Pa.
X |
r(Pa-OH) |
r(Pa−X) |
|---|---|---|
OH− |
2.134±0.002 |
|
F− |
2.115±0.010 |
2.142 |
Cl− |
2.094±0.006 |
2.706 |
Br− |
2.091±0.006 |
2.876 |
I− |
2.088±0.019 |
3.130 |
NCS− |
2.094±0.006 |
2.395 |
NO3− |
2.094±0.011 |
2.528±0.007 |
SO42− |
2.125±0.013 |
2.400±0.016 |
C2O42− |
2.132±0.008 |
2.343±0.001 |
X |
r(Pa−O) |
r(Pa-OH) |
r(Pa−X) |
r(Pa-OH2) |
ν(Pa−O) |
|---|---|---|---|---|---|
OH− |
1.879 |
2.164±0.034 |
|
2.550 |
771 |
F− |
1.871 |
2.137±0.025 |
2.181 |
2.521 |
779 |
Cl− |
1.857 |
2.117±0.028 |
2.730 |
2.498 |
795 |
Br− |
1.855 |
2.114±0.028 |
2.896 |
2.493 |
796 |
I− |
1.852 |
2.111±0.028 |
3.140 |
2.487 |
799 |
NCS− |
1.858 |
2.119±0.026 |
2.422 |
2.505 |
793 |
NO3− |
1.860 |
2.119±0.044 |
2.547±0.015 |
2.485 |
798 |
SO42− |
1.873 |
2.149±0.036 |
2.440±0.008 |
2.508 |
779 |
C2O42− |
1.881 |
2.165±0.040 |
2.372±0.021 |
2.525 |
763 |
Overall, these observations emphasize the importance of considering solvent effects when studying these complexes, as they can significantly impact the structural parameters and bonding characteristics of the molecules in a realistic solution environment.
Solvent effect on geometries with explicit solvation models
In the bare PaO(OH)2(X)(H2O) and Pa(OH)4(X) complexes, the coordination number of PaV can be either 5 or 6 depending on whether the ligand is monodentate or bidentate. However, it is worth noting that PaV can have a coordination number of up to 8.11, 24 This raises the possibility of accommodating additional water molecules in the first coordination sphere of PaV in the PaO(OH)2(X)(H2O) and Pa(OH)4(X) complexes. To investigate this hypothesis, we filled the first coordination sphere of PaO(OH)2(I)(H2O)n+1 and Pa(OH)4(I)(H2O)n complexes with up to n=3 water molecules, as depicted in Figure 3. Our results show that both complexes can accommodate 1 (n=1) and 2 (n=2) additional water molecules. However, when we introduce three water molecules (n=3), the third water molecule migrates to the second coordination sphere, where it forms a hydrogen bond with a first-coordination sphere hydroxide in both complexes, enhancing the overall stability. This suggests that the coordination number of PaV is 7 and with monodentate ligands, and could rise up to 8 with bidentate ligands.
Perspective views of PaO(OH)2(I)(H2O)n+1 and Pa(OH)4(I)(H2O)n complexes with n=0 (a), n=1 (b); n=2 (c); n=3 (d). Color code: navy blue (Pa), purple (I), red (O), white (H).
To assess the impact of these two additional water molecules on the relative stability of the PaO(OH)2(I)(H2O)n+1 and Pa(OH)4(I)(H2O)n complexes, we calculated the Gibbs free energies for the reaction PaO(OH)2(I)(H2O)(n+1) [R]→Pa(OH)4(I)(H2O)n [P] for n=0, 1, and 2. Note here that we are looking at difference with respect to the n=0 reaction, computing ΔΔGr (n)=ΔGr(n)−ΔGr(n=0). For n>0 (Table 3), we observed that first ΔΔGr are small, and second that the PaO(OH)2(I)(H2O)n+1 complexes remain more stable than the Pa(OH)4(I)(H2O)n ones, indicating that the addition of up to two water molecules has little impact on the relative stability of the PaO(OH)2(I)(H2O)n+1 and Pa(OH)4(I)(H2O)n complexes. Given the little impact and that explicit hydration is always tricky, there is no evidence that the corrected ΔGr(n) values are there significantly more accurate than the uncorrected one. Therefore, in the remainder of our study, we will focus on discussing the PaO(OH)2(X)(H2O) and Pa(OH)4(X) complexes, without considering explicit hydration.
n |
1 |
2 |
3 |
ΔΔGr-SO |
0.2 |
2.4 |
3.3 |
Effect of Spin-Orbit (SO) Coupling on reaction Gibbs free energies
The spin-orbit coupling (SOC) is typically considered to have a negligible effect on the ground-state properties of closed-shell molecular systems such as molecular geometries, which applies to our case. However, since both the compared complexes [P] and [R] display different bonding patterns, it is still possible that the SOC play a secondary but not negligible role on ΔGr. To test this hypothesis, we calculated the SOC contributions at the scalar relativistic geometries, which in fact amount almost the same order of magnitude to the electronic energies for the reaction PaO(OH)2(X)(H2O)→Pa(OH)4(X) with different ligands, as presented in Table 4. Notably, ΔESO is negative, in fact remarkably constant −5.7±0.4 kJ−1, indicating that SOC has a more significant stabilizing impact on the Pa complexes compared to the PaO ones. Due to the magnitude of the SOC contribution to ΔGr, and since we have not found an easy and obvious explanation for this from the 5f and 6d population analysis (see Table S8 of the SI), we just conclude that we cannot disregard the influence of the SOC for the precise determination of the thermodynamics of these reactions.
X |
ΔEr(SR) |
ΔΔEr(SO) |
ΔEr(SR+SO) |
|---|---|---|---|
OH− |
−48.3 |
−5.3 |
−53.6 |
F− |
−37.5 |
−5.6 |
−43.1 |
Cl− |
−27.5 |
−5.7 |
−33.2 |
Br− |
−25.4 |
−6.1 |
−31.5 |
I− |
−25.6 |
−6.7 |
−35.5 |
NCS− |
−24.7 |
−5.7 |
−30.4 |
NO3− |
−53.4 |
−5.9 |
−59.3 |
SO42− |
−87.2 |
−5.2 |
−92.4 |
C2O42− |
−68.6 |
−5.3 |
−73.9 |
Effect of ligands (X) on the geometries
The geometries optimized at the DFT/B3LYP level of Pa(OH)4(X) and PaO(OH)2(X)(H2O) complexes are reported in Table 1 and Table 2, respectively. It is noteworthy that in the case of the bidentate ligands NO3−, SO42−, and C2O42−, they form bonds with the PaV center through oxygen atoms. When considering NCS−, there are two possible binding configurations to the PaV center, either through the nitrogen atom or through the sulfur atom. Upon optimizing the Pa(OH)4(NCS) and Pa(OH)4(SCN) complexes at DFT/B3LYP level, it is observed that Pa(OH)4(NCS) is energetically more favorable by 33.5 kJ mol−1 compared to Pa(OH)4(SCN). This implies that the PaV center prefers to bind to NSC− through the nitrogen atom rather than the sulfur atom. A similar preference has been reported for An(IV) actinides (An=Th, U and Pu) in a study by Carter et al.25
For the PaO(OH)2(X)(H2O) complexes (see Table 2) and the Pa(OH)4(X) complexes (see Table 1), a noticeable trend is observed in the variation of the r(Pa−X) distance. The shortest Pa−X distance is found for the OH− ligand because it is the least bulky ligand. As the halides become heavier (F−<Cl−<Br−<I−), r(Pa−X) lengthens by up to 0.9 Å compared to the (Pa−F) bond length. Similarly, in the case of bulky ligands such as NO3−, SO42−, and C2O42−, which form bidentate bonds with Pa, the r(Pa−X) is longer by up to 0.4 Å compared to r(Pa−OH). When substituting one hydroxide ligand in the PaO(OH)3(H2O) and Pa(OH)5 complexes with X ligands, r(Pa-OH) becomes shorter by at most 0.05 Å in the different PaO(OH)2(X)(H2O) and Pa(OH)4(X) complexes again because OH− is the least bulky group. The distance to the water molecule, r(Pa-OH2), remains almost the same among the different PaO(OH)2(X)(H2O) complexes. In terms of the r(Pa−O) distance in PaO(OH)2(X)(H2O) complexes, it is relevant at this stage to compare the mono-oxo Pa−O bond distances to the dioxo U–Oy1 bond distances found in uranyl(VI) complexes with tetra- or pentavalent coordination (refer to values from the literature listed in Table S9 of the SI). In both the Pa and uranyl complexes, the shorter the An−X distance, the longer the An−O one. We will further discuss the relationship between the coordinated ligand and the Pa−O in the context of its energetic stability. In the literature, experimental values for r(Pa−O) are reported as shorter, such as 1.75 Å in the PaO(C2O4)33− complex.16 On the other hand, using the DFT/PBE0 approach,24 it is 1.86 Å, falling within the same range as r(Pa−O) distances we have reported for the PaO(OH)2(X)(H2O) complexes. The origin of this experimental/computational discrepancy is still unclear and requires further investigations both experimentally and computationally, as already mentioned elsewhere.24
Pa-ligand bonding analyses
NBO analysis
In uranyl (UO22+), both U−O formal bond orders are three.26 In the PaO3+ cation, the NBO analysis also reveals a triple bond character (see Figure 4), consisting of one σ bond and two π bonds between Pa and O atoms, all three having occupation numbers nearing 2. In these σ and π bonding orbitals both the 5f and 6d shells are involved in bonding, with the 5f shell formally receiving more electron from the ligands than the 6d one in both types of orbitals (see Table S10 in the Supporting Information). Note that we consider the Pa5+ ion as a reference, and that thus the population of the 5f and 6d shells is conceived as arising from donation from the ligands.
Plots of the σ (a) and two πx,y ((b) and (c)) PaO bonding orbitals within the bare PaO3+ cation. Color code: yellow (Pa), red (O). The isosurface cutoff is 0.03.
In the PaO(OH)2(X)(H2O) complexes, the Pa mono-oxo bond retains its triple bond character as confirmed by the NBO analysis presented in Table 5 and Figure 5. This analysis reveals that both the σ and two π Pa−O bonds are strongly assymetrical (polarized) toward the oxygen atom (≈83 % oxygen weight), as found in uranyl complexes27 and that both the 5f and 6d electron contributions from Pa compete in shaping the nature of these bonds. For the σ-bond, the 5f and 6d contributions decrease by approximately by 4 % and 3 %, respectively, when compared to the PaO3+ bare cation, implying that the σ bond is more borne by the oxygen atom in the complexes than in the bare PaO3+. In terms of the π bonds, the 5f contribution decreases slightly by 1.9 %, while the 6d contributions marginally increases by 0.6 % in the various PaO(OH)2(X)(H2O) complexes compared to PaO3+. Consequently, this makes the 5f and 6d contributions to the π orbitals nearly equivalent in all the studied PaO(OH)2(X)(H2O) complexes, and the Pa−O π bonds quite close to the limit of oxygen lone pairs.
|
σ |
π |
||||
|---|---|---|---|---|---|---|
X |
Pa(5 f) |
Pa(6d) |
O(s/p) |
Pa(5 f) |
Pa(6d) |
O(s/p) |
OH− |
16.1 |
5.9 |
77.3 |
8.4 |
7.9 |
83.5 |
F− |
16.6 |
5.7 |
77.0 |
8.6 |
7.9 |
83.3 |
Cl− |
17.4 |
5.6 |
76.2 |
8.9 |
8.2 |
82.6 |
Br− |
17.6 |
5.6 |
76.1 |
8.9 |
8.2 |
82.6 |
I− |
17.7 |
5.6 |
76.0 |
8.9 |
8.2 |
82.6 |
NCS− |
16.9 |
5.9 |
76.4 |
9.0 |
7.9 |
82.7 |
NO3− |
17.3 |
5.6 |
76.2 |
9.1 |
8.0 |
82.5 |
SO42− |
16.1 |
5.6 |
77.5 |
8.8 |
8.1 |
82.8 |
C2O42− |
15.7 |
5.8 |
77.7 |
8.5 |
8.0 |
83.2 |
Plots of the σ (a) and two π ((b) and (c)) Pa−O bonding orbitals within the PaO(OH)2(F)(H2O) complex. Color code: yellow (Pa), green (F), red (O), white (H). The isosurface cutoff is 0.03.
QTAIM analysis
To complement the NBO analyses, QTAIM analyses have been performed for the PaO(OH)2(X)(H2O) complexes. These analyses provide a range of bonding descriptors defined at the bond critical points (BCPs) which aid in the classification of the nature of the Pa mono-oxo bond, as proposed by Nakainishi et al.28 and Pilmé et al.29 for instance. QTAIM analysis was extensively used to assess the nature of actinide ligand bonds after the pioneering work by Ingram et al.30 In the Supporting Information (see Table S11, Table S12, Table S13, Table S14), we have compiled various bonding BCP descriptors including the electron density (ρ), the Laplacian of the density (
), kinetic energy density (G), the potential energy density (V), the ratio between the absolute value potential energy density to the kinetic energy one (
/G), and the charges of the different atoms. The delocalisation index (DI) between two bonded atoms is indicative of the bond order between them. A DI value equal to or lower than 1 suggests a single bond. This criterion applies to the Pa−X, Pa−OH and Pa−OH2 bonds within the different PaO(OH)2(X)(H2O) complexes. In contrast, the DI for the Pa−O bond is approximately 1.8, a value closely resembling that found in uranyl complexes (1.87 to 1.92),31 where the uranyl bond is recognized as a strongly dissymmetric triple bond. This similarity, in conjunction with the NBO analysis discussed previously, confirms that the Pa−O bond is a formal triple bond.
In terms of the electron density (ρ), a value of ρ>0.2 a.u. indicates a closed-shell covalent interaction. This criterion applies to the Pa−O bond, while the Pa−X, Pa−OH and Pa−OH2 bonds within the different PaO(OH)2(X)(H2O) complexes are best described as ionic bonds. This classification is further supported by the values of the Laplacian of the density 
at the BCPs, which are significantly smaller for the Pa−O bond in comparison to the Pa−X, Pa−OH and Pa−OH2 bonds. Moreover, the ratio between the absolute value potential energy density to the kinetic energy one (
/G) is a good indicator to describe the chemical bonds. A ratio exceeding 1 suggests a covalent interaction. Significantly, 
/G is higher by 0.5 for the Pa−O bond when compared to that of the Pa−X, Pa−OH and Pa−OH2 bonds. Thus all QTAIM descriptors collectively support the conclusion that the Pa−O bond exhibits a strong covalent character, while the Pa−X, Pa−OH, and Pa−OH2 bonds display an ionic character.
Effect of ligands (X) on the relative stabilities of the PaO(OH)2(X)(H2O) and Pa(OH)4(X) complexes
The primary objective of this study was to investigate the influence of inorganic and organic ligands on the relative stability of Pa5+ and PaO3+ complexes, aiming to identify which ligands can stabilize the PaV mono-oxo bond stable making it a truly actinide-like.
To determine the relative stability, Gibbs free energies for the reaction PaO(OH)2(X)(H2O)→Pa(OH)4(X) with different X ligands are compared (see Figure 6). A positive ΔGr translates into a preference for the PaO(OH)2(X)(H2O) over the Pa(OH)4(X) complex. This is the case for Cl−, Br−, I−, NCS−, NO3− and SO42− ligands. Conversely, a negative ΔGr indicates that the Pa(OH)4(X) complex is energetically favored over the PaO(OH)2(X)(H2O) complex. This is observed with OH−, F− and C2O42−. Note that for thiocyanate ligand, the ΔGr is close to zero and thus, may be not the most suitable candidate to explore the relative stability in real conditions. It is noteworthy that the trends in the relative stabilities found in the solvent mirror those in the gas phase (see Figure S1, and Table S17 of the Supporting Information).
Gibbs free energies (ΔGr) of the reaction PaO(OH)2(X)(H2O)→Pa(OH)4(X) for the different X ligands in the aqueous phase. The red bars refer to systems in which the X ligand stabilizes Pa(OH)4(X), and blue bars correspond to PaO(OH)2(X)(H2O) being energetically favored.
The relative stability of these two PaV forms can be explained by several factors. One key factor is the length of the Pa−O bond. When the PaO(OH)2(X)(H2O) complex is stabilized (as is the case with the Cl−, Br−, I−, NCS− and NO3− ligands), the Pa−O bond is shorter (see Table 2), with a difference of up to 0.03 Å, with respect to the OH−, F− and C2O42− ligands. Additionally, the stretching frequency of the Pa−O bond in these complexes is greater by up to 36 cm−1 compared to complexes with OH−, F− and C2O42− ligands. A shorter Pa−O bond and a higher stretching frequency indicate a stronger Pa−O bond. This phenomenon is observed with Cl−, Br−, I−, NCS−, and NO3− ligands where the PaO(OH)2(X)(H2O) complex is stabilized over the Pa(OH)4(X) complex.
Another crucial factor is the length of the Pa−X bond. The Pa−X bond length is longer by up to 0.9 Å with the Cl−, Br−, I−, NCS− and NO3− ligands compared to the one with the OH−, F−, SO42− and C2O42− ligands. Thus, when the PaO(OH)2(X)(H2O) complex is stabilized, the PaV center exhibits more affinity for the oxygen atom than for the X ligand (X=Cl−, Br−, I−, NCS− and NO3−), leading to the formation a mono-oxo bond. This is not the case of the OH−, F− and C2O42− where the Pa(OH)4(X) complex is stabilized and the Pa−X bond length is shorter indicating stronger bonding between the PaV center and these ligands.
In addition, from QTAIM analyses we obtain another important, not fully independent indicator: the DI. It increases as the bond becomes more covalent. This increase in DI is observed when the PaO(OH)2(X)(H2O) complex is stabilized over the Pa(OH)4(X) with Cl−, Br−, I−, NCS− and NO3− ligands (see Table S11 of the Supporting Information). In these cases, the DI is greater by 0.1, compared to the complexes with OH−, F− C2O42− ligands.
Concerning the SO42− ligand, even if the PaO(OH)2(X)(H2O) complex is slightly more stable than the Pa(OH)4(X) complex, we note that the Pa−O bond distance and the DI deviate from the values obtained for the other ligands Cl−, Br−, I−, NCS− and NO3−, suggesting a weaker Pa−O bond. Thus the SO42− ligand may not be a good candidate to observe the Pa mono-oxo bond in experimental conditions.
In summary, a shorter Pa−O bond, a higher stretching frequency, and a larger Pa−O DI all indicate a stronger Pa mono-oxo bond (see Figure 7). This helps explain why the PaO(OH)2(X)(H2O) complex is stabilized with Cl−, Br−, I−, NCS−, and NO3− ligands, while the Pa(OH)4(X) complex is favored with OH−, F− and C2O42− ligands.
Correlation between the Pa−O bond length (r(Pa−O)) and the delocalisation index of the Pa−O bond (DI(Pa−O)). The red circles refer to systems in which the X ligand stabilizes Pa(OH)4(X), and blue circles correspond to PaO(OH)2(X)(H2O) being energetically favored.
Conclusions
In our study, our primary objective was to delve into the stability of the Pa−O bond in the presence of various inorganic ligands. Employing advanced quantum chemical methods, we calculated the Gibbs free energy (ΔGr) for the reaction PaO(OH)2(X)(H2O)→Pa(OH)4(X) under standard conditions. Remarkably, even in closed-shell systems, the inclusion of spin-orbit (SO) coupling significantly impacted the relative electronic energies, and consequently the ΔGr values. To determine these electronic energies, we utilized the CCSD(T) method, known for its accuracy despite its computational expense. The solvent, water, played a substantial role in structural properties, necessitating geometry optimizations within a water continuum model. Our study introduced additional water molecules to saturate the first coordination sphere, uncovering variations in coordination numbers without affecting the relative stability. The COSMO-RS solvation model was employed for calculating solvation energy (ΔGsol). Additionally, we delved into the nature of the Pa−O bond in both the PaO3+ cation and PaO(OH)2(X)(H2O) complexes, confirming a triple bond reference (though it is strongly dissymetrical, as the uranyl di-oxo ones).
Predictions regarding the stability of the Pa−O bond indicated preferences for certain ligands, such as the heavier halides (chlorides, bromides, and iodides), as well as nitrates and sulfates. Conversely, hydroxide and oxalate ligands were found to trigger the preferential formation of Pa(OH)4(X) complexes. We anticipate that these theoretical predictions will serve as a catalyst for future experiments, validating and expanding our understanding of protactinium chemistry.
Computational Details
The geometry optimizations of PaO(OH)2(X)(H2O)n+1 and Pa(OH)4(X)(H2O)n complexes in their ground state were carried out with ADF.32, 33 These optimizations were performed at the density functional theory (DFT) level employing the B3LYP exchange-correlation functional.34, 35 The solvent effect is taken into account by Conductor-like Screening Model (COSMO).36-38 All atoms were described using triple-zeta plus polarization (TZ2P) basis sets39 without freezing core orbitals. To incorporate relativistic effects, two approaches were employed: the scalar relativistic (SR) and spin-orbit (SO) ZORA all-electron Hamiltonians.40-42 To evaluate the impact of the SOC on the geometries, optimizations were carried out with and without SO for complexes featuring ligands with light atoms (for instance X=OH−) and a heavier halides (for instance X=I−). The results, detailed in Table S15 of the Supporting Information, reveal that SO leads to a slight shortening of the Pa-ligand bond distances, with a maximum reduction of 0.015 Å. This effect is considered negligible, and therefore, structures optimized at the SR level were used. Nevertheless, it is worth noting that the SOC impact on the single-point electronic energies cannot be neglected and was introduced in the calculation of the ΔGr values by means of a simple correction to the electronic energy ΔEr, namely ΔESOC. To ensure that the optimized structures represent minima (no imaginary frequency), harmonic vibration frequency calculations were performed. These calculations also allowed for the determination of the thermodynamics contributions to the Gibbs free energy (ΔGcorr).
To calculate the solvation Gibbs free energies (ΔGsol), we have chosen the COSMO-RS43, 44 real-solvent continuum model, using the COSMO-RS atomic radii45 (Table S1) to construct the continuum model cavities, an approach that is superior to united atom models.46 COSMO-RS was also found to be superior to other continuum models for the prediction of oxidation potentials.47 We have validated the COSMO-RS model, by a comparison to other continuum models (PCM and COSMO) for the reaction of interest with X=OH− and X=C2O42−, as is discussed and justified in the Supporting Information.
The COSMO-RS solvation model43, 44 as implemented in the COSMOtherm program, utilized files generated by single-point calculations performed with the Gaussian 16 program.48 In this context the BP86 functional is used, together with def-TZVP basis sets and small core relativistic pseudopotential49 (60 core electrons) for Pa; and all other atoms were described with def2-TZVP basis sets.50
Recognizing that DFT may not provide the ultimate accuracy for determining electronic energies in chemical reactions involving heavy cations,51-54 additional single-point energy calculations were performed at the CCSD(T)55 level of theory (
). CCSD(T) is widely recognized as the reference method in quantum chemistry56 and is known for its exceptional accuracy, which has motivated the choice of Lontchi et al. to explore the PaV complexes stability.22 A discussion of the benchmarking of CCSD(T) versus DFT functionals given in the Supporting Information, supports this assessment.
The CCSD(T) calculations were carried out using the Molpro 2020 software.57 In the CCSD(T) calculations, relativistic effects were taken into account using all-electron Hamiltonians. Specifically, the choice between the exact two-component relativistic Hamiltonian (X2C)58 and the Douglas-Kroll-Hess (DKH) Hamiltonian59 depended in practice on the availability of adequate relativistic atomic basis sets. The aug-cc-pVTZ-X2C basis sets60-62 were applied for H, O, C, N, S, F, and Cl, while the aug-cc-pVTZ-DK basis sets63 were utilized for complexes containing Br64, 65 and I.66 Pa was described appropriately by cc-pVTZ-X2C or cc-pVTZ-DK basis sets.67 It is worth noting that in CCSD(T) calculations, all valence electrons were correlated, while the core electrons were frozen, except in the case of iodine, for which we had to correlate the outer-core 4d electrons. As it is recognized that CCSD(T) results are sensitive to the quality of the basis sets employed, a basis set quality effects exploration has been operated. Therefore, to attain convergence and determine the most appropriate basis sets, the energy of the reaction 2 with X=OH− was computed using two different basis sets: VTZ and VQZ. Subsequently, these results were extrapolated to the complete basis set (CBS) limit, which effectively represents an infinitely large basis set (further details are available in the Supplementary Information). The energies obtained for the reaction Equation 2 with X=OH− using either the VTZ or VQZ basis sets were found to be −48.3 kJ−1 and −48.7 kJ−1, respectively. When extrapolated to the CBS limit, the reaction energy was determined to be −48.5 kJ−1 (see Table S5 of the SI). This convergence study demonstrates that both the VTZ and VQZ basis sets yield reaction electronic energy values very close to the CBS limit. Consequently, it can be concluded that VTZ basis sets are sufficiently accurate for determining the reaction's energy at the CCSD(T) level.
(4)The Gibbs free energies reported in Table S16 change by at most 2.4 kJ when increasing the temperature from 298 K to T=319 K. Therefore in the rest of the article, only room temperature values will be discussed.
In order to investigate the nature of the chemical bond between Pa and O in the PaO(OH)2(X)(H2O) complexes and to assess the extent of involvement of the 5f electrons in chemical bonding, two complementary approaches are employed: natural bond orbital (NBO) analysis and the quantum theory of atoms in molecules (QTAIM), by performing single-point calculations with the B3LYP functional and the COSMO solvent using the ADF software where the NBO6 version68 is employed. This analysis provides insights into the bonding interactions within molecules, including bond types and electron density distributions. It can reveal the extent to which the 5f and 6d Pa orbitals participate in chemical bonding in the studied complexes. QTAIM provides information about the topology of electron density, such as bond critical points and bond paths. This analysis can help confirm and complement the findings from NBO analysis regarding the nature of chemical bonding in the complexes.
Supporting information
All quantum mechanics (QM) data, including the optimized coordinates for all species, are accessible on the open-access Zenodo repository with the following DOI: 10.5281/zenodo.10529027. Version v1.1. Additional results and details are provided in the supporting information PDF file.
Note
A preprint version of this work was deposited at ChemRxiv.69
Acknowledgments
This research received support from the PIA ANR project CaPPA (ANR-11-LABX-0005-01), the ANR CHESS project (ANR-21-CE29-0027), the I-SITE ULNE project OVERSEE (ANR-16-IDEX-0004), the French Ministry of Higher Education and Research, the Hauts de France regional council, and the European Regional Development Fund (ERDF) through projects CPER CLIMIBIO, ECRIN, WaveTech. Additionally, the authors express gratitude for the assistance provided by the French national supercomputing facilities (grants DARI A0130801859, A0110801859). The authors also appreciate the valuable discussions and feedback from ASP. Gomes, M. Maloubier, and C. Le Naour.
Conflict of interests
The authors declare no conflict of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are openly available in Zenodo at 10.5281/zenodo.10529027.
