# Is the protactinium(V) mono-oxo bond weaker than what we thought?

Tamara Shaaban, Hanna Oher, Jean Aupiais, Julie Champion, André Severo Pereira Gomes, Claire Le Naour, Melody Maloubier, Florent Réal, Eric Renault, Xavier Rocquefelte, et al.

<figure><img src="image_1.png" /></figure>

## To cite this version:

Tamara Shaaban, Hanna Oher, Jean Aupiais, Julie Champion, André Severo Pereira Gomes, et al. 2024, 60, pp.14376-14379. 10.1039/D4CC04522J. hal-04690060

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# Is the protactinium(V) mono-oxo bond weaker than what we thought?†

Tamara Shaaban,ª Hanna Oherᵇ, Jean Aupiais,ᶜ Julie Champion,ᵈ André Severo Peirera Gomes,ª Claire Le Naour,ᵇ Melody Maloubier,ᵇ Florent Réal,ª Eric Renault,ᵉ Xavier Rocquefelte,ᵉ Bruno Siberchicot,ᶜ Valérie Vallet,ª and Rémi Maurice*f

Received Date

Accepted Date

DOI: 00.0000/xxxxxxxxxx

The bond distance is the simplest and most obvious indicator of the nature of a given chemical bond. However, for rare chemistry, it may happen that it is not yet firmly established. In this communication, we will show that the formally-triple protactinium(V) mono-oxo bond is predicted longer than what was previously reported in the solid state and in solution, based on robust quantum mechanical calculations, supported by an extensive methodological study. Furthermore, additional calculations are used to demonstrate that the Pa−Ooxo bond of interest is more sensitive to complexation than the supposedly analogous U−Oyl ones, not only in terms of bond distance but also of finer bond descriptors associated with the effective bond multiplicity.

Protactinium (Pa, Z = 91) is an actinide with enigmatic physico-chemical properties¹,² that would differentiate the “transition-metal” like actinides (up to thorium, Th) from the heavier ones (starting with uranium, U)³. One of the key features of protactinium is its propensity to form a single oxo bond in solution in its pentavalent oxidation state⁴, while it is not observed for the “transition-metal” like actinides and while dioxo bonds are observed for the heavier elements such as uranium, neptunium (Np), plutonium (Pu) and americium (Am).

This single oxo bond has been characterized by X-ray absorption spectroscopy in a couple of systems⁵,⁶, in particular

[PaO(C₂O₄)₃]³⁻ and [PaO(SO₄)₃]³⁻, with a fitted Pa−Ooxo bond distance of ~1.72–1.75 Å, depending on the medium and conditions. The objective of the present article is to re-evaluate this bond distance from good theoretical grounds, by going well beyond our previous articles on molecular complexes that already pointed out a potential discrepancy between theory and experiment⁷,⁸. To be free of any ambiguity related to specification in solution, we include in our study the sole solid-state compound ever reported with an occurring Pa−Ooxo bond⁹, namely [C₈H₂₀N]₂[PaOCl₅]. However, we must stress that post-Hartree-Fock methods are not generally available in periodic codes, which is why we have also performed a detailed methodological study on both model and actual molecular systems (vide infra).

Experimental lattice parameters and bond distances are reported in Table 1. In this structure, the [PaOCl₅]²⁻ molecular unit emerges, with one shorter axial Pa−Clₓ bond distance and four longer equatorial Pa−Clₑq bond distances (non equivalent in the reported Cc space group), together with a Pa−Ooxo bond distance of interest of 1.74(9) Å. Periodic density functional theory (DFT) calculations were performed with the VASP code¹⁰,¹¹. Both lattice parameters and atomic positions were optimized with various setups (see Table 1). For all reported calculations, the same plane-wave energy cutoff of 550 eV was applied. From the generic PBE¹² calculation, the f levels can be effectively pushed up by an *ad hoc* Hubbard U term¹³ or finer described by using a hybrid exchange-correlation functional such as PBE0¹⁴, and on top of that a (post-SCF) dispersion correction may be applied¹⁵.

It is clear that for obtaining a fair agreement between the computed and experimental lattice parameters the introduction of a dispersion correction, namely D3(BJ)¹⁵, is required (see Table 1). Once it is applied, both the PBE and PBE0 functionals yield similar lattice parameters. While the Pa−Ooxo bond distance is typically increased by the +U correction, the introduction of Hartree-Fock exchange reduces it. Note that the dispersion correction keeps this bond distance untouched, with both the PBE and PBE0 func-

ChemComm Accepted Manuscript

<footnote>ª Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France</footnote>

<footnote>ᵇ Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France.</footnote>

<footnote>ᶜ CEA, Laboratoire Matière en Conditions Extrêmes, Université Paris-Saclay, F-91680, Bruyères-le-Châtel, France; CEA, DAM, DIF, 91297 Arpajon, France</footnote>

<footnote>ᵈ IMT Atlantique, Nantes Université, CNRS/IN2P3, SUBATECH, F-44000 Nantes, France</footnote>

<footnote>ᵉ Nantes Université, CNRS, CEISAM UMR 6230, F-44000 Nantes, France</footnote>

<footnote>f Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, F-35000 Rennes, France. E-mail: remi.maurice@univ-rennes.fr</footnote>

<footnote>† Electronic Supplementary Information (ESI) available: Additional calculations essentially of interest for methodological purposes. See DOI: 00.0000/00000000.</footnote>
ChemComm Accepted Manuscript

tionals. With the more accurate PBE0 functional, we obtain a Pa−Ooxo bond distance of 1.83 Å, which lies within the confidence interval of the experimental distance, 1.74±0.09 Å.

Given the computational cost and for comparison purposes, we retained the PBE+D3(BJ) method¹²,¹⁵ for probing two well-resolved, recent, uranium structures¹⁶,¹⁷, namely (C₄H₁₂N₂)[UO₂Cl₄] and (C₄H₁₂N₂)₂[UO₂Cl₄(H₂O)Cl₂. We note that a very good agreement with experiment is observed for the lattice parameters and for the U–Cl bond distances (see Table 2), which validates the chosen level of theory. Concerning the U−Oyl dioxo bond distances, we observe a standard overestimation of ~0.04–0.05 Å at this level of theory. If we correct the previous PBE+D3(BJ) Pa−Ooxo bond distance by the opposite amount, we obtain ~1.81–1.82 Å, which again lies within the experimental confidence interval. We thus conclude at this stage that the Pa−Ooxo bond distance is predicted to be slightly longer than 1.8 Å and thus also longer than the typical U−Oyl ones.⁸

Without entering yet in a detailed discussion concerning the Pa−Ooxo bond nature, we have performed additional periodic calculations with the PBE functional for the bare [PaO]³⁺ and [UO₂]²⁺ systems as well as determined integrated crystal orbital bond indices (ICOBIs)¹⁸ at the PBE+D3(BJ) level on the previous solid-state systems (see text below Table S1). Note that the reference bonds in [PaO]³⁺ and [UO₂]²⁺ are both formally triple⁸, with a subtle distinction: in [PaO]³⁺ bonding orbitals may display mixed 6d/5f Pa characters, whereas in [UO₂]²⁺, the 6d and 5f U characters are symmetry separated. In the bare systems, the Pa−Ooxo bond is slightly longer and displays a higher ICOBI. This is also true for the [C₈H₂₀N]₂[PaOCl₅] and (C₄H₁₂N₂)[UO₂Cl₄] solid-state systems (see Figure 1). Naturally, the ICOBIs are there smaller than in the bare systems (longer distances). We note that the full crystal environment induces a lengthening of the Pa−Ooxo bond by 0.037 Å, larger than that found in uranyl, 0.024 Å. This, plus the shorter Pa−Clₓ bond distance indicates that the Pa−Ooxo bond is more sensitive to complexation since the *trans* position is not protected, unlike in [UO₂]²⁺ and related compounds.

<figure><img src="image_4.png" /><figcaption>Fig. 1 Schematic representation of the PBE+D3(BJ) atomic arrangements of the [PaOCl₅]²⁻ (left) and [UO₂Cl₄]²⁻ (right) units (visualization performed with VESTA¹⁹). The ICOBIs are given in brackets.</figcaption></figure>

We now move on with complexes in solution. Static calculations, based on electronic structure theory and the application of a continuum dielectric model for solvation (implicit solvation

model), lead to longer Pa−Ooxo bond distances⁵,⁷ than what was reported by EXAFS in solution, by ~0.10–0.15 Å, i.e. by more than the expected sum of the experimental and computational errors. Since this discrepancy can originate from the relative simplicity of the model used to mimic the complex in solution, we have chosen to initiate our analysis by comparing results from static quantum chemical (QC) calculations (with isolated systems) and QC molecular dynamics (MD) simulations (with systems embedded in large simulation boxes containing around 100 water molecules). Calculations and simulations were performed with the Abinit code²⁰. For this part, we selected two prototypes: PaOF₃(H₂O)₃, previously included in an *ab initio* molecular dynamics (AIMD) study²¹, and the [PaO(C₂O₄)₃]³⁻ complex, previously studied by static approaches⁵,⁷. In both cases, the protactinium(V) ion displays a coordination number of 7, which practically seems to be the largest possible one in solution for this ion⁷,²¹, except in the peculiar [PaF₈]³⁻ case²².

First, we tested ten *pure* (i.e. nonhybrid) exchange-correlation functionals (see Table S2). For the bare [PaO]³⁺ system as well as for the isolated PaOF₃(H₂O)₃ and [PaO(C₂O₄)₃]³⁻ complexes, we found very homogeneous results for the Pa−Ooxo bond distance of interest. Therefore, any of those ten functionals could have been used for the AIMD study. We selected the PBE functional¹² for the sake of homogeneity across our reported results. As can be seen in Table 3, the combined influence of the water bath and molecular dynamics has minimal impact on the Pa−Ooxo bond distance. More importantly, these effects together slightly increase the bond distance (by 0.003–0.004 Å). Therefore, the previously mentioned discrepancy between theory and EXAFS on [PaO(C₂O₄)₃]³⁻ cannot be attributed to the static approach. Consequently, to facilitate a more in-depth methodological study, we will now exclusively use the static QC approach.

We have selected two protactinium(V) systems for this static study, namely [PaO]³⁺, for obvious reasons, and [PaO(C₂O₄)₃]³⁻ as our primary case in solution. The sulfuric case⁶ is intentionally excluded due to the unclear coordination modes of the sulfate groups (monodentate vs. bidendate fashions), though a similar issue arises for the Pa−Ooxo bond distance⁷. Calculations were performed with three computational chemistry codes, namely Gaussian²³, Molpro²⁴ and ADF²⁵.

Since detailed results are reported in the Supporting Information (see in particular Table S3 and Table S4), we only highlight our main conclusions here. First, both employed implicit solvation models lead to a slight Pa−Ooxo bond lengthening of less than 0.01 Å in the [PaO(C₂O₄)₃]³⁻ complex, which has a saturated protactinium(V) coordination sphere. Second, the spin-orbit coupling leads to an even more negligible Pa−Ooxo bond lengthening. Therefore, we report either scalar or spin-orbit relativistic values for comparison purposes, but to keep things simple, we have retained scalar relativistic values in Table 4. Third, we confirm that by going from PBE¹² to the hybrid PBE0¹⁴ functional, the Pa−Ooxo bond distance is reduced by ~0.03 Å, in accord with the already discussed solid-state results (*vide supra*). Fourth, hybrid functionals such as B3LYP²⁶ and PBE0¹⁴ show good agreement with the higher level CCSD(T) method²⁷, as does MP2²⁸. Last, the application of a dispersion correction¹⁵ is
<table><caption>Table 1 Optimized lattice parameters and relevant bond distances obtained for [C₈H₂₀N]₂[PaOCl₅] by periodic density functional theory calculations. Results are compared with experiment (Cc space group).</caption><thead><tr><th>[C<sub>8</sub>H<sub>20</sub>N]<sub>2</sub>[PaOCl<sub>5</sub>]</th><th>a (Å)</th><th>b (Å)</th><th>c (Å)</th><th>β (°)</th><th>d[Pa–O] (Å)</th><th>d[Pa–Cl<sub>ax</sub>] (Å)</th><th>d[Pa–Cl<sub>eq</sub>] (Å)<sup>a</sup></th></tr></thead><tbody><tr><td>PBE<sup>12</sup></td><td>14.281</td><td>14.951</td><td>13.596</td><td>91.34</td><td>1.859</td><td>2.648</td><td>2.689(6)</td></tr><tr><td>PBE+D3(BJ)<sup>12,15</sup></td><td>13.301</td><td>14.840</td><td>12.745</td><td>91.65</td><td>1.859</td><td>2.624</td><td>2.673(17)</td></tr><tr><td>PBE+U+D3(BJ)<sup>12,13,15</sup> (U<sub>eff</sub> = 4 eV)</td><td>13.295</td><td>14.797</td><td>12.825</td><td>91.36</td><td>1.890</td><td>2.631</td><td>2.690(14)</td></tr><tr><td>PBE0<sup>14</sup></td><td>13.996</td><td>14.799</td><td>13.350</td><td>91.29</td><td>1.832</td><td>2.624</td><td>2.674(7)</td></tr><tr><td>PBE0+D3(BJ)<sup>14,15</sup></td><td>13.153</td><td>14.665</td><td>12.518</td><td>91.59</td><td>1.832</td><td>2.608</td><td>2.659(19)</td></tr><tr><td>Expt.<sup>9</sup></td><td>14.131(8)</td><td>14.218(8)</td><td>13.235(9)</td><td>91.04(3)</td><td>1.74(9)</td><td>2.42(3)</td><td>2.64(6)</td></tr></tbody></table>

<sup>a</sup>The four distances are crystallographically independent.

<table><caption>Table 2 Optimized lattice parameters and relevant bond distances obtained for (C₄H₁₂N₂)[UO₂Cl₄] and (C₄H₁₂N₂)₂[UO₂Cl₄(H₂O)]Cl₂, two representative uranyl compounds, by periodic density functional theory calculations. Results are compared with experiment (P<span style="text-decoration: overline;">I</span> and Pnma space groups).</caption><thead><tr><th>(C<sub>4</sub>H<sub>12</sub>N<sub>2</sub>)[UO<sub>2</sub>Cl<sub>4</sub>]</th><th>a (Å)</th><th>b (Å)</th><th>c (Å)</th><th>α (°)</th><th>β (°)</th><th>γ (°)</th><th>d[U–O] (Å)</th><th>d[U–Cl] (Å)<sup>a</sup></th></tr></thead><tbody><tr><td>PBE+D3(BJ)<sup>12,15</sup><br>(dev.)</td><td>6.668<br>(+0.75%)</td><td>6.790<br>(+1.94%)</td><td>7.300<br>(–2.12%)</td><td>81.80<br>(–1.80%)</td><td>85.80<br>(–2.17%)</td><td>63.36<br>(+0.14%)</td><td>1.835</td><td>2.635(14)</td></tr><tr><td>Expt.<sup>16</sup></td><td>6.6183(6)</td><td>6.6609(6)</td><td>7.4578(6)</td><td>83.300(3)</td><td>87.703(3)</td><td>63.273(2)</td><td>1.786(3)</td><td>2.646(9)</td></tr><tr><th>(C<sub>4</sub>H<sub>12</sub>N<sub>2</sub>)₂[UO<sub>2</sub>Cl<sub>4</sub>(H<sub>2</sub>O)]Cl<sub>2</sub></th><th>a (Å)</th><th>b (Å)</th><th>c (Å)</th><th colspan="2"></th><th colspan="2"></th><th colspan="2"></th></tr><tr><td>PBE+D3(BJ)<sup>12,15</sup><br>(dev.)</td><td>12.172<br>(–0.34%)</td><td>12.418<br>(–0.22%)</td><td>13.409<br>(–0.36%)</td><td colspan="2"></td><td>2.513</td><td>1.8035(5)</td><td>2.768(3)</td></tr><tr><td>Expt.<sup>17</sup></td><td>12.2130(7)</td><td>12.4456(7)</td><td>13.4579(8)</td><td colspan="2"></td><td>2.499(3)</td><td>1.761(1)</td><td>2.765(3)</td></tr></tbody></table>

<sup>a</sup>The four distances are only crystallography equivalent two by two.

<sup>b</sup>The two distances are crystallography independent.

<table><caption>Table 3 Joint effect of explicit solvation and molecular dynamics on the Pa–O bond distance (Å) obtained with the Abinit code²⁰ and the PBE exchange-correlation functional¹².</caption><thead><tr><th>Computational setup</th><th>PaOF<sub>3</sub>(H<sub>2</sub>O)<sub>3</sub></th><th>[PaO(C<sub>2</sub>O<sub>4</sub>)<sub>3</sub>]<sup>3-</sup></th></tr></thead><tbody><tr><td>Static, isolated molecule</td><td>1.833</td><td>1.869</td></tr><tr><td>Dynamic (298 K), water bath, 1.5 ps</td><td>1.836</td><td>1.873</td></tr></tbody></table>

<table><caption>Table 4 Scalar-relativistic An–O (An = Pa, U) bond distances obtained with the ADF code²⁵, the COSMO implicit solvation²⁹ and the PBE0 exchange-correlation functional¹⁴, together with the corresponding delocalisation indices (δ's)³⁰ arising from the QTAIM³¹ analysis.</caption><thead><tr><th>Molecular system</th><th>d (Å)</th><th>δ</th></tr></thead><tbody><tr><td>[PaO]<sup>3+</sup></td><td>1.710</td><td>2.33</td></tr><tr><td>[PaO(C<sub>2</sub>O<sub>4</sub>)<sub>3</sub>]<sup>3-</sup></td><td>1.858</td><td>1.69</td></tr><tr><td>[UO<sub>2</sub>]<sup>2+</sup></td><td>1.702</td><td>2.15</td></tr><tr><td>[UO<sub>2</sub>Cl<sub>4</sub>]<sup>2-</sup></td><td>1.766</td><td>1.89</td></tr><tr><td>[UO<sub>2</sub>(C<sub>2</sub>O<sub>4</sub>)<sub>3</sub>]<sup>4-</sup></td><td>1.7815(15)</td><td>1.84</td></tr></tbody></table>

bland on the Pa–O<sub>oxo</sub> bond distance. All-in-all, we have reported the COSMO²⁹ scalar relativistic PBE0¹⁴ results in Table 4.

Before commenting on the obtained results with protactinium(V), we first assess the quality of the results obtained at the chosen level of theory based on uranyl systems, namely [UO₂]²⁺, the well-known [UO₂Cl₄]²⁻ molecular unit (already present in the (C₄H₁₂N₂)[UO₂Cl₄] solid-state system), and the [UO₂(C₂O₄)₃]⁴⁻ complex. The latter has been studied both experimentally and computationally³² and notably exhibits a uranium(VI) coordination number of 7, making it analogous to the [PaO(C₂O₄)₃]³⁻ case. As shown in Table S5, the influence of the spin-orbit coupling on the U–Oyl bond distance(s) is minimal, justifying our selection of a scalar relativistic level in Table 4. Note that the PBE0 gas-phase result for [UO₂]²⁺ (1.68 Å) is in fair agreement with the reference 1.71 Å value of de Jong *et al.*³³. For

[UO₂Cl₄]²⁻ and [UO₂(C₂O₄)₃]⁴⁻, our U–Oyl bond distance values in solution of 1.77 and 1.78 Å, respectively, are furthermore of quite exceptional match with the 1.77(1) and 1.79(4) Å experimental ones³²,³⁴. Thus, we conclude that the values reported in Table 4 are of sufficient quality to allow for reliable comparisons between the protactinium(V) and uranium(VI) cases.

From Table 4, it is evident that while the An–O bond distance in the bare [PaO]³⁺ system is slightly longer than that in [UO₂]²⁺, it is much longer in [PaO(C₂O₄)₃]³⁻ than in [UO₂Cl₄]²⁻ and [UO₂(C₂O₄)₃]⁴⁻. In other words, even if [PaO]³⁺ may be seen as a “half” [UO₂]²⁺ unit, the coordination-induced bond lengthening is much more pronounced in the case of protactinium(V) (ca. +0.15 Å) than in the uranium(VI) one (ca. +0.07 Å), being in practice doubled. Thus, we definitely conclude that [PaO]³⁺ exhibits a much stronger sensitivity to extra coordination compared to [UO₂]²⁺.

To further check if this perspective on bond distance corroborates with the bonding perspective, we have also determined delocalisation indices (δ's)³⁰ within the QTAIM framework³¹ (other indicators are given in Table S6). We recall that δ values, by definition, correspond to the number of electron pairs shared between two atoms, reflecting the effective bond multiplicity. In the bare [UO₂]²⁺ system, six bonding orbitals of σ<sub>u,g</sub> and π<sub>u,g</sub> are doubly occupied in the ground state³⁵, the *ungerade* ones involving 5f orbitals of U and the *gerade* ones involving 6d orbitals of U. Thus, the U–Oyl bonds are formally triple bonds. As shown in Table 4, δ in there much smaller than 3, which is due to the strong asymmetry of those bonds (“polar” character³⁶). Upon complexation, δ is reduced by ~0.3 in both [UO₂Cl₄]²⁻ and [UO₂(C₂O₄)₃]⁴⁻. Note that our 1.89 value for [UO₂Cl₄]²⁻ is consistent with the 1.87 one of Wellington *et al.*³⁶.

In the bare [PaO]³⁺ system, three bonding orbitals are populated in the ground state. Note that due to the absence of a
symmetry center, the 5f and 6d orbitals of Pa are not symmetry separated anymore. The obtained δ value, 2.33, is slightly higher than in $[UO_2]^{2+}$, which is 2.15. This means that the slightly longer Pa-Oxo bond distance goes together with a slightly more covalent Pa-Oxo bond in $[PaO]^{3+}$ compared to the U-Oyl ones in $[UO_2]^{2+}$. This is attributed to the smaller formal charge of protactinium(V) versus uranium(VI), hence a larger ionic radius. After complexation, δ is reduced by ~0.6 in $[PaO(C_2O_4)_3]^{3-}$. It is interesting to note that the observed factor of 2 in the complexation-induced bond lengthening perfectly correlates with the factor of 2 reduction in δ. Thus, these two bond descriptors point toward the exact same conclusion.

In this article, we have shown that the Pa-Oxo bond is more sensitive to complexation than the U-Oyl ones. We attribute this to the fact that the *trans* position is not protected in the $[PaO]^{3+}$ chemical moiety. This leaves room for coordination with specific bonding at this position in real chemical systems. For instance, it can occur in the solid-state $[PaOCl_5]^{2-}$ molecular unit (see Tables S7, S8 and S9 and the associated discussion on bonding) or in the $[PaO(C_2O_4)_3]^{3-}$ complex. Specifically, the distance to the *trans* ligands is expected to be shorter than to the *cis* ones due to the inverse *trans* effect already observed and analyzed in actinide complexes$^{37-41}$. Since the Pa-Oxo bond distance is predicted to be longer than the U-Oyl one, the previous experimentally reported Pa-Oxo bond distances must be revised. According to all of our calculations, this bond distance is in any case predicted to be slightly longer than 1.8 Å, indicating that it is weaker than previously thought. An obvious perspective of this work would consist in performing new experiments to confirm these findings. Furthermore, this work is already a key step in the exploration of the intriguing physico-chemical properties of the actinides since it confirms the peculiarity of protactinium, which definitely qualifies it as a trend separator within the actinide series.

## Author Contributions

This article is the result of a collective effort supported by the ANR CHESS project (contract No. ANR-21-CE29-0027). T.S. is the primary contributor for the performed calculations, completed by additional work by H.O., X.R. and B.S. The first draft was written by R.M. and each version was approved by all the co-authors.

## Data availability

The data supporting this article have been included as part of the Supplementary Information† and the optimized structures can be accessed at the Zenodo repository via the following DOI: 10.5281/zenodo.13494221.

## Conflicts of interest

There are no conflicts to declare.

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Data availability

The data supporting this article have been included as part of the Supplementary Information and the optimized structures can be accessed at the Zenodo repository via the following DOI: [10.5281/zenodo.13494221](https://doi.org/10.5281/zenodo.13494221).

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DOI: 10.1039/D4CC04522J