Poppy
Di Pietro
a and
Andrew
Kerridge
*b
aDepartment of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK
bDepartment of Chemistry, Lancaster University, Lancaster, LA1 4YB, UK. E-mail: a.kerridge@lancaster.ac.uk
First published on 1st June 2016
Calculations performed at the density functional level of theory have been used to investigate complexes of uranyl with the expanded porphyrin isoamethyrin and the bis-triazinyl-pyridine (BTP) ligands, the latter of which is well-known to be effective in the separation of trivalent lanthanides and actinides. Analysis has been performed using a range of density-based techniques, including the Quantum Theory of Atoms in Molecules (QTAIM), the Electron Localisation Function (ELF) and the reduced density gradient (RDG). The effects of peripheral alkyl substituents on UO2-isoamethyrin, known to be vital for proper replication of the experimental geometry, are considered. Evidence for comparable amounts of covalent character has been found in the largely ionic U–N bonds of UO2-isoamethyrin and [UO2(BTP)2]2+ and examination of the variation in the electronic characteristics of the uranyl unit upon complexation in both of these cases reveal striking similarities in the nature of the U–N bonding and the effect of this bonding on the U–Oyl interaction, as well as evidence of donation into the U–N bonding region from the uranyl unit itself.
A deeper understanding of actinide bonding is also of relevance to the nuclear industry, where current approaches to the remediation of spent nuclear fuel involve the chemical separation of its component radionuclides. This approach allows for the extraction of reusable uranium and plutonium from the uranium fission products. These fission products, which are considered as high level nuclear waste (HLW), include the long-lived minor actinides (MAs), primarily comprised of neptunium, americium and curium isotopes with half-lives >106 years, and the majority of the lanthanides, with half-lives typically on the order of decades.
Current research is focussed upon ligands suitable for the selective extraction of these minor actinides, the reasons being twofold. Firstly, separation of long- and short-lived radioisotopes can provide more economically viable waste storage and management strategies. Secondly, the minor actinides can be transmuted into usable nuclear fuel via neutron bombardment, but only if separated from the lanthanides, which have large neutron-absorption cross-sections. The chemistry of the MAs is very similar to that of the lanthanides, being dominated by the trivalent oxidation state,5 rendering selective extraction an exceedingly difficult challenge. The 5f shell of the actinides has a greater radial extent than the contracted, core-like, chemically inert 4f-shell of the lanthanides and current opinion29–32 suggests that this increased radial extent leads to enhanced covalent interactions which can be exploited to produce An(III) complexes with increased thermodynamic stability of over Ln(III) analogues. Sulphur-, phosphorus- and nitrogen-donor ligands have been demonstrated to preferentially coordinate An(III) (see ref. 29 and references therein) and, of these, the N-donors have received perhaps the most attention, partly due to the fact that they often satisfy the ‘CHON principle’: ligands composed only of carbon, hydrogen, nitrogen and oxygen can be fully combusted to environmentally safe gaseous products after use, minimising secondary waste. Of these N-donor ligands, 2,6-bis(1,2,4-triazine-3-yl)pyridine (BTP) was the first to be shown to exhibit excellent selectivity,33 although the related ligands 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) and 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline (BTPhen) have since demonstrated improved selectivity, stability and kinetics.34,35 The origin of this selectivity, however, remains elusive: covalency in complexes of the lanthanides and later actinides is weak,32,36 and variation in covalency is consequently very slight,37,38 making quantitative assessments extremely difficult. For this reason, uranium complexes are often considered as model systems39–43 in studies of actinide covalency, since there is a growing body of evidence that these complexes often exhibit increased covalent bonding when compared to those of other actinides.36–38,41,44,45
In this contribution we theoretically compare the bonding of two uranyl complexes, namely [UO2(BTP)2]2+22 and UO2IA,46 where IA = [24]hexaphyrin(1.0.1.0.0.0), commonly referred to as isoamethyrin (see Fig. 1). Isoamethyrin is a hexadentate nitrogen donor ligand that has previously been demonstrated to coordinate uranyl, neptunyl and plutonyl cations,28,47 suggesting its use as a potential colorimetric sensor for actinides in aqueous environments. It is anticipated that by examining in detail the electronic structure of uranyl as one moves from coordination by monodentate ligands20 to coordination by multidentate and macrocyclic ligands, so the effect of the equatorial coordination environment on the uranyl unit can be better understood. Here, we investigate two six-coordinate complexes of uranyl: one which features two tridentate ligands and a second which comprises a single hexadentate macrocyclic ligand. Although the electronic structure of uranyl, with its formally empty 5f-shell, differs significantly from that of lower oxidation state later actinides, we propose that if U–N bonding in UO2IA is of similar character to that in [UO2(BTP)2]2+, then there is scope for future investigations of IA as a potential separation ligand for the trivalent minor actinides.
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Fig. 1 Molecular structure of (a) BTP and (b) the isoamethyrin dianion, the two ligands considered in this study. Symmetry-distinct coordinating nitrogens are labelled. |
We aim to avoid the ambiguity which can arise from orbital based methods of characterising bonding32 by focussing solely on properties of the experimentally observable electron density. To this end we employ the Quantum Theory of Atoms in Molecules (QTAIM).48 QTAIM analysis partitions a molecule into a contiguous set of space-filling atomic basins, Ωi, the surfaces of which satisfy the condition ∇ρ(r)·n(r) = 0, where n(r) is the vector normal to the atomic surface. Evaluation of ∇ρ(r) = 0 reveals the set of critical points associated with the molecule. Each atomic basin (typically) contains a single nuclear critical point (NCP) at the position of the nuclear centre. A bond critical point (BCP) is found when the uniquely defined line of maximum density between two atoms has its minimum at the interatomic surface joining the two atomic basins: in this situation, the atoms are considered to be bonded to one another.49 The bond can be characterised by the values of the electron density and its Laplacian at the BCP: as a general rule, ρBCP > 0.20 a.u. and ∇2ρBCP < 0 for a covalent bond, whilst ρBCP < 0.10 a.u. and ∇2ρBCP > 0 indicates an ionic bond. More broadly, increasing values of ρBCP indicate increasing covalent character within a bond. Additional information can be obtained from the atomic partitioning by integrating one- and two-electron properties over the resulting basins. In this way, atomic populations N(i) as well as localisation λ(i) and delocalisation indices δ(i,j) can be defined. While λ(i) gives the number of electrons localised in the atomic basin Ωi, δ(i,j) gives the number of electrons shared between basins Ωi and Ωj, and so can be considered a quantitative measure of covalency. We have recently employed this approach in order to gain detailed insight into the variation in uranyl bonding due to equatorial bond covalency.20
We complement the QTAIM analysis with studies of the Electron Localisation Function (ELF).50 The ELF provides a measure of the likelihood of finding a localised pair of electrons at a given point in space. Of particular relevance to this study are the values at which the ELF isosurface bifurcates. The higher the ELF value at the bifurcation point, the higher the degree of electron sharing between the two spatial regions separated by the bifurcation.51 We also consider an approach to identifying regions of weak interaction52 which relates the density, ρ(r), to the reduced density gradient (RDG), defined as s(r) = |∇ρ(r)|/2(3π2)1/3ρ(r)4/3. Finally, we compare these results to explicit electron density differences resulting from complexation.
U–O and U–N bonds lengths are summarised in Table 1. Calculated U–O bond lengths are in good agreement with experimental values and, in the gas phase, show an elongation of ∼0.07 Å (∼0.06 Å) compared to uncoordinated uranyl when employing the PBE (B3LYP) functional: this elongation indicates a weakening of the U–O bond, and will be investigated in subsequent sections.
PBE | B3LYP | Expa,b | PBE/TZPc | ||||
---|---|---|---|---|---|---|---|
GP | DCM | GP | DCM | ||||
a Ref. 22 (averaged values). b Ref. 46. c Ref. 67. | |||||||
[UO2(BTP)2]2+ | U–O | 1.778 | 1.786 | 1.756 | 1.764 | 1.758 | — |
U–NT | 2.634 | 2.612 | 2.657 | 2.635 | 2.565 | — | |
U–NP | 2.655 | 2.636 | 2.676 | 2.656 | 2.602 | — | |
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2.641 | 2.62 | 2.663 | 2.642 | 2.577 | — | |
UO2IA | U–O | 1.777 | 1.787 | 1.758 | 1.767 | — | 1.79 |
U–NA | 2.625 | 2.614 | 2.633 | 2.619 | — | 2.627 | |
U–NB | 2.915 | 2.908 | 2.91 | 2.903 | — | 2.906 | |
U–NC | 2.799 | 2.792 | 2.796 | 2.788 | — | 2.786 | |
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2.78 | 2.771 | 2.78 | 2.770 | — | 2.773 | |
UO2IA′ | U–O | 1.787 | 1.799 | 1.766 | 1.777 | 1.760 | 1.799 |
U–NA | 2.586, 2.587 | 2.573, 2.573 | 2.602, 2.601 | 2.586 | 2.566 | 2.590 | |
U–NB | 2.772, 2.765 | 2.702, 2.693 | 2.790, 2.785 | 2.773, 2.766 | 2.677 | 2.773 | |
U–NC | 2.713, 2.705 | 2.755, 2.747 | 2.726, 2.724 | 2.716, 2.710 | 2.644 | 2.714 | |
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2.688 | 2.674 | 2.704 | 2.689 | 2.631 | 2.692 |
In the case of [UO2(BTP)2]2+, U–N bond lengths are slightly overestimated by ∼0.07 Å (∼0.09 Å) when employing the PBE (B3LYP) functional in the gas phase. Agreement with experiment is slightly improved when solvent effects are taken into account, reducing the calculated difference to ∼0.04 Å (∼0.07 Å) when using the PBE (B3LYP) functional. This demonstrates that the different model chemistries employed here are both capable of adequately modelling the relevant uranyl–ligand interactions. The U–N bonds lengths in UO2IA, however, are overestimated by up to 0.24 Å (0.23 Å) at the PBE (B3LYP) level. Inclusion of solvent effects slightly reduces this overestimation to 0.23 Å (0.23 Å) at the PBE (B3LYP) level of theory and introduces a very slight degree of non-planarity in the IA complex, but made no substantial qualitative difference to any complex considered here. We find that the shortest U–N bonds occur when the pyrolle unit lacks any meso-carbon bridging. These meso-carbons appear to give flexibility to the macrocycle, allowing the 2-2-bipyrrole subunit incorporating the NC-donors to approach closer than the groups incorporating the NB-donors, which exhibit maximum deviation from the experimental value. In UO2IA′, however, the presence of the peripheral alkyl substituents causes the ligand to distort slightly from planarity, allowing all U–N bonds to shorten. This low symmetry distorted complex exhibits six distinct U–N bond lengths. It remains the case that the shortest U–N bonds occur when the pyrolle unit lacks meso-carbon bridges. The U–NA bonds shorten by around 0.04 Å (0.03 Å) with the PBE (B3LYP) functional when compared to the UO2IA complex, bringing them into good agreement with experimental bond length of 2.566 Å. The U–NB bonds are significantly reduced by up to 0.15 Å (0.11 Å) with the PBE (B3LYP) functional, bringing them into better agreement with the experimental values of 2.677 Å, although these bonds are still overestimated by up to ∼0.10 Å (∼0.13 Å). Although inclusion of the alkyl groups improves the overall agreement with experiment, the overestimation of the U–O bond length is slightly increased, by ∼0.01 Å (∼0.02 Å) with the PBE (B3LYP) functional in the gas phase. Geometries obtained using the PBE xc-functional have slightly improved agreement with experiment than those obtained with B3LYP.
[UO2(BTP)2]2+ | UO2IA | UO2IA′ | |||||||
---|---|---|---|---|---|---|---|---|---|
U–NT | U–NP | U–NA | U–NB | U–NC | U–NA | U–NB | U–NC | ||
ρ BCP | PBE | 0.048 | 0.045 | 0.049 | 0.026 | 0.034 | 0.052, 0.052 | 0.035, 0.036 | 0.039, 0.400 |
B3LYP | 0.045 | 0.043 | 0.048 | 0.026 | 0.033 | 0.050, 0.050 | 0.034, 0.034 | 0.038, 0.039 | |
∇2ρBCP | PBE | 0.117 | 0.113 | 0.117 | 0.065 | 0.081 | 0.128, 0.129 | 0.088, 0.089 | 0.099, 0.100 |
B3LYP | 0.116 | 0.111 | 0.118 | 0.068 | 0.085 | 0.127, 0.128 | 0.087, 0.088 | 0.099, 0.100 | |
H BCP | PBE | −0.005 | −0.004 | −0.005 | −0.000 | −0.002 | −0.005, −0.005 | −0.002, −0.002 | −0.002, −0.003 |
B3LYP | −0.004 | −0.003 | −0.004 | −0.000 | −0.002 | −0.005, −0.005 | −0.001, −0.001 | −0.002, −0.002 | |
δ(U,N) | PBE | 0.305 | 0.290 | 0.348 | 0.221 | 0.264 | 0.354, 0.352 | 0.268, 0.272 | 0.283, 0.290 |
B3LYP | 0.272 | 0.262 | 0.313 | 0.198 | 0.241 | 0.318, 0.317 | 0.238, 0.240 | 0.256, 0.260 |
As expected, values of ρBCP are much lower for U–N bonds in all complexes (Table 3). The magnitude of these values, along with the near-zero energy densities, indicate largely ionic interactions, as might be expected. One trend can, however, be still be observed: shorter U–N bonds correspond to larger values of ρBCP and greater degrees of electron sharing, supporting the intuitive view that shorter, stronger bonds exhibit higher covalency, with a commensurate reduction of covalent character in the U–O bond. The effect of peripheral alkyl substituents on the QTAIM and structural parameters of the U–N bonds in the IA′ complex is far greater than the choice of exchange–correlation functional or solvation. The choice of functional does, however, appear to have small but noticeable effects on QTAIM parameters: use of the B3LYP functional results in a significant increase in ρBCP in the U–O bond in both complexes, along with a small reduction in electron sharing. Topological properties of the U–N bonds are largely unaffected by the change in functional, although there is a small systematic reduction in all properties. This implies that the hybrid functional, which includes a proportion of exact Hartree–Fock exchange, leads to increased electron localisation. The effect of solvation on QTAIM parameters is very small and implies a very slight weakening of the U–O bonds, accompanied by a minor strengthening of the U–N bonds, in agreement with structural parameters. However, since the dependence of these properties on the choice of exchange–correlation functional and solvation is small, from hereon we only report details of our analyses of gas-phase PBE results. Corresponding data obtained using the B3LYP functional, along with those obtained via the inclusion of a continuum solvent model, can be found in ESI.†
The lengthening of the U–O bond upon complexation may provide evidence that, whilst the degree of U–N electron sharing is small, it has a non-negligible effect on the U–O bond. To investigate this effect in more detail, the QTAIM parameters of the uranyl unit in isolation and when complexed by BTP and IA/IA′ have been evaluated (see Table 4). To enable comparison, the isolated uranyl calculations were performed at the complexed uranyl geometries. To further aid analysis, we define two new parameters:
[UO2(BTP)2]2+ | UO2IA | UO2IA′ | |||||||
---|---|---|---|---|---|---|---|---|---|
UO22+ | Complex | Δ | UO22+ | Complex | Δ | UO22+ | Complex | Δ | |
a Values averaged over both O centres. | |||||||||
N(U) | 88.92 | 89.21 | +0.28 | 88.92 | 89.16 | +0.23 | 88.94 | 89.17 | +0.24 |
N(O) | 8.54 | 8.81 | +0.27 | 8.54 | 8.83 | +0.29 | 8.53 | 8.85 | +0.31 |
N(UO2) | 106 | 106.82 | +0.82 | 106 | 106.81 | +0.81 | 106 | 106.86 | +0.86 |
λ(U) | 86.61 | 86.14 | −0.47 | 86.61 | 86.18 | −0.43 | 86.62 | 86.14 | −0.48 |
λ(O) | 7.31 | 7.62 | +0.31 | 7.31 | 7.67 | +0.36 | 7.31a | 7.69a | +0.38 |
λ(UO2) | 106 | 105.47 | −0.53 | 106 | 105.64 | −0.36 | 106 | 105.56 | −0.44 |
δ(U,O) | 2.32 | 1.99 | −0.33 | 2.32 | 2.01 | −0.31 | 2.32a | 1.97a | −0.35 |
The data in Table 4 gives considerable insight into the effect of equatorial complexation on U–O bonding. As can be seen from the calculated difference in properties upon complexation, the three complexes exhibit strong qualitative similarities. Firstly, approximately 0.8–0.9 a.u. of electronic charge is donated onto the uranyl unit. Of this donated charge, approximately equal amounts (0.2–0.3 a.u.) populate the uranium and each of the oxygen ions. This additional electronic charge on all ions increases electrostatic repulsion between them. Secondly, we can consider that, to a first approximation, the electronic charge localised on each centre dictates the degree of ionic interaction. In all complexes, electron localisation increases on the oxygen centre and decreases on the uranium centre, implying a more ionic U–O interaction upon complexation. Finally, there is a corresponding reduction in δ(U,O), indicating a reduction in covalent interaction. These three factors combine to explain the lengthening, and hence weakening, of the U–O interaction in the complexes.
Further insight into the U–N interactions can also be obtained. Whilst N(UO2) increases by approximately 0.8–0.9 a.u. upon complexation, λ(UO2) reduces to a value below that of the isolated dication, with this reduction more pronounced in the BTP complex (0.53 a.u. compared to 0.36 a.u. in UO2IA and 0.44 a.u. in UO2IA′). This is consistent with our previous studies of uranyl coordination by nitrogen donors.20 Since λ(UO2) takes into account U–O delocalisation, any differences between N(UO2) and λ(UO2) must therefore be due to electron sharing between the uranyl unit and the ligand, i.e. covalency in the U–N bonds. This difference is 1.35 a.u., 1.17 a.u. and 1.30 a.u. for the BTP, IA and IA′ complexes, respectively. Since the increase in electron localisation on the oxygen ions, λ(O), is approximately equal in magnitude but opposite in sign to the decrease in electron sharing in the U–O bond, δ(U,O) (+0.33 versus −0.33, +0.36 versus −0.31 and +0.38 versus −0.35 a.u. in the BTP, IA, and IA′ complexes, respectively), we can deduce that the increase in λ(O) is almost exclusively due to donation from the U–O bond. The reduction in electron localisation on the uranium centre, λ(U), is therefore almost entirely due to electron sharing in the U–N bond. Put simply, the ∼0.8–0.9 a.u. of charge donated upon complexation is contributed almost entirely into U–N bonding and also induces a donation of ∼0.4–0.5 a.u. of charge from the uranyl unit into the bonds. This donation cannot be back-bonding in the traditional sense, since U(VI) is formally 5f06d0. Nevertheless, this is clear evidence of a significant uranium contribution to the bonds.
[UO2(BTP)2]2+ | UO2IA | UO2IA′ | ||||||
---|---|---|---|---|---|---|---|---|
U–NT | U–NP | U–NA | U–NB | U–NC | U–NA | U–NB | U–NC | |
n C | 0.197 | 0.183 | 0.204 | 0.112 | 0.150 | 0.210, 0.209 | 0.149, 0.151 | 0.166, 0.170 |
Fig. 3 shows that, for n(r) below the lowest value of nC, the ELF surface consists of a single localisation domain. Above the highest value of nC, bifurcation occurs, resulting in three ([UO2(BTP)2]2+) or two (UO2IA/UO2IA′) localisation domains, corresponding to the uranyl unit and the ligand(s). This indicates that in both complexes the U–N bonding region exhibits the lowest degree of electron sharing, as expected in the otherwise covalently bonded complexes. In the case of the isoamethyrin complex, bifurcation occurs at a very low value, due to the long, weak, U–NB bond. Table 5 shows that the critical value associated with the U–NT bond is marginally higher than that of the U–NP bond, suggesting higher electron delocalisation and therefore covalency. This is commensurate with our other analyses, which show the U–NT bonds to be slightly shorter, with larger values of both ρBCP and δ(U,N), when compared to the U–NP bonds. This is more pronounced in UO2IA and UO2IA′. Here, the critical values associated with the U–N bonds are ordered as follows: U–NB < U–NC < U–NA. This ordering is in complete agreement with our structural and topological analysis which show the U–NA (U–NB) bonds to be shortest (longest) and most (least) covalent.
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Fig. 5 Isosurfaces of the reduced density gradient, s(r), mapped with values of ρ(r)sgn(λ2) for (a) [UO2(BTP)2]2+, (b) UO2IA and (c) (b) UO2IA′. Red regions indicate attractive interactions with weakly covalent character. Isosurfaces are rendered at s(r) = 0.35 a.u., corresponding to the horizontal lines in Fig. 4. |
We have considered four different methods for studying the bonding in these complexes, all based on analysis of the experimentally observable electron density. These analyses focus on the nature of U–N bonding in these complexes and the consequent effects on the highly covalent U–O bond of uranyl. These measures involve the use of the Quantum Theory of Atoms in Molecules and the Electron Localisation Function. We have also investigated regions of weak covalent interaction through analysis of the reduced density gradient, and complemented these studies with visualisation of the electron density difference induced via complexation of the uranyl unit by the IA, IA′ and BTP ligands. These four analyses were found to be in complete agreement: all demonstrated weak, but non-negligible, covalent character in the U–N bonding region of both complexes. As might be expected, the covalent character of the bonds was found to increase as the U–N bond length shortened. We have found that use of the B3LYP exchange–correlation functional leads to slightly increased electron localisation when compared to results obtained using the PBE functional. The B3LYP functional incorporates a degree of exact exchange, and it is known that this results in localisation of the electron density in the valence shell of transition metals and f-elements.71 This effect is sometimes used to reduce the well-known self-interaction error present in approximate exchange–correlation functionals. This spurious self-interaction leads to an overestimate of electron delocalisation, especially in strongly correlated systems. Nevertheless, our B3LYP-derived results still demonstrate substantial electron-sharing. We have also performed an in-depth analysis of the effect of removing peripheral alkyl substituents from isoamethyrin, a common simplification in computational chemistry, which, in this case, has a pronounced effect on both geometry and QTAIM parameters. Inclusion of solvent effects has small consistent effects in all complexes. U–N bond lengths are found to slightly decrease by around ∼0.01 Å and there is a corresponding increase in electron sharing. Similarly, there is a small lengthening of U–O bonds when solvent effects are considered, and correspondingly, a small decrease in electron sharing.
Our analyses revealed a strong effect on the uranyl U–O bonds upon complexation, namely a noticeable reduction in electron sharing in the U–O bonding region, with charge instead localising on the oxygen centres. This leads to an increase of ionic character in the U–O bond. This, of course, also corresponds to a reduction in covalency. Since the covalent interaction is stronger, this reduction explains the increased U–O bond lengths found in our structural analysis.
We have also demonstrated that the uranyl unit itself donates electronic charge into the U–N bonding region. This cannot be traditional back-bonding, since the U(VI) centre is formally 5f06d0, but instead is a contribution that is localised on the uranium centre in the isolated uranyl dication. This uranium donation appears to be a general feature of equatorial bonding in uranyl complexes.20
Finally, the results presented here show that, from an electronic perspective at least, multidentate expanded porphyrin ligands provide interesting model systems for investigating An–N bonding characteristics. The similarity in bonding character to that of BTP complexes supports the possibility of using such macrocycles as model systems in the investigation of the origins of selectivity of nitrogen donor ligands for trivalent actinides over lanthanides: we intend to explore these possibilities further in future work.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6cp01273f |
‡ Frequency analysis was not performed on the UO2IA′ complex when using the B3LYP xc-functional due to computational expense. |
§ Technically, this point is a saddlepoint on the ELF surface, characterised as a (3,−1) critical point in terms of the topology. It is only a minimum along the bond. |
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