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A DFT study of U(VI) hydroxy complexes was performed with special attention paid to the [(UO2)3(OH)5(H2O)4–7]+ and [(UO2)4(OH)7(H2O)5–8]+ species. It was established that the ionicity of the U=O bond increased when moving from [(UO2)(H2O)5]2+, [(UO2)2(OH)(H2O)8]3+, [(UO2)2(OH)2(H2O)6]2+, [(UO2)3(OH)5(H2O)4–6]+ to [(UO2)4(OH)7(H2O)5–8]+ species. In both [(UO2)3(OH)5(H2O)4–6]+ and [(UO2)4(OH)7(H2O)5–8]+ complexes, the U=O bond was observed to have a range of different lengths which depended on the composition of the first coordination sphere of UO2 2+. The cyclic structures of trimeric complexes were somewhat more stable than their linear structures, which was probably due to the steric effect.
The online version of this article (doi:10.1007/s10967-017-5305-z) contains supplementary material, which is available to authorized users.
Investigation of uranium complexes is very important from the practical point of view. Uranium is a toxic and radioactive element and its elimination from aqueous solutions near nuclear power plants or from underground waters in the neighborhood of uranium mines is a matter of global concern. The key to successful removal of this element is detailed information concerning the stability and structure of aqueous uranium complexes. Such information allows one to predict the migration of U ions with the different oxidation numbers in soil and the aqueous environment [1, 2]. The best known U compounds are those with oxidation number VI, and among them U(VI) hydroxy complexes, which are very attractive due to the large variation in the number and properties of the species they form. In acidic solutions, U(VI) exists in the form of ionic monomers UO2(H2O)52+ [3–6], whereas in neutral and alkaline solutions, a vast array of cationic and anionic species occur, in which the coordination number 4 or 5 is preserved for UO2 2+ ions [7–10]. The best known complexes: UO2(OH)+, (UO2)2(OH)3+, (UO2)2(OH)22+, (UO2)3(OH)42+, (UO2)3(OH)5+, (UO2)4(OH)7+, UO2(OH)2, UO2(OH)3−, and UO2(OH)42− have been investigated in detail, using different methods such as UV–vis [11–13], luminescence [14–16], FTIR [11, 17], Raman [11, 18], EXAFS spectroscopy [7, 19], potentiometry , and calorimetry . Parallel to the experimental investigations, computational techniques have been used to predict or confirm the structure of U(VI) hydroxy complexes. Different methods of quantum-chemical calculations can be employed in the analysis of the electronic structure and properties of 5-f elements. The Density Functional Theory (DFT) method can serve as a tool to complement experimental studies and confirm the information coming from experimental work. According to Schreckenbach and Shamov, who studied actinide elements, generalized gradient approximation (GGA) functionals provide accurate geometries and frequencies, while hybrid functionals are superior for energetics. Those authors have established that the best results for actinides can be obtained when the first coordination sphere is treated explicitly and the second one is represented using the continuum solvation models . They found that the application of the explicit model for the second coordination sphere of the actinides not only brought no clear advantages, but also made the calculations more time-consuming.
The aim of our contribution was to analyze the structure of U(VI) hydroxy complexes using the DFT method, with special attention being paid to the trimeric complexes (UO2)3(OH)5+ (henceforth referred to as 3.5) and the tetrameric complexes (UO2)4(OH)7+ (henceforth referred to as 4.7). Detailed studies of dimeric and trimeric complexes performed by Tsushima et al.  have shown that cyclic trimers with an oxo bond are stable. We decided to elucidate the structure of the linear species, keeping in mind the fact that in the real conditions they probably exist parallel to the cyclic isomers. Tetrameric complexes were investigated for the first time. Their concentration in aqueous solutions in the pH range of 5–6 is comparable to that of trimeric complexes (Fig. S1) , which means that the knowledge of their structure would help specialists understand the numerous complex equilibria present in the aqueous phase during various industrial processes, such as ion-exchange, solvent extraction, adsorption, etc., used for the reprocessing of uranium minerals or for the recovery of U from nuclear wastes [24–27].
All calculations for systems of uranium complexes were carried out using the Amsterdam Density Functional package (ADF2016) [28–30] at the relativistic level of theory, where the scalar coupling effects were considered using a two-component Hamiltonian with the zeroth order regular approximation (ZORA) [31–33]. Triple-ζ Slater basis set with two polarization functions were used for uranium and triple-ζ Slater basis set with one polarization function were used for oxygen and hydrogen . The frozen core approximation was applied, leaving the 5f, 6s, 6p, 6d and 7s electrons of uranium, and the 2s and 2p electrons of oxygen (as well as the 1s of H) for explicit treatment. All calculations were done using the PW91 generalized gradient approximation (GGA) functional proposed by Perdew and Wang . All structures were optimized in the aqueous phase by means of the Conductor like Screening Model (COSMO) of solvation as implemented in ADF package  using the Solvent Accessible Surface (asurf) of the solvent cavity.
The structures of uranium complexes were fully optimized without any constraint (except for [UO2(H2O)5]2+, where a symmetry point group (D5h) was applied). A frequency analysis showed that all the investigated structures had only positive frequencies confirming that these were local minima on the energy surface. The Mayer bond order  and atomic charges were obtained from fully optimized electronic structures.
The FT-IR spectra of UO2(NO3)2 aqueous solutions were recorded in the transmission mode at room temperature on a 1725X Perkin Elmer instrument using the KBr pellet technique at 4 cm−1 resolution. The KBr was dried in a drier at 200 °C for 24 h. The tablets (radius 1 cm, thickness 0.1 cm) were prepared using a hydraulic press. The 560 mg KBr was mixed with UO2(NO3)2 aqueous solution. Uranyl nitrate solutions were prepared from UO2(NO3)2·6H2O (Lachema n.p. Brno, p.a.). The U(VI) spectra were deconvoluted with the second-derivative method using Peak-Fit software V.4 (SeasolveSoftware Inc.).
The structures of all the investigated complexes are given in Figs. 1, ,22 and and3.3. The following species were examined: UO2(H2O)52+ (designated 1.0), (UO2)2(OH)3+ (2.1), (UO2)2(OH)22+ (2.2), (UO2)3(OH)42+ (3.4), (UO2)3(OH)5+ (3.5) and (UO2)4(OH)7+ (4.7). The parameters for the dimeric complexes (UO2)2(OH)3+ and (UO2)2(OH)22+ (designated respectively 2.1 and 2.2), i.e. U–U distances of 4.445 and 3.851 Å and O=U=O bond angles of 176° and 173.2°, respectively, are very similar to the values found by Tsushima, i.e. U–U 4.390 and 3.875 Å and U=O=U 175° for the 2.2 complex . A detailed comparison of the structures of isomeric trimeric and tetrameric hydroxy complexes with different numbers of H2O ligands is given in Table 1. For complex 3.5.5, the cyclic structures 3B and 3C are more stable than the linear ones, but the cyclic structure 3C with a tridentate OH bridge in the center is less stable than 3B, which does not have a bridge of this type. The differences in stability are probably a consequence of a tension among the U–OH bonds inside the structural ring resulting from electrostatic repulsion by the four hydroxyls situated in the vicinity. Generally, all cyclic structures are more extended in space than the linear ones, which means that their U–U distances are larger and the mutual repulsion of ligands is weaker, leading to greater stability. For example the U–U distances of 3.975, 4.447, 3.935 Å characteristic of the 3B complex are larger than the U–U distances of 3.778, 3.836 Å characterizing the 3D complex. In the case of complex 3.5.6, the U–U distances characteristic of the most stable species, 3E, are 3.927, 3.894, and 4.563 Å, whereas the distances calculated for 3F and 3G are 3.817, 3.865; 3.816, and 3.854 Å. 3G is the least stable of these complexes. Apart from having shorter U–U distances, it is also characterized by accumulation of the negative charge, originating from five hydroxyls, in the center of the structure. Complex 4.7.5 has two isomers. One of them (B) is less stable because it has an asymmetric structure with three uranyl ions with coordination number 4. The other isomer (A) has a symmetric form, and since it contains only two uranyls with coordination number 4, it is more coordinatively saturated. Two isomers of species 4.7.6 differ remarkably. One of them (C) has an oxo bridge in its structure and for this reason is much more stable than isomer D, which does not have this bridge. Between the two isomers of species 4.7.7, 4F is less stable because the water molecule in the center of the structure has been replaced by a hydroxyl which has increased the repulsion among the hydroxyls. For the same reason, isomer F of complex 4.7.8 is less stable than isomer G.
The changes in U=O bond length with the relative number nr U–OH of U–OH bonds and with the average Mulliken charge of O axial atoms are given in Fig. 4. U=O bond length was calculated as the average length of all U=O bonds in a particular complex. The relative number of U–OH bonds n r U–OH = n U–OH/n, where n r U–OH is the number of U–OH bonds and n denotes the sum of all bonds in the complex, i.e. the sum of U–OH, U=O, U–O, U–H2O, and O–H bonds. The length of U=O visibly increases with n r U–OH and decreases with the charge of axial oxygens. For structures 3E and 4C, the lengthening of the bond is especially pronounced due to the steric effect in the case of 3E, i.e. the presence of two uranyls with the coordination number 5, and due to the lowering of the number of U=O bonds in 4C resulting from the formation of an oxo bridge. The phenomenon of U=O bond change is consistent with the reports of many authors who noticed that U=O bonds weakened when some electron donors were present in the equatorial plane of the U(VI) complex , which was explained as a result of a concurrent π donation from 2p orbitals of axial and equatorial O atoms to the 5f and 6d orbitals of U atoms. Worth mentioning are the results of calculations done by Tsushima et al.  and Fujii et al. , who analyzed UO2(OH)2 and (UO2)2(OH)22+ species. The bend of the O=U=O bond is unquestionable and more pronounced for the latter species.
The increase of the Lewis acidity of the oxo uranyl ligand (U=O) under the influence of the different equatorial oxygen and nitrogen ligands may be exploited in the synthesis of the different adduct complexes in which the length of U=O bond changes in the range 1.8–1.9 Å . This is very close to the change in U=O bond, which can be found in our work, i.e. 1.77–1.82 Å. The most interesting is the formation of the hydrogen bond between the uranyl oxygen (U=O) and amines [40, 41] and this fact potentially is important from the point of view of U(VI) extraction from the aqueous environment. Sather, Berryman and Rebek  showed that tripodal receptor with carboxylate and amide groups in its structure forming the hydrogen bonds with uranyl oxygens (U=O), is able to extract selectively uranium from the sea water. Uranyl hydrated oxides and hydroxides form different structures with hydrogen bonded water in the interlayer regions  which is important in uranium processing and extraction in various steps of the nuclear fuel cycle.
According to the observations made in this present work, the change in O=U=O bond angle depends on the composition of the first coordination sphere of the UO2 2+ ion, and this angle is evidently wider for higher numbers of hydroxyls coordinating uranyl ions (Fig. 5). When a uranyl ion is coordinated exclusively by hydroxyls, the average O=U=O bond angle is close to 180°, in contrast to peripheric UO2 2+ ions in hydroxyl complexes of U(VI), in which this angle is visibly narrower. It seems that the π donation from 2p orbitals of axial O atoms is counterbalanced by the donation originating from the orbitals of the equatorial O atoms of hydroxyls. No such counterbalance is present when hydroxyl ligands are replaced by H2O ligands, which are weaker electron donors. The unsymmetrical and inhomogeneous environment of UO2 2+ ions in the first coordination sphere results in the shortening of the U=O bond paralleled by the reduction of the O=U=O bond angle. This observation is true of species 3.4 and 3.5, but does not apply to species 4.7. Although the average O=U=O angle for the peripheric uranium atoms is narrower than for the atoms in the center of the structure, the change in U=O bond length contradicts the above mentioned observation. For example for species 4A (4.7.5) the angles are: 173.9°, 177°, 177.8°, 176.2°, but the lengths of the U=O bonds form an unexpected sequence: 1.795, 1.802, 1.802, 1.811 Å, with a high value for the peripheric U atom which suggests that bond length is not a simple function of π donation from 2p orbitals of axial oxygen.
In our opinion, the formation of higher hydroxy complexes of U(VI) in moving from monomers to dimers to trimers to tetramers results in a spatial expansion of the species formed, which impedes the overlapping of 5f and 6d uranium orbitals with 2p orbitals of oxygen and increases the ionicity of U=O bonds by increasing the number of hydroxyl ligands in the first coordination sphere of UO2 2+.
The changes in average Mulliken population for 5f and 2p orbitals of U and axial O versus n r U–OH and Mayer bond order (MBO) of U=O bond, respectively, are shown in Fig. 6. The average Mulliken population of 2p orbitals increases with the increasing n r U–OH and with the decreasing Mayer bond order (MBO); this is in contrast to the population of 5f, which decreases with nr U-OH, providing evidence for some cancellation of f–p overlapping. The Mulliken populations for O in OH bridges (for trimeric and tetrameric species) are given in Table 1. It is easy to notice that for the cyclic structures 3B, 3C, and 3E, the Mulliken populations are higher than for the linear structures 3D, 3F, and 3G. A similar situation holds for structures 4B and 4A; this indicates that bridged U–OH bonds are more ionic in the cyclic structures than in the linear ones.
The HOMO–LUMO diagrams for isomeric trimers (UO2)3(OH)5+ and tetramers (UO2)4(OH)7+ are given in Fig. S2. Molecular orbital composition and energies are included in Table 2. The molecular orbitals HOMO (the Highest Occupied Molecular Orbital) are localized on O 2p orbitals originating from U=O, H2O, OH− and on p, f orbitals from U. The participation of p orbitals from OH− and H2O ligands in the overall energy of HOMO orbital is the highest. The energy gap for 3B, 3C cyclic trimers is higher in comparison with 3D linear trimer. The same, the sequence 3E(cyclic) > 3F, 3G (linear) is preserved, therefore, one can conclude that cyclic trimeric isomers are more stable than the linear ones. For the tetrameric complexes we have found the following sequences concerning HOMO–LUMO energy gap: 4A > 4B; 4C > 4D; 4E < 4F; 4G > 4H, which is the same as the sequence of the relative total bond energies of particular species, except for 4E/4F species pair. The LUMO (the Lowest Unoccupied Molecular Orbital) orbitals are localized mainly on U f orbitals for all analyzed trimeric and tetrameric structures. Generally, the energy gap for tetrameric complexes is lower than for the trimeric ones and for this reason one can presume that tetramers (UO2)4 (OH)7+ would show more chemical reactivity.
The deconvoluted FT-IR spectra of UO2(NO3)2 solutions with different pH values, characteristic of the predominance of 3.5 and 4.7 complexes in the U(VI) solution, are given in Fig. 7. The bands in the range 920–980 cm−1 are characteristic of different 3.5 and 4.7 species (Table 1), i.e. of the asymmetric O=U=O vibrations, however, it is very difficult to unequivocally determine whether they belong to trimeric or tetrameric species because trimers and tetramers have very similar U=O bond energies. One has to take into account the results obtained by Muller et al. , who found characteristic frequencies of 923 and 940 cm−1 for (UO2)3(OH)5+ and (UO2)2(OH)2 species, respectively. It is difficult to imagine that the frequencies 942, 947, and 943 cm−1 observed in our spectra could originate from a dimer, since only very small numbers of dimers are present in a U(VI) solution at pH range 5–6 (Fig. S1).
The length of a U=O bond increases with the number of hydroxyl ligands in the first coordination sphere of UO2 2+ ions, parallel to a decrease in the Mayer bond order and an increase in the Mulliken population on O 2p orbitals and a slight drop in this parameter on 5f U orbitals. The strengthening of the ionic character of the U=O bond, when it passes from UO2 2+ to the (UO2)4(OH)7+ complex, is therefore unquestionable.
The O=U=O bond angle is wider for uranyls coordinated exclusively by hydroxyl ligands compared with those which have a mixture of H2O and OH− ligands in the first coordination sphere.
For complex 3.5.5, the cyclic structures are more stable than the linear ones, which probably is the consequence of the steric effect, i.e. weaker repulsion of ligands in the first coordination sphere of the cyclic hydroxy complexes.
The values of U=O bond energy in (UO2)3(OH)5+ and (UO2)4(OH)7+ is very similar, which results in similar frequencies of O=U=O asymmetric stretching vibrations.
The ionic character of the bridged U–OH bond is stronger in cyclic structures 3.5.5 and 3.5.6 than in their linear counterparts. Further studies are necessary to support this conclusion and to extend it to species 4.7.5, 4.7.6, 4.7.7, 4.7.8.
The value of the energy gap of analyzed complexes suggests that cyclic trimeric isomers are more stable than the linear ones. HOMO orbitals are localized on O p and U p, f orbitals. LUMO orbitals are localized mainly on U f orbitals.
Below is the link to the electronic supplementary material.
The authors would like to thank Institute of Mathematics at Maria Curie Skłodowska University in Poland for facilitating their software and resources in Lunar cluster while preparing this manuscript.
Electronic supplementary material
The online version of this article (doi:10.1007/s10967-017-5305-z) contains supplementary material, which is available to authorized users.