Probing the Nature of Chemical Bonding in Uranyl(VI) Complexes with

Article pubs.acs.org/JPCA

Probing the Nature of Chemical Bonding in Uranyl(VI) Complexes with Quantum Chemical Methods Valérie Vallet,*,† Ulf Wahlgren,*,‡ and Ingmar Grenthe*,§ †

Université Lille 1 (Sciences et Technologies), Laboratoire PhLAM, CNRS UMR 8523, Bât P5, F-59655 Villeneuve d’Ascq Cedex, France ‡ Department of Physics, Stockholm University, AlbaNova University Centre, 10691 Stockholm, Sweden § Department of Chemistry, School of Chemical Sciences and Engineering, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden S Supporting Information *

ABSTRACT: To assess the nature of chemical bonds in uranyl(VI) complexes with Lewis base ligands, such as F−, Cl−, OH−, CO32−, and O22−, we have used quantum chemical observables, such as the bond distances, the internal symmetric/asymmetric uranyl stretch frequencies, and the electron density with its topology analyzed using the quantum theory of atoms-in-molecules. This analysis confirms that complex formation induces a weakening of the uranium−axial oxygen bond, reflected by the longer U−Oyl bond distance and reduced uranylstretching frequencies. The strength of the ligand-induced effect increases in the order H2O < Cl− < F− < OH− < CO32− < O22−. Indepth analysis reveals that the trend across the series does not always reflect an increasing covalent character of the uranyl−ligand bond. By using a point-charge model for the uranyl tetra-fluoride and tetrachloride complexes, we show that a significant part of the uranyl bond destabilization arises from purely electrostatic interactions, the remaining part corresponding either to charge-transfer from the negatively charged ligands to the uranyl unit or a covalent interaction. The charge-transfer and the covalent interaction are qualitatively different due to the absence of a charge build up in the uranyl−halide bond region in the latter case. In all the charged complexes, the uranyl−ligand bond is best described as an ionic interaction. However, there are covalent contributions in the very stable peroxide complex and, to some extent, also in the carbonate complex. This study demonstrates that it is possible to describe the nature of chemical bond by observables rather than by ad hoc quantities such as atomic populations or molecular orbitals.

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INTRODUCTION Chemical bonding has been discussed in terms of electrostatics and covalence since the appearance of Pauling’s The Nature of the Chemical Bond1,2 and by the introduction of Pearson’s3 “hardness/softness” concept for the description of the donor and acceptor atoms in complexes. In the present article, we will discuss chemical bonding in terms of electron delocalization, where we differentiate between covalency, charge-transfer processes, and electrostatics. The investigation has been done using quantum chemical methods (QM) on models of actinide complexes in the gas-phase. We have used the uranyl(VI) ion as a model acceptor and ligands containing H2O, F−, Cl−, OH−, CO32−, and O22− as Lewis bases. We have selected the uranylion because we expect the U−Oyl stretch frequency to be a sensitive indicator for the interactions between uranium and the ligands in the equatorial plane of the linear UO2-unit.4 By replacing the fluoride and chloride ligands with point charges, e−, we were able to compare the effects of the real ligands with a purely electrostatic model and in this way obtain information about the relative contribution of electrostatic and electron © XXXX American Chemical Society

delocalization on the U−Oyl bond distances and stretch frequencies. It is not meaningful to use a simple electrostatic model for the hydroxide, carbonate and peroxide complexes because of the charge delocalization within these ligands. There are a number of previous communications on electron delocalization5,6 based on orbital populations and charges on donor and acceptor atoms. However, the analysis of the bonding in molecules should as far as possible not rely on molecular orbitals since these are not observables and the choice of their representation (canonical orbitals, natural orbitals, natural-bonding orbitals, etc.) may result in different pictures of the interactions. However, there are observables that can be used to discuss these interactions, such as Raman/IR stretch frequencies of the uranyl(VI) ion and the electron density, ρ(r), measured by accurate X-ray diffraction experiments.7 The quantum theory of atoms-in-molecules (QTAIM), Received: September 13, 2012 Revised: October 29, 2012

A

dx.doi.org/10.1021/jp3091123 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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developed by Bader,8 provides the theoretical framework to study the topology of ρ(r), thus providing a rationale for describing the nature of interatomic interactions. This method has been used by Kaltsoyannis et al.9−13 to show that there is very little metal−ligand covalency in AnCp3, AnCp4, and uranium tris(aryloxides) complexes. We will apply this electronic density probe to scrutinize the trends in the internal uranyl bond and the bonds to the equatorial ligands. Our exploration of the uranyl−ligand interactions will begin by using gas-phase models as these will allow us to use the point-charge model to differentiate between purely electrostatic effects and electron delocalization. In the gas-phase, we can also study chemical bonding in complexes separated from solvent effects. Quantum chemical calculations of this type may require extensive computing time, and we have therefore made a comparison between different QM approximations in order to select the one that is appropriate for our purpose. Finally, we will discuss structures and frequencies computed within a continuum solvent model, for the purpose of comparing them to experimental data available in the literature, either in crystals or in solution.

package,27 which provides the appropriate wave function extended files (wfx) to be used by the AIMAll package.28

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RESULTS AND DISCUSSION Method Comparison and Bonding Analyses in the Gas Phase. In Table 1, we have compared gas-phase bond Table 1. Comparison of Bond Distances Optimized in the Gas-Phase for [UO2(OH)4]2− and [UO2Cl4]2− Calculated at Different Levels of Theory Using HF, B3LYP, MP2, CCSD, and CCSD(T) method UO2(OH)42− r(U−Oyl) r(U−OH) UO2Cl42− r(U−Oyl) r(U−Cl)

HF

B3LYP

MP2

CCSD

CCSD(T)

1.754 2.326

1.837 2.306

1.841 2.294

1.793 2.306

1.822 2.293

1.698 2.805

1.772 2.749

1.784 2.703

1.738 2.743

1.762 2.729

distances in UO2(OH)42− and UO2Cl42− at different levels of theory. The results obtained using the DFT functional B3LYP are in very good agreement with the CCSD(T) calculation, and B3LYP was therefore used in all following calculations. It may be noted that the CCSD bond distances differ by 0.03 Å from those obtained with CCSD(T), a somewhat surprising result. The accuracy of B3LYP geometries, in particular vs CCSD(T), has been investigated in several previous studies where similar results have been reported.29,30 However, it should be emphasized that energies obtained with B3LYP often are less satisfactory than those with correlated wave function methods, such as MP2 or CCSD(T), sometimes to the extent that conclusions based on B3LYP energies become flawed.17 In Table 2, we report bond distances and U−Oyl stretch frequencies in gas phase and for the bare uranyl-ion and complexes with H2O, e−, F−, OH−, Cl−, O22−, and CO32− in the equatorial plane. The data in Table 2 illustrates the well-known fact that both the U−Oyl distance and the corresponding stretch frequency, which reflect the strength of the chemical bond, vary with the ligands coordinated in the equatorial plane of the uranyl(VI) ion. For example, the U−Oyl distances increases from 1.739 Å in UO2(H2O)52+ to 1.803 Å in UO2O2(H2O)3, while the corresponding IR stretch frequency decreases from 1030 cm −1 to 882 cm −1 . Both these observations are consistent with a weakening of the U−Oyl bond when water molecules are replaced by negatively charged ligands. Part of this is a result of electron transfer/electron delocalization (covalence) and part by electrostatic repulsions between yl-oxygen and the coordinated ligands. We have tested how the sensitivity of these results depend on the uranium basis set, in particular, the number of polarization g functions, as the default Turbomole basis set only includes one such function. The differences in bond distances are noticeable but still within reasonable limits; the U−Oyl distances in UO2(OH)42− and UO2Cl42− differ by 0.006 and 0.008 Å between the basis sets with 1g and 3g functions at the B3LYP level. Nevertheless, we have chosen to use the larger 3g polarization set, as optimized by Cao et al.23 The point charge e− was used to quantify the purely electrostatic effect on the uranyl(VI) ion by being placed and constrained at the positions occupied by F− and Cl−, in uranyl tetra-fluoride and uranyl tetra-chloride, respectively. This allowed a comparison with the uranyl tetra-fluoro and tetra-

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THEORETICAL METHODS In the present study, we have used B3LYP14,15 to optimize geometries and to calculate frequencies. The quality of B3LYP applied to actinide complexes has been investigated previously, but in order to make sure that this method gives reliable results for the complexes studied in the present investigation, we compared geometries obtained with B3LYP and the ab initio methods HF, MP2, CCSD, and CCSD(T) for the UO2(OH)42− and UO2Cl42− complexes. For the methodological comparison, we used the Molpro16 program package. The conclusion from previous investigations17 was that B3LYP gives geometries with a high accuracy, while the calculated energies are not of the same quality, when compared to more accurate methods like CCSD(T). As will be seen in the Results section, we confirmed the good agreement between B3LYP and CCSD(T) for structure parameters and the former was therefore used in all following calculations. The investigations of the geometry of the uranyl(VI) ion in different surroundings was carried out for (i) the bare ion, (ii) the ion surrounded by fixed point charges, (iii) the different uranyl(VI) complexes in gas phase, and (iv) finally in a continuum solvent model. All structure optimizations in gas phase were done with the Turbomole program package,18 and the point-charge calculations with the Molcas 19−21 program system. In all calculations, the basis sets used were of triple-ζ valence plus polarization or better quality. Uranium was described by the small core potential suggested by Dolg et al.,22 with an associated uranium basis set23 with 10s, 9p, 5d, 4f, and 3g functions obtained from a segmented contraction of a 14s, 13p, 10d, 8f, and 6g primitive set of Gaussians. All light atoms in these calculations were described by the def2-TZVP basis sets24 with (5s1p)/[3s1p] contraction for hydrogen, (11s6p2d1f)/ [5s3p2d1f] contractions for carbon, oxygen, and fluorine, and (14s9p3d1f)/[5s5p2d1f] for chlorine. The calculations on structures in a polarizable continuum, Table 3, were made using the COSMO model 25 as implemented in the Turbomole18 program package with a solvent excluding cavity built from one sphere for each atom including hydrogen. Natural Population Analysis (NPA)26 was carried at the DFT level in the gas-phase. To perform the QTAIM analysis, we used the Gaussian09 (revision C.01) quantum chemistry B



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Table 2. Bond Distances and U−Oyl Symmetric and Asymmetric Stretch Frequencies Computed in the Gas-Phase at the B3LYP Level for the Bare Uranyl-Ion and Some Complexes; QTAIM and NPA Charges, the Latter within Brackets, Computed at the DFT Level; L Denotes the Ligands in the Equatorial Plane, e−, F−, Cl−, OH−, CO32−, and O22− d(U− Oyl) (Å)

d(U−L) (Å)

f(U−Oyl) (cm−1) Raman/IR

q(U)

q(Oyl)

bare UO22+ UO2F42− UO2(e−)42− at fluoride distance UO2Cl42− UO2(e−)42− at chloride distance UO2(H2O)52+ UO2(OH)42− UO2(OH)2(H2O)3

1.691 1.819 1.755

2.231 2.233

1047/1136 793/851 908/973

3.27 (3.28) 3.17 (2.03)

−0.63 (−0.64) −1.0 (−0.71)

−0.79 (−0.65)

1.773 1.722

2.749 2.753

854/935 981/1059

2.91 (1.41)

−0.92 (−0.62)

−0.77 (−0.54)

1.740 1.838 1.780

947/1028 762/832 866/934

3.15 (2.13) 3.06 (1.73) 3.05 (1.90)

−0.81 (−0.53) −1.05 (−0.65) −0.9 (−0.62)

−1.19 (−0.88) −1.22/0.48(−0.86) −1.19 (−0.91), −1.19 (−0.97)

UO2O2(H2O)3

1.804

2.497 2.305 2.202; 2.620, 2 × 2.742 2.152, 2.609

820/887

2.90 (1.70)

−0.97 (−0.65)

−0.56 (−0.44), −1.15 (−0.87)

0.64 (0.53) 0.48 (0.25) 0.56 (0.52), 0.61 (0.48) 0.60 (0.50)

UO2CO3(H2O)3

1.784

2.243, 2.600, 2.752

859/927

2.90 (1.89)

−0.98 (−0.62)

−2.55 (−0.71), −0.98 (−0.87)

0.59 (0.51)

complex

ligand

(OH)−, (H2O) (O2)2−, (H2O) O−CO3, (H2O), C− CO3

chloro complexes and could be used to estimate the electron delocalization contribution to the bonding in these complexes; for the remaining complexes, the distributed charge on the ligands made such a comparison less meaningful. A comparison of the U−Oyl Raman stretch frequencies between the complexes UO2F42− and UO2Cl42− and the corresponding quantities with point charges shows negligibly small differences in the frequencies, 2 cm−1 (122 cm−1 and 124 cm−1 for the fluoride and the chloride complexes, respectively), and the corresponding point-charge model. The same result, 2 cm−1, was obtained as the difference in frequency between the F− and the Cl− systems, (86 cm−1 and 84 cm−1, the former obtained with the point-charge model and the latter from the complexes). The difference in frequencies can thus not be used to distinguish between electrostatic and electron transfer contributions in these complexes. If we instead consider the uranyl bond distances, the difference between the fluoride and chloride complexes is more significant, 1.82 and 1.77 Å, respectively, for the two complexes, while the corresponding numbers for the point charges are 1.76 and 1.72 Å. Compared to the bare uranyl ion (1.69 Å), about half the change in the bond distance is due to electrostatic effects (a little more for fluoride than for chloride). This similarity is reflected by both the Raman and IR U−Oyl frequencies. In order to investigate the electrostatic effect on the U−Oyl distance and the corresponding stretch frequency, we varied the distance, d, between the point charges and uranium. As shown in Figure 1, there is a smooth decrease in the U−Oyl distance with increasing d and a corresponding increase in the stretch frequency. Both the bond distance and the frequency depend on the distance between the ligand and the uranyl ion, and, not surprisingly, the electrostatic effect of the negatively charged ligands is strongest for the shortest uranium−ligand distance. It may thus appear surprising that the frequencies in the fluoride and the chloride complexes are so similar. However, this observation can be clarified by considering the influence of the electronegativity of the ligand. In Table 2, we have included the NPA and QTAIM charges on the uranyl and the ligands. The difference between the uranium NPA charges in the fluoride and the chloride complexes is significant, 2.03 and 1.41, respectively (the QTAIM charges show a similar but smaller

q(L)

q(H)

Figure 1. (a) Axial U−Oyl distance as a function of the U−e−distance in UO2(e−)42−; (b) U−Oyl asymmetric stretch frequency as a function of the U−e− distance.

decrease). The different charges reflect the smaller electronegativity of chlorine vs fluorine, which gives rise to a larger ligand to uranyl charge transfer in the chloride complex that will weaken and lengthen the uranyl bond and thus result in a decrease in the uranyl stretch frequency; the smaller electrostatic effect on the frequencies in the chloride complex is thus compensated by the larger charge transfer. This is consistent with the similarity in the electron delocalization on the bond distances in the two complexes (an additional lengthening of about 0.05 Å of the U−Oyl bond). It is also interesting to note that, in the case of [UO2(H2O)5]2+, the same lengthening, 0.05 Å, is induced by the equatorial water molecules. We wish to emphasize that the electron delocalization is of the charge C



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transfer type rather than involving a substantial amount of covalency. This point is further discussed in the next section. Both the frequency shift and the change in uranyl bond distance in the peroxide and the carbonate complexes are similar to those in the chloride and fluoride complexes, but here, we cannot estimate the electrostatic effect with a simple point-charge model, as peroxide and carbonate are polyatomic ligands. This is also the case for the hydroxide complex, and the analyses of these systems should therefore be done using other indicators, as discussed in the following section. A formal relationship between the U−Oyl bond distances and stretching frequencies can be expressed with the Badger relationship,31 which relates the bond force constant k (megadyne/m) to the bond length r(U−Oyl) with the following expression: r(U−Oyl ) = d0 + β /k3

(1)

For this relationship to be valid in uranyl complexes, the underlying assumption is that the uranyl normal modes are essentially decoupled from those of the coordinated ligands, a condition that is fulfilled in most of the uranyl crystals studied by Raman and IR spectroscopy.32 Figure S1, Supporting Information, demonstrates that Badger’s rule is valid for all uranyl complexes, except for the hydroxide species, [UO2(OH)4]2− and [UO2(OH)2(H2O)3]. In contrast to most uranyl complexes, where the symmetric and antisymmetric frequencies correspond largely to motions of the yl-unit atoms, the hydroxide complexes are characterized by strong mixing of the uranyl−OH collective stretching motions with the yl-unit ones. To the best of our knowledge, this is the first illustration of deviations from Badger’s rule in uranyl complexes, illustrating that it may not be applicable to all such systems for bond distance derivations from measured frequencies. Gas-Phase Electron Densities. The gas-phase B3LYP data were used to calculate the electron density in the equatorial plane of the complexes in Table 2 and used in the corresponding QTAIM topology analysis. The calculated electron density in UO2(OH2)52+, UO2Cl42−, UO2F42−, UO2(OH)42−, UO2(OH)2(OH2)3, UO2O2(OH2)3, and UO2(CO3)(OH2)3, shown in Figure 2a−g, gives a pictorial representation of electron density in the equatorial plane of the complexes studied. The qualitative features are consistent with expectations; there is practically no build-up of electron density between water and uranium, consistent with an ion−dipole interaction. The electron density in the fluoride and chloride complexes is very similar to that in the aqua-ion, but with a minor electron accumulation between uranium and the ligands, still these complexes are best characterized as ionic. The same picture emerges for the hydroxide complex. The strongly bonded peroxide and carbonate complexes, UO2(O2)(OH2)3 and UO2(CO3)(OH2)3, show a significant electron density between their oxygen donor atoms and uranium, suggesting the more extensive electron delocalization expected for covalent metal−ligand interactions. In the peroxide complex, the accumulation of density and its rather homogeneous distribution in the region between the oxygen atoms and uranium suggests that the bond is best described as a three-center bond, a conclusion that was also reached by Bryantsev et al.33 This tendency, albeit weaker, can also be seen in the carbonate complex. Topological Analysis of Gas-Phase Electron Densities Using the QTAIM Model. The statements on the bonding

Figure 2. Gas-phase electron density in the equatorial plane of (a) UO2(OH2)52+; (b) UO2F42‑; (c) UO2Cl42−; (d) UO2(OH)42−; (e) UO2(OH)2(OH2)3; (f) UO2O2(OH2)3; and (g) UO2(CO3)(OH2)3. Contour maps of the electronic densities are shown as thin blue lines; the BCPs are shown as small green spheres; thin red lines indicate the interatomic paths that separate the atomic electron density basins; the values of the density (in e−/bohr3) at the BCPs are shown as well. D



ρb (e /bohr ) (e / Å3)

0.31 (7.46)

0.31 (7.56)

(6.69) (8.26) (7.65) (15.76) (7.12) (8.62) (7.56) 0.28 0.34 0.32 0.65 0.30 0.36 0.31

0.30 (2.00) 1.85 UO2CO3(H2O)3

a

1.85 UO2O2(H2O)3

0.99/0.80

0.28 (1.91)

2.02 1.72 1.89

0.99/0.81

(2.57) (1.83) (2.07) (1.70) (2.26) (1.74) (2.03) 0.38 0.27 0.31 0.25 0.33 0.26 0.30 0.93/0.78 1.01/0.81 0.98/0.80 0.96/0.82 0.96/0.78 1.02/0.82 0.98/0.80 2.29 1.78 1.92

d1/d2 (Å) DI(U,Oyl)

The first value, d1, is the distance between BCP and U and the second, d2, BCP between U−Oyl and U−L. ρb and ∇2ρb are the electron density and the Laplacian at the BCP given in e−/bohr3 and e−/ bohr5, respectively, with the corresponding values in e−/Å3 and e−/Å5 given in parentheses. DI(U,L) is the delocalization index. Hb (au) is the energy density at the critical point. The experimental values for Cs2UO2Cl4 are from Zhurov et al.7

−0.03 −4.5 × 10−4 0.27 (6.52) 0.15 (3.62) 0.10 (0.70) 0.04 (0.26) 1.24/1.01 1.43/1.17 −0.26

Hb (au)

−0.04 −2.3 × 10−4 0.35 (8.42) 0.14 (3.48) 0.12 (0.82) 0.04 (0.25) −0.23

0.29 0.62 0.73 0.18 0.87 0.21 0.71 0.21

(OH−) (OH2) (O22‑) (OH2) (CO3) (OH2)

1.20/0.96 1.44/1.18

(8.16) (2.85) (3.28) (4.44) (6.13) (7.92) 0.11 (2.58) 0.34 0.12 0.14 0.18 0.25 0.33 (0.59) (0.36) (0.49) (0.34) (0.57) (0.72) 0.03 (0.21) 0.09 0.05 0.07 0.05 0.09 0.11 1.24/0.99 1.40/1.35 1.40/1.28 1.37/1.13 1.26/1.04 1.21/0.99 1.49/1.26 0.55 0.53

−0.42 −0.21 −0.27 −0.23 −0.33 −0.19 −0.26

∇2ρb (e−/bohr5) (e−/ Å5) ∇ ρb (e /bohr ) (e / Å5)

Hb (au)

DI(U,L)

d1/d2 (Å)

ρb (e−/bohr3) (e−/Å3)

U−L BCP − 5

− 2

−

U−Oyl BCP

3

−

Table 3. Characteristics of the U−Oyl and U−L Bond Critical Points (BCP) for the Various Complexesa E

UO22+ UO2F42− UO2Cl42− Cs2UO2Cl4 (ref 7) UO2(H2O)52+ UO2(OH)42− UO2(OH)2(H2O)3

properties in the previous section can be further supported by quantitative analyses of the electron density using the QTAIM method, as reported in Table 3. According to the QTAIM theory, a chemical bond is characterized by the presence of a bond critical point (BCP), corresponding to the minimum in the electron density along the bond path connecting the bonded atoms. At the BCP, the gradient of the electron density is zero, while the Laplacian ∇2ρb might either be positive or negative; positive if there is a depletion of charge at the BCP and negative if there is a local concentration of charge. For single bonds, the latter is a sign of covalent interaction. For multiple bonds, the Laplacian is always positive at the BCP and another indicator for covalence, the delocalization index, DI(A,B), must be used. This integrates the electron density in the bonding region between atoms A and B and can be used as a measure of the bond order, noting that the computed values are always smaller than what is expected from the Lewis structures.8 Another quantitative indicator is the energy density Hb, the more negative the value, the more stabilizing (covalent) the interaction. In the naked uranyl bond, the BCP is closer to the yl-oxygen than to the uranium atom (see the rb-value in Table 3). The values of the density, 0.38 e−/bohr3 (2.57 e−/Å3) and the Laplacian 0.28 e−/bohr5 (6.69 e−/Å5) are in agreement with the findings reported by Michelini et al.,34 0.37 e−/bohr3 (2.49 e−/ Å3) and 0.28 e−/bohr5 (6.81 e−/Å5), respectively. It is noteworthy that ρb at the uranyl BCPs are similar to those of the M≡oxo (M = Cr, Mo, and W) triple bonds reported by Wang et al,35 thus confirming the concept of a strong covalent triple bond, even if the DI value, 2.2 in the bare uranyl-ion, is lower than the triple-bond value of 3. The evolution of the electronic density in the uranyl equatorial plane in the complexes can be seen not only in the projected density contour plots shown in Figure 2 but also from the characteristics of the U−L BCPs in Table 3. We have tested the influence of the level of theory on the computed BCP characteristics for [UO2Cl42−]. The results reported in Table S1 of the Supporting Information show that the only fluctuating quantity is the Laplacian at the critical point, when comparing B3LYP and CCSD densities. This simply reflects that minor changes in the local curvature of the density maps have a strong impact on the second derivatives. Nevertheless, these variations are not large enough to have the sign of the Laplacian changed from one method to the other. The U−Cl− BCP is located half way between uranium and the chloride ion, while the other BCPs are shifted toward the ligands in the water, fluoride, hydroxide, peroxide, and carbonate complexes, indicating that the bonds are polarized toward the ligands. In the water, fluoride, chloride, and hydroxide complexes, the Laplacian ∇2ρb is positive with ρb-values ≈ 0.05−0.09 e−/bohr3, close to 0.08 e−/bohr3 calculated for the ionic LiF molecule,36 suggesting only minor electron accumulations between uranium and the ligands. In addition, the energy density value is negative but in absolute value much smaller than the one in the uranyl bond. These observations from the QTAIM data suggest that the uranyl−ligand bonds are mainly ionic, which is also consistent with the small differences in the vibrational frequencies in the fluoride and chloride complexes as discussed in the previous section. From the analysis of various systems, Bader suggested that ρb is greater than 0.2 e−/bohr3 (1.35 e−/Å3) for covalent bonds and lower than 0.1 e−/bohr3 (0.67 e−/Å3) for closed-shell interactions that include ionic interactions. These limits are not

−0.02 −0.01 −0.03 −3 × 10−3 −0.02 −0.03 −3.3 × 10−4

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Table 4. Geometries and Frequencies for Different Uranyl(VI) Complexes Computed at the B3LYP Level with the COSMO Solvent Model; Comparison with Experimental Data from EXAFS in Solution and Single Crystal X-ray Data Are Also Included; Raman Data Are Denoted (R) complex UO22+ UO2(H2O)52+ UO2(OH)42−

UO2F42− UO2F4(H2O)2− UO2Cl42−

UO2(O2)(H2O)3 UO2(CO3)(H2O)3 UO2(O2)(CO3)24− [UO2(O2)2(H2O)]2− UO2(CO3)2(H2O)2− UO2(CO3)34−

[(H2O)3(UO2)(O2)(UO2)(H2O)3]2+ [(CO3)2(UO2)(O2)(UO2)(CO3)2]4−

method

d(U−Oyl) (Å)

d(U-L) (Å)

B3LYP-COSMO B3LYP-COSMO EXAFS soln37 B3LYP-COSMO EXAFS soln38,39 X-ray (s)11b B3LYP-COSMO B3LYP-COSMO EXAFS soln40 B3LYP-COSMO in CH3CN in ionic liq. Cs4UO2Cl4 X-ray B3LYP-COSMO B3LYP-COSMO B3LYP-COSMO K4UO2(O2)(CO3)2·2.5H2O43 B3LYP-COSMO B3LYP-COSMO B3LYP-COSMO Exafs soln44 Na4UO2(CO3)3(s)45 B3LYP-COSMO B3LYP-COSMO

1.704 1.76 1.77 1.84 1.83 1.815 1.82 1.82 1.80 1.78 1.77 1.77 1.776 1.81 1.78 1.84 1.826 1.89 1.80 1.82 1.81 1.811 1.77 1.80

2.44 2.41 2.27 2.25 2.261 2.21 2.23; 2.68 (H2O) 2.26; 2.48 (H2O) 2.71 2.6841 2.6942 2.669 2.18 (perox); 2.52 (H2O) 2.32 (carb); 2.49 (H2O) 2.24 (perox); 2.49 (carb) 2.238−2.256 (perox.); 2.429 - 2.473 (carb) 2.13, 2.32 (perox); 2.62 (water) 2.36, 2.38 (carb); 2.53 (water) 2.45 2.44 2.384−2.427 2.32, 2.44 2.34 (perox); 2.40 (carb)

rather good agreement with our values obtained for UO2Cl42− in the gas-phase. The differences observed might be related to the long-range crystal field influence on the UO2Cl42− cluster, which could be the origin of the different value of the Laplacian at the U−Cl BCP. Zhurov et al. conclude that the U−Cl− bond can be described as partially covalent. However, the small values of both ρb and Hb and the positive value of the Laplacian all suggest that the uranyl−chloride bond is ionic. Results in a Water Solvent. We have also compared vibration frequencies for a number of complexes in a water solvent, described by a polarizable continuous medium, with experimental data when available. The data in Tables 2 and 4 shows that the bond distances between the gas-phase and the solvent are very similar, within 0.02 Å for the U−Oyl distance, while the distance between uranium and coordinated water is systematically longer by 0.04 to 0.11 Å in the gas-phase. The symmetric U−Oyl stretch frequencies agree quite well between gas phase and solvent, with the largest deviation 43 cm−1 for UO2(OH2)52+ (Tables 2 and 5). QM models from gas phase and COSMO models should therefore be useful when discussing experimental data from aqueous solution. The entries marked with a star all derive from experimental Raman data in ref 4b. The frequencies deduced for the complexes are a result of deconvolution of broad experimental peaks into Gaussian components, sometimes with a separation less than 10 cm−1, and their accuracy is therefore not high. The situation is different for the aqua-ion and the limiting complexes UO2F42− and UO2(CO3)34− that are predominant in the test solutions. The authors in ref 4b suggest that a maximum of six chloride ligands can be coordinated; there is no other experimental data supporting this assumption. The high stretch frequency suggests that the complex is more like the

strict but result from studies across many molecular systems. The peroxide and carbonate complexes, UO2(O2)(OH2)3 and UO2(CO3)(OH2)3 with strong metal−ligand bonds have a larger electron density at the BCP than water, fluoride, chloride, or hydroxide. The uranyl−carbonate and uranyl−peroxide ρb value, 0.10 e−/bohr3 (0.70 e−/Å3) and 0.12 e−/bohr3 (0.82 e−/ Å3), lie just above the ionic threshold; the corresponding values of Hb are also slightly larger in absolute values than for the other ligands. These are signs that, in the U−L bonds, the major contribution is the ionic one. Another concept of interest is the bond ellipticity, which describes how cylindrical a bond is; an ellipticity of zero is expected for single and triple bonds, while it should be nonzero for double bonds. The ellipticity values are all small for U−F, U−Cl, U−water, and U−OH bonds, while the values for the uranyl−carbonate and the uranyl−peroxide bonds are 0.31 and 0.27, respectively. The first group of bonds thus includes essentially single bonds, while the latter show significant π-character. The BCPs characteristics of uranyl−ligand bonds are very similar to that reported for AnCp4,10 AnCp3,11 or uranium tris(aryloxides).12 The QTAIM analyses confirm that the fluoride and the chloride complexes are almost entirely ionic. The same conclusion can be drawn for the hydroxide complex based on the density plots. In both the peroxide and the carbonate complexes, the ionic character is still strong , but with some degree of covalency or charge delocalization effect, as illustrated not only by the density plots but also by values of DI(U,L) approaching 1, 0.87, and 0.71 in the peroxide and carbonate cases, respectively. The electron density distribution in Cs2UO2Cl4 has been measured by Zhurov et al.7 in a low temperature (20 K) X-ray diffraction experiment that was analyzed using the QTAIM theory. These experimental values reported in Table 2, are in F



Article

Cl− < F− < OH− < CO32− < O22− reflecting the increased stability (as measured by the equilibrium constants) across the series. In order to characterize the uranyl−ligand bonds, it was necessary to explore various models, to distinguish between the contributions from electrostatic interactions, electron transfer, and covalency. A point-charge model for the monatomic halides reveals that a significant part of the uranyl bond destabilization arises from purely electrostatic interactions, the remaining part corresponding mainly to electron transfer from the halides to the uranyl unit. The distinction between charge transfer mechanisms and covalency is inferred by exploring the electron density in the interatomic region. The aqua ion, tetra-fluoro, tetra-chloro, and tetra-hydroxide complexes are clearly ionic, while the increased electron density between uranium and the peroxide and to some extent carbonate suggest a significant covalent contribution. The results of this study suggests that one cannot draw direct conclusions on the nature of uranyl−ligands bonds by simply referring to correlations with the uranyl bond distances or symmetric and asymmetric stretching frequencies. However, qualitative and quantitative analyses of the electron density encompass fruitful information that is helpful in discussions of chemical bonding.

Table 5. Symmetric (Raman Active) and Asymmetric (Infrared Active) Stretching Frequencies of the Uranyl Unit for the Complexes in Table 3; The Star * Refers to Aqueous Solution Data B3LYP-COSMO

complex UO22+ UO2(H2O)52+ UO2(OH)42− UO2F42− UO2F4(H2O)2− UO2Cl42− UO2(O2)(H2O)3 UO2(CO3)(H2O)3 UO2(O2)(CO3)24− K4UO2(O2)(CO3)2·2.5H2O

νs (U−Oyl) (cm−1)

νas (U−Oyl) (cm−1)

1006 913 759 796 791 840 795 854 743

1064 961 786 818 818 898 840 897 767

exptl νs (U−Oyl) (cm−1) 8704b* 78638* 8224b* ∼8554b* 8514b*

766.543 [UO2(O2)2(H2O)]

2−‑

UO2(CO3)2(H2O)2− UO2(CO3)34− Na4UO2(CO3)3(s) [(H2O)3(UO2)(O2)(UO2)(H2O)3]2+

716

751

816 786

855 821

871, 877

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812.5,46 80947* 80848

ASSOCIATED CONTENT

S Supporting Information *

921, 922

Figure S1 illustrates whether U−Oyl bond distances and frequencies follow the Badger’s relationship. Table S1 compares the BCP characteristics in UO2Cl42− at different levels of theory. This material is available free of charge via the Internet at http://pubs.acs.org.

aqua-ion and might perhaps be best described as an outersphere ion-pair. Do Experimental Raman/IR Frequencies Provide Information on Chemical Bonding? It is quite clear from previous experimental observations and the QM data presented in Tables 2 and 4 that the U−Oyl frequency is strongly dependent on the equatorial ligands. However, the data in Table 2 and Figure 1 demonstrate that part of this difference is strongly dependent on electrostatic effects from the surrounding ligands; the stretch frequency for the point charge model is about 120 cm−1 larger than that for the fluoride and chloride complexes, and this is a significant difference compared to the variation in experimental stretch frequencies in Table 4. The large difference in the symmetric U−Oyl stretch frequency between the fluoride, chloride, and hydroxide complexes, 840, 937, and 827 cm−1, respectively, is nearly entirely an electrostatic effect due to the different uranium−ligand distance and not to a difference in covalency. However, the previous reasoning suggests that U−Oyl frequencies provide some information on chemical bonding, but this is at best qualitative. As the U − Oyl frequencies are strongly correlated with the U− Oyl distance, the same is true also for the latter. The best indication of differences in bonding arises from the close-up view at the electronic density and at its quantitative analysis through the QTAIM theory.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (V.V.); [email protected] (U.W.); [email protected] (I.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Most of the calculations were performed on the PhLAM cluster financed by the European Regional Development Fund (FEDER) through the “Contrat de Projets Etat Region” (CPER) 2007−2013. Additional computational resources have also been provided by the French supercomputing facility CINES “Centre Informatique National de l’Enseignement Supérieur” (CINES, Project No. phl2531).

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REFERENCES

(1) Pauling, L. J. Am. Chem. Soc. 1932, 54, 3570−3582. (2) Pauling, L. The Nature of the Chemical Bond; Cornell University: Ithaca, NW; 1st ed., 1939; 2nd ed., 1940; 3rd ed. 1960. (3) (a) Pearson, R. G. J. Am. Chem. Soc. 1963, 85, 3533−3539. (b) Pearson, R. G. Chemical Hardness: Applications From Molecules to Solids; Wiley-VCH: Weinheim, Germany, 1997. (4) (a) Nguyen-Trung, C.; Palmer, D. A.; Begun, G. M.; Peiffert, C.; Mesmer, R. E. J. Solution Chem. 2000, 29, 101−129. (b) NguyenTrung, C.; Begun, G. M.; Palmer, D. A. Inorg. Chem. 1992, 31, 5280− 5287. (5) Clark, A. E.; Sonnenberg, J.; Hay, P. J.; Martin, R. L. J. Chem. Phys. 2004, 121, 2563−2570. (6) Ingram, K. I. M.; Häller, J. L.; Kaltsoyannis, N. Dalton Trans. 2006, 2403−2414.

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CONCLUSIONS We have studied the nature of the chemical bond between uranyl and equatorial ligands, using observables such as the bond distances, vibrational frequencies, and the total electronic density. The QM data reported here support the experimental observations that the U−Oyl bond length and frequencies strongly depend on the equatorial ligands, reflecting the weakening of the yl-bond as strong Lewis bases are coordinated. The strength of the effect agrees with the trend reported by Nguyen-Trung et al.4 and follows the order H2O < G



Article

(7) Zhurov, V. V.; Zhurova, E. A.; Pinkerton, A. A. Inorg. Chem. 2011, 50, 6330−6333. (8) Bader, R. W. B. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (9) Arnold, P. L.; Turner, Z. R.; Kaltsoyannis, N.; Pelekanaki, P.; Bellabarba, R. M.; Tooze, R. P. Chem.Eur. J. 2010, 16, 9623−9629. (10) Tassell, M. J.; Kaltsoyannis, N. Dalton Trans. 2010, 39, 6719− 6725. (11) Kirker, I.; Kaltsoyannis, N. Dalton Trans. 2011, 40, 124−131. (12) Mansell, S. M.; Kaltsoyannis, N.; Arnold, P. L. J. Am. Chem. Soc. 2011, 133, 9036−9051. (13) Kaltsoyannis, N. Inorg. Chem. 2012, DOI: 10.1021/ic3006025. (14) Becke, A. D. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098. (15) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B: Condens. Matter 1988, 37, 785. (16) Werner, H.-J; et al. Molpro, version 2010.1, a package of ab initio programs, 2010. See the Supporting Information for a full author list. (17) Wåhlin, P.; Danilo, C.; Vallet, V.; Réal, F.; Flament, J.-P.; Wahlgren, U. J. Chem. Theory Comput. 2008, 4, 569−577. (18) TURBOMOLE, V6.4; University of Karlsruhe and Forschungszentrum Karlsruhe GmbH: Karlsruhe, Germany, 2012; available from http://www.turbomole.com. (19) (a) Aquilante, F.; De Vico, L.; Ferré, N.; Ghigo, G.; Malmqvist, P.-Å.; Neogrády, P.; Pedersen, T. B.; Pitonak, M.; Reiher, M.; Roos, B. O.; Serrano-Andrés, L.; Urban, M.; Veryazov, V.; Lindh, R. J. Comput. Chem. 2010, 31, 224. (20) Veryazov, V.; Widmark, P. O.; Serrano-Andrés, L.; Lindh, R.; Roos, B. O. Int. J. Quantum Chem. 2004, 100, 626. (21) Karlström, G.; Lindh, R.; Malmqvist, P.-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P.-O.; Cossi, M.; Schimmelpfennig, B.; Neogrády, P.; Seijo, L. Comput. Mater. Sci. 2003, 28, 222−239. (22) Küchle, W.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1994, 100, 7535−7542. (23) (a) Cao, X.; Dolg, M. J. Mol. Struct. 2004, 673, 203−209. (b) Cao, X.; Dolg, M.; Stoll, H. J. Chem. Phys. 2003, 118, 487−496. (24) (a) Weigend, F.; Häser, M.; Patzelt, H.; Ahlrichs, R. Chem. Phys. Lett. 1998, 294, 143. (b) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (25) Klamt, A.; Schuürmann, G. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799−805. (26) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735−746. (27) Frisch, M. J.; et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. See the Supporting Information for a full author list. (28) Keith, T. A. AIMAll, version 12.06.21; TK Gristmill Software: Overland Park, KS, 2012; available from aim.tkgristmill.com. (29) Réal, F.; Vallet, V.; Marian, C.; Wahlgren, U. J. Chem. Phys. 2007, 127, 214302. (30) Andrews, L.; Gong, Y.; Liang, B.; Jackson, V. E.; Flamerich, R.; Li, S.; Dixon, D. A. J. Phys. Chem. A 2011, 115, 14407−14416. (31) Badger, R. M. J. Chem. Phys. 1935, 3, 710. (32) Jones, L. H. Spectrochim. Acta 1958, 10, 395−508. (33) Bryantsev, V. S.; de Jong, W. A.; Cossel, K. C.; Diallo, M. S.; Goddard, W. A., III; Groenewold, G. S.; Chien, W.; Van Stipdonk, M. J. J. Phys. Chem. A 2008, 112, 5777−5780. (34) Michelini, M. C.; Russo, N.; Sicilia, E. J. Am. Chem. Soc. 2007, 129, 4229−4239. (35) Wang, C.-C.; Tang, T.-H.; Wang, Y. J. Phys. Chem. A 2000, 104, 9566−9572. (36) Bader, R. F. W. J. Phys. Chem. A 1998, 102, 7314−7323. (37) Wahlgren, U.; Moll, H.; Grenthe, I.; Schimmelpfennig, B.; Maron, L.; Vallet, V.; Gropen, O. J. Phys. Chem. A 1999, 103, 8257− 8264. (38) Clark, D. L.; Conradson, S. D.; Donohue, R. J.; Keogh, D. W.; Morris, D. E.; Palmer, P. D.; Rogers, R. D.; Tait, C. D. Inorg. Chem. 1999, 38, 1456−1466. (39) Moll, H.; Reich, T.; Szabó, Z. Radiochim. Acta 2000, 88, 411− 415.

(40) Vallet, V.; Wahlgren, U.; Schimmelpfennig, B.; Moll, H.; Szabó, Z.; Grenthe, I. Inorg. Chem. 2001, 40, 3516−3525. (41) Servaes, K.; Hennig, C.; Van Deun, R.; Görller-Walrand, C. Inorg. Chem. 2007, 46, 4212. (42) Gaillard, G.; Chaumont, A.; Billard, I.; Hennig, C.; Ouadi, A.; Wipff, G. Inorg. Chem. 2007, 46, 4815−4826. (43) Goff, G. S.; Brodnax, L. F.; Cisneros, M. R.; Peper, S. M.; Field, S. E.; Scott, B. L.; Runde, W. H. Inorg. Chem. 2008, 47, 1984−1990. (44) Ikeda, A.; Hennig, C.; Tsushima, S.; Takao, K.; Ikeda, Y.; Scheinost, A.; Bernhard, G. Inorg. Chem. 2007, 46, 4212−4219. (45) Li, Y.-P.; Krivovichev, S. V.; Burns, P. C. Miner. Mag. 2001, 65, 297−304. (46) Allen, P. G.; Bucher, J. J.; Clark, D. L.; Edelstein, N. M.; Ekberg, S. A.; Gohdes, J. W.; Hudson, E. A.; Kaltsoyannis, N.; Lukens, W. W.; Neu, M. P.; Palmer, P. D.; Reich, T.; Shuh, D. K.; Tait, C. D.; Zwick, B. D. Inorg. Chem. 1995, 34, 4797−4807. (47) Maya, L.; Begun, G. J. Inorg. Nucl. Chem. 1981, 43, 2827−2832. (48) Koglin, E.; Schenk, H. J.; Schwochau, K. Spectrochim. Acta, Part A 1979, 35, 641−647.

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Probing the Nature of Chemical Bonding in Uranyl(VI) Complexes with

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