Article pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Structure and Bonding in Uranyl(VI) Peroxide and Crown Ether Complexes; Comparison of Quantum Chemical and Experimental Data Valérie Vallet*,†,§ and Ingmar Grenthe*,‡,§ †
Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France School of Chemical Science and Engineering, Department of Chemistry, Royal Institute of Technology (KTH), S-10044 Stockholm, Sweden
‡
S Supporting Information *
ABSTRACT: The structure, chemical bonding, and thermodynamics of alkali ions in M[12-crown-4]+, M[15-crown-5]+, and M[18-crown-6]+, M[UO2(O2)(OH2)2]+4,5, and M[UO2(O2)(OH)(OH2)]n1−n (n = 4, 5) complexes have been explored by using quantum chemical (QC) calculations at the ab initio level. The chemical bonding has been studied in the gas phase in order to eliminate solvent effects. QTAIM analysis demonstrates features that are very similar in all complexes and typical for electrostatic M−O bonds, but with the M−O bonds in the uranyl peroxide systems about 20 kJ mol−1 stronger than in the corresponding crown ether complexes. The regular decrease in bond strength with increasing M−O bond distance is consistent with predominantly electrostatic contributions. Energy decomposition of the reaction energies in the gas phase and solvent demonstrates that the predominant component of the total attractive (ΔEelec + ΔEorb) energy contribution is the electrostatic component. There are no steric constraints for coordination of large cations to small rings, because the M+ ions are located outside the ring plane, [On], formed by the oxygen donors in the ligands; coordination of ions smaller than the ligand cavity results in longer than normal M−O distances or in a change in the number of bonds, both resulting in weaker complexes. The Gibbs energies, enthalpies, and entropies of reaction calculated using the conductor-like screening model, COSMO, to account for solvent effects deviate significantly from experimental values in water, while those in acetonitrile are in much better agreement. Factors that might affect the selectivity are discussed, but our conclusion is that present QC methods are not accurate enough to describe the rather small differences in selectivity, which only amount to 5−10 kJ mol−1. We can, however, conclude on the basis of QC and experimental data that M[crown ether]+ complexes in the strongly coordinating water solvent are of outer-sphere type, [M(OH2)n+][crown ether], while those in weakly coordinating acetonitrile are of inner-sphere type, [M-crown ether]+. The observation that the M[UO2(O2)(OH)(OH2)]n1−n complexes are more stable in solution than those of M[crown ether]+ is an effect of the different charges of the rings.
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will be 2-fold: first exploration of structures, chemical bonding, and the characteristics of ether and uranyl oxygen donors using gas-phase reactions (1), which is straightforward because these are not obscured by solvent effects; second, comparison of experimental solution chemical data for the alkali ion crown ether and M[UO2(O2)(OH)(OH2)]n1−n complexes using quantum chemical reaction energies and models of aqueous and nonaqueous solvents on the basis of the conductor-like screening model for the solvent abbreviated as COSMO:4
INTRODUCTION Since their discovery in 1967, the properties of alkali ion crown ether complexes have been extensively studied, as exemplified by a large number of publications and review articles summarized in ref 1. Of particular relevance for the present study are the experimental gas-phase reactions discussed by Armentrout, summarized in ref 2. One of the key issues in these studies was the origin of the cation selectivity that was assumed to result from a mismatch between the size of the metal ions and the crown ether cavity. This suggestion was based in part on solidstate structures, but mainly on equilibrium constants determined both in aqueous and nonaqueous solution. Similar ring-shaped structure elements, but with negative charge, “M[(UO2)(O2)A]n1−n” (n = 4−6), where M is an alkali ion and A different ligands, e.g. OH−, are found in clusters studied by Nyman, Burns, and co-workers;3 in the present communication we will discuss complexes where A = OH−. The focus © XXXX American Chemical Society
M+(g) + L(g) → ML+(g)
(1)
Crown ethers are uncharged, and for this reason we have used uncharged uranyl peroxide ligands [UO2(O2)(OH2)2]n (n = 4, 5) as models when discussing chemical bonding; the Received: October 8, 2017
A
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
The quantum-chemical modeling of this reaction can be made in one approach using a specific number of coordinated water molecules, a procedure followed when discussing reactions in the gas phase; a drawback is that the numbers of coordinated water, p and q, are not well-known. This problem is avoided in a second approach, where the interaction between solutes and solvent is described by using a continuum model such as COSMO. As we will demonstrate, this approach can describe experimental data from nonaqueous, weakly coordinating solvents quite well. The situation is different in strongly coordinating solvents such as water, where the entropy of reaction is strongly dependent on p and q. We demonstrate this by using a combination of a model with specific values of these quantities and the COSMO model. However, the agreement between experiment and model is not particularly good. Nevertheless, this model can be used to make the chemically important distinction between outer-sphere [M(OH2)p+][crown ether] and inner-sphere complexes, [M(OH2)q(crown ether)]+.
rings with n = 6 have not been studied because of the large number of conformers.5 Experimental solution chemical data for alkali ion complexes are only available for uranyl peroxide rings with negative charge and for this reason we have used [UO2(O2)(OH)(OH2)]nn‑ (n = 1, 4) as models. Our discussion will cover the following subjects: • bonding type (charge, polarity, and polarizability) • role of ligand topology (size, conformation, and flexibility) • comparison of the quantum chemical information with experimental solution chemical data
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QUANTUM CHEMICAL (QC) METHODS AND MODELS
Small-core relativistic effective core potentials (RECP) are used to account for the core electrons in the Rb, Cs, and U atoms.6,7 The valence orbitals of the uranium atom are described with the RECP segmented valence basis set of quadruple-ζ quality,8 while def2-TZVPP basis sets9 are used for all other elements. The structures are optimized at the DFT level with the TPSSh functional, as used in our recent study of uranyl peroxide complexes.10 Huang et al.11 have shown that this functional gives reasonably accurate geometries. The initial structures of the crown ethers and their complexes in the gas phase were taken from the conformers with lowest energy, identified in the comprehensive studies of Hill Glendening et al.12 and Armentrout et al.13 All geometries in the gas phase were optimized with symmetry constraints, as shown in Tables S1 and S2 in the Supporting Information. We also investigated these structures in water using the COSMO model, where for technical reasons the structure optimization was made without symmetry constraints. Single-point energy calculations were carried out at the MP2 level and corrected for basis set superposition error with the counterpoise correction.14 To compute reaction enthalpies, entropies, and free energies, the molecular partition functions at 298.15 K and 0.1 MPa are obtained from unscaled harmonic vibrational frequencies. When calculating reaction energies in water solution, we compared models with and without a specific number of coordinated solvent molecules. In nonaqueous solvents, we have assumed that all solute− solvent interactions can be described with the COSMO model alone, without specific coordinated solvent molecules. The solvation energy depends strongly on the choice of cavity radius that is based on the shape and radii of the solutes. The effective cavity radius for the hydrated alkali ions varies by about 1 Å between Li+ and Cs+ and was estimated using the hydration energies15 and turned out to be equal to rhydr = rHS + d, where rHS is the “hard-sphere” crystal radii16 and d ≈ 0.50 Å. We have assumed that the variation in the effective radius of M[crown ether]+ between Li+ and Cs+ is much smaller and determined mainly by the size of the crown ether. As solvation energies are not known for acetonitrile, we have assumed that the effective radii of the solvated alkali ions were equal to their “hard-sphere” radii plus a constant (0.50 Å) that was estimated from the experimental Gibbs energy of the reaction M+ + 18-crown ether → M[18-crown ether]+ in acetonitrile; details are reported in Tables S3 and S5 in the Supporting Information. Resolution of identity is used for all calculations for computational savings. All calculations were performed with the Turbomole quantum chemistry package.17 To characterize the nature of the interaction between the alkali ions and the crown ether or uranyl peroxide rings, both energy decomposition analysis18 and topological quantum theory of atoms in molecules (QTAIM) calculations have been performed.19 The electrostatic potentials and electron densities were visualized and drawn by the ADF package,20 by mapping them onto the electron density isosurfaces at 0.02 au (electrons per bohr3). Experimental solution chemical data on complex formation can be schematically described with reaction 2, from which it is apparent that both equilibrium constants and enthalpies and entropies of reaction are strongly dependent on changes in solvation of reactants and products.
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RESULTS AND DISCUSSION Structures of 12-crown-4, 15-crown-5, and 18-crown-6 ligands and Their Complexes with Alkali Ions, M[crown ether]+. The Cartesian coordinates of all structures optimized in the gas phase are reported in the ZIP file in the Supporting Information, and examples of structures of M[crown ether]+ complexes are given in Figure 1, with bond distances and angles in Table S1 in the Supporting Information that also includes examples of geometry optimization in the water solvent. The geometries of the different M+ complexes are in good agreement with those reported by Ray et al.,12b Armentrout et al.,13 and Glendening et al.12a with the exception of the Li[18-crown-6]+ complex, for which Glendening explored conformers with a symmetry higher than C1 used in the present study; they also obtained an asymmetrical geometry for the Na[18-crown-6]+ complex (C1 symmetry), in comparison to S6 symmetry (see Table S6 in the Supporting Information) in our study, where we noted that the difference between the S6 and C3v structures is very small, only 0.001 Å in bond distances (see Table S7 in the Supporting Information). There are also differences between the structures of the Cs[crown ether]+ complex, which presumably is a result of the different relativistic effective core potentials used. The distance between the ether oxygens, d(O−O), is approximately the same, 2.8 Å in all complexes, with the exception of the Li complexes, where it is significantly shorter, 2.6 Å. All M+ ions in the M[12-crown-4]+ complexes are coordinated outside the O4 ring plane, with no indication of steric constraints and no possibility of “molecular recognition”; we consider these M−O distances as “normal” because they follow the variation in the M+ “hard-sphere” ionic radii from Colin and Smith16 very well (Figure 2a). The solvent-optimized geometries are very similar to that in the gas phase, and the main difference in the solvent is slightly longer M−O bonds and the distance between M+ and the plane, [Oyl], formed by the coordinated uranyl oxygen atoms. In the M[15-crown-5]+ complexes the O5 ring is sufficiently large to allow coordination of Li+ and Na+ close to the ring plane, while K+, Rb+, and Cs+ ions are too large and are located outside. All M−O bond distances are “normal” except for Li[15-crown-5]+ (Figure 2b), which is about 0.10 Å longer than that expected from the ionic radius trend. In the M[18-crown-6]+ complexes, Li+ is only coordinated to three oxygen donors, because of the mismatch between its ionic radius and the crown ether cavity. Na+ and K+ are coordinated to all oxygen donors in the O6 plane, but the Na−O distances are about 0.40 Å longer than normal (Figure 2c); the ionic radii of Rb and Cs are
M(OH 2)p+ + crown ether → M(OH 2)q [crown ether]+ + (p − q)H 2O
(2) B
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 1. Structures optimized at the TPSSH level in the gas phase of (a) Li[12-crown-4]+ (C4), (b) Li[15-crown-5]+ (C1), and (c) Li[18-crown-6]+ (C1), demonstrating that only three Li−O bonds are formed, (d) K[18-crown-6]+ (S6), (e) K[18-crown-6]+ tilted to demonstrate that K+ is coordinated in the O6 plane, and (f) Cs[18-crown-6]+ tilted (S6), demonstrating that Cs+ is located above the O6 plane.
where only four oxygen donors are coordinated, resulting in C1 symmetry (Figure 3c), which is 25.0 kJ mol−1 more stable than that with C5 symmetry; a similar observation was made for Li[15-crown-5]+, where five-coordination was retained but where the Li−O distance was about 0.1 Å longer than normal. There is a good correlation between the M+−O distances and the M+ ionic radii (Figure 4). The complex M[(UO2)(O2)(OH)(OH2)]43− has been optimized in a COSMO water solvent, with geometry data given in Table S2 in the Supporting Information, where we note that the M−O bond distances are very nearly the same, within 0.02 Å, as in M[12-crown-4]+; the agreement with experimental X-ray data is also good, better than 0.10 Å. Nature of the M−O Interactions in M[12-crown-4]+, M[(UO2)(O2)(OH2)2]4+, and M[(UO2)(O2)(OH)]43− Complexes in the Gas Phase. Armentrout et al.2 have discussed the M−O bonding using experimental and QC data; the former relate to an enthalpy of reaction that does not provide information on “microscopic” details, which is the focus of our discussion. The M+−O interactions take place between a hard donor and a hard acceptor, suggesting that they are mainly electrostatic in origin. We have tested this assumption in the M[12-crown-4]+, M[(UO2)(O2)(OH2)2]4+, and M[(UO2)(O2)(OH)(OH2)]43− complexes by using QTAIM (Table S8 in the Supporting Information) and energy decomposition analyses (Table S9 in the Supporting Information) of the interactions between the M+ alkali ions and the ligand geometry in the complexes. The usefulness of the QTAIM in elucidating properties of uranyl complexes has been discussed in previous studies,24,25 where we also note that the method is consistent with experimental information.26 The small value of the electron density at the bond critical point, ρb ≈ 0.1 e−/Å3 and the very similar values of ρb, ∇2ρb (the Laplacian of the electron density), the energy density Hb, and the charges of M and O all reveal that the M−O bonds are essentially ionic in both crown
too large to allow coordination in the O6 plane, but their M−O distances are normal. The K+−O distances agree very well (0.02 Å difference at most) with X-ray data and EXAFS data in methanol.21,22 In addition, M−O distances for Rb+ and Cs+ agree within 0.04 Å with the EXAFS distances recorded in methanol (Rb+)22 and in acetonitrile (Cs+) for M[dibenzo-18crown-6]Br.23 As the M−O distances in the M[18-crown-6]+ complexes of K, Rb, and Cs are normal, there is no structural reason for the observed decrease in bond energy, K > Rb > Cs, in these complexes. However, longer than normal bond distances will result in less stable bonds as discussed below. Structures of M[UO2(O2)(OH2)2]n+ and M[UO2(O2)(OH)(OH2)]n1−n (n = 4, 5) and Their Complexes with Alkali Ions. Two models have been investigated, where the first, M[UO2(O2)(OH2)2]n+, has been used for comparison of chemical bonding with the corresponding crown ethers and the second, M[(UO2)(O2)(OH)(OH2)]43−, for comparison with experimental data. The coordinates of all M[UO2(O2)(OH2)2]n+ structures optimized in the gas phase are reported in the ZIP file in the Supporting Information, with interatomic distances given in Table S2 in the Supporting Information and examples of structures in Figure 3. The M−O bond distances are very similar but slightly shorter than those in M[12-crown-4]+ and M[15-crown-5]+, reported in Table S1 in the Supporting Information. An important feature in these structures is that the linear uranyl units are tilted with respect to the plane formed by the uranium atoms, {U}n, resulting in changes in the torsion angle U−Operox−Operox−U and in two sets of parallel planes formed by the uranyl oxygen atoms, Oyl, one at a distance of 1.63 Å and the other 1.43 Å from {U}n (Figure 3), where only the oxygens in the second set with O−O distances of about 3.1 Å are available for M+ coordination; the O−O distance in the first set, approximately 5.6 Å, is too large for coordination. The most stable geometry in the M[(UO2)(O2)(OH2)2]n+ complexes has Cn symmetry, with the exception of Li[(UO2)(O2)(OH2)2]5+, C
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 2. Average bond distance M+−O plotted as a function of the “hard-sphere” M+ ionic radii from Colin and Smith:16 (a) average TPSSH gas-phase M+−O distance in the M[12-crown-4]+ complexes; (b) average TPSSH gas-phase M+−O distance in the M[15-crown-5]+ complexes; (c) average TPSSH gas-phase M+−O distance in the M[18-crown-6]+ complexes. Note that Li is only coordinated to three oxygen donors. The slopes β are 1.18 and 1.02, respectively.
However, in M[(UO2)(O2)(OH)(OH2)]43−, the difference in electrostatic energy is not due to the M−O bond, but to the pure Coulombic attraction between M+ and the noncoordinated OH−. In the COSMO water solvent (see Table S9 in the Supporting Information), the total electronic energy ΔEtot/4 is virtually the same in the positively charged complexes M[12-crown-4]+ and [(UO2)(O2)(OH2)2]4+ complexes, while the large difference between the negatively charged M[(UO2)(O2)(OH)(OH2)]43− complex and the positively charged complex arises from the larger electrostatic interaction. Thermodynamics of the Interactions between Alkali Ions and Crown Ethers and Uranyl(VI) Peroxides, M(UO2(O2)(OH2)2)+, in the Gas Phase. The M−O bond energy given in Table 1 is defined as EM−O = (ΔEGP − ΔEdist)/n, where ΔEGP is the electronic energy of reaction in gas phase, ΔEdist is the ligand distortion energy, and n is the number of coordinated oxygen donors in the ligands. ΔEdist is defined as the difference in energy between the free ligand and the energy of the coordinated ligand at its geometry in the different complexes. Technically, the latter is obtained by a single-point calculation of the electronic energy after removing the metal ion from the complex. The gas-phase reaction enthalpies of reaction are in good agreement with those in studies of Ray et al.,12b Armentrout et al.,13 Hill et al.,12e and Glendening et al.12a that report complexation enthalpies (or rather ligand disssociation enthalpies)
ether and uranyl peroxide systems. The energy decomposition analysis of the gas-phase reaction energies (Table S9) splits the total reaction energy ΔEtot into chemically and physically relevant contributions: the classical electrostatic interaction ΔEelec, the exchange-repulsion ΔEexch‑rep, and the orbital relaxation energy ΔEorb. This analysis clearly demonstrates that the predominant component of the total attractive (ΔEelec + ΔEorb) energy contribution is the electrostatic component, ΔEelec, which is twice as large as the orbital polarization contribution ΔEorb in the complexes with uncharged rings, and 5−10 times as large in the negatively charged uranyl peroxide complexes. The orbital polarization contribution refers to electronic density changes from the complex to the isolated M+−ligand fragments, which can be illustrated by the 3D plots of the difference between the electrostatic potentials (Figure 5) or electron densities (Figure S1 in the Supporting Information) between the complex and the sum of the fragments. These 3D plots reflect the fact that Li+ induces a significant electron transfer from the ring and polarizes the latter much more than the heavier Cs+. The electronic energy, ΔEtot/4, is slightly more negative in M[(UO2)(O2)(OH2)2]4+ than in M[12-crown-4]+, which is a result of a larger electrostatic contribution in the M−O bond; this difference is even more pronounced in the M[(UO2)(O2)(OH)(OH2)]43− complexes, at the same time as the differences in ΔEexch‑rep/4 and ΔEorb/4, are small between the complexes. D
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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electrostatic. The difference in ΔEM−O is larger between the Li[UO2(O2)(OH2)2]4+ and Li[UO2(O2)(OH2)2]5+, complexes, 22.6 kJ mol−1, part of which seems to be related to the difference in the distortion energy, 25.5 kJ mol−1. For the corresponding Na complexes the difference in ΔEM−O is smaller, 13.3 kJ mol−1, in comparison to a difference of 6.9 kJ mol−1 in distortion energy. The distortion energy may give a significant contribution to the M−O bond energy and seems to be as important as geometric constraints in a discussion of ion selectivity; there is, however, still a clear trend of a weakening of the M−O bonds with increasing M+ ionic radius. The large difference in reaction energy between the M[UO2(O2)(OH2)2]4+ and M[UO2(O2)(OH)(OH2)]43− complexes refers not only to the M−O bond energy but also to the Coulomb interaction between M+ and OH− in the ligand ring. Gas-phase data do not display the selectivity of various crown ethers for alkali ions in comparison to that observed in solution.2 Discussion and Comparison with Experimental Data. Experimental data on the chemistry of the alkali ion crown ether and uranyl peroxide systems have been obtained from X-ray/EXAFS structures, from equilibrium studies in solution, and to some extent from preparative procedures. It is not straightforward to use QC data from reactions in solvents for comparison with these data, because the QC calculations require information on both the coordination of solvent to reactants and products, which is not known, and a model for the bulk solvent. The importance of information on the stoichiometry of reactants and products has been pointed out by Armentrout,2 but with no quantification; we have confirmed the importance of hydration by QC calculations at the MP2 level of the Gibbs energies and entropies of reaction for reactions 3−5 in the gas phase and water (cf. Table 3):
at 298 K in the gas phase given in Table 2. The largest deviations from experimental data are found for the M[18-crown-6]+ complexes, where the experimental data seem to refer to higher energy isomers of the 18-crown-6 rings as discussed by More et al.13c The data in Table 1 for the K, Rb, and Cs complexes, all of which have normal M−O bond distances, demonstrate that the M−O bond energy, ΔEM−O, for a given alkali ion is nearly constant in the different crown ether complexes. Longer than normal M−O distances result in a Li−O bond energy (per oxygen) that is 9.1 kJ mol−1 less negative in the 15-crown-5 complex than in 12-crown-4 and a Na−O bond energy that is 2.6 kJ mol−1 less negative in the 18-crown-6 complex than in 15-crown-5 (Table 1) the difference is not related to differences in ligand distortion energies that is 1.8 kJ mol−1; both observations are consistent with M−O bonds that are predominantly
Li(OH 2)4 + + 12‐crown‐4 → Li[12‐crown‐4]+ + 4H 2O (3)
Li(OH 2)4 + + 12‐crown‐4 → Li(OH 2)[12‐crown‐4]+ + 3H 2O
(4)
Li+ + 12‐crown‐4 → Li[12‐crown‐4]+
(5)
It is important to notice the very large entropy of reaction when there are changes in the number of coordinated and free water molecules, as this has a direct bearing on the constitution of the complexes.
Figure 3. Structures of (a) Na[(UO2)(O2)(OH2)2]4+, (b) Li[(UO2)(O2)(OH2)2]5+ in C1 symmetry (this is the most stable geometry), (c) Na[(UO2)(O2)(OH2)2]5+, and (d) Na[(UO2)(O2)(OH)(OH2)]43−. Color code: Li, silver; Na, blue; U, yellow; O, orange; H, white.
Figure 4. Average bond distance M+−Oyl as a function of the “hard-sphere” M+ ionic radii from Colin and Smith16 in (a) M[(UO2)(O2)(OH2)2]4+ (red, gas-phase TPSSH level) and M[(UO2)(O2)(OH)(OH2)]43− (blue, COSMO TPSSH level) and (b) M[(UO2)(O2)(OH2)2]5+ (red, gas-phase TPSSH level). The slopes (β) of the red lines are 1.05 and 1.07, respectively, while that for the blue line M[(UO2)(O2)(OH)(OH2)]43− equals 1.18. E
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 5. (a) 3D plots of the difference between the total electrostatic potential and that of the independent M+ and ring fragments (computed at the TPSSH gas-phase level) mapped on the 0.02 au (electron/bohr3) isosurface of the total electronic density in (a) Li[12-crown-4]+, (b) Cs[12-crown-4]+, (c) Li[(UO2)(O2)(OH2)2]4+, (d) Cs[(UO2)(O2)(OH2)2]4+, (e) Li[(UO2)(O2)(OH)(OH2)]43−, and (f) Cs[(UO2)(O2)(OH)(OH2)]43−, displayed with the same scale ranging from blue regions (−499 kJ mol−1) in which electrons are withdrawn to the red regions (78.77 kJ mol−1) in which electrons are accumulated.
as illustrated by reaction 2. The interactions between acetonitrile and alkali ions is much weaker than those with water, a measure given by their donor numbers that rank the relative strengths of the interactions between different donor molecules and a given acceptor. These values are 33 and 14.1 for water and acetonitrile, respectively;27 the lower donor number for acetonitrile suggests the formation of inner-sphere complexes, M[crown ether]+, with direct coordination between the alkali ion and the crown ether oxygen atoms as in reaction 6.
For reactions in water (Table 2 and Table S10 in the Supporting Information) the calculated Gibbs energies of reaction are very different from the experimental values but they are in much better agreement with the values in acetonitrile, which presumably is a result of the much smaller solvation energy in this solvent. In complex formation reactions, chemical bonds are broken in the solvated M+ ions and new bonds are formed with the oxygen donors in the crown ether and the uranyl peroxides. The driving force for the replacement of oxygen donors from coordinated water with oxygen from the ligand is expected to be small, because it involves the same type of atom; in addition the high concentration of “free” water will favor a shift in the equilibrium in reactions 3−5 from right to left, resulting in the formation of an outer-sphere complex, [M(OH2)p]+[crown ether],
M(OH 2)p+ + crown ether → M[crown ether]+ + pH 2O
(6)
This is also confirmed by solution EXAFS data from Kemner et al.23 in acetonitrile and Harada and Okada22 in F
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry Table 1. Average Bond Energies, EM−O = (ΔEGP−ΔEdist)/n, Calculated from the Electronic Energy for the Gas-Phase Reaction (1), ΔEGP, and the Ligand Distortion Energies, ΔEdist, All in kJ mol−1 12-crown-4, n = 4
a
15-crown-5, n = 5
18-crown-6, n = 6
M+
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
Li Na K Rb Cs
−354.4 −257.6 −192.0 −171.2 −158.4
56.1 34.6 28.7 27.3 26.7 M[UO2(O2)(OH2)2]4+
−102.6 −73.0 −55.2 −49.6 −46.3
−415.0 −315.5 −236.5 −211.0 −195.0
52.4 36.5 29.4 27.2 25.9 M[UO2(O2)(OH2)2]5+
−93.5 −70.4 −53.2 −47.6 −44.2
M
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
Li Na K Rb Cs
−463.8 −363.7 −284.5 −258.0 −241.6
10.0 12.5 13.0 11.9 10.4
−118.4 −94.0 −74.4 −67.5 −63.0
−444.1 −384.1 −322.1 −293.7 −274.8
35.5 19.4 22.5 23.7 22.8
−95.6 −80.7 −68.9 −63.4 −59.5
−1456.0 −1339.8 −1224.3 −1180.0 −1156.5
118.6 89.9 71.8 69.8 66.6
−393.6 −357.4 −324.0 −312.4 −305.8
ΔEGP (kJ mol−1)
ΔEdist (kJ mol−1)
EM−O (kJ mol−1)
35.6a −344.4 23.0 −61.2 −295.8 16.0 −52.0 −259.2 15.6 −45.8 −236.4 16.3 −42.1 M[UO2(O2)(OH)(OH2)]43−
Only four oxygens coordinated.
Table 2. Enthalpy and Gibbs Reaction Energy in the Gas Phase (GP) and in Acetonitrile and Water Solvent at 298 K for Reactions between Alkali Ions and Crown Ethersa ΔH°(GP) (kJ mol−1) this study
ΔG°(CH3CN) (kJ mol−1) ΔG°(GP) (kJ mol−1)
other studies
QC
exptl
M + 12-crown-4 ether → M[12-crown-4 ether]+ −341.3 −12.9 no data −251.0 −18.6 −191.4 −30.4 −175.0 −35.4 −164.9 −41.7 M+ + 15-crown-5 ether → M[15-crown-5 ether]+ −401.0 −19.4 −305.5 −16.3 −25.7 −230.4 −29.6 −25.1 −209.5 −34.1 −196.6 −41.1 −17.1 M+ + 18-crown-6 ether → M[18-crown-6 ether]+ −370.3 6.0 −335.6 −18.8 −24.5 −287.3 −35.1 −32.5 −255.7 −33.0 −28.5 −234.6 −38.3 −27.4
ΔG°(water) (kJ mol−1) QC
exptl
−5.6 −13.4 −26.7 −32.2 −38.9
very weak complexes
+
Li+ Na+ K+ Rb+ Cs+
−340.9 −246.2 −181.8 −161.4 −148.8
−378 ± 51b −247.0 ± 12.7c −184.2 ± 17.4c −153.0 ± 9.8c −138.2 ± 8.8c
Li+ Na+ K+ Rb+ Cs+
−400.7 −304.0 −226.0 −201.1 −185.5
−411.3d −299.1 ± −217.9 ± −176.8 ± −160.5 ±
Li+ Na+ K+ Rb+ Cs+
−359.8 −328.7 −281.9 −247.1 −224.6
−399.2f −335.9;f −299.2;f −243.1;f −203.8;f
15.5e 10.6e 9.7e 9.6e
300 235 192 170
± ± ± ±
19g 13g 13g 9g
−10.7 −9.7 −25.0 −30.0 −37.5 14.8 −11.3 −29.0 −27.6 −33.5
−3.6 −4.3 −4.7
−4.6 −11.6 −8.9 −5.7
a The change of standard state from a molar volume of 22.4 L in gas-phase to 1 L in the solvent is accounted for in ΔGsolv and ΔG°(acetonitrile). For comparison, the gas-phase enthalpies at 298 K measured by Ray et al.12b and Armentrout et al.13 or computed by Hill et al.12d,e and Glendening et al.12a are given in the column “other studies”. The experimental Gibbs energies of reactions are taken from Tables S10 and S11 in the Supporting Information. bExperimental value from Ray et al.12b cExperimental values from Armentrout et al.13a dMP2/aVTZ values from Hill et al.12e eExperimental values from Armentrout et al.13b fMP2 values from Glendening et al.12a gExperimental values from More et al.13c
Table 3. Gibbs Energies and Entropies of Reaction in the Gas Phase and in a Water COSMO Model, for Formation of Li[12-crown-4]+ with Different Numbers of Coordinated Water, Where the Change of Standard State from the Molar Volume of 22.4 L in the Gas Phase to 1 L in Solution Is Accounted for reaction + 12-crown-4 → Li[12-crown-4] + 4H2O + 12-crown-4 → Li(OH2)[12-crown-4]+ + 3H2O Li + 12-crown-4 → Li[12-crown-4]+; Li(OH2)4+ Li(OH2)4+ +
+
ΔG(GP) (kJ mol−1)
ΔS(GP) (kJ mol−1 K−1)
ΔG(water) (kJ mol−1)
ΔS(water) (kJ mol−1 K−1)
−26.2 −53.6 −341.3
289.3 186.5 1.2
−79.8 −52.5 −5.6
209.6 133.4 27.7
methanol (cf. Table S1 in the Supporting Information). Ozutsumi et al.28 used large-angle X-ray scattering (LAXS) to study the coordination of M[18-crown-6]+ complexes in very concentrated aqueous solutions (50% of the solvent water is
replaced by the complex) and tested different models, but with no firm conclusions on the structures. We also note that all experimental data for M[crown ether]+ complex formation reactions given in Tables S10 and S11 in the Supporting G
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
can achieve is qualitative statements on how the chemistry of these systems vary between different alkali ion complexes.
Information have negative entropies of reaction, suggesting that there are no, or only small changes in the number of coordinated water released, an indicator that outer-sphere complexes are formed. A detailed discussion of the thermodynamic characteristics of inner- and outer-sphere complexes is given by Ahrland,29 where he points out that negative entropies of reaction are strong indicators for the formation of outersphere complexes, as exemplified by the reactions in Table 3. Comparison between experimental and QC data for reactions in solvents should be made using Gibbs energies and entropies of reaction and not the corresponding enthalpies of reaction. In order to minimize solvent effects, we have made a comparison of the experimental and QC data for reactions in acetonitrile, which demonstrates that the Gibbs energies of reaction agree within 10 kJ mol−1 (Table 2) but that they do not describe the observed alkali ion selectivity, with the increase in stability from Na[18-crown-6]+ to K[18-crown-6]+ and then the decrease in stability for the corresponding Rb and Cs complexes. This is consistent with the QC observation of a general trend of decreasing in M−O bond strength in M[18crown-6]+ ether complexes from Li to Cs, but where the decrease between Na and K is smaller than the expected value because of 0.40 Å longer than normal Na−O distance (Figure 2c and Table S1 in the Supporting Information). The increase in stability from Na to K is significant, but the decrease from K to Cs is not very large. Because of the small changes in Gibbs energy, at most between 5 and 10 kJ mol−1, comparable to the accuracy expected in QC calculations, it is not surprising that the selectivity features can only be described quantitatively; nevertheless, the QC data provide strong support for the formation of inner-sphere complexes. In the aqueous uranyl peroxide systems, no free rings [UO2(O2)(OH)]nn− have been identified, only the precursor UO2(O2)(OH)(aq)−, and for this reason it is not possible to make a direct comparison between QC data and the equilibrium constants for reaction 7 reported in Table 4; the best we
M+ + 4[UO2 (O2 )(OH)(OH3)]− → M[UO2 (O2 )(OH)(OH 2)]4 3 −
(7)
The computed Gibbs energies of reaction are much more negative than those for the experimental values, but this is a result of problems to obtain reliable solvation energies for species with a high negative charge using the COSMO model, which can reach 350 kJ mol−1 for triply negatively charged species.30 The similar size of the complexes should result in similar solvation energies, which means that the trends can be compared with those observed experimentally; the agreement is reasonably good, at most within 5 kJ mol−1, if we assume a systematic error in the QC values of 250 kJ mol−1. Synthesis of Crown Ethers and Uranyl Peroxide Rings and Clusters. The synthesis of crown ethers from different precursors always takes place in an organic solvent, and the yield is strongly dependent on the presence of alkali ions acting as templates for the ring formation reactions.1a A similar effect is also noticed in the formation of uranyl peroxide rings in water, where small cations such as Li+ result in the formation of a four-membered rings Li[UO2(O2)(CO3)]47− and Na+ and K+ in the formation of Na/K[UO2(O2)(CO3)]59− and N(CH3)4+ in a mixture of complexes with five- and six-membered rings:31 that is, small cations promote the formation of small rings and large cations the formation of large rings.
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CONCLUSIONS Experimental structures and gas-phase reaction energies have been used to calibrate the quantum chemical methods used. The agreement is satisfactory, and on the basis of this observation we have analyzed structure details, chemical bonding, and reaction energies in water and acetonitrile solvents for alkali complexes between crown ethers and uranyl peroxide rings. The geometries of the different alkali complexes are similar, with all
Table 4. Electronic Reaction Energies ΔE, Enthalpies ΔH, and Gibbs Energies ΔG of Reaction in kJ mol−1 for the Formation of M[UO2(O2)(OH2)2]4+ and M[UO2(O2)(OH)(OH2)]43− from the Interaction between Alkali Ions and the Four-Membered Uranyl Peroxide Rings in the Gas Phase in a COSMO Water Solventa alkali ion
ΔG(GP) (kJ mol−1)
ΔE(water) (kJ mol−1)
ΔH(water) (kJ mol−1)
Li Na K Rb Cs
−438.4 −350.6 −280.4 −258.0 −244.4
Li Na K Rb Cs
−1444.5 −1336.9 −1226.8 −1187.4 −1166.9
Li Na K Rb Cs
−818.8 −711.3 −601.1 −561.8 −541.3
ΔG(water) (kJ mol−1)
M + [UO2(O2)(OH2)2]4 → M[UO2(O2)(OH2)2]4 −35.0 −23.7 −17.5 −37.2 −28.2 −32.0 −47.1 −39.1 −50.9 −47.9 −40.1 −55.8 −53.4 −45.8 −64.2 M+ + [UO2(O2)(OH)(OH2)]43− → M[UO2(O2)(OH)(OH2)]43− −49.2 −39.5 −45.6 −42.2 −33.8 −47.2 −46.6 −38.7 −57.0 −45.2 −37.5 −60.5 −50.5 −42.9 −68.8 M+ + 4[UO2(O2)(OH)(OH2)]− → M[UO2(O2)(OH)(OH2)]43− −526.3 −500.2 −307.8 −519.3 −494.4 −309.5 −523.7 −499.4 −319.2 −522.3 −498.1 −322.7 −527.6 −503.6 −331.0 +
ΔG(exptl) (kJ mol−1)
log10 K
−57.3 ± 2.3 −64.2 ± 1.7 −65.9 ± 2.0
10.0 ± 0.4 11.2 ± 0.2 11.5 ± 0.3
+
Thermodynamic data computed for the reaction in the gas phase and in water solvent for the reaction M+ + 4[UO2(O2)(OH)(OH2)]− → M[UO2(O2)(OH)(OH2)]43− are compared with experimental equilibrium constants and free energies of reaction for M[UO2(O2)(OH)(OH2)]43− in aqueous solutions at 25 °C, from Zanonato et al.10 a
H
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
Inorganic Chemistry alkali ions coordinated outside the crown ether and [UO2(O2)(OH2)2]n rings, with normal M−O bond distances when the cavity sizes are too small in comparison to the M+ ionic radii. When the cavity radius is much larger than the M+ radii, the M−O distances are longer than normal, or M+ is only coordinated to some of the oxygen donors, but now with normal distances. Analysis of the M−O bonds using reaction energies in the gas phase reveals that they are predominantly electrostatic with a significantly larger bond strength, about 20 kJ mol−1, for the M−Oyl bonds than for the M−O bonds in the crown ethers. The M−O bonds become progressively weaker from Li to Cs, which is consistent with their electrostatic origin. The bond energy depends on the M−O distance, but for a given alkali ion it is approximately the same, provided there are no geometrical constraints. Complex formation reactions in the gas phase, water, and acetonitrile have been compared using QC and compared with experimental information. The agreement is unsatisfactory for reactions in water, which is related to the poor performance of the COSMO model in this strongly coordinating solvent. However, entropy calculations provide a strong support for the formation of outer-sphere complexes, [M(OH2)n]+[crown ether]. The QC and experimental data for reactions in acetonitrile are in much better agreement with experiment, in general within about 10 kJ mol−1. The complexes are much stronger than those in water, and this fact together with EXAFS information demonstrates that they are of inner-sphere type, M[crown ether]+, in nonaqueous systems such as acetonitrile.
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ACKNOWLEDGMENTS
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REFERENCES
The authors would like to thank Pier Luigi Zanonato, Plinio Di Bernardo and Zoltán Szabó for fruitful discussions.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02584. Geometries of the various complexes between alkali ions and crown ether and uranyl peroxide rings, further details on adjustments of alkali ion cavity radii for the COSMO calculations and on the relative isomers of M[18-crown-6]+, population and energy decomposition analysis, and computed and experimental association constants for the crown ether and uranyl peroxide rings (PDF) Quantum chemical Cartesian coordinates (ZIP)
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Article
AUTHOR INFORMATION
Corresponding Authors
*E-mail for V.V.:
[email protected]. *E-mail for I.G.:
[email protected]. ORCID
Valérie Vallet: 0000-0002-2202-3858 Author Contributions §
V.V. and I.G. contributed equally.
Funding
The computations were performed on the PhLAM cluster financed by the CaPPA project (Chemical and Physical Properties of the Atmosphere) that is funded by the French National Research Agency (ANR) through the PIA (Programme d’Investissement d’Avenir) under contract “ANR-11LABX-0005−01” and by the Regional Council “Hauts de France” and the “European Funds for Regional Economic Development” (FEDER). Notes
The authors declare no competing financial interest. I
DOI: 10.1021/acs.inorgchem.7b02584 Inorg. Chem. XXXX, XXX, XXX−XXX
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