Analysis with the Quantum Theory of Atoms in Molecules

The electronic structure of the complexes considered in this chapter has been investigated in detail using the Quantum Theory of Atoms in Molecules to probe the electron density. Tables 4.2 presents various properties of the electron density at the U-O bond critical points (BCPs), as well as delocalisation indices for both the PBE and the B3LYP xc-functional in the gas phase, and Table 4.3 presents the same properties for the solvated structures. Looking first at the U-O bonds, it can be seen that the large values of  and large negative values of the energy density, H, found at the U-O BCP in [UO2(BTP2)]²⁺, UO2IA and UO2IA′ complexes are indicative of a typical covalent interaction (although the fact that ² BCP is positive is atypical of a covalent bond within the QTAIM definition), as has been found previously^394,396.

Further support for this comes from the high degree of electron delocalisation between the U and O ions. The strong similarity of the topological properties considered here, in addition to the very similar bond lengths presented in Table 4.1, allow a prediction that the equatorial coordination environments of [UO2BTP2]²⁺, UO2IA and UO2IA

Table 4.2: QTAIM–derived properties of the U-O bond of the three complexes considered in this study, derived from the gas phase electron densities obtained using both xc-functionals, PBE and B3LYP. BCP = electron density at BCP. ²BCP = Laplacian of BCP. HBCP = Energy density at BCP. (U,O) = delocalisation index between U and O centres. All reported quantities are in atomic units. ^* Average over both U-O bonds.

126

Table 4.3: QTAIM–derived properties of the U-O bond of the three complexes considered in this study, derived from solvated electron densities obtained using both xc-functionals, PBE and B3LYP. All reported quantities are in atomic units. ^* Average over both U-O bonds.

Tables 4.4 and 4.5 present various topological properties of the U-N bond critical points, with Table 4.4 containing the gas phase data for both functionals, and Table 4.5 containing the solvated data. When the U-N bonds are considered, it is found that, as expected, values of 𝜌_BCP are significantly lower than for the U-O bonds in all Table 4.4: QTAIM–derived properties of the U-N bond of the three complexes considered in this study derived from gas phase electron densities obtained using both functionals. BCP = electron density at BCP. ²BCP = Laplacian of BCP. HBCP = Energy density at BCP. (U,N)

= delocalisation index between U and N centres. All reported quantities are in atomic units (a.u.).

127 The small magnitude of 𝜌_BCP and the near-zero (but negative) energy densities, indicate that the U-N interactions are chiefly of ionic character, as might be expected, with an amount of electron sharing which is of similar character between complexes.

Shorter U-N bonds are found to correspond to larger values of 𝜌_BCP and greater degrees of electron sharing. This is supportive of the intuitive view that shorter, stronger bonds exhibit a greater degree of covalency. When the U-N bonds of IA and IA′ are considered, differences in the QTAIM and structural parameters due to choice of xc-functional or inclusion of solvation effects are minor compared to the effects Table 4.5: QTAIM–derived properties of the U-N bond of the three complexes considered in this study derived from complexes optimised with both functionals with the inclusion of solvation effects. All reported quantities are in atomic units.

Choice of functional appears to have consistent, small, but non-negligible effects on the QTAIM parameters. When B3LYP is used, there is an appreciable increase in 𝜌_BCP in the U-O bond of all complexes, and a small reduction in delocalisation. There is a small reduction in all properties measured at the U-N BCPs with B3LYP compared to PBE. The implication here is that B3LYP, comprising a proportion of exact Hartree-Fock exchange, leads to increased electron localisation as has been seen previously⁶¹. The effect of solvation on the topological parameters amounts to a slight reduction in the amount of electron sharing in the U-O interaction compared to the gas phase, with a commensurate minor increase in electron sharing in the U-N bonds.

128 The U-O bond is seen to lengthen upon complexation in all cases. This implies that whilst the U-N interaction is weak, with a small covalent component, there is a non-negligible effect on the U-O interaction. This effect can be further investigated by considering QTAIM parameters of the isolated uranyl unit and comparing them to those of the uranyl unit after complexation. This data is presented in Tables 4.6, 4.7, 4.8 and 4.9 for the PBE structures optimised in the gas phase, the B3LYP structures optimised in the gas phase, the PBE structures optimised with DCM, and the B3LYP structures optimised with DCM, respectively. The two additional parameters defined in Chapter 3 are used to aid analysis of the changes that occur upon complexation:

𝑁(UO₂) = 𝑁(U) + ∑ 𝑁(O_𝑖)

𝑖=1,2

(𝐸𝑞. 4.1)

𝜆(UO₂) = 𝜆(U) + ∑ [𝜆O_𝑖+ 𝛿(U, O_𝑖)]

𝑖=1,2

+ 𝛿(O, O) (𝐸𝑞. 4.2)

Where N(UO2) gives the uranyl electronic population (from which the charge q(UO2) can be derived) and (UO2) the number of electrons localised on the uranyl unit. In the case of isolated UO22+, N(UO2) = (UO2) = 106.

Table 4.6: QTAIM–derived properties of isolated and complexed uranyl. Isolated uranyl simulated at the complexed geometry.  gives the difference between isolated and complexed values. *Values averaged over both O centres. Properties derived from PBE/def(2)-TZVP densities. All quantities are in atomic units.

[UO2(BTP)2]²⁺ UO2IA UO2IA

UO22+ Complex  UO22+ Complex  UO22+ Complex  N(U) 88.92 89.21 0.28 88.92 89.16 0.23 88.94 89.17 0.24 N(O) 8.54 8.81 0.27 8.54 8.83 0.29 8.53 8.85 0.31 N(UO2) 106 106.82 0.82 106 106.81 0.81 106 106.86 0.86

(U) 86.61 86.14 -0.47 86.61 86.18 -0.43 86.62 86.14 -0.48

(O) 7.31 7.62 0.31 7.31 7.67 0.36 7.31^* 7.69^* 0.38

(UO2) 106 105.47 -0.53 106 105.64 -0.36 106 105.56 -0.44

(U,O) 2.32 1.99 -0.33 2.32 2.01 -0.31 2.32^* 1.97^* -0.35

129 Table 4.7: QTAIM–derived properties of isolated and complexed uranyl. Isolated uranyl simulated at the complexed geometry.  gives the difference between isolated and complexed values. *Values averaged over both O centres. Properties derived from B3LYP/def(2)-TZVP/SARC-TZVP gas phase densities. All quantities are in atomic units.

[UO2(BTP)2]²⁺ UO2IA UO2IA Table 4.8: QTAIM–derived properties of isolated and complexed uranyl. Isolated uranyl simulated at the complexed geometry.  gives the difference between isolated and complexed values. *Values averaged over both O centres. Properties derived from PBE/def(2)-TZVP/SARC-TZVP solvated densities. All quantities are in atomic units.

Table 4.9: QTAIM–derived properties of isolated and complexed uranyl. Isolated uranyl simulated at the complexed geometry.  gives the difference between isolated and complexed values. *Values averaged over both O centres. Properties derived from B3LYP/def(2)-TZVP/SARC-TZVP solvated densities. All quantities are in atomic units.

[UO2(BTP)2]²⁺ UO2IA UO2IA

130 The data in Tables 4.6 - 4.9 give further insight into the effect of equatorial complexation on U-O bonding, which can be summarised as in increase in the ionic interaction commensurate with a decrease in the covalent interaction. Looking first at the calculated differences in properties upon complexation, it can be seen that the three complexes exhibit strong qualitative similarities. The lengthening of the U-O bond upon complexation can be explained by three factors. Firstly, approximately 0.8 – 0.9 a.u of electronic charge for the PBE data and approximately 0.7-0.8 a.u for the B3LYP data, with these values being slightly greater when the effects of solvation are included, is donated onto the uranyl unit in each complex. This donated charge is split into approximately equal amounts (0.2 - 0.3 a.u.) which populate the uranium and each of the oxygen ions. This additional electronic charge on all ions reduces the electrostatic attraction between them, since the interaction is between a negative oxygen ion and a positive uranium. Secondly, the electronic localisation on each ion in the uranyl unit can be considered, to a first approximation, to dictate the degree of ionic interaction. In all complexes, electron localisation is observed to increase on each oxygen centre, while decreasing on the uranium centre, implying a more ionic U-O interaction upon complexation. Finally, a corresponding reduction in (U,O) upon complexation indicates a reduction in the covalent interaction. Combined, these factors explain the lengthening, and hence weakening, of the U-O interaction in the complexes.

Analysis of the quantities N(UO2) and (UO2) gives further insight into the U-N interactions upon complexation.. Whilst N(UO2) increases by approximately 0.8–0.9 a.u. upon complexation, (UO2) reduces to a value below that of the isolated dication.

This reduction is more pronounced in the BTP complex (0.53 a.u. compared to 0.36 a.u. in UO2IA and 0.44 a.u in UO2IA). This is consistent with the studies of uranyl coordination by nitrogen donors presented in Chapter 3. Since (UO2) takes into account U-O delocalisation, any differences between N(UO2) and (UO2) must therefore be due to electron sharing between the uranyl unit and the ligand, i.e.

covalency in the U-N bonds. When considering the data derived from the electron density optimised using the PBE xc-functional in the gas phase, this difference is 1.35 a.u., 1.17 a.u. and 1.30 a.u. for the BTP, IA and IA complexes, respectively, suggesting a degree of electron sharing in the U-N bonds consistent with that indicated by the U-N topological QTAIM parameters 𝜌_BCP and H. Since the increase in electron

131 localisation on the oxygen ions, (O), is approximately equal in magnitude but opposite in sign to the decrease in electron sharing in the U-O bond, (U,O) (+0.33 vs -0.33, +0.36 vs -0.31 and +0.38 vs -0.35 a.u. in the BTP, IA, and IA complexes, respectively), it can be concluded that the increase in (O) is almost exclusively due to donation from the U-O bond. The reduction in electron localisation on the uranium centre, (U), is therefore almost entirely due to electron sharing in the U-N bond. Put simply, the ~0.8-0.9 a.u. of charge donated upon complexation is almost entirely donated into the U-N bonds, and also induces a donation of ~ 0.4 - 0.5 a.u. of charge from the uranyl unit itself into the U-N bonds. This cannot be interpreted as

‘traditional’ back-bonding due to the formal 5f⁰6d⁰ occupation of U(VI), although there is still unambiguous evidence here of a significant contribution from the uranium atom to the equatorial U-N bonds.