Structural Data

Figure 6.5 shows the optimised geometry for the NpO2-cyclo[6]pyrrole complex optimised using the PBE xc-functional in the gas phase. No major structural differences were found between the uranyl, neptunyl and plutonyl complexes, so the neptunyl complex only is shown (for the uranyl complexes, see Figures 5.2 and 5.3,

194 Chapter 5). Table 6.21 shows averaged An-N and An-O bond lengths in cyclo[6]pyrrole complexes optimised using the PBE and B3LYP xc-functionals in the gas phase. In Chapter 5, the uranyl cyclo[6]pyrrole complex was compared to crystallographic data¹⁸⁷, with which excellent agreement was found. In general, there appears to be a small decrease in average An-N bond lengths as one moves from U to Np. Moving from the Np to the Pu complex using the PBE xc-functional in the gas phase, the average Pu-N bond length is found to be 0.003Å longer than the average Np-N bond length. It ought to be stressed that greater differences in An-Np-N bond length are induced by choice of functional than by changing the actinide species, and that all optimised complexes are very similar in terms of their An-N bonds. Calculated An-O bond lengths, on the other hand, decrease by up to ~0.1 of an Angstrom moving from U to Np, however moving from the Np to the Pu species optimised with the PBE xc-functional in the gas phase, where the Pu-O bond is in fact 0.001 Å longer than the Np-O bond. Lengthening of the An-O bond relative to the uncoordinated actinyls is most pronounced in the uranyl complexes, suggesting that the uranyl unit may be most affected by complexation.

U Np Pu

PBE B3LYP PBE B3LYP PBE B3LYP

𝑟̅̅̅̅̅̅̅̅_An−N 2.532 2.536 2.523 2.532 2.526 2.529

𝑟_An−O 1.799 1.781 1.772 1.758 1.773 1.745

Δ𝑟_An−O 0.088 0.085 0.063 0.067 0.076 0.068

Table 6.21: Average An-N and An-O bond lengths and Δ𝑟_An−O, the difference between the coordinated and uncoordinated An-O bond length, all in Å for complexes with the cyclo[6]pyrrole ligand, optimised with the PBE and B3LYP functionals in the gas phase

Figure 6.5: Optimised NpO2-cyclo[6]pyrrole complex, generated from data obtained using the PBE xc-functional in the gas phase.

195 6.3.4.2. QTAIM - Topological and Integrated Properties

Tables 6.22 and 6.23 shows topological QTAIM parameters for An-N bonds in cyclo[6]pyrrole complexes optimised with the PBE and B3LYP xc-correlation functionals in the gas phase. Tables 6.24 and 6.25 shows topological parameters of the An-O bonds for the same complexes.

First, covalency in the An-N bonds will be discussed for the calculations omitting spin constraint. As the central ion is changed from U to Np, it is noticed that all indicators point to the An-N bonds being very similar in terms of covalent character. There is some dependence on which xc-functional is used: for complexes optimised using the PBE xc-functional without spin constraint, the sum of ρBCP and HBCP point to the An-N bond character of the uranyl and neptunyl complexes being almost identical, while use of the B3LYP xc-functional appears to induce differences in ρBCP and HBCP of

~0.01 a.u. between the uranyl and neptunyl complexes, although it is apparent that the character of these bonds is very alike irrespective of which xc-functional is used. With both xc-functionals, without spin constraint, the average value of ²𝜌_An−N is approximately a thousandth of an a.u higher in the neptunyl complex than the uranyl complex, a difference of the order of 1%. There is a slightly larger increase in the value of ²𝜌_An−N between the neptunyl and plutonyl complexes. There is a notable increase in An-N delocalisation in the neptunyl complex compared to the uranyl complex, which is most significant when the PBE xc-functional is used. This may be an effect of the self-interaction error which is more pronounced with PBE than with a hybrid xc-functional such as B3LYP where the presence of exact exchange partially cancels the spurious self-interaction^343,373. Use of the B3LYP xc-functional results in slightly lower values of ρBCP and HBCP in the NpO2 complexes compared with UO2, which is at odds with the delocalisation data. Moving from Np to Pu, ρBCP and HBCP indicate a reduction in An-N covalency for the plutonyl complex compared to the uranyl and neptunyl complexes, while 𝛿(Pu,N) is very slightly (an increase of less than 1%) larger than 𝛿(U,N).

Spin constraint were subsequently applied and a single point energy calculation was run at the geometry previously optimised without spin constraint. When the PBE xc-functional was used, ∑𝜌_An−N was found to increase slightly compared to the

196 unconstrained systems, with the effect being most significant for the neptunyl complex. When the PBE xc-functional was used, ∑𝜌_An−N was found to increase more significantly compared to the unconstrained system for the neptunyl complex, whereas a slight decrease is calculated for the plutonyl complex. The average value of the laplacian of the electron density at the An-N BCP is slightly reduced by constraining the spin, such that for both the neptunyl and plutonyl complexes with both xc-functionals, ²𝜌_An−N is lower than the corresponding value in the uranyl complex. As with the isoamethyrin complexes, the magnitude of the energy density increases when spin constraint are used. When the delocalisation indices are considered, the neptunyl complex is the most significantly affected when the spin constraint is used, increasing by ~ 0.3 a.u. when the PBE xc-functional is employed and ~ 0.4 a.u. when the B3LYP xc-functional is employed. In the plutonyl complex with both xc-functionals, there are small decreases in the values of the delocalisation indices when the spin is constrained, but these changes are an order of magnitude smaller than those induced by the spin constraint in the neptunyl system. Overall, it appears that the inclusion of spin constraint seems to have a greater effect on topological parameters of the neptunyl complex than the plutonyl complex. This will be investigated further when the integrated properties and spin densities are analysed, although it is likely that full reoptimisations are needed in this case in order to fully rationalise these data.

xc-functional U Np Pu

∑ 𝜌_An−N Constrained 0.350 0.350 0.330

Unconstrained - 0.358 0.333

²𝜌_An−N Constrained 0.149 0.150 0.159

Unconstrained - 0.138 0.147

∑ 𝐻_An−N Constrained -0.042 -0.039 -0.030

Unconstrained - -0.058 -0.047

∑ 𝛿(An − N) Constrained 2.143 2.343 2.184

Unconstrained - 2.647 2.179

Table 6.22: QTAIM parameters for the An-N bond in the cyclo[6]pyrrole complexes, given as average or total values, in a.u. obtained using the PBE xc-functional, with and without spin constraint.

197

xc-functional U Np Pu

∑ 𝜌_An−N Constrained 0.344 0.337 0.334

Unconstrained - 0.350 0.330

²𝜌_An−N Constrained 0.152 0.154 0.161

Unconstrained - 0.136 0.149

∑ 𝐻_An−N Constrained -0.040 -0.036 -0.030

Unconstrained - -0.056 -0.047

∑ 𝛿(An − N) Constrained 1.970 1.985 1.973

Unconstrained - 2.342 1.962

Table 6.23: QTAIM parameters for the An-N bond in the cyclo[6]pyrrole complexes, given as average or total values, in a.u. obtained using the B3LYP xc-functional, with and without spin constraint.

When the An-O bonds are considered (Tables 6.24 and 6.25) without spin constraint, it is noticed that there is an increase in covalency as defined by QTAIM moving across the series from U to Pu. This is in keeping with previous studies⁴¹².

Differences between the values in Tables 6.24 and 6.25 and those of the uncomplexed actinyls indicate that reduction of covalent character in the An-O bond occurs upon complexation. When the unconstrained neptunyl and plutonyl systems are compared to the uranyl system, it appears that uranyl is the most affected by complexation with this ligand. This can perhaps be attributed to the larger ionic radius of uranium(VI) compared to neptunium/plutonium(VI). The An-N QTAIM parameters for the unconstrained systems suggest that the uranyl and neptunyl complex are very similar to one another while the plutonyl complex demonstrates less An-N covalency, in contrast with structural data which suggests that the largest differences are to be found between the uranyl complex and the neptunyl/plutonyl complexes.

When the spin constraint is applied, a reduction in the value of 𝜌_An−O is found with both xc-functionals for both the neptunyl and plutonyl complexes. This reduction is slight and maintains the trends from the unconstrained calculations: Np > Pu > U (Pu

> Np > U) when the PBE (B3LYP) xc-functional is employed. The laplacian is increased by the application of spin constraint, such that it increases in the order U >

Np > Pu regardless of xc-functional. The energy density is reduced when spin constraint are applied, by approximately the same amount as for the isoamethyrin

198 systems. Topological parameters, as expected, still indicate a reduction in covalent character upon complexation. Overall, the topological properties of the An-O bonds seem less significantly affected than those of the An-N bonds in the cyclo[6]pyrrole complexes.

PBE U Np Pu

𝜌_An−O Constrained 0.290 0.306 0.303

Unconstrained - 0.301 0.295

²𝜌_An−O Constrained 0.320 0.319 0.349

Unconstrained - 0.427 0.430

𝐻_An−O Constrained -0.253 -0.278 -0.268

Unconstrained - -0.254 -0.240

Table 6.24: QTAIM parameters for the An-O bond in the cyclo[6]pyrrole complexes measured in a.u., obtained using the PBE xc-functional, with and without spin constraint.

B3LYP U Np Pu

𝜌_An−O Constrained 0.304 0.318 0.327

Unconstrained - 0.312 0.318

²𝜌_An−O Constrained 0.274 0.271 0.276

Unconstrained - 0.367 0.369

𝐻_An−O Constrained -0.281 -0.301 -0.313

Unconstrained - -0.275 -0.280

Table 6.25: QTAIM parameters for the An-O bond in the cyclo[6]pyrrole complexes measured in a.u., obtained using the B3LYP xc-functional, with and without spin constraint.

Next, integrated properties of the electron density are examined. Tables 6.26 and 6.27 contain atomic populations for complexes optimised using the PBE and B3LYP xc-functionals, respectively. Tables 6.28 and 6.29 contain localisation and delocalisation data for the actinyl units in cyclo[6]pyrrole complexes optimised using PBE and B3LYP xc-functionals, respectively.

Looking first at the atomic populations obtained using the PBE xc-functional with both the spin-unconstrained and spin-constrained approach in Table 6.26, it can be seen for the complexes optimised using the PBE xc-functional in the gas phase without spin constraint, that upon complexation, a total of approximately 0.85-0.95 a.u. of charge is donated into the actinyl unit. This is reduced to 0.80-0.85 when the data obtained using the B3LYP xc-functional is considered (Table 6.27). When the spin constraint

199 are applied, the amount of charge donated into the neptunyl unit drops to 0.78 (0.71) a.u. when the PBE (B3LYP) xc-functional is employed, while there is a slight increase in the amount of charge donated into the plutonyl unit, 0.97 (0.84) a.u. with the PBE (B3LYP) xc-functional. As with the topological properties, it is the neptunyl complexes which are most significantly affected by the spin constraint.

U Np Pu spin-constrained and spin unspin-constrained approach for AnO2-cyclo[6]pyrrole

U Np Pu

Table 6.27: Atomic populations obtained using the B3LYP xc-functional with both the spin-constrained and spin unspin-constrained approach for AnO2-cyclo[6]pyrrole

Moving on to the actinyl localisation indices in Table 6.28 and 6.29, it is apparent that for all complexes, with both xc-functionals, and irrespective of spin constraint, there is an increase in localisation on the oxygen centres which is approximately equal in magnitude to the reduction of charge delocalised in all An-O bonds. The actinide centres themselves become more positively charged, and the total localisation, compared to the uncoordinated actinyls, decreases upon complexation by 0.5-0.9 a.u.

when the spin is not constrained, suggesting in all cases, substantial delocalisation between the actinyl unit and the ligand. Differences in the Pu systems induced by the application of spin constraint are minimal, however spin constraint significantly reduces the localisation on the Np centre compared to that of the unconstrained system.

200 λ(NpO2) for this system when the spin constraint is applied is ~ 0.45 (0.70) a.u. lower than for the unconstrained system when the PBE (B3LYP) xc-functional is employed, with λ(An), the value of which can be used to infer an oxidation state, suggesting a number of electrons localised on the neptunium centre closer perhaps to Np(VII) than Np(VI). This is particularly pronounced where the B3LYP xc-functional is employed.

This will be further investigated when the spin densities and spin populations are

When the unconstrained data is considered, N(AnO2) in particular is seen to increase by ~1 moving from U to Pu, consistent with the increase in the number of electrons formally present in the actinyl. This is not the case for λ(NpO2) where the constrained