Uranium(III)-carbon multiple bonding supported by arene δ-bonding in mixed-valence hexauranium nanometre-scale rings

Despite the fact that non-aqueous uranium chemistry is over 60 years old, most polarised-covalent uranium-element multiple bonds involve formal uranium oxidation states IV, V, and VI. The paucity of uranium(III) congeners is because, in common with metal-ligand multiple bonding generally, such linkages involve strongly donating, charge-loaded ligands that bind best to electron-poor metals and inherently promote disproportionation of uranium(III). Here, we report the synthesis of hexauranium-methanediide nanometre-scale rings. Combined experimental and computational studies suggest overall the presence of formal uranium(III) and (IV) ions, though electron delocalisation in this Kramers system cannot be definitively ruled out, and the resulting polarised-covalent U = C bonds are supported by iodide and δ-bonded arene bridges. The arenes provide reservoirs that accommodate charge, thus avoiding inter-electronic repulsion that would destabilise these low oxidation state metal-ligand multiple bonds. Using arenes as electronic buffers could constitute a general synthetic strategy by which to stabilise otherwise inherently unstable metal-ligand linkages.


Supplementary Tables
Supplementary Table 1

General Procedures
All manipulations were carried out using standard Schlenk and glove box techniques under an atmosphere of dry nitrogen. Toluene was dried by passage through an activated alumina tower and benzene was dried by refluxing over potassium. Both solvents were stored over potassium mirrors and degassed before use. Deuterated solvents were distilled from potassium, degassed by three freeze-

Choice of Model Systems
Geometry optimisations were only performed for the case where no ligand truncation is made, since the purpose of truncating the ligand was to study 3 and 4 where geometry optimisation is intractable for the  Figure S5 for a description of model systems and their labels.

Complex 2
Geometry optimisations were performed for 2 at the PBE/def-TZVP 6,7 level of theory as implemented in the Turbomole software package. 8 For uranium and iodide, the associated small core def-ECP was used to account for scalar relativistic effects. 9 The resolution of the identity (RI) approximation was employed when computing the two-electron integrals. 7,10 The optimised geometry was confirmed as local minima by means of harmonic vibrational analysis. While lower spin states were also explored, only the high spin S = 2 state was optimised as lower spin states suffered from spin contamination.

All Models
Single point energy calculations were performed using the same level of theory as 2 for the high spin state for all of the models. High spin for the models of 2 is S = 2, while the high spin for models of 3 and 4 is S = 9/2. Natural population analysis was performed to compute charges and molecular orbitals were plotted and shown below for select systems (Figures S17 to S24)

Complexes 3' and 4'
Additionally, Nalewajski-Mrozek bond orders [11][12][13][14][15] and MDC-q charges 16 were calculated using the Amsterdam Density Functional (ADF) software package 17 with density functional theory (PBE/TZ2P) 18,19 for 3' and 4'. Note that for both sets of DFT calculations, only the high spin state is reported since lower spin states all suffered from spin contamination. A small core was used in the calculations along with the zero-order regular approximation (ZORA) [20][21][22] to include scalar relativistic effects.

Computational Details
Cholesky decomposition and local exchange screening were used in all of the CASSCF/CASPT2 and RASSCF calculations to significantly reduce the cost of computing the two-electron integrals, 23 for each SCF iteration was too demanding; however, CASPT2 calculations were performed on a smaller active space with (9e,11o) (only including the unpaired electrons in the 5f orbitals) for the S = 1/2 to the S = 9/2 spin states.

Active Space Choice
Perhaps the most important choice in a CASSCF calculation is the active space. Ideally, all of the valence orbitals would be included; however, in most cases the inclusion of ligand orbitals in the active space is not required to properly describe the ground state of organometallic compounds. For actinidecontaining systems in higher oxidation states, only the 5f orbitals on the uranium centre must be included in the active space (e.g. including the 6d and 7s orbitals is not required). 34 Therefore, the best active space for 2 includes molecular orbitals that are linear combinations of the 5f orbitals on both metal centres resulting in an active space of eight electrons in fourteen orbitals, denoted (8e,14o). This would translate to an active space with 42 orbitals for 3 and 4, far beyond the limits of this method.
Therefore, we explored smaller active spaces to determine the minimum space required to best address our initial question of the nature of bonding within the U-arene-U group and the number of unpaired electrons in each arene group in 3 and 4. By removing orbitals with occupation numbers less than 0.03 from the (8e,14o) active space for 2, an active space of eight electrons in eight orbitals, (8e,8o), was identified and tested for 2. This smaller active space yields results consistent with the best active space of (8e,14o) (see Table S3).
Furthermore, 3 and 4 contain three U-arene-U group, tripling the size of the required active space compared to 2. Our testing in 2 indicates that no fewer than (8e,8o) per arene should be used in the ring complexes. Therefore, an initial guess at the best active space would be to include the 24 orbitals analogous to those in 2. However, recall that the ligand has been deprotonated in 3 and 4. As a result, there are fewer electrons associated with each U-arene-U group leading to an analogous active space of 21 electrons in 23 orbitals (21e, 23o). This active space is still too large to be treated with CASSCF; however, the RASSCF approach can be used. The RASSCF calculations use an active space of (21e,2e,2e;6o,11o,6o) where the notation of Sauri et al. 35 indicates a RAS space of (n,l,m;i,j,k) where n is the number of electrons in the active space, l is the maximum number of holes in RAS1, and m is the number of electrons allowed in RAS3. Similarly, i, j, and k are the number of orbitals in RAS1, RAS2, and RAS3 respectively. Calculations on 4'' were performed with C 2 symmetry, while all other calculations were in C 1 . RAS1 includes the δ-bonding orbitals, RAS2 includes the orbitals containing the unpaired electrons, and RAS3 includes the δ* orbitals.

Complexes 2, 2', 2'', and 2'''
The electronic structure of 2 and its models were explored using CASSCF/CASPT2 calculations. The ANO-RCC basis set was employed for uranium atoms using a contraction of triple-ζ quality, while the N, P, and C arene and H arene atoms were treated with a basis set of double-ζ quality and peripheral I, Si, C, and H atoms were treated with a minimal basis set. 32,33 The (8e,14o) and (8e,8o) active spaces were computed for 2 and the three models.

Complexes 2', 2'', 2''', and 4'''
For the models of 2, CASPT2 calculations were performed using the (8e,8o) active space and the smaller basis set that will also be employed in calculations of 4''' to assess not only the effect of truncating the active space but also the effect of using a small basis set. The Dolg ECP basis set 9 was used for all atoms except for H where the 3-21G basis set was employed. For uranium, the small core ECP was chosen. Finally, for 4'', a larger active space is required and therefore RASSCF calculations were performed; however, the ECP basis set is also used.

DFT and CASPT2 Results for 2
The PBE/def-TZVP geometry optimisation of 2 for the high spin S = 2 state gave structures in good agreement with experiment and previous density functional theory results (Table S1). For the optimised geometries, DFT single-points were performed for the S = 0 and S = 1 states. As expected, the closed shell singlet is high in energy; therefore, the broken symmetry singlet is also computed. Both the broken symmetry singlet and the triplet are higher in energy than the quintet state and have some spin contamination (Table S2). CASPT2 calculations were also performed and the results are given in Table   S3. Our best calculation used the ANO-RCC basis sets and the (8e,14o) active space. The bonding in 2 has four singly occupied natural orbitals composed of linear combinations of 5f orbitals localised on the uranium centres ( Figure S1). The two δ−bonding orbitals in 2 have occupation numbers of 1.85 and 1.86. This is consistent with the DFT study previously published concurrently with the synthesis of this molecule. The S = 0, 1, and 2 states are computed, where the singlet is the lowest in energy and the triplet lies only 0.03 kcal/mol higher (Table S3). The quintet state is also relatively close in energy at 2.41 kcal/mol. Each uranium center has an electron configuration of 5f 2 and was previously assigned as having two uranium(III) centers.
The (8e,14o) active space is compared with the (8e,8o) active space for 2 (see Table S3). Despite reducing the size of the active space, the overall picture remains the same but the occupation numbers of the δ−bonds increase from 1.85-1.87 to 1.94-1.95. Additionally, the relative energies at the CASPT2 level with the (8e,14o) space and those with the (8e,8o) space differ by less than 0.5 kcal/mol, well within the error of the method. The CASSCF energies were more sensitive than the CASPT2 energies but for this system the PT2 part can recover the energy missing by using the smaller active space. For these reasons, the (8e,8o) space is suitable for use in describing the ground state of 2. Additionally, Mulliken and LoProp charge analysis were performed on these compounds (Table S4) and reducing the active space does not qualitatively change the charges. Note that the Mulliken charges have a very low charge on the bridging arene compared to the LoProp charge.

Effect of Ligand Truncation in 2
The most significant approximation we make is the truncation of the BIPM ligand. In approaching this rather severe ligand truncation, there was the possibility that this could have serious implications in our calculations. Therefore, we first apply the ligand truncations to 2 to test if 1) the ligand truncation leads to qualitatively different results and 2) that truncating the active space to (8e,8o) has a minimal effect regardless of the model. In Table S5, the CASSCF and CASPT2 energies are reported for 2 and the three model systems for both the (8e,14o) and the (8e,8o) active spaces. Comparing 2 to the smallest charges as only a qualitative guide given their well-known deficiencies. We do note that both the LoProp and Mulliken chargers are not effected by truncating the active space.

CASPT2 Results for 2 and its Models with a Smaller Basis Set
Next, results from the calculations with the ECP basis set are compared to those using ANO-RCC. In this case, only the (8e,8o) active space was computed since for 4'' neither the ANO-RCC basis set nor such a large active space will be applied. In Table S7, the relative energies are again in agreement by less than 0.5 kcal/mol. The active orbitals and occupation numbers (Figures S14 to S16) are the same for the ECP basis as they were with ANO-RCC when the same active space is used. While it is well known that Mulliken charges are sensitive to the basis set (and we certainly see this in our results), it is important to emphasise that the trends between the charges for the charge models are consistent whether the ANO-RCC or ECP basis set is used. For example, in Table S8, the charges for the system with the largest number of basis functions, 2, has LoProp charges that compare well with the other models; however, the Mulliken charges on the arene group are very small in 2 and we attribute this to the well-known problems associated with Mulliken charges. By studying 2 and its representative model systems, three main conclusions arise: 1) the (8e,8o) active space is large enough to properly describe the ground state; 2) the Dolg ECP basis set gives results in qualitative agreement with the ANO-RCC basis; 3) truncating the ligand does not change the nature of the ground state qualitatively.

RASSCF Results for 4'''
Relative energies with RASSCF for 4'' are given in Table S9. Since RASPT2 calculations with the large basis set required more memory than was feasible on our resources, only RASSCF energies are reported for our largest active space. However, a smaller active space can be employed in which the δbonding orbitals with the highest occupation numbers (and their corresponding anti-bonding orbitals) were removed from the active space. This (9e,17o) active space can be used to perform CASPT2 calculations. While this is an approximation, we can use this smaller active space to compute CASPT2 energies (see Table S10). Note that the figures of the active orbitals for RASSCF were reported in the main text.

DFT Results for 2 and its Models
PBE/def-TZVP calculations were performed for 2 and its three models for the high spin state only.
Natural population analysis (NPA) as implemented in the Turbomole program package was performed to compute charges.

DFT Results for 3' and 4' and its Models
Finally, DFT calculations were performed for 3', 4', and 4'''. Furthermore, no symmetry was imposed in the DFT calculations whereas the RASSCF calculations were performed in C 2 symmetry. The δ and 5f orbitals are drawn in Figure S21 and S23 while the orbitals with contributions from the 2p orbitals on the carbene are plotted in Figures S22 and S24 for 3' and 4', respectively. Charge analysis was performed with natural population analysis (NPA) using density functional theory (PBE/def-TZVP).
The charges on uranium are lower than with the other approaches and once again we see that changing the charge model has a larger effect than the ligand truncation. Additionally, since previous DFT studies by some of the authors have used DFT to compute MDC-q charges as implemented in the ADF program package, single point energy calculations were performed for 3' and 4' for comparison with the literature.