Introduction

Three-coordinate lanthanide and actinide complexes of the type MX3 are typically pyramidal rather than the trigonal planar shape which would be anticipated to minimise steric congestion in complexes where bonding is primarily ionic1,2,3,4,5,6,7. This unexpected deviation from the highest symmetry is also widespread in low-coordination number p- and d-block complexes8.

Electronic structure manipulation through geometry for f-block complexes is an emergent field, with potential applications in molecular- and quantum-scale sensing and computing applications9. For example, planarization of the three-coordinate lanthanide complex K[LuII(OC6H2(Ad)2−2,4-tBu-6)3] places the effective S = 1/2 spin in an s/d hybrid orbital that affords the molecule with one of the largest hyperfine interactions for a molecular system, Aiso  =  3,467  ±  50 MHz, and a very large associated clock transition, that make it competitive with a trapped ion qubit for quantum information storage10.

Potentially competing factors have been suggested to account for an unexpected deviation from the geometry which should minimise steric overlap, such as pyramidalization, Fig. 1. The tendency towards pyramidalization can arise from the generation of a dipole moment that gives additional electrostatic stabilisation (the so-called polarisable ion model) (Fig. 1b), the optimisation of dispersion forces between peripheral groups on the ligands (Fig. 1c) or the formation of additional weak or agostic bonds between metal and ligand (Fig. 1d). Dispersion is increasingly recognised as providing a significant stabilising force in many unusual new p- and d-block molecules that have been reported over the past decade11, and its effect increases rapidly (as the 6th power of distance) at short inter atomic separations. In a pyramidal geometry, the metal’s d orbitals can only be involved in σ-type bonding on symmetry grounds, Fig. 1e, whereas a planar geometry enables involvement of metal d-orbitals in π-type bonding. This has been investigated computationally for a series of small X (H, Me, Hal, NH2) in group 3 and 4 complexes12. However, for An which exhibit greater bonding covalency than group 3, and for heavier heteroatom-bound ligands, with more available X(p) π-orbitals, greater planarity would be expected from this argument. For example, the S-donor MX3 molecules (X = SAr = S-tBu3−2,4,6-C6H2, M = U, La, Ce, Pr, Nd13; M = Sm14) are essentially isostructural with shallower pyramidal geometries, leaving the questions still unanswered.

Fig. 1: Summary of the pyramidal molecules studied in this work and the factors thought to contribute to pyramidalization in Ln and AnX3 complexes.
figure 1

a Out of plane (oop) distance between the M and the X3 plane is described as oop, shown in blue, is used to provide a simple measure of pyramidalization in US3 and UX3. Contributing factors to pyramidalization in MX3 include b dipole moment, c ligand-ligand interactions, d metal-ligand agostic interactions and e M(d)-X(p) π overlap. UN3 = U(N(SiMe3)2)3 and US3 = U(SAr)3 where SAr = arylthiolate S-tBu3−2,4,6-C6H2.

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The importance and effects of covalency in bonding in the actinides, as well as its definition15, is a contemporary problem and has widespread ramifications in energy technologies such as f-block ion separations. For example, understanding the differences in M-X bonding with sulfur-based X ligands might help answer the fundamental question of why the commercial S-donor extractant chelator Cyanex301, bis(2,4,4-trimethylpentyl)dithiophosphinic acid, shows a separation factor of over 1000 for AmIII over EuIII which have the same ionic radius and electronegativity16,17.

Systems in which energetically competitive structures are related by subtle changes such as weak metal-ligand interactions, or ligand-ligand interactions may be sensitive to external conditions such as temperature or pressure. We studied the effect of high pressure (up to 5 GPa) on low-valent uranium complexes with bulky amido (N″ = N(SiMe3)2 and aryloxide (Odtbp) ligands18. We found, supported by Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) calculations, evidence of genuine agostic U···H bond formation at high pressure.

In this work, we have undertaken variable pressure single crystal X-ray diffraction studies on two contrasting pyramidal compounds, Fig. 1; the highly symmetrical, uranium(III) tris(amide) U(N(SiMe3)2)3 (UN3) and the less well-studied, more polarisable U(SAr)3 (SAr = arylthiolate S-tBu3-2,4,6-C6H2) (US3)13,19. These are combined with NBO and QTAIM analyses of DFT-derived electronic structures, in order to evaluate the structural drivers set out in Fig. 120,21. The study of uranium rather than rare earth MX3 complexes enables us to explore all the potentially contributing factors hypothesised to favour pyramidalization. The actinide can make use of four different types of atomic orbitals (s, p, d and f) in metal-ligand bonding, in contrast to lanthanides, where f-orbital participation in bonding is tiny22.

Results and discussion

Single crystal X-ray diffraction studies of US3 and UN3

Complexes UN323,24 and US313 were prepared and the single crystal X-ray structures of UN3 as its cyclohexane solvate and US3 were determined at ambient temperature and pressure, and then at increased pressure steps up to 4.09 GPa and 5.25 GPa, respectively. Figure 2 summarises the changes observed.

Fig. 2: The change in pyramidalization observed for UN3 and US3 with pressure.
figure 2

a Increased pyramidalization of UN3 with pressure, and planarization of US3 with pressure. b Key distances and angles and their change with pressure for the two compounds, with computed values in brackets. UN3 = U(N(SiMe3)2)3 and US3 = U(SAr)3 where SAr = arylthiolate S-tBu3−2,4,6-C6H2.

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The experimental structure of UN3 shows uranium disordered equally over two positions above and below the plane of the three heteroatoms, Fig. 2. At ambient pressure six U-C(H) metal-ligand close contacts in the cavity above the pyramid (U-C range 2.943(7)–3.301(8) Å) are found. With increasing pressure, pyramidalization increases, evidenced by the U-N3 oop distance increasing by 0.075(3) Å. There is also a significant shortening of the U-C(H) close contacts. In the solid state, UN3 has unequal U-N-Si angles of 110.17(10)° and 123.60(11)° since the Si-C bond of one of each amido ligands is closer to the U centre [U···Cγ 3.055(5) Å; U···Si 3.2800(12) Å]. At 4.09 GPa the closest U-C(H) contact distance of 3.055(5) Å (there are three, still equivalent by symmetry) shortens to 2.939(7) Å (Fig. 3), and the corresponding U···Si shortens to 3.2809(8) Å. These can be attributed to stabilisation by agostic M···Si-Cγ interactions, similar to [U{CH(SiMe3)2}3] and SmN34,25. The U-N bond length does not change significantly with pressure (from 2.289(3) Å at ambient pressure to 2.277(6) Å at 4.09 GPa).

Fig. 3: High pressure structure of UN3.
figure 3

a Solid state structure of UN3 from top at 4.09 GPa, b side view of the solid-state structure of UN3 showing pyramidalization and U-CH agostic interactions at 4.09 GPa (red = close contacts, grey = longer contacts). UN3 = U(N(SiMe3)2)3. Atom colour code: Green = U; blue = N; gold = Si; grey = C.

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At ambient temperature and pressure, Fig. 4, US3 is essentially isomorphous with the 100 K structure reported for it and Ln = La, Ce, Pr, Nd, Sm13,14. The U-S3 oop distance is 0.216(1) Å with a propeller-like SAr arrangement. In the ambient pressure structures of US3 and all the LnS313, except SmS3 which contains a smaller metal14, there is a small boat-distortion of the arene ring, with the ipso-carbon the furthest from the ring plane (0.070 to 0.086 Å).

Fig. 4: Solid state structure of US3 under ambient conditions and at high pressure.
figure 4

a Solid state structure of US3 at ambient pressure with intramolecular U-C contacts drawn in blue, b solid state structure of US3 at ambient pressure with intramolecular S-H contacts drawn in red, c solid state structure of US3 at 5.25 GPa along the US3 plane. Atom colour code: Green = U; orange = S; grey = C; white = H. US3 = U(SAr)3 where SAr = arylthiolate S-tBu3−2,4,6-C6H2.

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The U-S distances in US3 (range 2.7057(19)–2.7143(18) Å) are similar to those in Meyer’s recently reported UIII adduct of a chelating tris-thiophenolate (U-S distance = 2.7083(8) Å), both of which are much shorter than the few other UIII-S compounds in the literature (range 2.77–2.87 Å)19,26,27,28. The M-S-Cipso angles in US3 are more acute (78.7(2)–86.68(16)°) than all including the tris-thiophenolate (92.31(9)°)27,28. The short U-C contacts in US3 are benzylic-type interactions with the ipso and one ortho carbon in each ligand ring (Fig. 3, top-left) (average U-Cipso 3.045(115) Å, average U-Cclosest ortho 3.279(89) Å at ambient T, p). The alternating ring bond lengths further support this, and the effect is more prominent for U than for the Ln congeners, in agreement with the use of more diffuse orbitals by uranium.

US3 also has several short U-H contacts, (range 2.47 to 2.82 Å), which were characterised as agostic interactions through NBO analysis by Ephritikhine and co-workers (see below). In contrast to UN3, these favourable U-HC agostic interactions can form both above and below the US3 core. The crystallography suggests that there are four short S-HC contacts within each ligand (range 2.55–2.67 Å), (Fig. 3, top-right). Weak sulfur-containing hydrogen bonds (SCHBs) can play a cumulative stabilising and structure-directing role29,30,31,32,33, but our calculations do not find that they play a noticeable role in this case (see below).

Planarization with increasing pressure is evidenced by the U-S3 oop distance decreasing from 0.216(1) Å to 0.034(1) Å at 5.25 GPa, Fig. 3, bottom. The average U-S distance does not significantly change (2.7109(5) at 0 GPa to 2.717(22) Å at 5.25 GPa) although the difference between shortest and longest increases from 0.009 Å to 0.041 Å. Instead, the U-S-Cipso angle becomes more acute; from a range of 78.7(2)-86.68(16)° (ambient) to 76.2(3)–81.6(2)° (5.25 GPa). The average U-Cipso distance shortens from 3.045(115) Å to 2.950(82) Å, and the average U-Cortho distance shortens even more dramatically from 3.279(89) Å to 3.048(161) Å by 5.25 GPa. Some of the S…HC contacts shorten to <2.4 Å as the tBu groups rotate to improve packing; these are well within the sum of the van der Waals bond radii of sulfur and hydrogen (3.0 Å).

Computational studies

Computational studies were carried out on structures derived from the crystallographic data. The geometries of UN3 and US3m, where US3m is a computationally more tractable model for US3 in which the para tBu groups are replaced by H atoms, were calculated using scalar relativistic, hybrid density functional theory (PBE0), incorporating Grimme’s dispersion corrections with the Becke-Johnson damping parameters. Both systems optimise to pyramidal structures, confirmed as true minima by harmonic vibrational frequency analysis. Geometry optimisation of US3 and US3m using a smaller basis set confirmed that the presence of the para tBu groups has minimal structural effect: pyramidalization varied by 0.01 Å and U-X distances by no more than 0.008 Å. Further calculations located planar at U (UN3) or near planar at U (US3m) transition state structures, each possessing a single imaginary vibrational mode associated with interconverting two pyramidal conformers, with modest energy barriers of 5.6 and 9.8 kJ mol−1 respectively, confirming that a planar geometry is achievable. For comparison, the experimentally determined inversion energy for NH3 is 24.2 kJ mol−1 34.

The computed dipole moments at the optimised pyramidal geometries are large for both UN3 and US3m, 2.54 and 2.03 D, respectively. For comparison, experimentally determined values in bent p-block molecules are rather lower (H2O: 1.84, NH3: 1.44, PH3: 0.55, PCl3: 1.16 D)35. At the transition states, the dipole moments are much reduced, to 0.43 and 0.60 D respectively for UN3 and US3m. The large dipole moments for the pyramidal forms of both systems will contribute to the stability of those geometries, and the reduction at the transition states will oppose planarization, albeit to a significantly lesser extent in US3m than UN3.

In their 2006 contribution, Roger et al. used second order perturbation theory analysis within the NBO framework to explore the electronic structure of a model for US3. They concluded that there are stabilising interactions resulting from donations from (i) a Cipso-Cortho bond to empty U f (ii) a S-Cipso bond to empty U f and (iii) tBu C-H to empty U d/f (an agostic effect enhanced by slight hyperconjugation between Cipso-Cortho and C-C of tBu). They also identified delocalisation from a S lone pair to Cipso-Cortho π* bond. Unfortunately, only the agostic effect was quantified, providing “a stabilisation of roughly c. 5 kcal mol−1”. We have conducted a similar analysis on both the pyramidal and transition state structures of UN3 and US3m, details of which are collected in the SI. Overall, we find quite different results for US3m that those of Roger et al., most likely arising from substantial advances in computational methodology over the last 15 years. The principal difference between pyramidal and transition state US3m is a significant reduction in agostic interactions in the latter, indicating that the high pressure behaviour of US3 is not the result of enhanced agostics. Note that there are no sulfur containing hydrogen bond interactions in either form of US3m larger than the NBO default cut off of 0.25 kcal mol−1 (1.046 kJ.mol−1). Although QTAIM analysis does locate S-H bond paths and bond critical points, the electron and energy densities at these critical points are very low (< 0.02 and c. 0.000 au respectively) suggesting that these interactions are at most very weak, in agreement with the NBO perturbation theory analysis. In UN3, the energies associated with the NBO donor-acceptor interactions are much less than for the sulfur system, though we do find evidence of slightly stronger agostic interactions in the transition state than the pyramidal form. As with US3m, these agostics do not appear to determine the high-pressure behaviour of UN3. The boat-distortion in the ligand arenes mentioned above for US3, which was previously ascribed to the benzylic U-C interactions disrupting the bonding in the ring, is attributed in these calculations to donation from the U-S bonds to the Cipso-Cortho π*orbital of the arene.

To assess the U-N and U-S bonding, and in particular the way in which it changes between the pyramidal and transition state structures, we have analysed both Quantum Theory of Atoms in Molecules metrics and Natural Localised Molecular Orbital composition data. These are presented and discussed in the SI, page 18. While there are clear differences in the bonding between UN3 and US3m, there are only very minor changes between the pyramidal and transition state structures (with marginally weaker bonding in the latter), from which we conclude that bonding changes (including in the d-orbital contribution to the NLMOs, and the metal-ligand overlap) are insufficient to drive the differences in the high pressure behaviour of UN3 and US3m.

Volume discussion

The molecular volumes (isodensity surface of 0.001 electrons/Bohr3) of UN3 and US3m were determined for the optimised pyramidal and transition state structures. For UN3, there is a small increase, 1% between the pyramidal and planar forms. Experimentally, the volume defined by the van der Waals surface of the pyramidal molecules of UN3 in the experimental crystal structures shows a modest reduction between ambient pressure and 4.80 GPa (Fig. 15 in the SI), but a systematic trend is rather difficult to discern, with most points scattered within 0.5% of the ambient pressure volume. The combination of the computational and experimental data implies that the molecular volume of the pyramidal form of UN3 is quite insensitive to pressure, but would increase slightly on becoming planar. A planar form of UN3 would therefore not be promoted by application of pressure.

By contrast, the molecular volume of US3 in the experimental crystal structures shows a linear decrease between ambient pressure and 5.25 GPa, with a 2% reduction in volume as the molecule changes from a pyramidal to a planar geometry (Fig. 4). The volume reduction in the theoretical structures is still more marked, with the volume of the 0.001 electrons/Bohr3 isosurface of US3m being 7% smaller in the planar than in the pyramidal form. A volume reduction of this magnitude would strongly stabilise the planar form relative to the pyramidal alternative at high pressure.

Summary

To summarise, upon pressurisation in the solid state, UN3 becomes more pyramidal, whereas US3 becomes planar. Until now, it has been presumed that larger ligands are needed to enforce a planar geometry36, but sterics are not the dominant factor in determining the geometry of these complexes. The SAr ligand is significantly smaller than the N(SiMe3)2 ligand, and at least for the rare earth elements and the actinides, multiple factors beyond sterics need to be considered when choosing ligands that can usefully control geometry in unusually low-coordinate complexes. The opposing pressure responses of UN3 and US3 have helped to reveal the dominant reasons why the molecules’ normally favoured conformation is pyramidal. The increasing pyramidalization of UN3 with pressure is favoured by an increased dipole moment and reduction in molecular volume, while the planarization of US3 with pressure is promoted by the slight reduction in molecular volume achievable. We find that agostics do not determine the pressure behaviour for either molecule and that the bonding changes that occur with changes in the degree of pyramidalization of UN3 or US3 (including in the d-orbital contribution to the NLMOs, and the metal-ligand overlap) are insufficient to drive the differences in their high-pressure behaviour.

Methods

UN3 and US3 were synthesised according to literature procedures: further details are included in the supplementary information file under the methods section1,2. Diffraction data at ambient pressure were collected at 270 K with the crystal mounted under a film of oil protect the crystal from the air while maintaining a steady position on its mount. Data sets at high pressure were collected in a Merrill-Bassett diamond anvil cell using Boehler-Almax cut diamonds, a tungsten gasket and ruby as a pressure marker. The solubility of the compounds necessitated the use of fluorinert (FC70) as the medium between 0 and 1 GPa. Fluorinert has a hydrostatic limit of 0.6 GPa36, and so no data could be collected between 1 and 2.37 GPa. Above 2 GPa, pressure was applied using a 1:1 mixture of pentane and isopentane as a hydrostatic medium. The maximum pressure reached was 4.09 Gpa for UN3 and 5.25 Gpa for US3. Data at ambient pressure and 0.87 GPa were collected using MoKα radiation, those at higher pressures were collected at Diamond Light Source on Beamline I19 (Experimental Hutch 2) with X-rays of wavelength 0.4859 Å. Shaded regions of the detector were omitted during integration of the diffraction images, and a multi-scan correction was used to account for absorption, gasket shading and other systematic errors.