Isomerisation of nido-[C2B10H12]2– dianions: unprecedented rearrangements and new structural motifs in carborane cluster chemistry

The formation and isomerisation of nido-[C2B10H12]2– species is investigated through DFT calculations, which reveal novel basket and inverted nido intermediates and unusual inverconversion pathways, including basket collapse and pivoting triangles and diamonds.


Introduction
As predicted by Wade's Rules, 1 the addition of a skeletal electron pair (SEP) to a closo polyhedron (with [n + 1] SEPs, where n is the number of vertices) results in the formation of the corresponding nido cluster ([n + 2] SEPs). A key synthetic route that relies upon this is the polyhedral expansion method, whereby 2-electron reduction of a closo precursor (normally a 12-vertex carborane) results in the formation of a nido fragment, which can then be capitated with a {BR} or {M} fragment. Application of this method led to both the rst 13-vertex metallacarborane 2 and the rst 13-vertex carborane. 3 In 2007 we showed that the polyhedral expansion of a single carborane precursor, [1,12-Ph 2 -1,12-closo-C 2 B 10 H 10 ], with {M} ¼ {Ru(p-cymene)} led to the formation of ve isomeric supraicosahedral metallacarboranes of the form RuC 2 B 10 ( Fig. 1). 4 This implies the presence of ve isomeric nido fragments following reduction, i.e. 1,7-, 3,7-, 4,7-, 7,9-and [7,10-Ph 2 -7,10-nido-C 2 B 10 H 10 ] 2À . A concurrent computational study on [1,12-closo-C 2 B 10 H 12 ] (para-carborane) suggested the rst nido-fragments formed upon reduction were [1,7-nido-C 2 B 10 H 12 ] 2À (termed 1,7 in the following) and [4,7-nido-C 2 B 10 H 12 ] 2À (4,7). At the time, the further isomerisation of these species to the remaining nido species was not considered, however computing these directly provided relative energies, H (enthalpies, 0 K) of +29.5, +24.0, +22.0 and +1.4 kcal mol À1 for 1,7, 3,7, 4,7 and 7,10 respectively, all relative to 7,9 at 0.0 kcal mol À1 . In contrast, related experimental studies adopting ortho-or meta-carborane precursors show that 7,9 is the only nido species formed. 2,[5][6][7] The thermal rearrangement of 12-vertex closo (hetero) boranes has been the subject of continued investigation. Starting from ortho-carborane, the conversion to meta-carborane at 450 C and then to para-carborane at 700 C has been known for over 50 years and indeed was the route to their rst syntheses. [8][9][10] The processes involved in their rearrangement have been studied for many years, both theoretically [11][12][13][14][15][16] and experimentally through labelling studies. [17][18][19] In 1966, Lipscomb 13 introduced the diamond-square-diamond (DSD) mechanism (Scheme 1a), while in the same year, Zakharkin and Kalinin 16 suggested the triangular face rotation (TFR) mechanism, which can also be described as three concerted DSD processes (Scheme 1b). The DSD process in particular has since been recognised as key to carborane rearrangement. Wales 15 adopted an eigenvector following method to map the potential energy surface of C 2 B 10 H 12 at the Hartree-Fock (HF) level. Multi-step DSD-derived processes were found to dominate, however two TFR-type pathways were also located. High symmetry processes involving multiple simultaneous DSDs (e.g. the hextuple DSD process leading to a cuboctahedral geometry suggested by Lipscomb 13 ) were discounted due to their unfeasibly high activation energies. Later studies also demonstrate an energetic preference for low symmetry processes. 11,12,14 Wales also ruled out the closo-nido-closo rearrangement pathway, which requires opening of the cage to a high energy pseudo-nido intermediate.
More recently, Brown and McKee 11 showed, through density functional theory (DFT) calculations, that a single step TFR process was favoured in the ortho-to meta-carborane isomerisation, while a two-step DSD pathway was preferred for isomerisation from meta-to para-carborane. Brown and McKee had discounted a two-step pathway from ortho-to meta-carborane, due to a high initial barrier between ortho-carborane and the intermediate involved. We later showed that the equivalent intermediate was formed upon the oxidation of 7,9 and characterised a lower energy process to form ortho-carborane, in agreement with experiment. 12 Most recently, Sugden and co-workers 14 investigated both of these isomerisation pathways through ab initio molecular dynamics (DFT-MD) adopting the PBE functional.
In stark contrast, few computational studies have involved reduced 12-vertex carboranes, despite the isomeric form of the reduced species ultimately dictating the isomer of the supraicosahedral product. McKee et al. 20 computed 7,9 directly, through HF calculations, for comparison with plausible protonated [nido-C 2 B 10 H 13 ] À structures. Later, Hermansson and co-workers 21 showed in a study of the electron affinities of carboranes (also at the HF level) that sequential addition of two electrons to meta-carborane resulted in 7,9, while geometries produced from reduction of ortho-and para-carborane showed only minor distortions and did not resemble nido fragments. More recently, 12-vertex nido carboranes and (bis)carboranes have featured in our investigations of the aforementioned oxidation of 7,9 to ortho-carborane, 12 the room-temperature C-C activation of an arene at a 13-vertex metallacarborane, 22 co-production of isomeric 13-vertex cobaltacarboranes from polyhedral expansion of a tethered carborane precursor 23 and in the rational design of derivatives of 7,9 stabilised towards aerial oxidation. 24 Herein we report a computational study of the isomerisation processes that follow from the initial 2e reduction of para-carborane and formation of 1,7 and 4,7, revealing pathways interconnecting all ve nido fragments inferred experimentally (see Fig. 1). The reduction of ortho-carborane is shown to initially produce 7,8, before rearranging to the experimental product, 7,9. meta-Carborane reduction proceeds to 7,9 directly, where the barrierless rearrangement process is rationalised by relation to the nido isomerisation pathways. In the completion of this work, we uncover and rationalise new dianionic 12-vertex carborane structures which we refer to as basket and inverted nido intermediates and characterise new, unexpectedly complex processes interconnecting nido species, ultimately linking all intermediates to the global minimum, 7,9.

Formation of 1,7 and 4,7
DFT calculations were performed at the BP86/6-31G** level using Gaussian 03 and we report zero-point corrected electronic energies, H, for all computed species relative to 7,9 (see Computational details). In order to model the reduction of para-carborane, rst the neutral geometry was optimised, then two electrons were added and the system was re-optimised. This resulted in an initial reduced minimum, Int(A) (H ¼ +34.   decreasing the B 3 /B 6 distance causes the 4-membered face to close via TS2(A-4,7) (H ¼ +38.9 kcal mol À1 ) in what is effectively a barrierless process. Thereaer, a DSD process occurs in the C 1 -B 3 -B 6 -B 5 diamond, breaking the C 1 -B 6 connection and forming the B 3 -B 5 connection, allowing C 1 to become 3-connected and furnishing the nido geometry, 4,7. These energy proles suggest that processes decreasing the number of connections to carbon vertices and increasing the number of connections to boron vertices are favoured. The lower barrier to formation of 4,7 than of 1,7 also suggests that processes involving movement of boron are easier than those involving movement of carbon. This is supported by electronegativity arguments; the radial orbitals of the carbon vertices, being more contracted than those of boron, do not allow stabilisation of higher-connected sites or longer connections. The movement of vertices from the initial para-carborane geometry to give Int(A) can be rationalised by visualisation of the LUMO of paracarborane (Fig. 3). This features a p-antibonding interaction along the C 1 -B 6 connection and a further antibonding interaction between B 3 and B 4 . Therefore the 2e occupation of this orbital is consistent with the breaking of these interactions to give a 4-membered

Onward isomerisations of 1,7 and 4,7: general strategies
The geometries of 1,7 and 4,7 were considered as starting points towards formation of the remaining nido species, 3,7, 7,9 and 7,10. Initially, we considered the possibility of TFR processes linking nido isomers (Scheme 2); in 1,7, rotation of the C 1 -B 3 -B 4 triangle could be envisaged to interconvert 1,7 and 3,7 and rotation of the same triangle again, or C 3 -B 9 -B 4 , would exchange 3,7 and 4,7. Likewise, in 4,7, rotation of the C 4 -B 9 -B 10 triangle could give 7,9 and 7,10. However, attempts to characterise such processes through potential energy surface searching (linear transits) were unsuccessful from either 1,7 or 4,7. Several atoms had to be xed in position in order to prevent non-targetted rearrangement of the cluster. This suggested that the TFR process, though relevant to closo carborane isomerisation, was higher in energy than other processes available to the more exible nido species. It was noted that the lowest energy vibrational mode of all nido species computed involves rotation of the 6-membered face above the 5-membered 2-3-4-5-6 belt, where the largest displacement is seen in the 7-position. Taking the lead from the mode-following approach of Wales, 15 we used the transition state (TS) optimisation option in Gaussian 03, 25 which follows the lowest energy vibrational mode to a saddle-point on the PES, thus allowing low energy transition states to be sought a priori, direct from selected minima. The present C 2 B 10 H 12 clusters (which lack polyatomic exopolyhedral substituents) lend themselves to mode-following since the lowest energy vibrational mode always involves displacement of cluster vertices and so is productive towards cluster rearrangement. Mode-following was therefore always attempted in the rst instance for any transition state search (see Computational Details). From 1,7 and 4,7 this revealed surprising and contrasting isomerisation processes, which see rearrangement of 1,7 to 7,9 in a single step and 4,7 to 7,10 in a multi-step process.
2.1 Formation of 7,9 via isomerisation of 1,7. Modefollowing from 1,7 provided a transition state, TS(1,7-7,9) (H ¼ +41.2 kcal mol À1 ; Fig. 4), connecting 1,7 directly to 7,9, through a barrier of just 11.7 kcal mol À1 . TS (1,9) is formed through a DSD process in the C 7 -B 12 -B 6 -B 2 diamond and exhibits a 3-connected boron vertex, B 12 , which protrudes from the 6-membered open face by 0.81Å w.r.t. the C 7 -B 8 -B 9 -B 10 -B 11 least-squares mean plane (for comparison, C 7 protrudes by 0.28Å and 0.27Å from the open faces of 1,7 and 7,9 respectively). Visualisation of the single imaginary vibrational mode of TS(1,7-7,9) sees movement of B 12 relative to the open face, where the B 12 /B 9 distance is 3.01Å at the transition state geometry. Characterisation of TS (1,9) via IRC calculations revealed a remarkable and unanticipated process in which the cluster inverts in one step from 1,7, which has a CB 5 6-membered open face, to 7,9, with a C 2 B 4 open face. Fig. 4 shows the isomerisation process, with atom labelling consistent with the formal numbering of 1,7 to allow vertex movement to be followed; two snap-shots, SS1 (1,9) and SS2 (1,9), are shown to further aid in visualising the process and a movie is provided in the ESI. † The initial movement away from TS(1,7- Scheme 2 TFR processes considered to interconvert nido geometries. 7,9) involves pivoting about the long C 7 /B 11 diagonal of the C 7 -B 6 -B 11 -B 12 diamond. SS1 (1,9) illustrates the midpoint of this process. The pivoting continues, opening the C 1 -B 2 -C 7 -B 6 -B 11 -B 5 face and closing the C 7 -B 8 -B 9 -B 10 -B 11 -B 12 face of the starting structure. At SS2 (1,9) the original open face has closed to give a geometry resembling a mirror image of TS (1,9), but with both C-vertices now on the open face. Finally, a barrierless DSD process in the C 7 -B 6 -B 12 -B 8 diamond moves C 7 into the 3-connected site to give 7,9.
2.4 Remaining isomerisation pathway; 7,10 to 7,9. At this stage isomerisation processes have been characterised that rationalise the formation of all ve nido species targeted. However, for completeness, it is desirable to connect all species to 7,9, the global minimum. 1,7 connects to 7,9 directly, whereas 3,7 connects to 7,9 via 1,7 and 4,7 connects to 7,9 via 7,10 (see Discussion section). The remaining isomerisation, from 7,10 to 7,9, is discussed below and shown in Fig. 7. Starting from 7,10, mode-following results in a degenerate process where the 3-connected C 7 becomes 4-connected and B 8 and B 9 (or equivalent B 12 and B 11 ) become 3-connected. This is similar to the initial movement of vertices seen for the formation of 3,7 from 1,7, however here it does not lead to an isomerisation process. A linear transit was therefore adopted, increasing the C 7 -B 2 distance, to cause a DSD process in the C 7 -B 8 -B 2 -B 12 diamond. This gave TS1(7,10-7,9) (H ¼ +27.7 kcal mol À1 ) which leads to a basket intermediate, Int (7,9) (H ¼ +2.8 kcal mol À1 ), where C 7 -B 11 forms the basket handle. Int (7,9) is related to 7,9 through a DSD process in the C 7 -B 11 -B 6 -B 12 diamond, which was characterised through location of TS2(7,10-7,9) (H ¼ +21.4 kcal mol À1 ). The isomerisation from 7,10 to 7,9 therefore involves two DSD processes, through a basket intermediate, with an overall barrier of 26.3 kcal mol À1 .

Reductions of orthoand meta-carborane
The experimental reductions of ortho-and meta-carborane each lead to 7,9. 2,5-7 Hermansson et al. 21 showed in a study of carborane electron affinities that, at the HF level of theory, sequential addition of two electrons to meta-carborane produced a 7,9 nido geometry, whereas ortho-carborane was only slightly distorted. Through the present DFT calculations, we have now characterised the rearrangement processes undergone by both of these species following 2e reduction, ultimately giving 7,9, which can be rationalised by relating them to the processes seen above. By analogy to the computational treatment of the reduction of para-carborane, 2e were added to the optimised geometry of ortho-carborane and the structure reoptimised as a dianion. This gave Int(B) (H ¼ +18.4 kcal mol À1 above 7,9; Fig. 8). Int(B) is another example of a basket intermediate, where here the geometry is C 2 symmetric and the C 1 and C 2 vertices form the basket handle. The C 1 -C 2 connection in Int(B) is shortened to 1.52Å w.r.t. 1.64Å in ortho-carborane, indicative of single bond character. From Int(B), a basket collapse process was characterised through TS(B-7,9) (H ¼ +52.9 kcal mol À1 ; see Fig. 8, grey pathway) and involves DSD processes in the C 1 -B 5 -B 10 -B 6 diamond (with C 1 /B 10 and B 5 /B 6 distances of 2.44Å and 2.58Å respectively) and breaking of the C 1 -C 2 connection to give 7,9 in a single step. However, this process exhibits a high overall barrier of 34.5 kcal mol À1 , consistent with it being dominated by the breaking of a C-C connection with single bond character. An alternative basket collapse process was characterised through mode-following (Fig. 8, black pathway). This pathway initially maintains the C 1 -C 2 connection, giving 7,8 through a low barrier of 15.5 kcal mol À1 in which the C 1 -C 2 connection is shortened still further to 1.45Å. Mode-following from 7,8 led to a degenerate rearrangement involving a DSD process in the C 1 -C 2 -B 4 -B 5 diamond (as numbered in Fig. 8), forming a C 2 -B 5 connection through a barrier of 14.8 kcal mol À1 . Linear transits were therefore conducted to discover a pathway leading to 7,9. A low energy transition state, TS1 (7,9) (H ¼ +27.4 kcal mol À1 ) was located, and provided a basket intermediate, Int1 (7,9). From here, C 1 -C 2 bond breaking proceeds through TS2 (7,9) at over 10 kcal mol À1 lower than TS(B-7,9) (H ¼ +42.5 kcal mol À1 ), giving a barrier of 29.9 kcal mol À1 from 7,8. This process leads to Int2 (7,9) at H ¼ +2.8 kcal mol À1 , which is identical to Int (7,9). Therefore the basket collapse process described above to give 7,9 is repeated in this pathway; here forming the C 1 -B 7 connection through a DSD process in the C 1 -B 11 -B 7 -B 6 diamond of the Int2 (7,9) basket. The nido-7,8 isomer is implicated experimentally in the synthesis if 4,1,2-MC 2 B 10 species from ortho-carborane, where exopolyhedral hydrocarbyl or silyl tethers connecting the C-vertices ensure the C positions remain adjacent. 3,26,27 With the removable silyl tether Fig. 8 2e addition to ortho-carborane followed by isomerisation to 7,9 through a one-step pathway (grey) or a multi-step pathway, via 7,8 (black). Numbering of CH vertices (blue) and BH vertices (black) consistent with ortho-carborane. Inset shows key computed structures along the pathway. Selected distances inÅ and energies relative to 7,9 in kcal mol À1 . H atoms omitted for clarity. metallation with M ¼ {CoCp} leads to the concurrent formation of the expected 4,1,2-MC 2 B 10 species, but also the 4,1,6-MC 2 B 10 isomer, indicating that isomerisation of the nido-7,8 fragment to the 7,9 form is possible. 23 The initial strengthening of the C 1 -C 2 connection in Int(B) cf. ortho-carborane contrasts with the 2e addition to 1,2-Ph 2 -1,2-closo-C 2 B 10 H 10 (towards [7,9-Ph 2 -7,9nido-C 2 B 10 H 10 ] 2À ), where the C 1 -C 2 connection breaks due to a s-C-C antibonding component in the LUMO orbital of the neutral species. 24 In the LUMO of ortho-carborane (Fig. 9a) a p-antibonding interaction is seen between the C vertices, suggesting the connection would indeed be lengthened on occupation of the orbital. Further antibonding interactions are seen between C 2 and the B 3 -B 7 edge and those equivalent by C 2v symmetry (C 1 -{B 3 -B 4 }, C 1 -{B 5 -B 6 } and C 2 -{B 6 -B 11 }) and along the B 4 -B 5 (and B 7 -B 11 ) connections. Upon visualising the optimisation an initial lengthening of connections with antibonding interactions was noted (see ESI † for Movie). A snapshot of this (Fig. 8, SS(o-B)) shows the C 1 -C 2 connection initially lengthens from 1.64Å in ortho-carborane to ca. 1.7Å. In addition, the distances from the C vertices to B 3 and B 6 and the B 4 -B 5 and B 7 -B 11 connections are also lengthened at SS(o-B). As the optimisation continues the C 2v symmetry is reduced to C 2 by reformation of the C 2 -B 3 (1.55Å), C 1 -B 5 (1.71Å) and C 1 -C 2 (1.52Å) connections in Int(B).
Addition of 2e to meta-carborane led directly to the location of 7,9 (Fig. 10a) (see ESI † for movie). During the optimisation the structure initially distorts with retention of C 2v symmetry, consistent with the population of the LUMO of meta-carborane ( Fig. 10b and see snap-shot geometry SS1(m-7,9) in Fig. 10a). Subsequently, B 6 -C 7 lengthens and the symmetry is lost. At  SS2(m-7,9), a B 6 -B 4 connection is formed and the connections from C 7 to B 8 , B 11 and B 12 have reformed. SS2(m-7,9) is equivalent to SS2(1,7-7,9) (Fig. 4) and indeed undergoes a related DSD process, here in the B 3 -B 4 -B 6 -C 1 diamond to give 7,9.

Discussion
Polyhedral expansion of closo-C 2 B 10 carboranes with metal fragments produces a range of MC 2 B 10 species which imply the intermediacy of 1,7-, 3,7-, 4,7-, 7,9-and 7,10-isomers of the nido-[C 2 B 10 ] 2À species. Here we have used DFT calculations to characterise the isomerisation pathways that link these various nido isomers. Our study has revealed several unusual new intermediates and their unforeseen rearrangement pathways which are categorised and rationalised below.
Following the addition of two electrons to the optimised geometry of para-carborane, 1,7 and 4,7 are formed as the initial nido species (Scheme 3). Thereaer, 1,7 connects to 7,9, through a single transition state, with a barrier of 11.7 kcal mol À1 . In contrast, the isomerisation of 4,7 proceeds through a facile multi-step process to form 7,10, but with a similar overall barrier of 11.0 kcal mol À1 . The remaining nido species, 3,7, is formed in an alternative 3-step process from 1,7 with a barrier of 17.6 kcal mol À1 . In order to connect all nido species to the global minimum, 7,9, additional pathways were sought from 7,10, 3,7 and 4,7. From 7,10, a two-step process was characterised with a barrier of 26.3 kcal mol À1 . From 3,7, while a single step process was characterised for isomerisation to 7,9 with a barrier of 28.5 kcal mol À1 (see ESI Fig. S2 †) this is higher than the reverse process from 3,7 to 1,7 (above; DH ‡ ¼ 23.1 kcal mol À1 ) and therefore 3,7 likely isomerises to 7,9 via 1,7. Similarly, a direct pathway from 4,7 to 7,9 was not found and so formation of 7,9 from 4,7 is thought to proceed through 7,10 (DH ‡ ¼ 11.0 kcal mol À1 ). An additional nido species, 7,8, was found to be formed following 2e addition to ortho-carborane and isomerises to 7,9 through a barrier of 29.9 kcal mol À1 . 2e reduction of meta-carborane leads directly to 7,9. Degenerate pathways, where the start and end points of a rearrangement are the same nido species, were characterised for 7,9 (DH ‡ ¼ 10.7 kcal mol À1 ), 7,10 (DH ‡ ¼ 11.1 kcal mol À1 ),  A family of basket intermediates, which are oen energetically comparable to conventional nido fragments, were located along several of the characterised pathways. In a basket intermediate, two vertices form a basket handle bridging the remaining 10 vertices, with examples located in this study including Int(A), Int(A-4,7), Int (7,9), Int1 (7,9) and Int2 (7,9) (all with C 1 symmetry) and Int2 (4,10) and Int(B) (with C 2 symmetry with the CH vertices in the bridgehead positions and basket handle positions respectively). As shown in Scheme 4a, starting from the docosahedron, a C 1 -basket may be produced through removal of one of the 5-connected vertices 6-9 (red), with lengthening of the 1-4 distance to produce the requisite 4-and 5-membered faces. The C 2 -basket intermediates are related to the relevant C 1 -basket by a DSD in the 1-2-5-9 diamond and lengthening of the 3-4 distance. Two additional key intermediates, Int1(4,7-7,10) and Int2(1,7-3,7), we refer to as inverted nido geometries, due to the 6-membered belt of vertices, rather than the 5-membered belt, being capped by a single vertex. The inverted nido motif is derived from the docosahedron by removal of a 5-connected vertex (10 or 11, green). A classical nido geometry is produced through removal of a 6-connected vertex (4 or 5, blue). 28 In order to test the validity of this empirical observation, the idealised [B 13 H 13 ] 2À docosahedron was computed, the appropriate vertices removed and the structure re-optimised as [B 12 H 12 ] 4À fragments. The nido and inverted nido were located as minima (H ¼ 0.0 and +25.8 respectively; see ESI †). The basket geometry was found to collapse to a nido structure, suggesting the C vertices are required to stabilise the distorted geometry, however, the C 2 basket was located as a transition state that exchanges equivalent nido structures (H ¼ +18.6 kcal mol À1 ; see ESI †).
The structural types discussed above tend to access specic rearrangement processes. From nido species, the initial step in the isomerisation is most oen to move the 3-connected C 7 vertex into a 4-connected position. This then triggers movement of the neighbouring vertices resulting in net rotation of the 6-membered belt of vertices above the 5-membered belt. Such processes are also responsible for the degenerate exchanges characterised in 7,8, 7,9 and 7,10. Three additional processes are found (Scheme 4b): a common DSD process by which basket intermediates undergo basket collapse to give nido species (Scheme 4b, upper le); the pivoting of a 4-vertex diamond about its long diagonal to directly exchange nido geometries (Scheme 4b, right; seen in the isomerisations from 1,7 to 7,9, from 1,7 to 3,7 and in the higher energy degenerate process at 3,7 (see ESI, Fig. S1 †)) and the pivoting of two triangles about a shared vertex exchanging inverted nido and nido geometries (Scheme 4b lower le; seen in the isomerisations of 4,7 to 7,10 and 1,7 to 3,7). Scheme 3 Interconnection of 12-vertex nido carborane dianions and their relation to 12-vertex closo carboranes. Relative energies of nido species and the barriers associated with rearrangement processes (denoted ‡ ) given in kcal mol À1 . Scheme 4 (a) Relationship between the docosahedron and nido, basket and inverted nido geometries with numbering consistent with the docosahedron. (b) Processes characterised that interconvert these geometries.
In the characterisation of these isomerisation processes, where possible through a priori mode-following calculations, a series of common intermediate topologies as well as the unexpectedly complex processes by which they interconnect have been uncovered and rationalised. Basket intermediates (e.g. Int(A), Int(A-4,7), Int2(4,7-7,10), Int (7,9) and Int(B)) are characterised by a two-vertex basket handle bridging the remaining 10 vertices; inverted nido intermediates (Int1(4,7-7,10) and Int2(1,7-3,7)) exhibit a 5-membered belt and a 6-membered belt capped by the remaining vertex. The geometries of these new intermediates, like nido species themselves, are related to the 13-vertex docosahedron by removal of a single vertex. The pathways through which carborane dianions isomerise, driven by the thermodynamic preference for low-connected C vertices, are most oen initiated by movement of the 3-connected C 7 vertex, common to all nido species, into a 4-connected position through a DSD step, forcing a B vertex into a destabilised 3-connected site and leading to rearrangement of the cluster. Isomerisation continues through processes such as the pivoting of a 4-vertex diamond about its long diagonal. This can directly lead to a nido geometry or produce a basket or inverted nido intermediate. Basket intermediates can undergo a basket collapse process, characterised by DSD steps, giving rise to a nido geometry, while inverted nido intermediates convert to nido geometries through the pivoting of two 3-vertex triangles about a shared vertex.

Computational details
Calculations were performed using Gaussian 03, Revision D.01 employing the BP86 functional 29,30 and 6-31G** basis sets 31 for B, C and H atoms. Zero-point corrected energies, H, are reported in kcal mol À1 relative to 7,9. Analytical frequency calculations were used to conrm geometries as minima (all positive eigenvalues) or transition states (one negative eigenvalue). Transition states were further characterised through IRC calculations. 32,33 Mode-following calculations used the 'OPT ¼ TS' option in Gaussian along with the GDIIS algorithm, where convergence constraints were set to 'verytight' in order to force the optimisation to move away from a formally minimum energy starting geometry, itself optimised with default convergence constraints. Synchronous Transit-Guided Quasi-Newton (STQN) calculations were run with the 'QST2' option (two intermediate geometries given as input) and the structure generated used as input in a transition state optimisation.