What Can We Learn from the Crystal Structures of Metallacarboranes ?

The determination of the molecular structures of metallacarboranes by X-ray diffraction remains critical to the development of the field, in some cases being the only viable way in which the overall architecture and the isomeric form of the molecule can be established. In such studies one problem frequently met is how to distinguish correctly {BH} and {CH} vertices, and this review begins by describing two relatively new methods, the Vertex-Centroid Distance (VCD) and Boron-Hydrogen Distance (BHD) methods, that have been developed to overcome the problem. Once the cage C atoms are located correctly, the resulting metallacarborane structure can frequently be analysed on the basis that cage B has a greater Structural Trans Effect (STE) than does cage C. In the absence of significant competing effects this gives rise to unequal M–L distances for a homogeneous ligand set and to a preferred Exopolyhedral Ligand Orientation (ELO) for a heterogeneous ligand set. ELO considerations can be used, amongst other things, to rank order the STEs of ligands and to identify suspect (in terms of cage C atom positions) metallacarborane structures.

Crystals 2017, 7, 234 2 of 19 closure of a 13-vertex precursor.This makes it impossible to predict with confidence the correct isomeric form of the 12-vertex cobaltacarborane by either chemical intuition or NMR spectroscopy and means that recourse to crystallographic study is necessary.At the time of writing, six of the eight known isomers of [CpCoC2B9H11] have been characterised crystallographically [9][10][11][12][13][14].

Distinguishing B and C Vertices
The structural studies we have performed on the isomers of [CpCoC2B9H11] highlight an important point-since the isomers are distinguished only by the positions of the {BH} and {CH} fragments, in a crystallographic study can one be completely confident which non-metal vertices are boron and which are carbon?This is a relevant and long-standing question in structural studies of carboranes and heterocarboranes because the atomic scattering factors for X-rays, f, of B and C are similar due to the adjacency of these elements in the Periodic Table .Consistent with it being an established problem, two early methods were developed to locate the C atoms in carboranes and heterocarboranes in cases where the C atom does not carry a non-H substituent (typically alkyl or aryl group): i.
Make use of the conventional wisdom that the lengths of cage connectivities are C−C < C−B < B−B.The basis of this is simply that C has a smaller atomic radius than B since the valence electrons experience a greater effective nuclear charge (Zeff) through imperfect shielding. ii.
Refine all the potential cage C and cage B atoms as B (the Prostructure) and identify the C atoms by their relatively small Ueq values, since if insufficient electron density has been assigned to an atom, the process of least-squares refinement compensates by condensing the available electron density, shrinking Ueq.

Distinguishing B and C Vertices
The structural studies we have performed on the isomers of [CpCoC 2 B 9 H 11 ] highlight an important point-since the isomers are distinguished only by the positions of the {BH} and {CH} fragments, in a crystallographic study can one be completely confident which non-metal vertices are boron and which are carbon?This is a relevant and long-standing question in structural studies of carboranes and heterocarboranes because the atomic scattering factors for X-rays, f, of B and C are similar due to the adjacency of these elements in the Periodic Table .Consistent with it being an established problem, two early methods were developed to locate the C atoms in carboranes and heterocarboranes in cases where the C atom does not carry a non-H substituent (typically alkyl or aryl group): i Make use of the conventional wisdom that the lengths of cage connectivities are C-C < C-B < B-B.The basis of this is simply that C has a smaller atomic radius than B since the valence electrons experience a greater effective nuclear charge (Z eff ) through imperfect shielding.ii Refine all the potential cage C and cage B atoms as B (the Prostructure) and identify the C atoms by their relatively small U eq values, since if insufficient electron density has been assigned to an atom, the process of least-squares refinement compensates by condensing the available electron density, shrinking U eq .
Both these approaches to cage C atom identification have merit but they also have limitations.Everything else being equal, the paradigm C-C < C-B < B-B is perfectly sound.Thus, unambiguous crystallographic studies of the three icosahedral carborane isomers [closo-  , in which the cage C atoms were clearly identified by H-bonding interactions [15], afforded C-C 1.630(8) Å, C-B 1.705( 14) Å and B-B 1.772(11) Å.Therefore, in an icosahedral metallacarborane derived from [closo-1,2-C 2 B 10 H 12 ] in which the cage C atoms retain their adjacency, and whose crystal structure is free from disorder [16], it should be fairly obvious which vertices are C from inspection of the lengths of the cage connectivities.It necessarily becomes less clear when the cage C atoms are not adjacent, but in such cases cage C should still be distinguishable.
Problems arise, however, in species in which the degree of each vertex (the number of cage connectivities it makes), is not equal.In an icosahedral cluster, all vertices are degree-5, but in sub-icosahedral clusters some vertices are degree-4, whilst in supraicosahedral clusters some are degree-6, and since the lengths of the connectivities increase with the degree of a vertex the simple pattern C-C < C-B < B-B can be overturned.Thus, for example, in the 7-vertex anion [3-Cl-closo-2-CB 6 H 6 ] − , shown in Figure 2a, the C2-B1 and C2-B7 distances (between degree-4 C and degree-5 B) are significantly longer than the B4−B5 and B5−B6 distances (between two degree-4 B atoms) [17], and in the 10-vertex carborane [8-Br-closo-1,6-C 2 B 8 H 9 ], Figure 2b, all the connectivities from degree-5 C6 to degree-5 B atoms are longer than those from degree-4 B10 to the degree-5 atoms B7 and B9 [18].In the 14-vertex cobaltacarborane [1,13-Cp 2 -closo-1,13,2,9-Co 2 C 2 B 10 H 12 ], Figure 3a, the C9-B14 distance is actually longer than the B11-B14 distance, even though C9 and B11 are both degree-5 and B14 is degree-6 [19].Clearly it would be challenging to predict with confidence the cage C atom positions in cases like these on the basis of connectivity lengths alone.icosahedral metallacarborane derived from [closo-1,2-C2B10H12] in which the cage C atoms retain their adjacency, and whose crystal structure is free from disorder [16], it should be fairly obvious which vertices are C from inspection of the lengths of the cage connectivities.It necessarily becomes less clear when the cage C atoms are not adjacent, but in such cases cage C should still be distinguishable.Problems arise, however, in species in which the degree of each vertex (the number of cage connectivities it makes), is not equal.In an icosahedral cluster, all vertices are degree-5, but in subicosahedral clusters some vertices are degree-4, whilst in supraicosahedral clusters some are degree-6, and since the lengths of the connectivities increase with the degree of a vertex the simple pattern C−C < C−B < B−B can be overturned.Thus, for example, in the 7-vertex anion [3-Cl-closo-2-CB6H6] − , shown in Figure 2a, the C2−B1 and C2−B7 distances (between degree-4 C and degree-5 B) are significantly longer than the B4−B5 and B5−B6 distances (between two degree-4 B atoms) [17], and in the 10-vertex carborane [8-Br-closo-1,6-C2B8H9], Figure 2b, all the connectivities from degree-5 C6 to degree-5 B atoms are longer than those from degree-4 B10 to the degree-5 atoms B7 and B9 [18].In the 14-vertex cobaltacarborane [1,13-Cp2-closo-1,13,2,9-Co2C2B10H12], Figure 3a, the C9−B14 distance is actually longer than the B11−B14 distance, even though C9 and B11 are both degree-5 and B14 is degree-6 [19].Clearly it would be challenging to predict with confidence the cage C atom positions in cases like these on the basis of connectivity lengths alone.Using Ueq values to identify cage C atoms can also be problematic, simply because the Ueq of an atom is influenced by its local environment.In particular, heavy atoms frequently suppress the Ueq icosahedral metallacarborane derived from [closo-1,2-C2B10H12] in which the cage C atoms retain their adjacency, and whose crystal structure is free from disorder [16], it should be fairly obvious which vertices are C from inspection of the lengths of the cage connectivities.It necessarily becomes less clear when the cage C atoms are not adjacent, but in such cases cage C should still be distinguishable.Problems arise, however, in species in which the degree of each vertex (the number of cage connectivities it makes), is not equal.In an icosahedral cluster, all vertices are degree-5, but in subicosahedral clusters some vertices are degree-4, whilst in supraicosahedral clusters some are degree-6, and since the lengths of the connectivities increase with the degree of a vertex the simple pattern C−C < C−B < B−B can be overturned.Thus, for example, in the 7-vertex anion [3-Cl-closo-2-CB6H6] − , shown in Figure 2a, the C2−B1 and C2−B7 distances (between degree-4 C and degree-5 B) are significantly longer than the B4−B5 and B5−B6 distances (between two degree-4 B atoms) [17], and in the 10-vertex carborane [8-Br-closo-1,6-C2B8H9], Figure 2b, all the connectivities from degree-5 C6 to degree-5 B atoms are longer than those from degree-4 B10 to the degree-5 atoms B7 and B9 [18].In the 14-vertex cobaltacarborane [1,13-Cp2-closo-1,13,2,9-Co2C2B10H12], Figure 3a, the C9−B14 distance is actually longer than the B11−B14 distance, even though C9 and B11 are both degree-5 and B14 is degree-6 [19].Clearly it would be challenging to predict with confidence the cage C atom positions in cases like these on the basis of connectivity lengths alone.Using Ueq values to identify cage C atoms can also be problematic, simply because the Ueq of an atom is influenced by its local environment.In particular, heavy atoms frequently suppress the Ueq Using U eq values to identify cage C atoms can also be problematic, simply because the U eq of an atom is influenced by its local environment.In particular, heavy atoms frequently suppress the U eq of atoms directly bonded to them, meaning that this approach to discriminating between B and C atoms can be particularly unreliable for metallacarboranes.As an example, consider the cobaltacarborane [1,13-Cp 2 -closo-1,13,2,10-Co 2 C 2 B 10 H 12 ] [19].Figure 3b shows the Prostructure and Table 1 lists the U eq values of vertices 2-12 and 14 in this Prostructure.Vertices 2 and 10 correspond to C atoms (U eq underlined) but whilst vertex 2 has the smallest U eq of all the vertices, the U eq of vertex 10 is larger than that of seven B atoms (U eq italicised).Vertex 2 is directly connected to both Co atoms and all B atoms with U eq values smaller than that of vertex 10 are bound to at least one Co, whilst vertex 10 is directly connected to neither, clearly illustrating the influence of an adjacent metal on the magnitude of U eq .In summary, both of the established methods (connectivity lengths and U eq values) for distinguishing between {BH} and {CH} fragments in (hetero)carboranes generally, and metalla(hetero)carboranes specifically, have deficiencies and should be used with caution.Because of this we have developed two further approaches to the problem which we term the Vertex-Centroid Distance (VCD) method and the Boron-Hydrogen Distance (BHD) method.

The VCD Method
The basis of the Vertex-Centroid Distance method, similar to that of the connectivity length approach, is that carbon has a smaller atomic radius than boron.In the VCD method the centroid of the cluster is calculated and the distances from each vertex to the centroid are measured.Since carbon is smaller than boron, the C atoms will lie closer to the centroid and are therefore identified by the VCDs.The advantage of this method over the connectivity length approach is that (i) a single parameter is associated with each vertex (greatly simplifying analysis), and (ii) it is independent of the isomer, working just as well for species in which two C atoms are separated as those in which the C atoms are adjacent.
We first described the VCD method in 2013, carefully validating it against a large number of carborane and metallacarborane structures in the literature in which the cage C atoms were located unambiguously [19].The method is independent of whether a particular vertex has been refined as B or C (this only affects U eq of the vertex not its position), so we were able to use the VCD approach to identify literature cases in which cage C had been wrongly positioned, to suggest B/C disorder that had been overlooked and to refute erroneously assigned disorder.
In the VCD method some care needs to be taken in calculating the position of the polyhedral centroid and in interpreting the VCDs.In the case of the 11-vertex nido polyhedron in Figure 4a only vertices 2-11 should be used to define the centroid, since to include vertex 1 would bias the centroid towards it.Equally, in the 10-vertex closo metallacarborane in Figure 4b, the metal vertex 1 should be excluded from the centroid calculation (since metal atoms generally lie further from the centroid than do B or C atoms) and, for balance, the antipodal vertex 10 should also be excluded.Note, however, that even if a vertex is excluded from the set from which the centroid is calculated, the VCD from that vertex can still be used.When using VCD it is important that only VCDs from equivalent vertices (as defined by symmetry-equivalence with respect to the parent closed polyhedron) are compared.Thus, in the polyhedron shown in Figure 4b only VCDs from the degree-5 vertices 2-9 should be compared (the VCD from the degree-4 vertex 10 will be considerably longer), and in the dodecahedral cluster of Figure 4c VCDs from the degree-4 vertices 1, 2, 7, and 8 should be compared as one group and those from the degree-5 vertices 3-6 compared as a separate group.dodecahedral cluster of Figure 4c VCDs from the degree-4 vertices 1, 2, 7, and 8 should be compared as one group and those from the degree-5 vertices 3-6 compared as a separate group.Centroids and VCDs are easily calculated using standard software such as Mercury [20] or Olex2 [21].Roughly speaking, within a set of equivalent vertices a VCD to carbon will be typically 0.1-0.15Å shorter than a VCD to boron, as demonstrated by the entries in Table 2 for the carborane [closo-1,7-C2B10H12] in which the positions of the cage C atoms are unambiguously known by their involvement in intermolecular H-bonding [15].One caveat to the VCD approach to identifying cage C positions that we have recently identified concerns carborane cages in which a cage C atom is σ-bonded to a metal atom.These C atoms have longer VCDs than equivalent C atoms not involved in M−C bonding, making the distinction between B and C less obvious (the VCD to this C atom may even exceed that to B), and Table 3 demonstrates this effect in the case of [1-{CpRu(PMe2Ph)2}-2-Me-closo-1,2-C2B10H10] [22].In such cases, however, the presence of M−C bonding should be clearly inferred from NMR spectroscopy.This notwithstanding, we have found that the VCD method is a quick and effective addition to the techniques available to distinguish B and C atoms in carboranes and heterocarboranes.One useful Centroids and VCDs are easily calculated using standard software such as Mercury [20] or Olex2 [21].Roughly speaking, within a set of equivalent vertices a VCD to carbon will be typically 0.1-0.15Å shorter than a VCD to boron, as demonstrated by the entries in Table 2 for the carborane [closo-1,7-C 2 B 10 H 12 ] in which the positions of the cage C atoms are unambiguously known by their involvement in intermolecular H-bonding [15]. 1 The C atoms are at vertices 1 and 7.

Vertex
One caveat to the VCD approach to identifying cage C positions that we have recently identified concerns carborane cages in which a cage C atom is σ-bonded to a metal atom.These C atoms have longer VCDs than equivalent C atoms not involved in M-C bonding, making the distinction between B and C less obvious (the VCD to this C atom may even exceed that to B), and Table 3 [22].In such cases, however, the presence of M-C bonding should be clearly inferred from NMR spectroscopy.This notwithstanding, we have found that the VCD method is a quick and effective addition to the techniques available to distinguish B and C atoms in carboranes and heterocarboranes.One useful benefit is that because VCD uses only atomic coordinates the method can be used to check published carborane and heterocarborane structures, useful in analysis of literature compounds [23].

The BHD Method
The basis of the Boron-Hydrogen Distance method is that crystallographic refinement of an atom at which insufficient electron density has been assigned will compensate for this by moving a bound H atom artificially close to that atom.Thus, in the Prostructure, if a vertex which is really C has been refined as B, not only will U eq be relatively small but an unusually short vertex-H distance will be observed.In a carborane or heterocarborane, a typical B-H bond length is ca.1.1 Å and a typical C-H distance ca.1.0 Å.But if a C atom has been refined as B, the vertex-H distance will usually be shortened to between 0.2 and 0.5 Å, clearly identifying the vertex as a C atom.Short bonds to H are clearly visible at vertices 2 and 10 of Figure 3b, and Table 4 summarises all the vertex-H bonds in this Prostructure.On correctly assigning the vertices as C, further refinement subsequently affords perfectly sensible vertex-H bond lengths. 1 For each vertex the left entry is for the Prostructure, the right entry for the final, correctly assigned, structure.
We first described the BHD method in 2002 [24] and reported on it more comprehensively in 2014 [25].It relies on crystallographic data of reasonable precision (and certainly the ability to refine H atoms positionally) but given that a standard crystallographic experiment typically now involves data collected at low temperature on a CCD-equipped diffractometer precise diffraction data should be routinely achieved.Moreover, the practice of including F 2 data in CIFs means that the BHD method can now be used to check recent literature structures.
It is now standard operating procedure in our laboratory to use both the VCD and BHD methods to help distinguish between {BH} and {CH} fragments using the Prostructures of carboranes and heterocarboranes, in conjunction with the established practices of inspection of the lengths of cage connectivities and the values of U eq .When all four methods lead to the same conclusion, we can have a high level of confidence that the C atoms are correctly located.Being confident about C atom positions is a vital prerequisite for an analysis of metallacarborane structures, discussed below.

Structural Trans Effects in Metallacarboranes
By far the most common carborane ligand is [nido-7,8-C 2 B 9 H 11 ] 2− , easily derived from [closo-1,2-C 2 B 10 H 12 ] by a straightforward deboronation reaction.When this anion is bound η 5 to a metal atom the resultant metallacarborane is the 3,1,2-MC 2 B 9 isomer.There are hundreds of examples of such metallacarboranes [3], very many of which have been subject to crystallographic study (a search for the {3,1,2-MC 2 B 9 H 11 } fragment in the Cambridge Structural Database (CSD) [26] affords nearly 400 hits).What useful information can we glean from these many structural studies?
A fundamental issue is that, although the carborane is bound η 5 , the C and B atoms in the upper pentagonal face do not bind equally strongly to the metal atom.Since Z eff C > Z eff B, the C atoms contribute disproportionately more to the core molecular orbitals and the facial B atoms contribute more to the frontier molecular orbitals (FMOs) of the carborane ligand, leading to relatively weak M-C bonding [27].However, this relatively weak M-C bonding is not directly obvious from crystallographic studies due to the smaller radius of C compared to B (see above).Thus, for example, in

Exopolyhedral Ligand Orientation
In cases where the non-carborane ligand is η-bonded but asymmetric or in cases where the κ 1 -bound ligand set is heterogeneous, the STE in metallacarboranes gives rise to a preferred Exopolyhedral Ligand Orientation (ELO) of the non-carborane ligand(s).In the absence of significant competing effects, the preferred ELO will be that in which the exopolyhedral ligand (or part of ligand) with the greater or greatest STE lies approximately trans to cage C, whilst that with smaller or smallest STE lies approximately trans to cage B. Thus, the differing STEs of the cage C and cage B atoms control the orientation of the exopolyhedral ligand(s).

ELO of η-Bound Ligands
A striking example of preferred exopolyhedral ligand orientation comes from comparison of the structures of metallacarboranes with pyrrolyl and boratabenzene as exopolyhedral ligands.7a, the orientation of the pyrrolyl ring is such that the N heteroatom lies above the C1-C2 connectivity of the carborane ligand [32], whilst in [3-(C 5 H 5 BMe)-closo-3,1,2-RhC 2 B 9 H 11 ], Figure 7b, the boratabenzene ligand is oriented such that its B heteroatom is positioned trans to C1-C2 [33].Given that Z eff N > Z eff C > Z eff B, in the pyrrolyl ligand the N atom will contribute least to the π-FMOs and have the smallest STE, whilst in the boratabenzene ligand the B atom will contribute most to the π-FMOs and have the greatest STE.Hence the observed, very different, exopolyhedral ligand orientations are rationalised.

Exopolyhedral Ligand Orientation
In cases where the non-carborane ligand is η-bonded but asymmetric or in cases where the κ 1bound ligand set is heterogeneous, the STE in metallacarboranes gives rise to a preferred Exopolyhedral Ligand Orientation (ELO) of the non-carborane ligand(s).In the absence of significant competing effects, the preferred ELO will be that in which the exopolyhedral ligand (or part of ligand) with the greater or greatest STE lies approximately trans to cage C, whilst that with smaller or smallest STE lies approximately trans to cage B. Thus, the differing STEs of the cage C and cage B atoms control the orientation of the exopolyhedral ligand(s).

ELO of η-bound ligands
A striking example of preferred exopolyhedral ligand orientation comes from comparison of the structures of metallacarboranes with pyrrolyl and boratabenzene as exopolyhedral ligands.In [3-(C4H4N)-closo-3,1,2-CoC2B9H11], Figure 7a, the orientation of the pyrrolyl ring is such that the N heteroatom lies above the C1−C2 connectivity of the carborane ligand [32], whilst in [3-(C5H5BMe)closo-3,1,2-RhC2B9H11], Figure 7b, the boratabenzene ligand is oriented such that its B heteroatom is positioned trans to C1−C2 [33].Given that Zeff N > Zeff C > Zeff B, in the pyrrolyl ligand the N atom will contribute least to the π-FMOs and have the smallest STE, whilst in the boratabenzene ligand the B atom will contribute most to the π-FMOs and have the greatest STE.Hence the observed, very different, exopolyhedral ligand orientations are rationalised.In indenyl, naphthalene, and related η-bonded ligands the π-atomic orbitals of the ring-junction C atoms are simultaneously involved in two aromatic systems and consequently are relatively weakly bound to the metal atom (small STE) compared to the non-ring-junction C atoms.In metallacarborane complexes of these ligands this gives rise to a preferred ELO.Thus in [3-(C9H7)closo-3,1,2-CoC2B9H11], Figure 8a, the η 5 -indenyl ligand is oriented such that the ring-junction atoms are cisoid to the cage C atoms (cisoid describes the orientation in which atoms are as close to each other as possible given the overall staggered conformation of η 5 -indenyl and η 5 -carborane rings) [12].In the analogous iron species [3-(C9H7)-closo-3,1,2-FeC2B9H11] the two rings are eclipsed and the ringjunction C atoms sit directly above the cage C atoms [34], rationalised by a significantly greater distance between the rings in the iron complex (3.23 Å) compared to that in the cobalt complex (3.09Å).One η 5 -fluorenyl metallacarborane is known [35].In the fluorenyl ligand are two pairs of ring- In indenyl, naphthalene, and related η-bonded ligands the π-atomic orbitals of the ring-junction C atoms are simultaneously involved in two aromatic systems and consequently are relatively weakly bound to the metal atom (small STE) compared to the non-ring-junction C atoms.In metallacarborane complexes of these ligands this gives rise to a preferred ELO.Thus in [3-(C 9 H 7 )-closo-3,1,2-CoC 2 B 9 H 11 ], Figure 8a, the η 5 -indenyl ligand is oriented such that the ring-junction atoms are cisoid to the cage C atoms (cisoid describes the orientation in which atoms are as close to each other as possible given the overall staggered conformation of η 5 -indenyl and η 5 -carborane rings) [12].In the analogous iron species [3-(C 9 H 7 )-closo-3,1,2-FeC 2 B 9 H 11 ] the two rings are eclipsed and the ring-junction C atoms sit directly above the cage C atoms [34], rationalised by a significantly greater distance between the rings in the iron complex (3.23 Å) compared to that in the cobalt complex (3.09Å).One η 5 -fluorenyl metallacarborane is known [35] A final example of the preferred orientation of an η-bonded ligand in a metallacarborane is when that η-bonded ligand is another carborane.Without doubt the single most studied metallacarborane is

ELO of κ 1 ligands
A significant number of [L3MC2B9H11] metallacarboranes (where the metallacarborane is the 3,1,2-MC2B9 isomer) are known in which the three ligands L are not all the same, and within examples which have been studied crystallographically, a well-represented sub-group is that with two phosphine ligands and one chloride ligand.When M = Co or Rh these are neutral, 18-e species.For M = Ru an 18-e monoanion is known, but there is also a series of 17-e neutral species for both Fe and Ru.All these compounds, together with their CSD refcodes and the torsion angles (θ) for each of the exopolyhedral ligands, are listed in Table 5. Entries in italics refer to 17-e compounds.

ELO of κ 1 ligands
A significant number of [L3MC2B9H11] metallacarboranes (where the metallacarborane is the 3,1,2-MC2B9 isomer) are known in which the three ligands L are not all the same, and within examples which have been studied crystallographically, a well-represented sub-group is that with two phosphine ligands and one chloride ligand.When M = Co or Rh these are neutral, 18-e species.For M = Ru an 18-e monoanion is known, but there is also a series of 17-e neutral species for both Fe and Ru.All these compounds, together with their CSD refcodes and the torsion angles (θ) for each of the exopolyhedral ligands, are listed in Table 5. Entries in italics refer to 17-e compounds.

ELO of κ 1 Ligands
A significant number of [L 3 MC 2 B 9 H 11 ] metallacarboranes (where the metallacarborane is the 3,1,2-MC 2 B 9 isomer) are known in which the three ligands L are not all the same, and within examples which have been studied crystallographically, a well-represented sub-group is that with two phosphine ligands and one chloride ligand.When M = Co or Rh these are neutral, 18-e species.For M = Ru an 18-e monoanion is known, but there is also a series of 17-e neutral species for both Fe and Ru.All these compounds, together with their CSD refcodes and the torsion angles (θ) for each of the exopolyhedral ligands, are listed in Table 5. Entries in italics refer to 17-e compounds. 1These structures differ in that NITWOC contains solvate; 2 dppp 3 = diphenylphosphinopropane; 3   1 These structures differ in that NITWOC contains solvate; 2 dppp3 = diphenylphosphinopropane; 3 2,4-dppp5 = 2,4-diphenylphosphinopentane; 4 1,5-dppp5 = 1,5-diphenylphosphinopentane.
It is immediately apparent that in all cases the ligand with the lowest |θ| (ca.0-20°) is always Cl, whilst one P atom has |θ| ca.95-115° and the other P has |θ| ca.125-145°.There is therefore a clear orientational preference for a {MClP2} fragment in a 3,1,2-MC2B9 metallacarborane in which the Cl ligand is located cis to the cage C atoms, fully consistent with the STE of Cl being smaller than that of phosphine.
How strong is this orientational preference?Using DFT calculations we have computed the energy of the model compound [3,3-(PH3)2-3-Cl-closo-3,1,2-RhC2B9H11] as a function of |θCl| [49], and the results are plotted in Figure 10.The global minimum is the conformation with |θCl| = 0°, ca. 15 kcal mol −1 more stable than the conformation with |θCl| = 180°.The strength of this orientational preference is therefore of the order of strong H-bonding implying that, in the absence of significant inter-or intramolecular forces (which could be either attractive or repulsive), the exopolyhedral ligand orientation should be controlled by the relative structural trans effects of the ligands.The |θCl| values of the 12 compounds in Table 5 all fall within the small circle superimposed on Figure 10.In all the above cases the 3,1,2-MC 2 B 9 metallacarborane contains two exopolyhedral ligands with relatively large STEs and one with a relatively small STE.Fewer examples exist of the reverse situation; two ligands with relatively small STEs and one with a relatively large STE.In [3,3-(PPh 3 ) 2 -3-H-closo-3,1,2-RuC 2 B 9 H 11 ] − , shown in Figure 11a, the ligand with the smallest |θ| is one of the relatively weak PPh 3 ligands [44], whilst the other PPh 3 ligand at greater |θ| has a significantly shorter Ru-P bond length, consistent with it lying less trans to boron.The ligand with the greatest |θ| is the relatively strong H.A similar situation pertains in [3,3-(κ 2 -tmeda)-3-CO-closo-3,1,2-RuC 2 B 9 H 11 ], Figure 11b [52].Here the relatively atoms are the N atoms of the tmeda ligand and the strong ligand is CO.One N has the smallest |θ| whilst the other N is significantly closer to the metal atom.The CO ligand is oriented with the greatest |θ|.A secondary feature of both these structures is that since the single ligand with the greater STE (H and CO, respectively) is positioned essentially directly trans to C1, the Ru-C1 connectivity is significantly longer than Ru-C2.In all the above cases the 3,1,2-MC2B9 metallacarborane contains two exopolyhedral ligands with relatively large STEs and one with a relatively small STE.Fewer examples exist of the reverse situation; two ligands with relatively small STEs and one with a relatively large STE.In [3,3-(PPh3)2-3-H-closo-3,1,2-RuC2B9H11] − , shown in Figure 11a, the ligand with the smallest |θ| is one of the relatively weak PPh3 ligands [44], whilst the other PPh3 ligand at greater |θ| has a significantly shorter Ru−P bond length, consistent with it lying less trans to boron.The ligand with the greatest |θ| is the relatively strong H.A similar situation pertains in [3,3-(κ 2 -tmeda)-3-CO-closo-3,1,2-RuC2B9H11], Figure 11b [52].Here the relatively weakly-bound atoms are the N atoms of the tmeda ligand and the strong ligand is CO.One N has the smallest |θ| whilst the other N is significantly closer to the metal atom.The CO ligand is oriented with the greatest |θ|.A secondary feature of both these structures is that since the single ligand with the greater STE (H and CO, respectively) is positioned essentially directly trans to C1, the Ru−C1 connectivity is significantly longer than Ru−C2.

Applications of ELO
There are a number of ways in which the recognition of exopolyhedral ligand orientation can be useful in metallacarborane chemistry.In the following sections, we discuss only a few selected examples to illustrate the potential value of ELO considerations in this area.

Rank Ordering the STEs of Exopolyhedral Ligands
We have noted that the preferred orientation of exopolyhedral ligands in mixed-ligand 3,1,2-MC2B9 metallacarboranes is consistent with STEs in the relative order H > PR3 > Cl.This is as expected since there is general agreement in the literature that H is a strong STE ligand, phosphines have a moderate STE, and Cl is invariably weak [53,54].Rankings of the STEs of ligands are usually made on the basis of extensive compilations of M−X distances, where X is a probe ligand trans to the ligand in question.In contrast, analysis of metallacarborane structures allows the STEs of ligands to be compared very quickly, based on a simple orientational preference.
CO and PPh3 are both considered as moderate STE ligands.Coe and Glenwright order their STEs as CO > PPh3 on the basis of analysis of [M(CO)5PPh3] structures [53], whilst See and Kozina conclude the reverse ordering, PPh3 > CO, from analysis of the structures of complexes in which these ligands are trans to Cl [54].We recently surveyed the preferred ELO in mixed carbonyl-phosphine 3,1,2-

Applications of ELO
There are a number of ways in which the recognition of exopolyhedral ligand orientation can be useful in metallacarborane chemistry.In the following sections, we discuss only a few selected examples to illustrate the potential value of ELO considerations in this area.

Rank Ordering the STEs of Exopolyhedral Ligands
We have noted that the preferred orientation of exopolyhedral ligands in mixed-ligand 3,1,2-MC 2 B 9 metallacarboranes is consistent with STEs in the relative order H > PR 3 > Cl.This is as expected since there is general agreement in the literature that H is a strong STE ligand, phosphines have a moderate STE, and Cl is invariably weak [53,54].Rankings of the STEs of ligands are usually made on the basis of extensive compilations of M-X distances, where X is a probe ligand trans to the ligand in question.In contrast, analysis of metallacarborane structures allows the STEs of ligands to be compared very quickly, based on a simple orientational preference.
An understanding of the unexpected ELOs in TAKCUD and LICDOQ is afforded by a detailed examination of their structures, revealing intramolecular H-bonding between the O atom of the acetyl or methoxyalkylidene ligand and the protonic H atom(s) on cage carbon.In TAKCUD, Figure 12a, the H-bond is between O1 and H2 whilst in LICDOQ, Figure 12b ) and concluded that, at least in this class of compound, the STE of CO is greater than that of PPh3 [55].
An understanding of the unexpected ELOs in TAKCUD and LICDOQ is afforded by a detailed examination of their structures, revealing intramolecular H-bonding between the O atom of the acetyl or methoxyalkylidene ligand and the protonic H atom(s) on cage carbon.In TAKCUD, Figure 12a, the H-bond is between O1 and H2 whilst in LICDOQ, Figure 12b

Rapid Identification of Suspect Structures
Since, in the absence of intramolecular H-bonding or steric crowding, the ELO is a direct consequence of the cage C positions, literature structures with an unexpected ELO may signify that the cage C atoms are wrongly placed.One such example concerns the rhodacarborane [3,3-(κ 2 -NO3)-3-PPh3-closo-3,1,2-RhC2B9H11], the original structure of which was published in 1979 [61].It was clear from the high e.s.d.s that this was a relatively imprecise structure (room temperature data collection on a serial diffractometer), but what was particularly striking was the orientation of the nitrato and phosphine ligands, with the latter apparently cis to the cage C atoms, Figure 14a.Nitrate is a very weak ligand compared to PPh3, so this orientation was certainly suspicious.

Rapid Identification of Suspect Structures
Since, in the absence of intramolecular H-bonding or steric crowding, the ELO is a direct consequence of the cage C positions, literature structures with an unexpected ELO may signify that the cage C atoms are wrongly placed.One such example concerns the rhodacarborane [3,3-(κ 2 -NO 3 )-3-PPh 3 -closo-3,1,2-RhC 2 B 9 H 11 ], the original structure of which was published in 1979 [61].It was clear from the high e.s.d.s that this was a relatively imprecise structure (room temperature data collection on a serial diffractometer), but what was particularly striking was the orientation of the nitrato and phosphine ligands, with the latter apparently cis to the cage C atoms, Figure 14a.Nitrate is a very weak ligand compared to PPh 3 , so this orientation was certainly suspicious.VCD analysis supported the possibility that the cage C atoms were misplaced.Consequently, we resynthesised the compound and redetermined the structure (at low temperature using a CCD-equipped diffractometer), locating the cage C atoms unambiguously and at different vertices to those of the original structure [19].The new structure, Figure 14b, is fully consistent with ELO expectations since in both crystallographically-independent molecules the PPh 3 ligand now lies at large |θ| values, 168.9 and 174.VCD analysis supported the possibility that the cage C atoms were misplaced.Consequently, we resynthesised the compound and redetermined the structure (at low temperature using a CCDequipped diffractometer), locating the cage C atoms unambiguously and at different vertices to those of the original structure [19].The new structure, Figure 14b, is fully consistent with ELO expectations since in both crystallographically-independent molecules the PPh3 ligand now lies at large |θ| values, 168.9 and 174.3°.

Exploring the STEs of Cage Heteroatoms
Since the ELOs of a heterogeneous set of ligands of differing STEs are a consequence of the differing STEs of boron and cage heteroatoms, it should be possible to use the ELOs to comment on the STEs of those cage heteroatoms, relative to boron.Figure 15  Finally, there is some evidence that consideration of ELO can allow comment on the relative STEs of cage vertices of differing degrees.In the 13-vertex stannacarborane [1,10-Me2-4,4-(κ 2 -Me2bipy)-closo-4,1,10-SnC2B10H10], shown in Figure 16a, the Sn4 centre has a κ 2 -dimethylbipyridine ligand and a stereochemically-active lone pair of electrons.The orientation of the dimethylbipyridine, lying cis to the degree-4 atom C1 and trans to the degree-5 atom C10, implies that degree-4 C has a larger STE than degree-5 C, which is intuitively reasonable [65].On thermolysis of the analogous bipyridine species the cage undergoes isomerisation from 4,1,10-SnC2B10 to 4,1,12-SnC2B10, affording [1,12-Me2-4,4-(κ 2 -bipy)-closo-4,1,12-SnC2B10H10], Figure 16b, and the bipyridine ligand "flips" so that it now lies trans to C1 and cis to B10.This suggests that, in terms of STE, degree-5 B > degree-4 C, which is not intuitively obvious.Note that even though in these stannacarborane molecules the cage Finally, there is some evidence that consideration of ELO can allow comment on the relative STEs of cage vertices of differing degrees.In the 13-vertex stannacarborane [1,10-Me 2 -4,4-(κ 2 -Me 2 bipy)-closo-4,1,10-SnC 2 B 10 H 10 ], shown in Figure 16a, the Sn4 centre has a κ 2 -dimethylbipyridine ligand and a stereochemically-active lone pair of electrons.The orientation of the dimethylbipyridine, lying cis to the degree-4 atom C1 and trans to the degree-5 atom C10, implies that degree-4 C has a larger STE than degree-5 C, which is intuitively reasonable [65].On thermolysis of the analogous bipyridine species the cage undergoes isomerisation from 4,1,10-SnC 2 B 10 to 4,1,12-SnC 2 B 10 , affording [1,12-Me 2 -4,4-(κ 2 -bipy)-closo-4,1,12-SnC 2 B 10 H 10 ], Figure 16b, and the bipyridine ligand "flips" so that it now lies trans to C1 and cis to B10.This suggests that, in terms of STE, degree-5 B > degree-4 C, which is not intuitively obvious.Note that even though in these stannacarborane molecules the cage C atoms carry Me substituents, space-filling models suggest that intramolecular steric crowding is minimal and consequently that the exopolyhedral ligand orientation is electronically-controlled.

Conclusions
What can we learn from the crystal structures of metallacarboranes?It goes without saying that, in common with such studies generally, crystallographic structure determination provides absolute proof of the identity and isomeric nature of the metallacarborane that, in the vast majority of cases, can be correlated with the synthetic procedure used, the spectroscopic properties, and chemical reactivity of the compound and, increasingly, the structure optimised by computational means.In addition, however, this review has demonstrated that the heterogeneity of a carborane ligand, manifest in the differing structural trans effects (STEs) of carbon and boron, leads to heterogeneity in the bonding of exopolyhedral ligands and preferred orientations of these ligands.Recognition of this can be used, amongst other things, to establish quickly and simply the relative STEs of exopolyhedral ligands and to identify literature structures which are suspicious.All of this, however, is predicated on the cage C atoms being correctly identified in the crystallographic study.This sometimes remains a challenge, but new approaches such as the VCD and BHD methods have been developed to overcome that challenge, and have proven to be useful in many cases.Unfortunately, most papers which report (hetero)carborane crystal structures give no indication as to how the cage C and cage B atoms were distinguished, whether it be by one of the newer methods or by the more established approaches of analysis of the lengths of the cage connectivities and/or Ueq values of the vertex atoms.Such detail, although minor, would be a welcome addition to published work.

Figure 4 .
Figure 4. Choosing the correct vertices to define the polyhedral centroid and comparing vertexcentroid distances (VCDs) within an appropriate group: (a) A nido 11-vertex polyhedron-the centroid is defined by only vertices 2-11 but all VCDs can be compared as a single group; (b) A closo 10-vertex polyhedron with a metal atom at vertex 1-the centroid should be defined by vertices 2-9 only, and only VCDs from these vertices should be compared; (c) A closo 8-vertex polyhedron-all vertices are used to calculate the centroid but the VCDs from vertices 1, 2, 7, and 8 and from vertices 3-6 should be considered separately.

Figure 4 .
Figure 4. Choosing the correct vertices to define the polyhedral centroid and comparing vertex-centroid distances (VCDs) within an appropriate group: (a) A nido 11-vertex polyhedron-the centroid is defined by only vertices 2-11 but all VCDs can be compared as a single group; (b) A closo 10-vertex polyhedron with a metal atom at vertex 1-the centroid should be defined by vertices 2-9 only, and only VCDs from these vertices should be compared; (c) A closo 8-vertex polyhedron-all vertices are used to calculate the centroid but the VCDs from vertices 1, 2, 7, and 8 and from vertices 3-6 should be considered separately.

Figure 6 .
Figure 6.The orientation of the ligand L is defined by the modulus of the torsion angle θ where θ = L−M3−A−B; A is the centroid of the metal-bound C2B3 face (green dot) and B is the centroid of the C1−C2 bond (purple dot).

Figure 6 .
Figure 6.The orientation of the ligand L is defined by the modulus of the torsion angle θ where θ = L−M3−A−B; A is the centroid of the metal-bound C2B3 face (green dot) and B is the centroid of the C1−C2 bond (purple dot).

Figure 6 .
Figure 6.The orientation of the ligand L is defined by the modulus of the torsion angle θ where θ = L-M3-A-B; A is the centroid of the metal-bound C 2 B 3 face (green dot) and B is the centroid of the C1-C2 bond (purple dot).

[ 3 -
Co(1,2-C2B9H11)2] − (trivial name CoSAN) because its stability and tailorability has led to a vast number of applications.Like the very first metallacarboranes, CoSAN is a sandwich complex, formally composed of two [nido-7,8-C2B9H11] 2− anions and a Co 3+ metal centre.There are 73 crystallographic determinations of the [3-Co(1,2-C2B9H11)2] − anion in the CSD and in the vast majority of these the conformation is cisoid.This cisoid conformation, Figure 9, has been shown to be the most thermodynamically stable by DFT calculations performed on the isoelectronic complex [3-Ni(1,2-C2B9H11)2] [37], but it can be very easily rationalised by STE/ELO arguments with the large STE B atoms of one cage lying trans to the small STE C atoms of the other.

Figure 13 .Figure 14 .
Figure 13.(a) The structure of [3,3,3-(CO)3-3-PPh3-closo-3,1,2-MoC2B9H11] (Ph groups omitted for clarity) showing the phosphine at low |θ|; (b) The structure of [1,2-Me2-3,3,3-(CO)3-3-PPh3-closo-3,1,2-MoC2B9H9] (Ph groups omitted for clarity) in which the phosphine is displaced to a high |θ| value by steric crowding between it and the cage Me substituents.Rapid Identification of Suspect StructuresSince, in the absence of intramolecular H-bonding or steric crowding, the ELO is a direct consequence of the cage C positions, literature structures with an unexpected ELO may signify that the cage C atoms are wrongly placed.One such example concerns the rhodacarborane [3,3-(κ 2 -NO3)-3-PPh3-closo-3,1,2-RhC2B9H11], the original structure of which was published in 1979[61].It was clear from the high e.s.d.s that this was a relatively imprecise structure (room temperature data collection on a serial diffractometer), but what was particularly striking was the orientation of the nitrato and phosphine ligands, with the latter apparently cis to the cage C atoms, Figure14a.Nitrate is a very weak ligand compared to PPh3, so this orientation was certainly suspicious.
3 • .Exploring the STEs of Cage Heteroatoms Since the ELOs of a heterogeneous set of ligands of differing STEs are a consequence of the differing STEs of boron and cage heteroatoms, it should be possible to use the ELOs to comment on the STEs of those cage heteroatoms, relative to boron.Figure 15 shows the structures of three icosahedral metallaheteroboranes in which a metal-ligand fragment is bonded to a {B 10 X} cage.From the orientation of the hydride ligands in [2,2-(PPh 3 ) 2 -2-H-closo-2,1-RhNB 10 H 11 ] [62], Figure 15a, and [2,2-(PEt 3 ) 2 -2-H-closo-2,1-PtCB 10 H 11 ] [63], Figure 15b, we conclude that both N and C have smaller STEs than boron.Recall that in Section 3.1.1 the STE ranking B > C > N was deduced from the orientations of pyrrolyl and boratabenzene ligands in metallacarboranes.Also note that, in principle, the orientation of the {PtHP 2 } fragment in the platinacarborane could be used to identify the position of the cage C atom, as an interesting complement to the established methods previously discussed.From the structure of the rhodathiaborane [2,2-(PMe 2 Ph) 2 -2-Cl-closo-2,1-RhSB 10 H 10 ] [64], Figure15c, it is clear that S also has a smaller STE than boron since the ligand with the largest |θ|, P1, makes a significantly shorter Rh-P bond than does P2.