When is a vertex not a vertex? An analysis of the structures of [MB₁₀H₁₂] metallaboranes

There are two extreme descriptions of the bonding between metal fragments and the {B₁₀H₁₂} ligand. In the first the metal is regarded as a full cluster vertex in an 11 vertex nido metallaborane; the B₁₀ residue is formally arachno-{B₁₀H₁₂}^4-. In the second the metal is a poor cluster vertex and does not significantly perturb the borane fragment architecture, formally nido-{B₁₀H₁₂}^2-. nido-{B₁₀H₁₂}^2- and arachno-{B₁₀H₁₂}^4- have exactly the same pattern of connectivities, but their structures may be distinguished by root mean square (r.m.s.) misfit calculations. Applications of these calculations to [MB₁₀H₁₂] metallaboranes reveals clear examples of both extreme formalisms, and in [(C₆H₁₁)₃PAuB₁₀H₁₂] ^- and [(OC)₃CoB₁₀H₁₂]^- the formal metal oxidation states (Au⁺, Co³⁺) that follow directly from these descriptions of the {B₁₀H₁₂} ligand agree well with independent measurement. In addition, however, several metallaboranes are found to have structures in which the B₁₀ residue lies between that of {B₁₀H₁₂}^2- and {B₁₀H₁₂}^4-. The verticity of a metal fragment is introduced as a convenient way of describing its relative degree of incorporation into the metallaborane as a true cluster vertex. By analysis of the results of extended-Hückel molecular orbital-fragment molecular orbital (EHMO-FMO) calculations verticity is found, to a first approximation, to be directly related to the number of available valence orbitals the metal fragment possesses. Metal fragments that are one-orbital sources are poor vertices, whilst those that are three-orbital sources are good vertices, but the boundary between good- and poor-metal vertex is not well defined and there is, in essence, a continuum of verticity.