Abstract :
Metal-free carboranes having 13 vertices are anomalous since their closo polyhedra having the expected 28 skeletal electrons are not the usual deltahedra with exclusively triangular faces but instead polyhedra with one or two trapezoidal faces obtained by removal of one or more edges from the corresponding 13-vertex deltahedron. Removal of such edges converts degree 6 boron vertices in the 13-vertex deltahedron into more favorable degree 5 boron vertices while lowering the degree of nearby carbon vertices. Thus the anomaly of the 13-vertex carborane closo polyhedron can be rationalized by the preference of boron for degree 5 vertices. The 12-vertex tetracarbon carborane (CH3)4C4B8H8 with a nido electron count of 28 skeletal electrons but with two quadrilateral faces has a solid state structure derived from a 13-vertex “closo” polyhedron with one quadrilateral face by removal of a degree 4 vertex to give the second quadrilateral face. However, the corresponding tetraethyl derivative (C2H5)4C4B8H8 has a different solid state structure derived from removal of a degree 6 vertex from an unusual 13-vertex deltahedron with three degree 6 vertices to give an open hexagonal face rather than two quadrilateral faces. In contrast to the 13-vertex closo polyhedra, the 14-vertex closo polyhedron is a true deltahedron, namely the D6d bicapped hexagonal antiprism, which is found in a carborane derivative as well as in several dimetallacarboranes with the metal atoms always at the degree 6 vertices. However, the 15-vertex closo polyhedron, so far found only in the metallaborane 1,2-μ-(CH2)3C2B12H12Ru(η6-p-cymene), is a non-deltahedron with one quadrilateral face.
