Defective vertices in closo- and nido-borane polyhedra

Boron polyhedra can be described in terms of the deviation of their local vertex environments from the degree 5 vertices found in ideal icosahedra. Vertices of degrees other than 5 can be considered to be defective vertices. The most favorable structures for borane polyhedra are those in which the defective vertices are isolated as much as possible, similar to the Frank-Kasper polyhedra found in metal alloy structures. Using this criterion, the 9- and 10-vertex borane deltahedra are seen to be more favorable than the other nonicosahedral deltahedra in the boranes B(n)H(n)(2-) (6 < or = n < or = 12) in accord with experimental observations. Extension of such ideas to neutral boron hydrides of the type B(n)H(n+4) accounts for the relatively high stability of B(10)H(14), the formation of metal complexes of B(6)H(10), and the stability of B(18)H(22). In addition, the borane B(12)H(16) is predicted to form stable transition-metal complexes.