Defective vertices in closo- and nido-borane polyhedra

Boron polyhedra can be described in terms of the deviation of their local v ertex environments from the degree 5 vertices found in ideal icosahedra. Ve rtices of degrees other than 5 can be considered to be defective vertices. The most favorable structures for borane polyhedra are those in which the d efective vertices are isolated as much as possible, similar to the Frank-Ka sper polyhedra found in metal alloy structures. Using this criterion, the 9 -and 10-vertex borane deltahedra are seen to be more favorable than the oth er nonicosahedral deltahedra in the boranes BnHn2- (6 less than or equal to n less than or equal to 12) in accord with experimental observations. Exte nsion of such ideas to neutral boron hydrides of the type BnHn+4 accounts f or the relatively high stability of B10H14, the formation of metal complexe s of B6H10, and the stability of B18H22. In addition, the borane B12H16 is predicted to form stable transition-metal complexes.