Localization of MOs and electronic populations in closo-carboranes 1, 5-C2B3H5 and 1,6-C2B4H6

We have analyzed the electronic populations of chemical bonds and atoms in the highly symmetric closo-carboranes 1,5-C2B3H5 (I) and 1,6-C2B4H6 (II). The overlap populations σ/sub XY/ are compared with the corresponding Mulliken indices. We note substantial nonadditivity of the populations σ/sub XY/ for closed three-center bonds BCB' and the closeness of the total overlap populations σ/sub t/ to its maximum value. We have established the localization of the natural MOs on the bonds CH, BH, and BCB', and for molecule I also on the CBC' bonds. The effects of conjugation of bonds in the closo-carborane polyhedron are apparent in the linear dependence of these MOs. The corresponding nonorthogonal hybrid AOs of carbon and boron are also linearly dependent. We have formulated the concept of unshared population of an atom