A unifying electron-counting rule for macropolyhedral boranes, metallaboranes, and metallocenes

A generally applicable electron-counting rule-the mno rule-that integrates macropolyhedral boranes, metallaboranes, and metallocenes and any combinati on thereof is presented. According to this rule, rn + n + o number of elect ron pairs are necessary for a macropolyhedral system to be stable. Here, m is the number of polyhedra, n is the number of vertices, and a is the numbe r of single-vertex-sharing condensations. For nido and arachno arrangements , one and two additional pairs of electrons are required. Wade's n + 1 rule is a special case of the mno rule: where in = 1 and a = 0. B20H16. for exa mple has m = 2 and II = 20, leading to 22 electron pairs. Ferrocene, with t wo nido polyhedral fragments, has nr = 2, n = 11, and a = I, making the tot al 2 + 11 + 1 + 2 = 16. The generality of the mno rule is demonstrated by a pplying it to a variety of known macropolyhedral boranes and heteroboranes. We: also enumerate the various pathways for condensation by taking icosahe dral B-12 as the model. The origin of the mno rule is explored by using fra gment molecular orbitals. This clearly shows that the number of skeletal bo nding molecular orbitals of two polyhedral fragments remains unaltered duri ng exohedral interactions. This is true even when a single vertex is shared , provided the common vertex is large enough to avoid nonbonding interactio ns of adjacent vertices on tither side. But the presence of more than one c ommon vel tex results in the sharing of surface orbitals thereby, reducing the electronic requirements.