A generally applicable electron-counting rule-the mno rule-that integrates macropolyhedral boranes, metallaboranes, and metallocenes and any combination thereof is presented. According to this rule, m + n + o number of electron pairs are necessary for a macropolyhedral system to be stable. Here, m is the number of polyhedra, n is the number of vertices, and o is the number 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 m = 1 and o = 0. B20H16, for example has m = 2 and n = 20, leading to 22 electron pairs. Ferrocene, with two nido polyhedral fragments, has m = 2, n = 11, and o = 1, making the total 2 + 11 + 1 + 2 = 16. The generality of the mno rule is demonstrated by applying it to a variety of known macropolyhedral boranes and heteroboranes. We also enumerate the various pathways for condensation by taking icosahedral B12 as the model. The origin of the mno rule is explored by using fragment molecular orbitals. This clearly shows that the number of skeletal bonding molecular orbitals of two polyhedral fragments remains unaltered during exohedral interactions. This is true even when a single vertex is shared, provided the common vertex is large enough to avoid nonbonding interactions of adjacent vertices on either side. But the presence of more than one common vertex results in the sharing of surface orbitals thereby, reducing the electronic requirements.

before joining Princeton University in 1973 for his Ph.D. degree under the supervision of Professor Paul von Rague ´Schleyer. During his years at Princeton, Jemmis spent a semester at the University of Munich (fall 1974) and two years at the University of Erlangen-Nurnberg (1976−77). After a two-year postdoctoral fellowship at Cornell with Prof. Roald Hoffmann, Jemmis returned to India in 1980 as a lecturer at the

Boron carbide, usually described as B 4 C, has the mysterious ability to accommodate a large variation in carbon composition (to as much as B 10 C) without undergoing a basic structural change. We systematically explore how the bonding varies with carbon concentration in this structure and the origin of the fundamental electron deficiency of the phase. As the carbon concentration is reduced, we find that the exo-polyhedral B Eq -C bonds of the icosahedra in the structure become increasingly engaged in multiple bonding, and the repulsive steric interactions between the bulky B 12 units surrounding the carbon atom are reduced. The short bond lengths observed within the three-atom yC-B-Cx chains are then due to substantial p-bonding, while the carbon deficiency weakens its s-framework significantly. We conclude that the idealized framework of boron carbide has to expel some electrons in order to maximize its bonding; disorder in the structure is an inevitable consequence of this partial oxidation. The localization of electronic states arising from the disorder leads to the semiconducting nature of boron carbide throughout its composition range.

A recently proposed system with a central planar tetracoordinate carbon linking two three-membered rings, C(5)(2-), lends itself to extension in one, two, and three dimensions. Our construction of potential realizations begins with an analysis of the electronic structure of C(5)(2-). Dimers such as C(10)Li(3-), C(10)Li(4), and a trimer C(15)Li(6) are then examined, and their geometries are optimized to find clues for ways the C(5)(2-) unit may polymerize in the presence of countercations. Coordination through the terminal carbons is favored in the oligomers and polymers; several electronically and structurally reasonable systems of the stoichiometry C(5)M(x) (M = Li, x = 2; M = Be, Pt, Zn, x = 1) emerge from band structure calculations and energetic considerations.