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.

Graphene oxide exhibits extensive disorder with a multitude of functional groups and holes making its structure an abstract concept. Multiple structural models make it a dark horse and hamper its utility despite its synthetic ease, maneuverability, and promising applications. Here we probe the impact of the epoxidation process, which is arguably the first kinetic step in graphene oxidation, to identify the induced vulnerabilities of its backbone and to cognize possible pathways for further oxidation. Probing the topological and geometrical variations in the distribution of epoxide on the graphene lattice, we find that the conformational entropy, driven by the combinatorial growth of isomers, aids and abets disorder. Graph theoretical enumeration gives 16 distinct epoxide environments within symmetrically equivalent epoxides. Their stability is primarily influenced by the steric repulsion between the oxygen lone pairs and overlap compatibility of the interepoxy C–C bond. Avoiding steric repulsion either by topology or by equatorial splaying of oxygens leads to stability, without which the network is weakened either by elongation of C–C bonds or by axial splaying of oxygens leading to uneven C–O bonds. The proposed unzipping of the underlying epoxy C–C bond through the cooperativity of strain from three-membered rings and conjugative stabilization from residual sp2 character are found to be incongruous. With an improved bonding model of epoxide, we account for the observed variations in C–C bond lengths and energetics of epoxides in different environments that facilitate strategic mechanistic control for further oxidation.

The effect of removing two protons, hydrogen atoms, or hydrides from the stable icosahedral B(12)H(12)(2-) is investigated theoretically. The resulting B(12)H(10)(q) (q = 4-, 2-, 0) isomers show interesting and understandable bond distance and stability variations, as well as special deformations associated with the apex-ring configuration typical of the underlying polyhedron. The dianions are analogous to o-, m-, and p-benzyne and have the special feature of distinct singlet and triplet states not far removed from each other in energy.

Ring stacking in some closo-borane dianions and the hypothetical capped borane nanotubes, predicted to be stable earlier, is analyzed in a perturbation theoretic way. A "staggered" building up of rings to form nanotubes is explored for four- and five-membered B(n)H(n) rings. Arguments are given for the stacking of B(5)H(5) rings being energetically more favorable than the stacking of B(4)H(4) rings. Elongated B[bond]B distances in the central rings are predicted for some nanotubes, and the necessity to optimize ring-cap bonding is found to be responsible for this elongation. This effect reaches a maximum in B(17)H(17)(2-); the insertion of additional rings will reduce this elongation. These closo-borane nanotubes obey Wade's n + 1 rule, but the traditional explanation based on a partitioning into radial/tangential molecular orbitals is wanting.

According to the n + m electron counting rule for condensed polyhedral boranes (Balakrishnarajan, M. M.; Jemmis, E. D. J. Am. Chem. Soc. 2000, 122, 4516.), an edge-shared bis-nido structure with a B19 skeleton requires 23 electron pairs for skeletal bonding (19 + 2 + 2 for bis-nido arrangement). B19H20 reported recently (Dopke, J. A.; Powell, D. R.; Gaines, D. F. Inorg. Chem. 2000, 39, 463.) lacks two electrons. We propose that the observed structure has the molecular formula B19H22 -. The geometry of B19H20 3- based on the calculations at the B3LYP/6-31G* level is given here.