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June 4, 2001
Volume 79, Number 23
CENEAR 79 23 pp. 53-54
ISSN 0009-2347
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Extension of Wade's rule outlines connections between boranes, metallocenes, elemental boron


A new electron-counting rule derived from Wade's rule for predicting the structure and bonding requirements of cage-type compounds has been devised by chemistry professor Eluvathingal D. Jemmis and coworkers at the University of Hyderabad in India [J. Am. Chem. Soc., 123, 4313 (2001)]. The rule is expected to be a useful extension of Wade's rule to cover condensed polyhedral boranes and the many possible products created by merging boranes and metallocenes into single macromolecules.

In a subsequent paper in the same issue of JACS (page 4324), Jemmis and postdoctoral researcher Musiri M. Balakrishnarajan use the new rule to describe the electronic requirements of -rhombohedral boron, a 105-atom allotrope containing boron polyhedra building blocks. The goal of the work is to determine missing links between polyhedral boranes and complex boron allotropes, similar to the structural and bonding connections between benzene, condensed aromatic systems, and graphite.

Chemists have used electron-counting rules for many years to associate bonding patterns in different classes of compounds, such as the familiar octet rule for first- and second-row elements, the 18-electron rule for transition metals, and the Hückel 4n + 2 rule for aromatic compounds. However, these rules don't readily apply to electron-deficient molecules such as boranes that utilize multicentered bonding--a pair of electrons shared between more than two atoms--so other rules have been formulated.

One such rule was devised in 1954 by Nobel Laureate William N. Lipscomb, now emeritus professor of chemistry at Harvard University, who came up with the styx numbers to rationalize the cage structures of boranes. Each letter in styx represents one type of building block or structural linkage in boranes.

In 1971, chemistry professor Kenneth Wade of the University of Durham, in England, built on the collective observations of Lipscomb and other chemists to formulate his well-known n + 1 rule. Wade's rule states that a cage molecule with a geometry based on a closed (closo) polyhedron constructed of triangles with n vertices will possess n + 1 skeletal bonding electron pairs. 

WADE'S RULE and its corollaries--collectively known as Wade's rules--have been refined and extended by a number of researchers. When coupled with spectroscopic studies and theoretical calculations, Wade's rules have been successful in showing the structural interconnections between boranes, carboranes, other heteroboranes, carbocations, organometallic complexes, and transition-metal cluster compounds .

The new rule devised by Jemmis, Balakrishnarajan, and graduate student Pattath D. Pancharatna--called the mno rule--states that m + n + o skeletal electron pairs are necessary for a closed macropolyhedral system to be stable. Here, m is the number of condensed polyhedra; n is the number of vertices, as in Wade's rule; and o is the number of single-atom bridges between two polyhedra. When two polyhedra are condensed and share an edge or a face, o is zero. The mno rule adds extra electrons for open-cage classes of compounds--nido (nestlike, slightly open cage) and arachno (weblike, more open)--with p number of vertices missing, in accordance with Wade's rules.

Jemmis and Balakrishnarajan had earlier formulated an n + m rule where m formally replaces the 1 in Wade's rule [J. Am. Chem. Soc., 122, 4516 (2000)]. Wade's rule is thus a special case of the mno rule when m = 1 and o = 0, Jemmis points out. The 4n + 2 rule is also a special case of the mno rule when condensation of two compounds is restricted to edge sharing in two dimensions, such as in polycyclic aromatic hydrocarbons. The addition of o in the new rule is a more important extension with regard to exploring the structural and bonding requirements in fused cage compounds.

"Jemmis draws together a number of corollaries to Wade's rules into a single, easily employed general rule," comments Thomas P. Fehlner, a professor of chemistry at the University of Notre Dame. Fehlner has been a major contributor to this field with his work on unsaturated metal-boron clusters. Without Wade's rule, his work would not have been possible in a systematic way, Fehlner says, and the application of the mno rule should similarly help provide a continuity of borane chemistry to understand the complex structure required for elemental boron.

Boron exists in more than a dozen allotropic forms, with -rhombohedral boron (B105) being the most thermodynamically stable. These compounds have very interesting properties: B105 melts at about 2,450 C, is stronger than steel and harder than corundum, but is lighter than aluminum, according to Jemmis. It acts as a p-type semiconductor and can be made an n-type semiconductor by doping with metal atoms. Thus, there are many potential applications for B105 and other boron allotropes in structural and electronic materials. 

THESE ALLOTROPES are mostly exotic species, however, formed during the thermal decomposition of polyhedral boranes. Although they have been studied primarily by solid-state physicists, Jemmis suggests that recent findings such as the high-temperature superconductivity of MgB2 (C&EN, March 5, page 13), which contains alternating layers of boron and magnesium in a graphite-type structure, will draw more chemists to this line of research.

Jemmis and Balakrishnarajan in the second JACS paper explore the electronic and structural requirements for B105 to be stable. They begin with a model based on icosahedral B12H122-, which is the most stable polyhedral borane known and functions as the equivalent of benzene in borane chemistry. But unlike electronically neutral benzene as a building block for condensed aromatics and graphite, B12H122- as a building block accumulates negative charges, which must be accounted for in the structure of the resulting allotrope.

The researchers used the mno rule along with molecular orbital theory and X-ray structure data to determine that B105 requires lattice defects to satisfy its electronic requirements. "The distribution of partial lattice occupancies and extra atoms in -rhombohedral boron, as explained by the mno rule," Jemmis says, "provides a new dimension in understanding the unusual properties of boranes and new strategies to maneuver the diverse and technologically important features of boron-rich solids." The results also suggest that a closer look should be taken at vacancies and extra occupancies in solids before ignoring them as purely defects, Jemmis adds, since they may be required by the electronic structure.

APPLICATION In the mno rule for counting skeletal electron pairs, m is the number of condensed polyhedra, n is the number of polyhedral vertices, and o is the number of single-atom bridges between two polyhedra. Extra electron pairs are added for open polyhedra that have p number of vertices missing, such as the one missing vertex in each cyclopentadienyl ligand in ferrocene. The lines joining atoms outline the shape of the polyhedral structures and aren't necessarily bonds.

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