Skeletal bonding topology

In 1977 we reported a method based on graph theory for study of the skeletal bonding topology in polyhedral boranes, carboranes, and metal clusters Q). Subsequent work has shown this method to be very effective In relating electron count to cluster shape for diverse metal clusters using a minimum of computation. Discrete metal clusters treated effectively by this method Include post-transition metal clusters (, ) > osmium carbonyl clusters (O, gold clusters, platinum carbonyl clusters (J., 7 ) > and... 

Most clusters, however, caimot be described adequately in terms of two-center, two-electron bonds because the coimectivity of the vertices exceeds the number of valence orbitals that are available for bonding. Early efforts to rationalize such systems, such as Lipscomb s styx approach and Kettle s Topological Equivalent Orbital Method, are described by Mingos and Johnston. In these more difi cult cases, the simple valence-bond picture is inappropriate examples are deltahedral clusters composed of B-H vertices or conical M(CO)3 fragments, both of which usually have only three orbitals available for skeletal bonding. Theoretical models for describing these systems will be discussed in the next section. 

II.D). Thus, consider the bonding topology in a an isocloso metallaborane deltahedron with n vertices, which can be shown by Euler s theorem to have 2/7 — 4 faces and 3/7 — 6 edges such as the corresponding closo deltahedron with the same number of vertices. If each vertex (e.g., a neutral BH vertex or isoelectronic/isolobal equivalent) contributes three skeletal (internal) orbitals and two skeletal electrons (i.e., a 2/7 skeletal electron system), then the numbers of skeletal orbitals and electrons are correct for 3c-2e bonds in n of the 2/7 — 4 faces leaving /7 — 4 faces without 3c-2e bonds. 

As has been shown above, a polymeric chain can be simulated with the aid of Equation 2.10. This equation allows both crosslinked polymer topology (the values and are functions of the chemical crosslinking density v ) and its molecular characteristics (the value is defined by skeletal bond length f and characteristic ratio C, which serves as an indicator of the chain statistical flexibility and also depends on Z ) to be accounted for [131]. 

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