Graph Theory in the Study of Metal Cluster Bonding Topology: Applications to Metal Clusters Having Fused Polyhedra.
Abstract
The energy levels in delocalized two- or three-dimensional chemical structure are related to the eigenvalues of the graph representing the corresponding bonding topology. Such relatively crude but computationally undemanding graph theory derived models provide a clear demonstration of the close relationship between two-dimensional aromatic systems such as benzene and three-dimensional aromatic systems such as deltahedral boranes, carboranes, and metal clusters. The basic building blocks for the three dimensional aromatic systems are deltahedra having no degree 3 vertices. Delocalized bonding in such systems having v vertices requires two electrons for a multicenter core bond as well as 2v electrons for pairwise surface bonding. A problem of particular interest is how metal cluster polyhedra can fuse together leading ultimately to the infinite structures of the bulk metals. As a model for such processes the fusion of rhodium carbonyl octahedra is examined using graph theory derived methods. These lead to reasonable electron-precise models for the bonding topologies in the 'biphenyl analogue' (Rh12(CO)30)2-, the 'naphthalene analogue' (Rhg(CO)19)3-, the 'anthracene analogue' H2Rh12(CO)25, and the 'perinaphthene analogue' (Rh11(CO)23)3-. Similar models can also be developed for clusters based on centered larger rhodium polyhedra as exemplified by the centered cuboctahedral clusters of the type (Rh13(CO)24H5-q)q- (q = 2, 3, 4) representing a fragment of the hexagonal close packed metal structure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 02, 1986
- Accession Number
- ADA166623
Entities
People
- R. B. King
Organizations
- University of Georgia