SYMMETRY PROPERTIES OF CHEMICAL GRAPHS .9. THE VALENCE TAUTOMERISM IN THE P7(3-) SKELETON
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We investigate the intramolecular rearrangement of the P73 ion in which PP bonds are continuously broken and reestablished resulting in a dynamic structure with all seven phosphorus atoms being chemically equivalent. This leads to 7/3 = 1680 valence tautomers. The P73 ion is a typical fluctuating molecule, distantly related to C10H10 bullvalene. In order to determine the symmetry of the process we first consider the problem of the construction of the rearrangement graph. Initial steps toward this goal are illustrated, and additional characterizations of the graph are derived after its construction by computer. A number of properties of this rather complicated graph having 1680 vertices and 2520 edges are discussed: in particular the occurrence of various cycles, the maximal distance between vertices, the count of neighbors at different distance, and finally its symmetry. Copyright 1986 John Wiley & Sons, Inc.