Theoretica chimica acta

, Volume 48, Issue 3, pp 207–214 | Cite as

The enumeration of electron-rich and electron-poor polyhedral clusters

  • R. Bruce King
  • Dennis H. Rouvray
Original Investigations


We present as dual processes the capping of closed triangulated polyhedra with apical atoms and the making of holes in such polyhedra either by puncture of the surface or by excision of atoms and their edges. These processes are shown to generate stable chemical species containing respectively less or more than 2n + 2 skeletal electrons. The former species are designated as electron-poor whereas the latter are called electron-rich. Pólya's enumeration method is used to enumerate the distinct ways of capping and excising the closed, triangulated polyhedra to yield systems containing from four to twelve vertices. For the enumeration of cappings the appropriate cycle index is that of the dual of the polyhedron being capped, whilst for the enumeration of the excisions the cycle index is that of the polyhedron being excised.

Key words

Boranes Carboranes Polyhedral clusters Pólya's enumeration theorem Electron counts 


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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • R. Bruce King
    • 1
  • Dennis H. Rouvray
    • 2
  1. 1.Department of ChemistryUniversity of GeorgiaGeorgiaUSA
  2. 2.Institut für Strahlenchemie im Max-Planck-Institut für KohlenforschungMülheim an der RuhrFederal Republic of Germany

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