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Automorphic NMR spin symmetries of cage structures: exclusively combinatorial correlative mappings for specific (Ln ⊃ G ≡ I natural embedding pertinent to higher t−I13C-fullerenes

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  • Temme, F.P.

Abstract

A strong correspondence is shown to exist between spin cage-cluster systems to which Cayley's theorem applies, such as [13C]60z2 for z integer higher fullerenes, and the occurrence of exclusively combinatorial [χi] (Ln ↓G) invariance (ECI) sets which determine their NMR spin symmetry. The n = 60 z2, z a small integer, higher t-icosahedral cage clusters, [X13C]n and various further nested-endohedral forms represent a wide range of model systems. Their [[λ] → Γ (Ln ↓ A5 ≡ I)]correlative mapping aspects follow directly from the nature of the monocluster ECI sets. These allow one to derive the SU2 × Ln ↓ A5 spin symmetry for (bi) cluster NMR of 13C-fullerene compounds, and also the generalised wreath-product spin symmetry for endohedral “nano-onionic”-structured fullerenes. Further aspects of the “n versus sub-group cardinality” Cayley relationship for spin cage clusters, inherent in the spin symmetry automorphisms onto certain (pseudo) regular (t-)polyhedral “geometric solids”, are examined in the context of the direct natural Ln ⊃ G (≡ I) embeddings.

Suggested Citation

  • Temme, F.P., 1996. "Automorphic NMR spin symmetries of cage structures: exclusively combinatorial correlative mappings for specific (Ln ⊃ G ≡ I natural embedding pertinent to higher t−I13C-fullerenes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(3), pages 314-324.
    • Handle: RePEc:eee:phsmap:v:227:y:1996:i:3:p:314-324
    DOI: 10.1016/0378-4371(95)00347-9
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