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Exclusively combinatorial invariance aspects of a non-J model (reg.-t) polyhedral 13C-fullerene: Cayleyan [A]24 (SU(2 ⩽ m) × L24↓O) NMR (R-V) spin symmetries and their correlative mappings

Author

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  • Temme, F.P.

Abstract

In the physical context of symmetry-adapted bases for NMR spin (sub) systems and the spin statistics of ro-vibrational spectra, [A]24 (SU2 × L24↓O) exo-cage cluster spin symmetry is derived, utilising both the corresponding isomorphic t-Octahedral cage rotational symmetry of certain specific isotopomeric fullerenes - e.g., [13C]24+/−, or [12C]nn [X]24 (SU(m)×L24↓O) - and the specifics of Cayley's theorem for [A]24 models, or for [13C..]60 symmetry [from Molec. Phys. 79 (1993) 934]. In consequence for n = 24 identical to |G| for G = O, within a further rotational symmetry isomorphism implicit in the (6, 6, 4) and (8, 8, 3) regular t-Octahedra of the [4–6] and [3–8] (bis-cyclo) cages, the analytic (i.e. totally combinatorial) forms are determined for the spin invariance sets and their {[λ] → Γ} correlative mappings inherent in a fully determinate (L24 ⊃ O) natural embedding. The confluence between geometry and combinatorical algebra over a spin (site) invariance set, reported herein, is especially rare in non-icosahedral Ln-embedded symmetries.

Suggested Citation

  • Temme, F.P., 1996. "Exclusively combinatorial invariance aspects of a non-J model (reg.-t) polyhedral 13C-fullerene: Cayleyan [A]24 (SU(2 ⩽ m) × L24↓O) NMR (R-V) spin symmetries and their correlative mappings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 313-323.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:1:p:313-323
    DOI: 10.1016/0378-4371(96)00037-4
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