Group-embeddings for NMR spin dual symmetries, to λSA|-Π: Determinate [10BH]2-12 (SU(m≤12)xS12↓I) natural subduction via symbolic Sn combinatorial generators: Complete sets of bijective maps, CNP-weights
Mathematical Chemistry and Theory Group, Department of Chemistry, Queen's University,
Kingston-ON, Canada, K7L 3N6
Corresponding author: a Temmef@chem.queensu.ca
Published online: 15 September 1999
Modelling of the properties of high-spin isotopomers, as polyhedra- on-lattice-points which yield various symbolic-computational -encodings of nuclear permutation (upto some specific SU(m) branching level), is important in deriving the spin-ensemble weightings of clusters, or cage-molecules. The mathematical determinacies of these, obtained here for higher m-valued SU group embeddings, are compared with that of an established group embedding, in order to collate the spin physics of with that for -analogue. The most symmetrical form of anion provides a pertinent example of the physics discussed in [CITE]. Retention of determinacy in the two cases is correlated to the completeness of the 1:1 bijective maps for natural embeddings of automorphic dual group NMR spin symmetries. The Kostka transformational coefficients of a suitable model ( module, Schur fn.) play a important role. Our findings demonstrate that determinacy persists (to branching levels) more readily for embeddings derived from (automorphic) finite groups dominated by odd-permutational class algebras, such as the above , or the case discussed in [16a,15,3d], compared to other examples -(e.g. as respectively, in press, and in [17b]): , . Generality of the symbolic algorithmic difference approach is stressed throughout and the corresponding dodecahedral maps are outlined briefly -for the wider applicability of SF-difference mappings, or of comparable -symbolic methods, (e.g.) via [CITE].
PACS: 02.10.-v – Logic, set theory, and algebra / 33.20.Vq – Vibration rotation analysis / 36.40.Mr – Spectroscopy and geometrical structure of clusters / 33.25.+k – Nuclear resonance and relaxation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999