par Brocas, Jean 
Référence Journal of the American Chemical Society, 108, 6, page (1135-1145)
Publication Publié, 1986
Référence Journal of the American Chemical Society, 108, 6, page (1135-1145)
Publication Publié, 1986
Article révisé par les pairs
| Résumé : | When a molecular skeleton with n sites and symmetry group G carries nx ligands of type X, ny of type Y, etc., the resulting isomers are distributed among several symmetries. We show that the numbers υγGB of isomers of symmetry γ obey a system of linear and inhomogeneous equations, as shown by eq 12. The linear coefficients pβγG and the independent terms pβBSn appearing in this system are related to the double-coset structure of G and Sn, respectively, and are easy to calculate by standard group theoretical methods. Unfortunately, the rank of pβγG is smaller than the number of υγGB unknowns. Hence, the system can only be solved if some of the unknowns are calculated independently. However, in practice, some of the υγGB numbers are easy to obtain either because they are vanishing for any ligand partition (phantom subgroups of G) or because they are readily found by inspection, as it is the case when isomers of high symmetry γ have to be enumerated. Therefore, the relations established in this paper do yield an efficient method to enumerate permutational isomers of fixed symmetry. It is remarkable that the calculations required only involve enumeration of double cosets. The present method is applied to the dodecahedrane skeleton. The number of isomers of fixed symmetry and corresponding to the formula C20H20-nXn have been obtained (n = 0, 1, 2, ..., 10). © 1986 American Chemical Society. |
