CHEMICAL ALGEBRA .2. DISCRIMINATING PAIRING PRODUCTS

The algebra of stereogenic pairing equilibria is presented in a very g eneral context. Starting from the notions of fuzzy subgroup and conjug acy link, chemical pairing constants between molecular species u and v having a skeletal symmetry group G are formulated as ''pairing produc ts'' on a G-Hilbert space. ''Discriminating pairing products'' K are d efined by the conditions: ''K greater-than-or-equal-to 1'' and ''K = 1 double-line arrow pointing left and right the representative vectors of the paired species are G-equivalent''. When G has only two elements , the pairing product is always discriminating. For several skeletal s ymmetries, if the vectors are ''enantiomorphic (v = sigmau, sigma2 = e , sigma is-not-an-element-of G), then K is greater than 1 and reaches 1 only if u is ''achiral'': ''chirality indexes'' and general ''permut ational indexes'' are then defined from K(u, sigmau). The general mode l is illustrated by some examples.