Chemical algebra. II: Discriminating pairing products

The algebra of stereogenic pairing equlibria is presented in a very general context. Starting from the notions of fuzzy subgroup and conjugacy link, chemical pairing constants between molecular speciesu andv having a skeletal symmetry groupG are formulated as pairing products on aG-Hilbert space. Discriminating pairing productsK are defined by the conditions: K 1 and K = 1 the representative vectors of the paired species areG-equivalent. WhenG has only two elements, the pairing product is always discriminating. For several skeletal symmetries, if the vectors are enantiomorphic (v = u, ² =e, G), thenK is greater than 1 and reaches 1 only ifu is achiral: chirality indexes and general permutational indexes are then defined fromK(u u). The general model is illustrated by some examples.