ISSN:
1572-8897
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
,
Mathematics
Notes:
Abstract The search for a definition of distances over sets of skeletal analogs (identified to G-Hilbert spaces of vector ligand parameters) is initiated from the algebraic formulation of the constant of stereogenic pairing equilibria (pairing product). A basic definition equation is devised from thermodynamical speculations. The equation is proved to have always a single potential distance solution Dp as soon as the pairing product is discriminating. The equation of Dp is constructed in order to satisfy three consistency requirements: completeG-invariance (arbitrary orientations selected to describe skeletal analogs do not affect the value of Dp); extension properties (Dp coincides with two standard completelyG-invariant distances or with the Euclidean distance in borderline cases); all the distance properties except, perhaps, the triangular inequality. The latter point remains challenging in general, and is computationally verified in some examples.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01169213
