Constrained and unconstrained chirality functions. A new method, going from discrete to continuous space, to find the best overlap between enantiomer atoms

This paper provides two different functions for quantifying geometric chirality. Both are based on Euclidean distances between enantiomer atoms and the best associated RMS, but, depending on the function, atoms are paired without or with constraint. In the first, the best match between the enantiomer atoms is sought by means of a completely new method in which one enantiomer is fitted onto a spline approximation of the other. This method reestablishes the continuity between similarity and dissimilarity, broken in discrete space by atom-per-atom shape recognition treatments. In the second, each enantiomer atom is paired with its mirror image and only the mirror location is optimized. Congruity-based chirality measures are grouped into two classes according to whether the discrimination function between the chiral object and the reference object takes some constraint into account (second class) or does not (first class). In this paper, our constrained or unconstrained chirality function is compared with the continuous chirality measure (second class). It is inferred that only chirality scales of the same class can be correlated.