On quantifying chirality — Obstacles and problems towards unification

Abstract

Recently there has been an ever growing interest and activity in the attempts on quantifying chirality which is causing this concept to become a diverse and uncorrelated entity. Possible reasons for this complication are presently discussed. It is shown that it becomes necessary to distinguish between geometric and physical chiralities. For geometrical chiral sets it is necessary to distinguish between equi- and sub-dimensional sets where the metrization of their chirality can be generalized and unified only for equi-dimensional sets. This is accomplished by the method of overlap. For sub-dimensional sets there exists no general and unique mode of quantifying chiralities, except for discrete and finite sets of points such as the comers of polyhedron, for which the approach of Hausdorff distances proves to be an efficient method of quantifying the chirality presented by their distribution. The domain of physical chiralities, although being of natural significance, is still in a premature state of development. Each physical property may have a different chiral measure so that there is no sense in a claim of unification. Equi- and sub-dimensionality exist also for physical chiralities and they can be quantified by the overlap method for equi-dimensional sets.