The concept of ‘syntopy’
Paul G. Mezey, J. Maruani · Molecular Physics · 1990
Point symmetry is essentially a discrete concept, whereas molecular structures and their conformational changes display continuous features, even within semi-classical models. Using the formalism of fuzzy-set theory, we propose a continuous extension of the point-symmetry concept for quasi-symmetric structures. For each point k of the reduced nuclear configuration (metric) space M of the set of all molecular systems having a specified stoichiometry, and for an energy criterion ϵ suggested by the statics or the dynamics of the systems, we define membership functions μ i (k, ϵ) which generate fuzzy subsets Si (ϵ) of the metric space M. These fuzzy subsets are used to obtain a continuous extension of the symmetry point groups of formal, classical, nuclear configurations.