The fundamental syntopy of quasi‐symmetric systems: Geometric criteria and the underlying syntopy of a nuclear configuration space

Abstract

AbstractPoint symmetry is a discrete concept; A nuclear configuration for a given stoichiometry either has or has not a particular point symmetry. By contrast, both static and dynamic properties of actual molecules exhibit continuous features. Using the formalism of fuzzy‐set theory, we had previously proposed the concept of syntopy as a continuous extension of the symmetry concept for quasi‐symmetric systems: This was based on an energetic criterion taking into account the energy costs of nuclear rearrangements. This extension of symmetry was necessarily dependent on the considered electronic state: For a given geometric arrangement of the nuclei, the energy cost of some rearrangement is dependent on the actual potential surface, that is, on the electronic state, in the Born–Oppenheimer approximation. In the extension of the syntopy model reported in the present work, we consider a syntopy criterion that is common to all electronic states. The syntopy thus defined—called the fundamental syntopy of the reduced nuclear configuration space—is independent of the potential surface and of the electronic state: It is defined only in terms of a geometric condition, which makes it more appropriate to rationalize mesoscopic structures. This new syntopy model provides a connection between all possible syntopies generated by the various potential‐energy surfaces supported by the considered family of atomic nuclei. © 1993 John Wiley & Sons, Inc.