ELECTRONIC AND TOPOLOGICAL CHIRALITY INDEXES FOR DISSYMMETRIC MOLECULAR-SYSTEMS

A new quantitative measure of molecular dissymmetry is proposed that is based on quantum-mechanical counterparts of notions extracted from differential geometry. Starting with the so-called torsion of a curve, we arrive at a chirality operator and appropriate average as the chirality index dipthong ae. The essential properties of dipthong ae are its additivity and also its ability to vanish for the racemic mixture of chiral structures. Some quantum-chemical approaches to calculating dipthong ae are presented, e.g., a typical one using only the adjacency matrix and the coordinates of atoms. Quasi-continuous and continuous systems, such as helices and Mobius-like structures, are studied.