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 æ. The essential properties of æ are its additivity and also its ability to vanish for the racemic mixture of chiral structures. Some quantum-chemical approaches to calculating æ 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 Möbius-like structures, are studied.