Algebraic chirality criteria and their application to chirality classification in rigid molecular systems

The ''configurational'' approach is shown to shift several stereochemical problems to the analysis of combinatorial rather than geometrical objects. On the basis of this approach, algebraic chirality criteria for point 3D configurations and their superpositions (labeled, graph, and molecular configurations) are deduced, The application of the suggested criteria makes it possible to elaborate a new classification system which is directly applied to rigid chiral objects (i.e., to fixed spatial realizations of complete and hydrogen-depleted molecular graphs and to skeleton, framework, and core graphs as well). Several examples of rigid F-, G-, N-, P-, and S-chiral molecules are briefly considered; the simple designation system for nonrigid molecular entities is also outlined.