Generalized structural geometry

Abstract

Arbitrary combinations of bond lengths, bond angles and torsion angles can be used as generalized coordinates for describing molecular models. It is shown how these and the conventional Cartesian or fractional unit-cell coordinates can be interconverted. Algorithms are also given for the geometrical analysis of rigid structures of links joined by flexible connectors (where only bond lengths are specified). Properties of the connectivity matrix, as an alternative complete description of a structure, are developed. Several applications of the above procedures are described.