SHAPE GROUP STUDIES OF MOLECULAR SIMILARITY: SHAPE GROUPS AND SHAPE GRAPHS OF MOLECULAR CONTOUR SURFACES

The earlier, symmetry-independent group theoretical characterization of the shapes of three-dimensional molecular functions, such as electrostatic potentials, electronic charge densities, or molecular orbitals, is extended and compared to a new family of shape descriptors. The incidence graphs and shape graphs, defined by the curvature properties of various molecular contour surfaces, provide an easily visualizable, alternative mathematical technique for a computer-based, non-visual evaluation of molecular shape and molecular similarity. The invariance domains of incidence graphs, shape graphs and shape groups within the dynamic shape space D provide the mathematical basis for the development of a general method for a dynamic description of molecular shapes.