Shape group studies of molecular similarity: Shape groups and shape graphs of molecular contour surfaces

Abstract

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 spaceD provide the mathematical basis for the development of a general method for a dynamic description of molecular shapes.