MOLECULAR SHAPE PROFILES

We introduce a scheme that gives a numerical characterization for a molecular shape and shapes in general! A sequence that represents molecular shape is derived from the powers of interatomic distances for all atoms at the atomic periphery. One may view the derived sequence, which we call shape profile, analogous to a power series expansion of a function. The elements of the sequence are given as the average contribution from all atoms at the molecular periphery. We illustrate the shape profiles for smaller benzenoid systems and use them in a discussion of molecular similarity for benzenoidal shapes. The approach can be extended to other molecular forms, including nonplanar structures. The ''resolution'' of the characterization of the shapes can be increased by increasing the number of points (not necessarily atoms) on the molecular periphery.