Shape-similarity relations based on topological resolution

Shape-similarities of electron density clouds of molecules provide importan t clues concerning chemical and physical properties, including information about their reactivities in biochemical systems. The concept of topological resolution is used for quantifying molecular similarities: within a hierar chy of finer and cruder topologies, the crudest topology that already provi des discrimination between two objects (such as two fuzzy electron density clouds) is used to define a measure of their similarities. The finer this t opology, the more similar the two objects. This approach, the method of top ological resolution-based similarity measures (TRBSM), can be combined with a geometrically motivated resolution-based similarity measure (RBSM) withi n a metric space. Some of the relations between these two approaches are di scussed in this contribution, with special emphasis on applications to elec tron densities.