Shape‐similarity relations based on topological resolution

Abstract

Shape‐similarities of electron density clouds of molecules provide important 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 hierarchy of finer and cruder topologies, the crudest topology that already provides discrimination between two objects (such as two fuzzy electron density clouds) is used to define a measure of their similarities. The finer this topology, the more similar the two objects. This approach, the method of topological resolution‐based similarity measures (TRBSM), can be combined with a geometrically motivated resolution‐based similarity measure (RBSM) within a metric space. Some of the relations between these two approaches are discussed in this contribution, with special emphasis on applications to electron densities.