Ring perception definitions

Having resolved the molecular perception problem and achieved a unique representation of all atoms, bonds, and rings in the molecule, the second major step is the definition of the most useful measure for local similarity of atoms and atomic environment. For the purpose of COSMO/rag, we need to achieve the state that atoms are considered as most similar, if their partial molecular surfaces and surface polarities, i.e., polarization charge densities, are most similar. But since the latter is not known, at least for the new molecule under consideration, we have to ensure that the local geometries and the electronic effects of the surrounding atoms are most similar. Obviously, two similar atoms should at legist be identical with respect to their element and their hybridization. Turning this information into a unique real number, a similarity index of the lowest order (zeroth order) can be defined for each atom from the atom element numbers and... 

The substituted azulene 3 possesses Kekul resonance forms, but would not be perceived as aromatic in a system that restricted aromaticity to six-membered rings. Indole 4 possesses a double bond in the five-membered ring that displays substantial aromatic character in its chemical reactions, yet this ring in indole would not be perceived as aromatic by most systems. As soon as a system introduces fuzzy chemical concepts, such as a definition of aromaticity based on chemical reactivity, into a system based on graph-theoretic concepts, such as perception of Kekul resonance forms, incompatibilities and errors, conversion and searching will result. 

---