HOMA Index Establishes Similarity to a Reference Molecule

The article shows that the definition of the HOMA index of geometrical aromaticity satisfies the axioms of a similarity function between the examined and benzene ring. Consequently, for purely mathematical reasons, the index works exceptionally well as an index of aromaticity: it expresses a geometric similarity to the archetypal aromatic benzene. Thus, if the molecule is geometrically similar to benzene, then it is also chemically similar, and therefore, it is aromatic. However, the similarity property legitimizes using the HOMA-like indices to express similarity to molecules other than benzene, whether cyclic or linear and existing or hypothetical. The paper demonstrates an example of HOMA-similarity to cyclohexane, which expresses a (relaxed)-saturicity property not accompanied by strong structural strains or steric hindrances. Further, it is also shown that the HOMA index can evaluate the properties of whole molecules, such as 25 unbranched catacondensed isomers of hexacene. The index exhibits a significant quadratic correlation with the total energy differences of planar isomers from which the nonplanar ones deviate. Moreover, the HOMA index of hexacene isomers significantly correlates with the Kekulé count connected to the resonance energy in the Hückel approximation. As a result, the study shows that the HOMA index can be used not only for aromaticity analyses but also as a general chemical descriptor applicable to rings, chains, composed molecular moieties, or even whole molecules.