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.