HOMA Index Establishes Similarity to a Reference Molecule

Abstract

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.

Figure 1

Structures for which the HOMA_B and HOMA_C indices were calculated (Table 1).

Figure 2

Relationships between indices calculated using benzene (B) and chair cyclohexane (C) reference molecules. The HOMA indices (a) and the HOMA indices truncated to single EN (black points) and GEO factors (red points) (b).

Figure 3

Structures in which the central 6-membered ring has HOMA_B ≈ 0, but only 2, 3, 6, 9, and 10 have this ring are similar to cyclohexatriene according to the HOMA_CHT^Δ criterion (see Table 2).

Figure 4

Structural formulas of all unbranched catacondensed hexacene isomers. Total energy differences vs benzo[c]picene are in blue and parentheses (kcal/mol), HOMA_B of the entire structure are in red, and the Kekulé count are in black and brackets. Point group symmetry and the PAH 3-digit code are in the second row in black.

Figure 5

(a) Linear correlation between the total energy difference and the natural logarithm of the Kekulé count ln(K) for 25 unbranched catacondensed isomers of hexacene calculated at the B3LYP/D3/6-31G** level. (b) Logarithmic correlation between the total energy difference and the HOMA_B index calculated for entire molecules and (c) the linear correlations between the HOMA_B index calculated for entire molecules and the Kekulé count for all 25 structures (in blue) and only for the planar ones (in red). Blue empty cycles correspond to the nonplanar molecules (Figure 4).