The NICS(1) magnetic aromaticity index is split into NICS(1) and NICS(−1) indices when the points 1 Å above and below the ring center are inequivalent by symmetry. The two indices characterize the aromaticity of the two ring faces rather than the ring itself.

HOMA (Harmonic Oscillator Model of Aromaticity) is a simple, successful, and widely used geometrical aromaticity index. However, HOMA can also be used as a general molecular descriptor appropriate for any type of molecule. It reaches the global maximum for benzene, whereas the potent magnetic aromaticity NICS index has no lower or upper limits. Hence, questions arise and go beyond mere differences between the geometric and magnetic aspects of aromaticity: (1) Does a molecule of aromaticity greater than that of benzene, but undisclosed by the HOMA definition, exist? (2) Can the Kekuléne cyclohexatriene moiety with HOMA = 0 exist as a part of a larger system? (3) Can the geometrical aromaticity index be defined better? Our answer to the first query is “It is not likely enough”, to the second, “Why not define HOMA using a less mysterious molecule than cyclohexatriene?”, and to the third, “It is possible to construct another fair geometrical index, but is it better for evaluating aromaticity?” To find these answers, we have studied: (1) the HOMA and NICS indices of over 50 hexahomosubstituted benzenes, (2) the HOMA, as well as EN and GEO, indices of over 100 triply fused hexasubstituted benzenes, and (3) the HOMA and new Geometrical Auxiliary Index (GAI) , of different unsaturated and saturated, aromatic and aliphatic hydrocarbons including all alkane constitutional isomers composed of up to nine carbon atoms.

Interactions of 21 fentanyl derivatives with μ-opioid receptor (μOR) were studied using experimental and theoretical methods. Their binding to μOR was assessed with radioligand competitive binding assay. A uniform set of binding affinity data contains values for two novel and one previously uncharacterized derivative. The data confirms trends known so far and thanks to their uniformity, they facilitate further comparisons. In order to provide structural hypotheses explaining the experimental affinities, the complexes of the studied derivatives with μOR were modeled and subject to molecular dynamics simulations. Five common General Features (GFs) of fentanyls’ binding modes stemmed from these simulations. They include: GF1) the ionic interaction between D147 and the ligands’ piperidine NH⁺ moiety; GF2) the N-chain orientation towards the μOR interior; GF3) the other pole of ligands is directed towards the receptor outlet; GF4) the aromatic anilide ring penetrates the subpocket formed by TM3, TM4, ECL1 and ECL2; GF5) the 4-axial substituent (if present) is directed towards W318. Except for the ionic interaction with D147, the majority of fentanyl-μOR contacts is hydrophobic. Interestingly, it was possible to find nonlinear relationships between the binding affinity and the volume of the N-chain and/or anilide’s aromatic ring. This kind of relationships is consistent with the apolar character of interactions involved in ligand–receptor binding. The affinity reaches the optimum for medium size while it decreases for both large and small substituents. Additionally, a linear correlation between the volumes and the average dihedral angles of W293 and W133 was revealed by the molecular dynamics study. This seems particularly important, as the W293 residue is involved in the activation processes. Further, the Y326 (OH) and D147 (Cγ) distance found in the simulations also depends on the ligands’ size. In contrast, neither RMSF measures nor D114/Y336 hydrations show significant structure-based correlations. They also do not differentiate studied fentanyl derivatives. Eventually, none of 14 popular scoring functions yielded a significant correlation between the predicted and observed affinity data (R < 0.30, n = 28).

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.