Raw computational data for the carbocyclic structures presented in Figure 1 of J. Org. Chem. 90(2025)8674 manuscript. All calculations were carried out with Gaussian 16 using the B3LYP, TPSSh, and ωB97X-D methods together with the D3 dispersion correction and aug-cc-pvtz basis set.
The data are ordered by the three computational methods and for each method, the results include:
- optimized geometries and vibrational frequencies (folder: OPT),
- chemical shift (folder: NMR),
- spin-spin coupling (folder: SPIN),
- and NICS indices (folder: NICS).
The NICS and HOMA indices were calculated only at the B3LYP level. The NICS folder contains log in which the properties are calculated for the ring center and above and below it. Geometries of optimized molecules in the form of the Cartesian xyz coordinates (extracted from *log files located in the OPT folder) are collected in Table S7. Based on the calculated bond distances (R), the HOMA(R) index (Harmonic Oscillator Model of Aromaticity) was calculated (Tables S1 and S4). The optimised structures from Gaussian calculations were then transferred to AIMALL program where Electron Density Parameters at BCPs (Bond Critical Points) and RCPs (Ring Critical Points) are obtained. Based on these values, HOMA(AIM/BCP) were calculated (Table S1). Moreover, in the Tables S1 and S4, HOMA(13C NMR) and HOMA(SPIN) data are shown which were determined on the *log files collected in the folders NMR and SPIN, respectively.
Based on the collected data the following correlations were calculated and presented in Figures:
- correlations between HOMA(R) and HOMA(AIM/BCP) indices based on the AIM results (Figures 2 and 3);
- correlations between HOMA and HOMA(σ(¹³C)) (Figure 4);
- correlations between HOMA and HOMA(¹J(CC)) (Figure 5), and
- correlations between the INICS index and HOMA (Figure 6).
The HOMA geometrical aromaticity index is unique. It is simple, based on observable bond distances, and can be defined using experimental or computational bond values. Moreover, its mathematical form expresses geometric similarity to the archetypal aromatic benzene. Here, we show that HOMA is simply a kind of mean of the errors squared (MSE). This is why the index is such a good measure of aromaticity. Thus, only a slight modification grounds the HOMA index on electronic or magnetic properties, producing an electronic or magnetic molecular measure expressing electronic or magnetic similarity/dissimilarity to benzene. Based on an analysis of over 70 neutral or charged carbocyclic rings, we compare the HOMA indices based on bond distances, selected electron density properties in bond or ring critical points, chemical shifts, and spin−spin coupling constants. We conclude that using electronic and magnetic variables discloses separate trends that are invisible if CC bond lengths are used. Such new HOMA indices can be used to study different facets of aromaticity and as more general molecular structure descriptors.
(2026)
