Aromaticity HOMA

The aromaticity of 1,2,4-triazoles has been investigated and quantified using the harmonic oscillator model of aromaticity (HOMA) index, where a value of 1 is assigned to a molecule that is fully aromatic, 0 for a nonaromatic molecule, and a negative value for a molecule that is antiaromatic the data obtained were compared to other small-molecule heteroaromatics. It was determined that different tautomers of substituted and unsubstitued 1,2,4-triazoles have individual HOMA indices <2000JST(524)151>. 

Studies on the statistical deviation from an ideal bond order support the relatively high aromaticity of 1,2,5-thiadiazole (Table 7). The harmonic oscillator model of aromaticity (HOMA) value for 1,2,5-thiadiazole has not yet been reported. 

In addition to the above prescriptions, many other quantities such as solution phase ionization potentials (IPs) [15], nuclear magnetic resonance (NMR) chemical shifts and IR absorption frequencies [16-18], charge decompositions [19], lowest unoccupied molecular orbital (LUMO) energies [20-23], IPs [24], redox potentials [25], high-performance liquid chromatography (HPLC) [26], solid-state syntheses [27], Ke values [28], isoelectrophilic windows [29], and the harmonic oscillator models of the aromaticity (HOMA) index [30], have been proposed in the literature to understand the electrophilic and nucleophilic characteristics of chemical systems. 

In a more recent study, the problem of n delocalization in porphyrins and metalloporphyrins was reinvestigated using two different aromaticity indexes, HOMA andNICS [37], The harmonic oscillator model of aromaticity (HOMA) [31] quantifies the aromaticity of a system on the basis of the calculated deviation of its... 

We have used a different approach to compare the aromaticities of phosphole (8) and pyrrole (10) [23, 24], From literature data on derivatives of 8 and 9 it is known that the inversion barrier of phosphole is about 67 kJ mol-1 (70.2 kJ mol-1 at the B3LYP/aug-cc-pVTZ level) [25] while that of tetrahydrophosphole amounts to 163 kJ mol-1. This is explained by the fact that the planar transition state of 8 is highly aromatic. Pyrrole (10) is planar and pyrrolidine has a calculated inversion barrier of 15-17 kJ mol-1. Several aromaticity indices were used in this study, based on different criteria of aromaticity energetic (aromatic stabilization energy, ASE), geometric (harmonic oscillator model of aromaticity, HOMA, and /5), and magnetic (NICS). 

Quantum-chemical calculations for pyrylium including one, two, or three water molecules using DFT and 6-31 + G(d,p) basis set revealed that the aromaticity (estimated by harmonic oscillator stabilization energy, HOSE natural resonance theory, NRT harmonic oscillator model of aromaticity, HOMA and nucleus-independent chemical shifts, NICS) is not influenced by water molecules [82],... 

A theoretical evaluation of the aromaticity of the pyrones pyromeconic acid, maltol, and ethylmaltol along with their anions and cations was carried out at several levels (Hartree-Fock, SVWN, B3LYP, and B1LYP) using the 6-311++G(d,p) basis set <2005JP0250>. The relative aromaticity of these compounds was evaluated by harmonic oscillator model of aromaticity (HOMA), nucleus-independent chemical shifts (NICSs), and /6 indexes and decreases in the order cation > neutral molecule > anion. 

Harmonic oscillator model of aromaticity (HOMA) — This is a geometry-based index of aromaticity that takes into account two effects. These are the increase in bond-length alternation (GEO term) and the increase in mean bond length in the system (EN term) such that HOMA= 1-EN-GEO <2004PCP249>. For examples see Sections 2.2.42.3, 2.3.42.3, and 244.2.3. 

The harmonic oscillator model of aromaticity (HOMA) index and Bird aromaticity indices (/5,15 6, and /A) for selected heterocycles are shown in Table 35 and Figure 15. The theoretical background to these indices is discussed in Section 2.2.4.2.3. To facilitate direct comparison between ring systems, Bird introduced a unified aromaticity index /A that is related to the indices for five- and six-membered rings and fused rings by the expression ... 

Several aspects of aromaticity have been studied <2002JOC1333> using statistical analyses of quantitative definitions of aromaticity. ASEs, REs, magnetic susceptibility exaltation (A), nucleus-independent chemical shift (NIGS), the harmonic oscillator model of aromaticity (HOMA), (/j) and (Aj), evaluated for a set of 75 five-membered 7t-electron systems and a set of 30 ring-monosubstituted compounds (aromatic, nonaromatic, and antiaromatic systems) revealed statistically significant correlations between the various aromaticity criteria, provided the whole set of compounds is used. The data in Table 9 have been found for arsole (AsH) 1 (E = As, R = H), its anion (As ), and protonated species (AsH2 ). 

Polarizability anisotropy of the 7t-electrons is regarded as the best available polarizability-based aromaticity index from a comparison of Pozharskii s index AA, Bird s index /a, the harmonic oscillator model of aromaticity (HOMA) index, the parallel polarizability a, the polarizability anisotropy, and the 7t-electron counterparts a < and Aa" <2004MI427>. 

Several reviews on various aspects of oxazole chemistry have been published. Cicchi and co-workers and Gilchrist reviewed synthesis and reactions of oxazoles. Walsh and co-workers " reviewed the biosynthesis of thizazole and oxazole peptides, including microcin B17 1196. Kawase and co-workers reviewed the synthesis of 5-(trifluoromethyl)oxazoles via Dakin-West chemistry. Suga and Ibata reviewed much of their work on [3 - - 2] cycloadditions of 5-alkoxyoxazoles. In addition, Mrozek and co-workers applied the harmonic oscillator model of aromaticity (HOMA) index to live-membered ring heterocycles, including oxazoles. 

Tropolone is another famous nonalternant system whose aromaticity has long been disputed. Recent studies of its anion and two conformers of protonated tropolone have given us a good opportunity to analyze how the aromaticity is affected by the protonation. The HOMA for tropolone is equal to 0.642. Its anion is definitely less aromatic, HOMA = 0.176, whereas cis and trans conformers of protonated... 

Analysis of the experimental molecular geometry (X-ray) of l,4-dichloro-2,6[5]metacyclophane shows its high aromaticity (HOMA = 0.985), despite substantial distortions from the planar conformation, as shown in Figure 16. This is in line with the H NMR signals of the ring protons but against the increased reactivity of this compound. ... 

I-GH2+ and 2 GH2+ anthracenes differ from each other dramatically. The substituted ring in the I-GH2+ derivative has a less aromatic character (HOMA = 0.348) than in the parent molecule (0.519), but the ring in the 2-CH2 derivative is much more dearomatized (HOMA = 0.179). Two other rings in the case of 2- CH2 derivatives are much less aromatic (HOMA = 0.668 and 0.652) than in the case of the 1-CH2 derivative (HOMA = 0.767 and 0.715). The CC bond, via which the quinoidal structure may propagate over the whole molecule, is equal to 1.401 A in the case of the 1-CH2 derivative as compared with the value of 1.375 A in the case of the 2-CH2 derivative (both bonds marked in bold lines in Chart 8). 

The least effect of CH2+ on the adjacent rings is observed in the case of 9-derivatives. The substituted ring is of low aromaticity (HOMA = 0.174), but the other two are markedly more aromatic, even more so than in the parent compound (HOMA = 0.892). This observation is in line with the well-known fact that 9-hydroxyanthracene easily tautomerizes to its... 

Krygowski 5 harmonic oscillator model of aromaticity (HOMA) as structural index of aromaticity S... 

Krygowski et al defined the Harmonic Oscillator Model Of Aromaticity (HOMA) index as. 

On the basis of geometrical considerations, molecules should show a decrease in aromatic character when they possess a high degree of bond alternation and deviate significantly from planarity. Several quantitative measures of this bond alternation have been proposed. Among the most important ones, we mention the Julg aromaticity index and the harmonic oscillator model of aromaticity (HOMA). " ... 

In addition to the e/-method, other criteria of cyclic conjugation and local aromaticity have also been utilized, all based on accurate DFT calculations. These were the harmonic oscillator model of aromaticity , HOMA [144—146], nucleus-independent chemical shifts , NICS [147, 148], and six-center indices , SCI [149, 150]. (For details on multi-center indices of aromaticity, see [99].)... 

---