Aromaticity HOMA index

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>. 

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. 

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 ... 

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. 

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

Hydrogen-bonding can modify the aromatic character, and the role of solvents has been demonstrated by changes in the HOMA index caused by differences in the hydration of sodium and magnesium salts of... 

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... 

The important field of ionic liquids, in most cases 1,3-dimidazolium salts (143) has been studied by IR and Raman spectroscopies supported by B3LYP calculations. Additionally, calculations of the heteroaromaticity (HOMA index) showed that cation formation causes a decrease of the aromaticity of the imidazole ring. However, when the R groups at positions 1,3 are benzyl or adamantyl, the aromatic nature of the heterocyclic moiety increases. Moreover, the electron distribution performed using the GAPT method indicated the positive charge delocalization in the imidazolium ring [143],... 

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. 

Surprisingly, the HOMA index classifies pyrrole as being more aromatic than thiophene but the Bird index gives the order thiophene > pyrrole > furan. Both pyrrole and thiophene are much more aromatic than furan and according to the Bird index indole and isoindole are significantly more aromatic than their oxygen and sulfur analogues. 

Oxygen-containing heterocycles are always less aromatic than their sulfur and nitrogen counterparts, e.g., imidazole thiazole >> oxazole and pyrazole > isothiazole > isoxazole. These trends follow those of pyrrole, thiophene and furan (Section 2.3.4.2). 1,2,3-Oxadiazole is unknown and all attempts to synthesize this compound have been unsuccessful. Although it is not the least aromatic of the oxadiazoles based on the HOMA index (cf. 1,3,4-oxadiazole), its instability can be attributed to easy isomerization to the acyclic valence tautomer (i.e., 85 - 86). 

HOMA index (. Harmonic Oscillator Model of Aromaticity index)... 

The HOMA index for the feth aromatic bond type can be decomposed in two terms describing two different contributions to a decrease in aromaticity one contribution, due to the bond elongation, is called EN and the other one, due to the bond length alternation, is called GEO ... 

Some correlation between NICS index and HOMA index was found out [Szatylowicz, Krygowski et al., 2007]. However, criticism about the use of NICS as aromaticity descriptor is made by Lazzeretti [Lazzeretti, 2004], concluding that. a quantitative theory of aromaticity based on NICS is epistemologically inconsistent. ... 

Among geometry-based indices, the HOMA index works most effectively not only does it measure the decrease in aromaticity due to an increase in bond alternation (the GEO term), but it also estimates the decrease due to bond elongation (the EN term). 

Chermahini et al. (2007JMST(822)33) also studied substituent effects on the aromaticity (expressed by HOMA and NICS indices) of anionic and protonated forms of C5-X tetrazole derivatives (with X = NH2, OH, OMe, SMes, H, Me, F, Cl, BH2, CF3, CN, NO, and NO2). They have shown that the stability order of protonated forms is related to the nature of the substituent. For electron-withdrawing substituents, the stability follows the sequence 1,3-H > 1,4-H > 2,3-H > 1,2-H, but in the case of electron-donating groups the order of the stabihty changes to 1,4-H > 1,3-H > 1,2-H > 2,3-H. NICS(O) values suggest that the anionic forms of tetrazoles are less aromatic than IH- tautomers, whereas the obtained NICS(l) and HOMA values indicate that the aromaticity of anionic forms lies between those found for IH- and 2H- tautomeric forms. In the case of protonated tetrazole derivatives, the most aromatic are the 2,3-H forms, whereas 1,4-H tautomers are the least aromatic. Based on the HOMA index analysis the authors concluded that the aromaticity of protonated systems can be related to the nature of the substituent. However, a closer look on their results suggests that the Tt-electron delocalization of all the studied protonated systems hardly depends on the nature of the substituent at the position C5. 

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