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. 

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... 

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],... 

By determining the bond lengths in 2,4,6-triphenylpyrylium salts with various substituents at the para position of the 4-phenyl ring, Krygowski and coworkers found a practically linear dependence between the HOMA index and the Hammett cp parameter, indicating for amino substituents a considerable bond localization (with corresponding decrease of HOMA) [79-81],... 

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 ... 

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 non linear dependence of Arp on HOMA results from the definitions of these parameters the first one is a quadratic function of the differences of bond lengths, whereas the other is a linear one. It is worth mentioning here that the main contribution to the variability of HOMA index for chelate chain comes out from the GEO term, i.e., it is due to changes in bond length alternation, whereas the contribution due to the bond elongation is chaotic and insignificant. Figure 7 presents the dependence of EN and GEO on Arp. 

When the HOMA index calculated for the phenol rings is plotted against the C-O bond length (an approximate measure of H-bonding strength) for 664 H-bonded phenol derivatives retrieved from the Cambridge Structure Database, the dependence looks as in Fig. 10 [36]. 

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. ... 

A large field of applications of the HOMA index has recently been presented in two reviews [25,72], so there is no need to repeat them. The most important achievement is that the HOMA index can be analytically separated into two terms [26, 85] which account for the energetic and geometric contributions, EN and GEO, respectively. Originally this was done for carbocyclic systems [26], then the formula was modified to account for heterocyclic systems as well [85]. This more general formula is presented by eq. (13) ... 

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. 

The recently developed eq 8 cannot be used directly for the heterocyclic systems since the averaging procedure is meaningless for heterogenic data (the same limitation as in the case of Julg s index ). Therefore, in the case of hetero- -electron systems, a further modification of the HOMA index was made. The bonds with heteroatoms are represented by the Pauling bond numbers... 

Table 6. Structural Parameters of the HOMA Index in Its Separated Form (8) for. r-Electron Systems with Heteroatoms. n,pt — a Value of the Bond Number for Ropt...

Finally, the r(n) values from eq 13 may be applied in eq 8. leading to the HOMA index and its components EN and GEO. Table 6 collects all the constants used for the carbo- and heterocyclic systems. 

Figure 3. Linear dependence of HOMA index on the Cohen Benson ASE // (E). Correlation coefficient i = 0.989. (Reprinted with permission from ref 104b. Copyright 2000 Elsevier Science.)...

Until the mid-1990s, the CSD base archived 4079 derivatives of cyclopentadienyl and cyclopentadiene bound to almost all elements from Li to Tl. Table 21 presents the values of HOMA index estimated as a mean value for the subsamples built up of the compounds of cyclopentadiene or cyclopentadienyl moieties with particular elements. In most cases the data observed are greatly dispersed hence, statistical characteristics are given as averages and the interquartile ranges of HOMA values as well as the mean C—X interatomic distances are given with their interquartile ranges (variances could not be used for... 

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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