Aromaticity index, and

However, they are of greater interest as intermediates not only do they undergo a variety of reactions, but the A -oxide entity decreases the aromaticity index " and substantially affects reactivities at other positions. 

A new index of aromaticity has been proposed and applied to neutral and mesoionic five-membered heterocycles. The aromaticity index is based on data from experimentally determined bond lengths which yield statistically evaluated bond orders. A reasonable parallel exists between the aromaticity index and resonance energies <85T1409>. 

It is impractical to determine the cetane number of residual fuels in the ASTM D-613 cetane engine. Because of this, the Calculated Carbon Aromaticity Index and the Calculated Ignition Index were respectively developed by Shell and BR These values can be determined from the following equations where d = Density in kg/m3 59°F (15°C) and v = Viscosity in cSt 122°F (50°C). 

Bird, C.W. (1985). A New Aromaticity Index and its Application to Five-Membered Ring Heterocycles. Tetrahedron, 41,1409-1414. 

The bond energy E y and the bond length r are related by E y= 1/r thus, there should be a correlation between aromaticity indexes and resonance energies. Accordingly, a unified aromaticity index 7a has been defined (reference benzene 7a=100), and 7a=77 for 1, 86 for 1,2,4- and 100 for 1,3,5-triazine <1992T335>. From molecular dimensions, 7a = 77 has also been calculated for both 4,6-dimethyl- and 4-methyl-6-phenyl-l,2,3-triazine, 73.4 for 4,6-dimethyl-l,2,3-triazine 2-oxide, 76.0 for 4-methyl-6-phenyl-l,2,3-triazine 2-oxide, and 68.95 for 6-methyl-4-phenyl-1,2,3-triazine 1-oxide <1993T8441>. In this sense, N-oxidation is accompanied by a reduction in aromatic character. 

Figure 1 Correlations between HOMA aromaticity index and resonance substituent constant (cjr) for substituted benzene (Bz), pyrazole (Pz), and imidazole (Im) derivatives. HOMA, harmonic oscillator model of aromaticity. Reprinted with permission from (20nJPCA(ii 5)8571). Copyright 2011 American Chemicai Society.

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). " ... 

Bird, C. W. 1985. A new aromaticity index and its application to five-membered ring heterocycles. Tetrahedron Al 1409-1414. 

There are variations in representation of rings in different disciplines. The dye industry does not designate aromaticity or double bonds in rings. AH double bonds and aromaticity are shown in the Encyclopedia as a matter of course. For example, tetralin has an aromatic ring and a saturated ring and its stmcture appears in the Encyclopedia with its common name. Registry Number enclosed in brackets, and parenthetical CA index name, ie, tetralin [119-64-2] (1,2,3,4-tetrahydronaphthalene). With names and stmctural formulas, and especiaHy with CAS Registry Numbers, the aim is to help the reader have a concise means of substance identification. 

A second theoretical index, and one for which there appears to be more justification in its application to free-radical reactions, is the atom localization energy. This index is a measure of the energy required to localize one electron of the 7r-electron system in the aromatic molecule at the point of attack of the radical. The formation of the intermediate adduct in a free-radical aromatic substitution may be regarded as the sum of two processes one, the localization of an electron at the point of attack and the other, the pairing of this... 

One can read letters through the porous PVA-PVAc film in benzene, but one cannot do so in cyclohexane nor in the case of the blank. This is supported by the fact that the refractive indices of benzene are close to that of PVA, but the refractive index of cyclohexane is far from that of PVA. When the porous film was dipped in a mixed solvent of benzene and cyclohexane (8.0 2.0 in weight), it became semi-transparent. To make this point clearer, the refractive index and the dispersive power of polymers and organic solvents were measured. The results are shown in Table 3, which shows that the refractive index of PVA is near that of benzene and that the dispersion power of aliphatic compounds is lower than that of aromatic compounds. 

The n-d-M correlation is an ASTM (D-3238) method that uses refractive index (n), density (d), average molecular weight (MW), and sulfur (S) to estimate the percentage of total carbon distribution in the aromatic ring structure (% C ), naphthenic ring structure (Cj,), and paraffin chains (% Cp). Both refractive index and density are either measured or estimated at 20°C (68°F). Appendix 4 shows formulas used to calculate carbon distribution. Note that the n-d-M method calculates, for example, the percent of carbon in the aromatic ring... 

Increase in naphthene, olefin, and aromatic concentration, which is indicated by an increase in the refractive index and decreases in aniline point and K factor... 

The order of aromaticity of these compounds is benzene > thiophene > pyrrole > fiiran, as calculated by an aromaticity index based on bond-distance measurements. This index has been calculated for five- and six-membered monocyclic and bicyclic heterocycles Bird, C.W. Tetrahedron, 1985, 41, 1409 1986, 42, 89 1987, 43, 4725. 

Total additive loadings rarely exceed 1% of the finished resin. The criteria for ignition resistance are based on oxygen index and UL-94 ratings. The mode of action of the flame retardants is reported to be consistent with that of aromatic sulfonates as proposed by Webb (27). 

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... 

Sulfur. Thiophene and benzo[ >] thiophene are both aromatic heterocycles, as discussed earlier in this review. Isothiazole is a planar molecule with an aromaticity comparable with those of thiazole and pyrazole, and higher than those of isoxazole and oxazole,122 140 as evaluated on the basis of Bird s aromaticity index A, based upon the statistical degree of uniformity of the bond orders of the ring periphery. Theoretical calculations and experimental data in connection with the aromaticity of isothiazole have been reviewed.141 Thiazole is also viewed as an aromatic molecule, similar to thiophene. It lacks an experimental aromaticity value, but the heat of formation together with bond lengths and angles have been calculated by various computational meth-... 

Several aromaticity indices (bond lengths, bond orders, Jug and Francois s aromaticity index) indicate that, despite the nonplanarity of the five-membered ring in 2,5-diphenylthiophene-l-oxide (108), this compound is intermediate in aromaticity between the corresponding thiophene 107 and the nonplanar 1,1-dioxide 109 (Scheme 48).149 The theoretical calculations were supported by experimental electrochemical data.150... 

Other congeners of phosphinins—arsenin, antimonin, and bismin—have been shown to be definitely less aromatic than benzene by diverse theoretical treatments that have been reviewed.236 For instance, the Bird aromaticity index for arsenin was found to be 67, compared to 100 for benzene.123 Table 4 summarizes a few parameters used to estimate the aromaticity of heterobenzenes resonance energies... 

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