Aromaticity electronic indices

Another index of delocalization, devised and widely applied by Schleyer et al.,163 is the nuclear-independent chemical shielding (NICS) value. When calculated above the ring, this value corresponds to the -contribution which is a significantly negative quantity for situations with aromatic delocalization . Scheme 21 shows the A and NICS values computed by Schleyer et al.141 for benzene, hexasilabenzene, and hexazine. The three species are seen to possess equally aromatic electron sextets, as indeed anticipated from the appreciable vertical resonance ener-... 

Cyclic systems with 4m + 2 carbon atoms are characterized by the aromatic index m. At the lowest level (m = 0) ethylene formally corresponds to a 2-membered ring. The electronic structure shown in Figure 6.1 is consistent with aromatic electron distribution. Benzene (m = 1) is the prototype of properly cyclic aromatics. The molecular o-a-m conserves the sum of atomic angular momenta. The odd couples with the screening function are delocalized around the ring, with zero o-a-m. 

An interesting comparison between several aromaticity indices (harmonic oscillator model, nucleus-independent chemical shift, para-delocalization index, aromatic fluctuation index, multicenter indices, atoms-in-molecules theoretical indices and graph-theoretical indices) concluded that the most reliable ones are based on electron delocalization (08JCC1543). 

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>. 

Sola "" aromatic fluctuation index (FLU) (describing the fluctuation of electronic charge between adjacent atoms in a given ring) ... 

Matito E, Duran M, Sola M (2005) The aromatic fluctuation index (FLU) a new aromaticity index based on electron delocalization. J Chem Phys 122 014109... 

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

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... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

In aromatic diazonium compounds containing an ionized hydroxyl group ( —O-) in the 2- or 4-position, it is necessary to consider delocalization of electrons and, therefore, two mesomeric structures (1.7a-1.7b) (see Sec. 4.2). This fact has implications for nomenclature compounds of this type are considered as quinone derivatives following IUPAC Rule C-815.3 (Exception) compounds of this class are called quinone diazides. As a specific compound 1.7a-1.7b is indexed in Chemical Abstracts as 4-diazo-2,5-cyclohexadien-l-one. If reference is made specifically to mesomeric structure 1.7b, however, it is called 4-diazoniophenolate. 

As shown, for example, by calculations of the structural index A, the aromaticity of alumobenzene (112) is still lower than that in borabenzene. Calculations (MNDO) have shown the ground state of this molecule to be, in contrast to benzene, triplet (3B,). Even so, the 67r-electron structure of (112) is more stable than the 47r-electronic one. However, the difference between their energies (36.6 kcal/mol) is nearly twice as small as that for the corresponding structures of borabenzene. 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

The refractive index, d, is a measure of induced polarizability. Dispersion forces are especially high for aromatic hydrocarbons, which have highly polarizable k electrons. This is reflected in the high refractive indices of aromatic compounds, often 0.1 to 0.2 units higher than comparable nonaromatic compounds (table 3.5). Solvents with high polarizabilities are often good solvents for soft anions (i.e., those with high polarizabilities) such as SCN, F, and fF... 

---