Julg index

Figure 5 Julg index J for the (nonplanar) minimum and (pianar) transition state ring struotures of HEC4H4 at the MP2 and B3LYP ievei of theory. From S. Peizer, K. Wichmann, R. Wesendrup, and P. Schwerdtfeger, J. Phys. Chem., 2002,106, 6387.

Since all bonds in benzene are equal in length, the bond alternation ratio and the Julg aromaticity index for benzene is one. The Julg index has been modified to account for resistance to circulation of the 7j-electrons which is a major factor in electronegative heteroatoms . This correction factor A2 is given by Equation (3). 

Based on this, the new Julg index A = A1A2. This index however, has a few setbacks, the main one being the difficulty in evaluating the 7r-charges for molecules with heavy heteroatoms. The aromaticity indices of thiophene and benzene as determined by geometric criteria are shown in Table 18. 

The ideas of equality of carbon-carbon bond lengths as a characteristic attribute of a stable aromatic molecule (61JCS859 64PAC363) were embodied in the form of the aromatic stability index of Julg (76TCA249). 

Borete, calculations, 56, 361, 362 Borins, calculations, 56, 359 Borin, Julg A index, 56, 339 Borin, 1-carbonyl complex, calculations, 56, 362... 

As structural criteria of aromaticity, indexes N= + b (where R are bond lengths, and a and b are parameters characteristic for a given pair of atoms) and Julg s parameter J = 1 — 225/ S,s(l —d Jdf (where n is the number of peripheral bonds rs, are their lengths, and d is their mean length) have been applied. The less the value SaA and closer to 1 the value J, the greater is the aromaticity of a heterocycle. Polarizability exaltations F = M — M , where M and M arc the mean dipole polarizability and the mean atomic or group polarizability, respectively. 

Based on the idea that bond alternation causes the aromatic character to decrease, the first aromaticity index based on the —> molecular geometry was proposed by Julg and Frangois [ Julg and Franfois, 1967] as... 

Joshi steric descriptor > Julg-Eran9ois index ... 

Julg and co-workers have attempted to use structural criteria as a quantitative tool for assessing aromatic character and they have developed52 an aromaticity index Ai which is a measure of the degree of averaging of the peripheral bonds in an aromatic skeleton. The index is defined as... 

The Julg aromaticity index (/4i) <67TCA249> is based on taking the mean square deviations of the C—C bond lengths as a measure of aromaticity, and is calculated by the formula shown in Equation (2). 

An obvious limitation of the model is the fact that it can be applied only to carbocyclic systems. Sometimes this approach has been used on species with heteroatoms, and then only CC bonds were taken into account. This limitation results in exclusion of the contributions which are directly due to the interactions between heteroatoms and carbon—heteroatoms leading to a potential misinterpretation of aromaticity of these systems. Julg s index was applied to numerically describe the aromaticity of some jr-elec-tron systems and served also to test the correctness of other aromaticity indices such as HOMA as well as supporting other already accepted measures of aromaticity such as aromatic stabilization energy, ASE, and magnetic susceptibility exaltation. A. ... 

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... 

An aromaticity index, Aj has been defined by Julg and Francois 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). " ... 

Structural criteria In the structural criteria, several aromaticity indexes were developed by different groups of researchers. Earlier in 1967, Julg and Francois [7] proposed the first aromaticity index based entirely on the molecular geometry. The idea came from the fact that an increase in bond alteration signifies decrease in aromatic behavior. The index, Aj, is given by the following expression ... 

In Table 40 we have collected B indices for a number of smaller benzenoid hydrocarbons. For comparison, we also show the corresponding aromaticity indices based on bond lengths. According to Julg, one can derive an index of aromatic character from the differences between the actual CC bond lengths in a benzenoid hydrocarbon and the average CC bond distance d) using the expressions... 

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