Aromatic Character Derived from Molecular Geometry

AROMATIC CHARACTER DERIVED FROM MOLECULAR GEOMETRY 

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)  

The values of rgv and r in eq. 11 are obtained for XY bond types using the Pauling concept of bond number [15] all bonds with heteroatoms are in this way recalculated into virtual CC bonds. For CC bonds themselves the values of rj are equal to the experimental bond lengths rav stands for an averaged value. 

Katritzky et al. [88] and Jug [89] and others [14,22,57] have shown recently that aromaticity is a multidimensional phenomenon. For this purpose they applied statistical methods (the principal component or factor analyses [51,90,91]) which need application of many indices of aromaticity estimated (experimentally or calculated theoretically) for many molecular systems. Thus their conclusion is of great general importance but no information may be extracted for any individual molecule or its fragment. The method presented above, the separation of HOMA value into EN and GEO terms, allows us to describe numerically which of these two factors is 

An interesting aspect of aromaticity is its relation to the planarity of the n-electron system in question. As it was shown using the geometry of m-cyclophane [94] and of per-substituted naphthalenes, even a substantial folding of the ring in the former case or of the bicyclic system in the latter, does not lead to the loss of aromatic character. It happens rather suddenly when a considerable deviation from coplanarity 

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AROMATIC CHARACTER DERIVED FROM MOLECULAR GEOMETRY... 

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