Bond length alternation indexes

Harmonic oscillator model of aromaticity (HOMA) — This is a geometry-based index of aromaticity that takes into account two effects. These are the increase in bond-length alternation (GEO term) and the increase in mean bond length in the system (EN term) such that HOMA= 1-EN-GEO <2004PCP249>. For examples see Sections 2.2.42.3, 2.3.42.3, and 244.2.3. 

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. 

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 ... 

Another approach in which the bond length alternation is taken into account is based on the sum of squared differences of the sequential bond lengths. The index called BAG (bond alternation coefficient) reads ... 

Zhao and coworkers [82,83] have also reported on the dibenzo-annulated radiaannulene compounds 87 and 88 containing DT rings at their terminal positions (Figure 8.25). From the X-ray crystallographic analyses, the central radiaannulenes units in both 87 and 88 adopt almost planar structures. In addition, the bond length alternation (BLA) indexes of 87 and 88 are found to be 0.165 and 0.155 A, respectively, owing to a moderate it-delocahzation of the central cyclic... 

The geometric aromaticity criteria are related to the observations of the equalized bond length of benzene, which is in contrast with that of the conjugated polyenes, having alternating bond lengths (and bond orders). The extent of the equalization can be measured statistically, and perhaps the most widely used method is that proposed by Bird [66]. The Bird index (BI), which can also be applied for heteroatoms (including... 

This index solves the problem for monocyclic system but becomes complex for polycyclic systems (as it involves the sequential bond lengths). Also it cannot be applied for systems containing heteroatoms and, to some extent, for systems in which the localization of double bonds is not alternating. 

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