Based Measures of Aromaticity

IV. Magnetism-Based Measures of Aromaticity A. Ring Currents... 

The aromaticity of five-membered rings with two or more heteroatoms was discussed in detail in earlier reviews.52 100 111 In a comprehensive survey on the quantitative measurements of aromaticity,112 it has been shown that basicity-based quantification of aromaticity gave more reproducible resonance energies than other methods, such as heats of formation, ring currents, magnetic susceptibilities, and theoretical indices. 

A limited amount of energy data is available for this class of heterocycle. Table 38 shows empirical resonance energies (ERE) and Hess-Shaad resonance energies (HSRE) for a limited list of azoles. Also included in Table 38 are aromatic stabilization energies (ASEs). The ASE is a more recent measure of aromaticity based on homodesmotic and isodes-motic reactions. ASE values for a wide range of five-membered heterocycles are available <2003T1657>. 

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). 

Zhou, Parr, and Garst showed that absolute hardness correlates well with theoretical measures of aromaticity but that the value of tj by itself does not allow the categorization of aromaticity. Zhou and Parr later defined the relative hardness of a species as the difference between its hardness and the hardness of an acyclic reference compound. Based on these correlations, the authors proposed that a compound is aromatic if its Hiickel absolute hardness (determined from the Hiickel HOMO-LUMO gap) is less than -O.ip, antiaromatic if the value of tj is less than -0.15j8, and nonaromatic if rj is between those two values. The corresponding division based on relative hardness is 0. That is, a cyclic molecule that is harder than an acyclic analog is aromatic, while one that is not as hard as an acyclic analog is antiaromatic. 

Another popular electronic measure of aromaticity is the fluctuation index (FLU) (2005JCP014109). It measures electron fluctuation differences with respect to an aromatic reference system by comparing the contiguous electron delocalization indices (1999JPCA304) along cychc structure. The FLU index is close to 0 in aromatic species and departs from this value in nonaromatic ones. The drawback in this case is similar to that for geometry-based indices, namely the dependence on the reference systems. 

Although known for almost a couple of centuries there exists no direct measure of aromaticity mainly because it is neither an experimental observable nor it is a theoretically defined quantity. In this chapter various types of aromatic systems with a special emphasis to all-metal aromatic clusters have been discussed. Different indirect aromaticity measures have been analyzed with special emphasis to some chemical reactivity based aromaticity indices within a conceptual density functional theory... 

Zhou, Parr, and Gharst put forward the absolute hardness as a measure of aromaticity. Their argumentation is based on the fact that both aromaticity and hardness are measures of high stability and low reactivity. In their contribution, a simple proof for this fact was given. Gonsider a species S. The energy change for the process... 

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