Electronic Criteria for Aromaticity

As discussed in the Introduction, Huckel s rule is an electronic criterion for aromaticity, and is based on the configuration of the rr electrons. Another characteristic of aromatic compounds is a relatively large HOMO-LUMO gap, which indicates the absence of high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds to electrophilic reagents. This facet of electronic configuration can be expressed in terms of hardness (see p. 96 for the definition of hardness in terms of DFT theory).  

The numerical value of hardness obtained by HMO calculations correlates with the stability of aromatic compounds. The energy gap can also be compared with polyene reference molecules to give relative hardness. By this measure, the relative hardness of benzene is 0.765(3 when butadiene is assigned as 0. MNDO calculations have also been used in this context.  

The correlation can be given an experimental basis when hardness is related to molar refractivity  

Molar refractivity is easily derived from the refractive index. Hardness measured in this way correlates with other aromaticity criteria such as resonance energy per electron for a variety of hydrocarbons and heterocyclic molecules (see p. 141)  

An experimental measure of the HOMO-LUMO gap is the reduction and oxidation potential of the ring. A range of benzenoid and nonbenzenoid reduction potentials correlates with the LUMO energy, as calculated by a modified HMO method.  

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