The Energy Criterion for Aromaticity

One approach to evaluation of the aromaticity of a molecule is to determine the extent of thermodynamic stabilization. Attempts to describe stabilization of a given aromatic molecule in terms of simple HMO calculations have centered on the delocalization energy. The total rr-electron energy of a molecule is expressed in terms of the energy parameters a and 6 that are used in HMO calculations. This energy value can be compared to that for a hypothetical localized version of the same molecule. The HMO energy for the tt electrons of benzene is 6a + 86. The same quantity for 

The isodesmic reaction method (see Section 1.2.6) has also been applied to the calculation of the resonance stabilization of benzene. Homodesmotic reactions, a special version of isodesmic reactions, can also be used. Homodesmotic reactions 

Isodesmic and homodesmotic reactions can use either experimental thermochemical data or energies obtained by MO or DFT calculations. There have been many specific reaction schemes and computational methods applied to calculation of stabilization energies. With the above homodesmotic sequence, calculations at the MP4(SDTQ)/6-31G((i,/ ) level give the following stabilization (AF) values.  

This particular calculation may underestimate the relative stabilization, since it uses 1,3-butadiene as the model, rather than the cis geometry that is incorporated into cyclic structures. For example, the homodesmotic reaction below gives a stabilization energy of 30.5 kcal/mol relative to cyclohexadieneA A feature of this scheme is that it incorporates many of the structural features of the system, such as ring strain, into both sides of the equation so that they should largely cancel. The net stabilization has been called the aromatic stabilization energy. 

Another refinement of the isodesmic approach to defining aromatic stabilization is to compare methyl-substituted aromatics with the corresponding 

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