Resonance Energy and Absolute Hardness

There are two other approaches to defining aromaticity that we will consider. The first is based on a comparison of the heat of formation of an organic compound with the heat of formation calculated for a nondelocalized reference system. The difference between those two values would then be the resonance energy for this system. 

At first glance this approach would seem to be dependent on uncertain reference systems. However, it was given firm footing by the work of Dewar, and Baird elaborated Dewar s approach. Calculated values of resonance energy can thus be based only on knowledge of the molecular 

Structure and experimental data for a few reference compoimds. The resonance energy so calculated is denoted the Dewar resonance energy (DRE). For a completely imsaturated compoimd with the formula CnH OpO, where p is the number of carbonyl-type oxygens and q is the number of ether-t5rpe oxygens, Baird showed that the DRE can be calculated as in equation 4.69  

This approach allows one to calculate indirectly the heat of formation of C(sp )-C(sp ) single bonds, which is difficult to determine directly. With this approach, the definition of aromaticity is that an aromatic compound has DRE 0, an antiaromatic compound has a DRE 0, and a compoimd that is neither aromatic nor antiaromatic has a DRE near 0. Results of DRE calculations by Baird are listed in Table 4.2.  

4 APPLICATIONS OF MOLECULAR ORBITAL THEORY AND VALENCE BOND THEORY 

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