Hess-Schaad Reference Structure

REPEs for the annulenes using the Hess—Schaad reference structure are in Figure 11. These of course are for the planar annulenes with all C—C bonds of equal length. Nevertheless, Figure 11 does appear to predict with reasonable accuracy what is known about the actual systems. 

Column 4 of Figure 6 shows the predicted order of aromaticity of our set of 11 compounds using the simple Hiickel energy calculation but with the Hess— Schaad reference structure. Thus, the only difference between the results in column 1 and column 4 is the choice of reference structure. This difference has a large consequence, and it seems to us that while the computed order of aromaticity in column 1 is poor, the order in column 4 is quite satisfactory. Benzene is at the top followed by naphthalene. Calicene and azulene are predicted to be more weakly aromatic, followed by the nonaromatics, butadiene, fulvene, and heptalene. The antiaromatics pentalene, benzocyclo-butadiene, and fulvalene follow with cyclobutadiene, the most antiaromatic, at the bottom. 

This definition of resonance energy makes a clear distinction between aromatic (positive DRE), antiaromatic (negative DRE) and nonaromatic (near zero DRE) conjugated molecules. Extensive tables of resonance energies were also obtained in the framework of the HMO approximation by Hess and Schaad [Hess Jr. and Schaad, 1971a Hess Jr. and Schaad, 1971b Hess Jr. et al, 1972 Hess Jr. and Schaad, 1973]. Moreover, extensions and modifications of the calculations of the reference structure energy were proposed by other authors [Baird, 1969 Baird, 1971]. 

Schaad and Hess [95] investigated the ori n of the reference structures with the two-bond and the eight-bond parameters. They treated acyclic reference structures as collections of perturbed ethylene molecules. A perturbation treatment through second order produced the two-bond parameter scheme (- c-c = 0.5 Ec=c = 2), whereas a perturbation treatment through the fourth order produces the eight-bond parameter... 

The theory was described as being parameter-free in a sense that it avoids the use of empirical parameters for reference structure bond energies based on least-squares fitting of numerical data and that it does not need the distinction of eight bond references for hydrocarbon used in the Hess—Schaad scheme. The first papers were on hydrocarbons and gave similar results to the Hess—Schaad resonance energy (HSRE) method. The same, of course, is true for the papers by Aihara. ° It is clear, however, that such a theory cannot be parameter-free if heteroatoms are involved. These concern the /tx and /cc-x parameters of HMO theory. ... 

Encouraged by the success of the Hess—Schaad approach on the Hiickel level, a topological approach was advanced by the Zagreb group " and by Aihara. It is based on the computation of an acyclic polynomial in the framework of graph theory. This is used to describe the acyclic polyene-like reference structure. The topological resonance energy (TRE) is defined as... 

Ett, loc ot the localized reference structure, the RE, and the REPE of different aromatic compounds. The calculated values were compared with the available data of Hess and Schaad and appeared to be in excellent agreement with one another. Figure 113 gives a graphic representation of the lowering of the REPE in the different heterocyclic systems. 

Tkble V. Values for a Series of Aromatic Heterocyclic Systems of the Hiickel tt Energy, hmo> the loc of the Localized Reference Structure as Determined by Hess and Schaad, the RE, and the REPE... 

Similarly, Figures 11 and 12 show that the Hess— Schaad and graph-theoretical reference structures give very similar predictions of aromaticity for the annulenes. Without a more precise experimental definition that is generally accepted, we cannot say which of these two reference structures is better. Both appear to give at least roughly correct predictions of aromaticity. 

We have applied the Hess—Schaad version of the Dewar reference structure to the systems listed in Table 2. Theoretical investigations of the REPE index were also published. Changes in the energy of the o electrons in a series of compounds were found to vary linearly with though in opposite direction to ji energies. This provides some explanation of why jr-elec-tron-only models of conjugated systems can be as successful as they are. Reference structures were investigated."" " and comparisons were made with other recent theoretical aromaticity indices. ... 

If other models of aromaticity are taken, which are also based on Hiickel jt energies but use more elaborate reference structures, opposite results were obtained, with benzene being more aromatic than Ceo-The Hess—Schaad scheme, in which the reference structure is given in terms of six independent parameters, gives a HSRE/e which is about one-half that of benzene (Table 4). A scheme developed by the Zagreb group affords values comparable to those obtained with the Hess—Schaad model. ... 

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