Hess-Schaad model

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. ... 

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. ... 

A recent Hflckel calculation based on the proper choice of models correctly accounts for the observed differences in w-electronic makeup between lff-azonine (26a) and oxonin (24a) which were calculated to possess resonance energies of 0.139 and 0.0010, respectively [B. A. Hess, L- J. Schaad, and C. W. Holyoke, Tetrahedron 28, 3657 (1972)]. In terms of simple Hiickel theory the differences between 26a and 24a were attributed chiefly to the lower LVMO energy of the latter (A. G. Anastassiou, in Topics in Nonbenzenoid Aromatic Chemistry (T. Nozoe, R. Breslow, K. Hafner, S. Ito, and I. Murata, eds.), Vol. I, pp. 1-27. Hirokawa Publ., Tokyo, 1973). 

According to a recent HQckel calculation based on properly chosen models, thionin (24 X = S) should be endowed with a well-delocalized (RE = 0.118/3) periphery (see Hess and Schaad ). 

The total -electron energy is one of the most important parameters of a conjugated molecule that can be obtained from the Huckel MO calculations [65]. It can be used selectively, to relate to the thermodynamic stability of conjugated structures. A parametrization scheme, based on thermodynamic data, by Hess and Schaad [66], has produced agreement with experiment to the same d ee of qumititative accuracy as the much more sophisticated SCF r-MO procedure developed by Dewar (67). In addition. Schaad and Hess [68] have shown that in many instances Bir follows linearly the total (thermodynamically measurable) energy of the conjugated molecule. The physical reasons leading to the answer as to how it Is possible that a model as simple as the Huckel model can ve not only qualitative, but sometimes also fair quantitative... 

The estimated stabilization energies from the HOSE model are in line with those obtained in other ways. It was shown that HOSE correlates well with the Hess and Schaad resonance energies (correlation coefficient R = 0.991 for 22 alternant TT-electron hydrocarbons R= 0.937 for 12 nonalternant hydrocarbons). In the last case, the Hess and Schaad RE values were given for nonalternant hydrocarbons whereas geometries used to calculate the HOSE values originated from substituted species. Since the substituent effect in nonalternant systems is quite considerable, these aspects will be discussed later. 

P. L. Polavarapu and D. F. Michalska, /. Am. Chem. Soc., lOS, 6190 (1983). Vibrational Circular Dichroism in fSJ-(-)-Epoxypropane. Measurement in V por Phase and Verification of the Perturbed Degenerate Mode Theory. P. L. Polavarapu and D. F. Michalska, Mol. Phys., 52, 1225 (1984). Mid Infrared Vibrational Cin r Dichroism in fS)-(-)-Epoxypropane Bond Moment Model Predictions and Comparison to the Experimental Results. P. L. Polavarapu and D. F. Michalska, Mof. Phys., 55, 723 (1985). Errata Mid Infrared Vibrational Circular Dichroism in f5J-(-)-Epoxypropane Bond Moment Model Predications and Comparison to the Experimental Results. P. L Polavarapu, B. A. Hess, and L. J. Schaad, /. Chem. Phys., 82, 1705 (1985). Vibrational Spectra erf Epoxypropane. 

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