Cyclic polyenes resonance energy

By contrast, the Dewar resonance energy represents solely the contribution coming from the cyclic electron (bond) delocalization since the model reference structure is represented not by a system of isolated 7r-bonds, but by a hypothetical cyclic polyene with the number of tr- and tr-bonds equal to that in a given molecule. Making use of the additivity of bond energies in acyclic polyenes (65JA692), one may calculate the total energy... 

Pyridine and benzene conform to Hiickers rule, which predicts that planar cyclic polyenes containing (4n + 2) -electrons ( = 0, or an integer) should show added stability over that anticipated for theoretical polyenes composed of formal alternate single and double bonds. This difference is sometimes called the empirical resonance energy. For example, benzene, where n = 1, is estimated to be 150 kJ moT more stable than the hypothetical molecule cyclohexatriene (Box 1.8) for pyridine, the empirical resonance energy is 107 kJ mol . ... 

CM) is shown in Scheme 22, and it is seen to involve cyclic conjugation, but all the interactions between the "T-bond units have a polyenic character. The relative energy of the two structures, as in eq 7, is defined as the Dewar resonance energy (DRE) of the cyclic molecule. 

More sophisticated calculations indicate that cyclic An systems like cyclobutadiene (where planar cyclooctatetraene, for example, is buckled by steric factors and is simply an ordinary polyene) are actually destabilized by n electronic effects their resonance energy is not just zero, as predicted by the SHM, but less than zero. Such systems are antiaromatic [17, 46]. 

Model the transition states of Reactions (4.1)-(4.4) by the conjugated molecules 8, 9, 10 and 11, and use the PMO method to calculate their resonance energies (defined as the difference between the energy of the cyclic structure and its open chain polyene counterpart). Hence, deduce the feasibility of Reaction (4.1). 

To produce more reliable predictions of aromaticity, Hess and Schaad (following a suggestion of Dewar) calculated delocalization (resonance) energies of cyclic hydrocarbons by comparing the compounds Htickel-theory with a value calculated for a hypothetical acyclic conjugated polyene with the same number and kinds of bonds as in a localized structure of the cyclic hydrocarbon. [B. A. Hess and L. J. Schaad, J. Am. Chem. Soc., 93, 305, 2413 (1971) 94, 3068 (1972) 95, 3907 (1973) B. A. Hess, L. J. Schaad, and C. W. Holyoke, Tetrahedron, 28, 3657, 5299 (1972) Schaad and Hess,... 

Exercise 5.19 a) Extend the above analysis to calculate the lEPA resonance energy for a cyclic polyene with N — 2n (N >6) carbon atoms. As before, argue that all particle energies are the same so that... 

Since the polyene is cyclic, the zeroth ethylenic unit is the same as the nth while the (n + l)th is just the first. In this model, the exact resonance energy of benzene is 2)3, while asymptotically, the exact resonance energy is... 

Thus the resonance energy calculated for a cyclic polyene with N >6 up to fourth order is (1/4 -t-1/64) = 0.2656NP, which compares very favorably with the asymptotically exact value of 0.2732N)J (i.e., 97%). 

The for benzene is +19.82 kcal/mol, or 3.3 kcal/mol per CH unit (Fig. 13.14). Therefore, benzene is about 5.6 kcal/mol more stable per CH unit than a cyclic polyene with no special stability (8.9 — 3.3 = 5.6 kcal/mol). Because there are six CH units in benzene we can estimate the special stability (resonance or delocalization energy) to be 6 X 5.6 = 33.6 kcal/mol. Note that the two methods, which use the related heats of hydrogenation and heats of formation, are in rather good agreement. 

Topological resonance energies are Dewar resonance energies comparing cyclic systems to acyclic polyenes within the Hiickel scheme and have been reported for 1-10 as shown in Table 2. " Negative values (in units) indicate reduced conjugative stability relative to acylic models, and this criterion indicates destabilization in all these species. These values are not normalized for different numbers of electrons. 

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