Resonance energy definition

A number of resonance energy definitions are based on theoretical quantum-chemistry approaches. It was also recognized that the main difference between the proposed approaches lies in the definition of the nonconjugated reference structure, not in the use of different MO theories. 

Write an essay of approximately 2000 words on the history and the various definitions of the concept of resonance, resonance energy, and aromaticity. 

A modified definition of resonance energy has been introduced by Dewar (66T(S8)75, 69JA6321) in which the reference point is the corresponding open-chain polyene. In principle this overcomes the difficulties inherent in comparing observed stability with that of an idealized molecule with pure single and double bonds, as thermochemical data for the reference acyclic polyenes are capable of direct experimental determination. In practice, as the required data were not available, recourse was made to theoretical calculations using a semiempirical SCF-MO method. The pertinent Dewar Resonance Energies are listed in Table 30. 

Other congeners of phosphinins—arsenin, antimonin, and bismin—have been shown to be definitely less aromatic than benzene by diverse theoretical treatments that have been reviewed.236 For instance, the Bird aromaticity index for arsenin was found to be 67, compared to 100 for benzene.123 Table 4 summarizes a few parameters used to estimate the aromaticity of heterobenzenes resonance energies... 

The definition used depends on the phenomenon under study. For instance, the intensity-averaged lifetime must be used for the calculation of an average colli-sional quenching constant, whereas in resonance energy transfer experiments, the amplitude-averaged decay time or lifetime must be used for the calculation of energy transfer efficiency (see Section 9.2.1). 

Earlier definition of resonance energies comes down to an evaluation of the QMRE within the framework of the Hiickel MO method (HMO) (61MI1 75MI1 86MI1). Hiickel resonance energy (HRE) is defined as... 

We may perform the same analysis for the allyl radical and the allyl anion, respectively, by adding the energy of 4>2 to the cation with each successive addition of an electron, i.e., H (allyl radical) = 2(a + V2/3) + a and Hn allyl anion) = 2(a + s/2f) + 2a. In the hypothetical fully 7T-localized non-interacting system, each new electron would go into the non-interacting p orbital, also contributing each time a factor of a to the energy (by definition of o ). Thus, the Hiickel resonance energies of the allyl radical and the allyl anion are the same as for the allyl cation, namely, 0.83/1. 

Another aspect of delocalization, the mixing of Kekule structures and the energetic gain associated with it, will also be quantitatively investigated, and finally our results will be placed into the context of the thermochemical properties of hydrocarbons and the current definitions of resonance energy. 

For cyclobutadiene, keeping the K0 term as necessary to describe the background exerted by a skeleton, the average of the two Kekule structures is K0-Ja-Jb. Correspondingly, for benzene, confined also to Kekule structures, the non-resonant part can be conventionally defined as K0-3Ja/2-3Jb/2. In this way we estimate a resonance stabilization for benzene of — 8.56 kcal/mol, comparable with the CASVB calculation [22] giving — 7.4 kcal/mol. Here one should note that with respect to the adopted definition and the method of estimation, the resonance energy is disputed in a very large interval (— 5 to — 95 kcal/mol) [23]. The representation in... 

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