Huckel Resonance Energy

HUckel resonance energies units of fi) of cyclic conjugated polyenes... 

Simple HUckel calculations predict the resonance energy of the benzocyclopropenyl cation (273) (3.65 P) to be higher than that of the tropylium ion (274) (2.99 P) and that of the cyclopropenyl cation (275) (2.00 P). Recent ab initio calculations at the 3.2 IG level attribute the same stability to 273 and 275 with respect to their hydrocarbon precursors The enthalpy change in going from 1 to... 

The Huckel approximation is defined by a set of simplicafions to the form of the Hamiltonian in the LCAO-MO description of planar conjugated molecules. Although the Huckel approximations are quite severe, nevertheless they produce results that rationafize qualitatively the resonance energies and spectra of these molecules. 

On the other hand, we should perhaps not be too surprised if values of fi derived from different kinds of measurements do not agree exactly, and indeed this is the case. We have seen above that/ obtained from the vertical resonance energy of benzene is about 37 kcal/mol, whereas Platt first showed that the best overall fit to the spectra of benzene and other unsaturated hydrocarbons was obtained in the framework of the Huckel approximation by taking / to be 55-60 kcal/mol. This high value, which has subsequently been widely adopted to estimate actual differences in energies between MOs, is generally known as the spectroscopic value of / . 

There is, however, an important difference between examples 27 and 41. The later compound forms a Huckel-aromatic orbital system in 41b while the former compound adopts a Mobius orbital system with 4q + 2 electrons, i.e. 27 is Mobius antiaromatic although six electrons participate in cyclic delocalization (see Section III. B). This is in line with a destabilizing resonance energy of 9.9 kcalmol"1 (Table 2) calculated with the MM2ERW method41-42. 

In his first publications Huckel has already pointed out the possibility of the calculation of the transition frequencies from the calculated energy levels. An objection to this was, however, that in the so-called zeroth approximation (p. 279) the value of the parameters both in the valence bond and in the molecular orbital method had to be chosen quite different in order to calculate either the resonance energy or the transition frequencies in agreement with observation (Sklar, Forster)26. 

Early MO descriptions of homoaromatic compounds were based on Huckel MO (HMO) theory. Through-space interactions between interacting C centres were modelled by assuming a value for the resonance integral For example, in the case of the homotropenylium cation, Winstein took P (C1,C7) = 0.5 and obtained a resonance energy comparable to that of the tropenylium cation. He concluded that, despite the insertion of the CH2 group into the Ti-system of the tropenylium cation, delocalization of TT-electrons is largely retained. 

Here two C fullerene structures are r ard l as distinct if they have different Huckel theory resonance enei es and/or HOMO-LUMO energy separations. This definition discounts the fact that identical resonance energies and HOMO-LUMO energy separations might conceivably be obtained for two different C fullerene molecular graphs. 

There is another way to test chemical stability hat can be applied to aromatic organic compounds. Aromaticity is usually taken to mean high stability and low reactivity. It can be quantified by calculating the resonance energy per electron (REPE). These values are usually calculated by simple Huckel theory, but they correlate well with experimental measures of reactivity. ... 

The resonance energy, RE, is a rather enduring concept [12] which has served for many years as a theoretical measure of the aromatldty of conjugated systems [87,88]. The RE concept has been the raison d etre for the continuous use of Huckel theory by organic chemists. For example, many recent developments of Huckel theory were indeed stimulated by a desire to remedy the failure of traditional forms of the theory in predicting the aromatic behaviour of conjugated molecules. 

A number of concepts can be taught using Huckel theory resonance energy, bond order, and predicted sites for nucleophilic and electrophilic attack. This method has the advantage that the computer programs are very simple to use, 8,29 g d so the user can concentrate on the chemistry as well as the methodology of solving simultaneous linear equations. 1 2... 

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