Conjugation—Huckel Theory

Alder reactions to give the endo adduct as in (18) ->(19) rather than the exo one as in (18) ->(20)] in terms of qualitative perturbation theory. Similar methods were used by Hoffmann and his co-workers in discussion of favourable and unfavourable conformations of conjugated systems,93 and of relative stabilities of isomers.94 All these treatments are based, implicitly or explicitly, on extended Huckel theory,... 

Huckel theory - A simple approximation for calculating the energy of conjugated molecules in which only the resonance integrals between neighboring bonds are considered. Also called CNDO method (complete neglect of differential overlap). 

The last decade has produced a number of results which indicate that the successful longevity of Huckel theory is based on the fact that this theory contains intrinsic Information about the internal connectivity in the conjugated structures, i.e. it reflects the nrighbourhood of the atoms in the conjugated systems [5,16]. Here we will be concerned with the rdationship between Huckel theory and the topology of the molecular x-network. 

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. 

Simple molecular orbital theory provides a useful pictorial view of the electronic structure of molecules. It is particularly valuable in predicting the distribution of electronic charge over a molecule, and for planar w-electron systems predictions of molecular stability are often very accurate. By judicious choice of parameters the simple molecular orbital theory can also account for the gross features of the electronic spectra of conjugated molecules as, for example, in Huckel theory. 

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 Huckel 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) Schaad and Hess, J. Chem. Educ., 51, 640 (1974) Hess and Schaad, Pure Appl. Chem., 52,1471 (1980) Schaad and Hess, Chem. Rev., 101, 1465 (2001).]... 

For monocycUc conjugated polyenes (such as cyclobutadiene and benzene) with each of Nq carbon atoms contributing an electron in a 2p orbital, simple Huckel theory gives the following expression for the energies of the resulting it molecular orbitals ... 

Huckel theory for PPV or other polymers with para-conjugated phenyls gives a simple explanation for their reversed 2A/IB ordering relative to polyenes [39]. We label phenyl sites in Fig. 6.2 adjacent to one bridgehead as 1, those adjacent to the other bridgehead as 2. The new orbitals... 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

Previously in Chapter 3 we introduced the Huckel molecular orbital theory and applied it to the n system of a number of conjugated polyene chains. In this section we will apply this approximation to cyclic conjugated polyenes, taking advantage of the symmetry properties of these systems in the process. 

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