Cyclic polyene theory

B and Q bands, but did provide qualitative data on how skeletal variations affect porphyrin absorption spectra. The stage was now set for the strengths of all these theories to be unified. Martin Gouterman did this by using configuration interaction, a technique vital in free electron and cyclic polyene theories, to describe the porphyrin excited states generated by Hiickel theory. He called this new synthesis the four-orbital model. ... 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

Nonbenzenoid cyclic conjugated hydrocarbons are conveniently classified into two categories conjugated hydrocarbons composed of odd-membered rings called, in terminology of molecular orbital theory, nonalternant hydrocarbons, and cyclic polyenes currently known as annulenes. 

The localized many-body perturbation theory (LMBPT) applies localized HF orbitals which are unitary transforms of the canonical ones in the diagrammatic many-body perturbation theory. The method was elaborated on models of cyclic polyenes in the Pariser-Parr-Pople (PPP) approximation. These systems are considered as not well localized so they are suitable to study the importance of non local effects. The description of LMBPT follows the main points as it was first published in 1984 (Kapuy etal, 1983). 

Dewar s theory. In recent years more and more popular in organic chemistry becomes the theory of perturbation molecular orbitals (PMO) worked out by the American chemist M.J.S. Dewar. Using that theory, many complex problems of organic chemistry can be tackled, including the problem of aromaticity. Since it is impossible to describe this theory here, we are citing only some of the conclusions concerning the cyclic polyenes, drawn from it. 

These ideas were introduced by Hiickel, who used a molecular orbital approach to calculate the energy of cyclic polyenes. According to this theory, the molecular yr-orbitals of a regular m-sided polygon of carbon atoms may be classified by a quantum number j which may take any of the values = 0,... 

To introduce notation, we briefly review the application of Huckel theory to a cyclic polyene with N In carbon atoms. Each carbon atom contributes one electron to the n system of the molecule. The total Hamiltonian is approximated as a sum of one-particle terms as... 

Exercise 6,6 Consider a cyclic polyene with N = 4v + 2, v = 1, 2,... carbons. Instead of assuming that all the bonds are identical, suppose they alternate in length. In the context of Huckel theory this means that the resonance integrals between adjacent carbons are not all equal to P but alternate between Pi and Pi- For example, for benzene we have... 

Algebraically, the levels of the cyclic polyenes may be derived using simple Hiickel theory. The general result is given in equation 12.9 for the energy of the jth level for a cyclic system containing N atoms... 

The concept of the Mobius strip was explained earlier (see p. 55). The basis of the Zimmerman analysis is an extension of this idea. A cyclic polyene is defined as a Hiickel system if its basis molecular orbital (i.e. the lowest filled TT-level as in the case of benzene, for example) contains zero or an even number of phase dislocations. Mbbius systems possess an odd number of phase dislocations in the basis molecular orbitals. In accordance with the rules predicting aromaticity for these systems, which results from the application of the Hiickel molecular orbital theory, it may be inferred that since cyclic conjugation also arises in the transition states of pericyclic reactions, the foDowing conclusions apply ... 

Monocyclic conjugated polyenes are referred to as annulenes, and there exists ample experimental evidence to support the conclusions based on application of HMO theory to neutral and charged annulenes. The relationship between stability and structure in cyclic conjugated systems will be explored more fully in Chapter 9. 

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