Pericyclic reactions analysis

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

By retrosynthetic analysis, identify a precursor that could provide the desired product by a single pericyclic reaction. Indicate appropriate reaction conditions for the transformation you identify. 

Cope himself formulated this transformation as what would now be called a synchronous pericyclic reaction . This interpretation was supported by Woodward-Hoffmann s analysis of pericyclic processes. The Cope rearrangement of 1,5-hexadiene derivatives was regarded therefore for a long time as a classical example of an allowed pericyclic reaction... 

Application of CM theory to explain pericyclic reactions was first attempted by Epiotis and coworkers (Epiotis, 1972, 1973, 1974 Epiotis and Shaik, 1978b Epiotis et al 1980). The following analysis is a much-simplified treatment of that approach. Let us compare, therefore, the CM analysis for the [4 + 2] allowed cycloaddition of ethylene to butadiene to give cyclohexene with the [2 + 2] forbidden dimerization of two ethylenes to give cyclobutane. For simplicity only the suprafacial-suprafacial approach is considered, although this simplification in no way weakens the argument. 

A component analysis of pericyclic reactions proceeds by the following steps, which are illustrated for each of the classes of reaction in Figure 12.4 ... 

Figure 12.4. Procedure for general component analysis illustrated for each of the three types of pericyclic reactions.

Pericyclic reactions are described in Chapter 12 as a special case of frontier orbital interactions, that is, following Fukui [1]. However, the stereochemical nomenclature supra-facial and antarafacial and the very useful general component analysis of Woodward and Hoffmann [3] are also introduced here. 

The conclusion we may draw from this analysis is that in pericyclic reactions of these kinds we shall always be able to discover the inherent symmetry of the interaction topologically by considering the system as being made up of suitable components, even when there is no actual symmetry maintained in the molecule as a whole. We shall therefore be able to analyze the situation in terms of the... 

The Goldstein-Hoffmann approach to aromaticity, which was discussed in Section 10.4, is also applicable to pericyclic reactions, although the main emphasis in their development was the analysis of alternative geometries for ground-... 

This opens up the possibility of a systematic investigation of pericyclic reactions not only for model cases of parent unsubstituted systems, but for inclusion if zwitterionic contributions also enable the analysis of the eventual mechanistic changes induced by the polar substitution. As an example, the push-pull substituted Diels-Alder system will be analysed, in which the diene component is substituted in position 1 by a donor, and dienophilic component in position 6 by an acceptor substitution. In order to avoid the problems with the relative wieght of individual limiting structures of the intermediate (Eq. 30), the coulombic integrals modelling the substitution in the HMO wave function were arbitrarily set to a = 3/ and a = — 3) so that there is sufficient polarity in the system to secure the approximation of the intermediate by pure zwitterionic structure Z,. 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

The so-called aromaticity rules are chosen for comparison, as they provide a beautiful correspondence with the symmetry-based Woodward-Hoffmann rules. A detailed analysis [92] showed the equivalence of the generalized Woodward-Hoffmann selection rules and the aromaticity-based selection rules for pericyclic reactions. Zimmermann [93] and Dewar [94] have made especially important contributions in this field. 

The following sections present an empirical approach to applying the selection rules. The chapter continues with a basic introduction to the analysis of symmetry properties of orbitals and the application of orbital correlation diagrams to the relatively simply cyclobutene-butadiene interconversion it concludes with some examples of the frontier orbital approach to pericyclic reactions. 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Pukui... 

Whether we have a benzene-like system, catalyzed or non-catalyzed pericyclic reactions with an even ntimber of centers, or the Demjanow-reaction. structure-theoretical analysis always results in a ccHTesponding m-dimensional reaction lattice crmtaining an (m — 11-dimensional, dynamic sub-lattice, which is also Boolean (see Figures 3.12 and 3.13). 

Using benzene-like aromatic systems and pericyclic reactions with an even number of centers, the principles of graph-theoretical structure theory are described and extended to conjugated heterocycles and cyclic systems with an odd number of centres. With topological analysis of the graphs of these systems as a foundation, a graph-theoretical definition of the idea of aromaticity in regard to monocyclic compounds is presented. 

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