Molecular orbital theory, pericyclic reaction analysis

We then present ab initio molecular orbital theory. This is a well-defined approximation to the full quantum mechanical analysis of a molecular system, and also the basis of an array of powerful and popular computational approaches. Molecular orbital theory relies upon the linear combination of atomic orbitals, and we introduce the mathematics and results of such an approach. Then we discuss the implementation of ab initio molecular orbital theory in modern computational chemistry. We also describe a number of more approximate approaches, which derive from ab initio theory, but make numerous simplifications that allow larger systems to be addressed. Next, we provide an overview of the theory of organic TT systems, primarily at the level of Hiickel theory. Despite its dramatic approximations, Hiickel theory provides many useful insights. It lies at the core of our intuition about the electronic structure of organic ir systems, and it will be key to the analysis of pericyclic reactions given in Chapter 15. 

Throughout this book we have often referred to the importance of the HOMO and LUMO in understanding a molecule s properties. Fukui reasoned that these frontier molecular orbitals might play an especially important role in concerted, pericyclic reactions. We have also noted before that it is always favorable to mix filled molecular orbitals wi th empty molecular orbitals. Combining these ideas led to frontier molecular orbital (FMO) theory, an elegant analysis of the types of reactions of importance here. Quite simply, frontier molecular orbital theory states that if we can achieve a favorable mixing between the HOMO of one reactant and the LUMO of another reactant, a reaction is allowed. If we cannot, the reaction is forbidden. 

Perhaps most importantly, though, the analysis of thermal pericyclic reactions introduced to organic chemists the power of orbital-based arguments in analyzing reaction pathways. Prior to this work, many experimentalists were justifiably skeptical that full molecular orbital theory could seriously impact their research. Those days are now long gone. 

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 ... 

From the foregoing discussion it appears that the frontier orbital method is at once a simple, concise, and accurate method for assessing the stereochemical outcome of pericyclic reactions. Furthermore, it is a method that is equally applicable to symmetrical and to unsymmetrical systems. There are some disadvantages in the theory, however. Firstly, it is necessary to derive the general phase characteristics of the HOMO and LUMO levels. Hiickel molecular calculations can be used for tliis purpose, but there are available a number of approximate methods, for example the electron-in-a-box model, which are usually satisfactory even if they are more difficult to apply to more complex systems. Nevertheless, frontier orbital analysis is quicker and more simple than the formalized correlation diagram approach, and with a little practice one can intuitively arrive at the correct relative phase relationsliips in the HOMO and LUMO levels. 

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