Qualitative theories Woodward-Hoffmann rules

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

Although sophisticated electronic structure methods may be able to accurately predict a molecular structure or the outcome of a chemical reaction, the results are often hard to rationalize. Generalizing the results to other similar systems therefore becomes difficult. Qualitative theories, on the other hand, are unable to provide accurate results but they may be useful for gaining insight, for example why a certain reaction is favoured over another. They also provide a link to many concepts used by experimentalists. Frontier molecular orbital theory considers the interaction of the orbitals of the reactants and attempts to predict relative reactivities by second-order perturbation theory. It may also be considered as a simplified version of the Fukui function, which considered how easily the total electron density can be distorted. The Woodward-Hoffmann rules allow a rationalization of the stereochemistry of certain types of reactions, while the more general qualitative orbital interaction model can often rationalize the preference for certain molecular structures over other possible arrangements. 

MO theory has been used to draw qualitative conclusions about the course of chemical reactions. The most fruitful applications have come from the Woodward-Hoffmann rules, which predict the preferred path and stereochemistry for many important classes of organic reactions. As an example of the application of these rules, we consider the cycliza-tion of a substituted i-cw-butadiene to a substituted cyclobutene. The reaction can take two possible steric courses described as conrotatory or disrotatory, depending on whether the terminal groups rotate in the same or opposite senses as the reaction proceeds. Note the difference in products in Fig. 17.11. 

Results such as these have tended to restrict use of the EH method to qualitative predictions of conformation in molecules too large to be conveniently treated by more accurate methods. However, just as the simple Huckel method underwent various refinements (such as the cjo technique) to patch up certain inadequacies, so has the EH method been rehned. Such refinements have been shown to give marked improvement in numerical predictions of various properties. The EH method has been overtaken in popularity by a host of more sophisticated computational methods. (See Chapter 11.) However, it is still sometimes used as a first step in such methods as a way to produce a starting set of approximate MOs. The EHMO method also continues to be important as the computational equivalent of qualitative MO theory (Chapter 14), which continues to play an important role in theoretical treatments of inorganic and organic chemistries (as, for example, in Walsh s Rules and in Woodward-Hoffmann Rules). 

The above molecular orbital theory is always widely used either quantitatively by performing explicit calculations of molecular orbitals or qualitatively for rationalizing various kinds of experimental or theoretical data. As nicely shown by Gimarc (1979) in his comprehensive book Molecular Structure and Bonding, qualitative MO theory allows an approach to many chemical problems related to molecular shapes and bond properties. Its most important achievement is the determination of reaction mechanisms by the well-known Woodward-Hoffmann (1970) rules and the general orientation rules proposed by Fukui (1970). 

Having learnt about the concerted reactions, we can now undertake the theory of these reactions. The development of the theory of concerted reactions has been due chiefly to the work of R.B. Woodward and R. Hoffmann. They have taken the basic ideas of molecular orbital theory and used them, mainly in a qualitative way, to derive selection rules which predict the stereochemical course of various types of concerted reactions. These rules are best understood in terms of symmetries of interacting molecular orbitals. Here are will see some of the most important theoretical approaches and see how they are interrelated. 

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