Qualitative molecular orbital theory rules

To create group orbitals or delocalized molecular orbitals, we need to understand how to combine atomic orbitals properly. Therefore, the starting point in developing our second model of organic bonding is a set of rules that lead by inspection to group orbitals and molec-ular orbitals. This procedure is called qualitative molecular orbital theory (QMOT). 

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. 

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. 

In this chapter, we discuss the various applications of group theory to chemical problems. These include the description of structure and bonding based on hybridization and molecular orbital theories, selection rules in infrared and Raman spectroscopy, and symmetry of molecular vibrations. As will be seen, even though most of the arguments used are qualitative in nature, meaningful results and conclusions can be obtained. 

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). 

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. 

A simple description of electrons in a solid is the model of a free electron gas in the lattice of the ions as developed for the description of metals and metal clusters. The interaction of electrons and ions is restricted to Coulomb forces. This model is called a jellium model. Despite its simplicity, the model explains qualitatively several phenomena observed in the bulk and on the surface of metals. For a further development of the description of electrons in solids, the free electron gas can be treated by the rules of quantum mechanics. This treatment leads to the band model. Despite the complexity of the band model, Hoffmann presented a simple description of bands in solids based on the molecular orbital theory of organic molecules that will also be discussed below. 

Frequently, chemistry textbooks present simultaneously different approaches for the interpretation of chemical reactions. Using the transition state theory (TST), concepts and rules have been derived from the qualitative valence bond as well as from the molecular orbital theory. Both quantum chemical approaches represent useful tools in learning and understanding certain aspects of chemistry by a qualitative consideration of particular electronic configurations and interactions. However, for an explicit treatment of all factors influencing a chemical reaction, it is initially unavoidable to utilize the numerical results of potential energy calculations with respect to the most relevant parts of the PES. 

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. 

---