Orbital symmetry rules and the mechanisms of inorganic reactions

Abstract

In the last few years symmetry arguments have been used very effectively to predict the course of chemical reactions. The Woodward—Hoffmann rules are famous examples. A complete, but simple, theory of how symmetry enters into a chemical process can be given. Use is made of group theory and secondorder quantum mechanical perturbation theory. The resulting simple equations can be reduced even further to a consideration of the symmetry of the molecular orbitals of the reactants. The relevant orbitals are the highest filled (HOMO) and the lowest empty (LU MO) with the correct symmetries to match the symmetry of the reaction coordinate. The closer in energy these orbitals are, the lower the activation energy. An orbital symmetry forbidden reaction is one where no orbitals of the right symmetry exist within a reasonable energy range of each other. In the usual case it is unnecessary to know the molecular orbital scheme of the products. For bimolecular and trimolecular reactions, the reaction coordinate must be totally symmetrical, therefore the symmetry requirement for the HOMO and LUMO is that they have a net positive overlap. For unimolecular reactions, the reaction path need not be totally symmetrical. The direct product of the HOMO and LUMO symmetries determines the symmetry of the reaction coordinate. The HOMO and LUMO also must correspond to bonds that are to be broken and bonds that are to be made; if they are bonding MOs the reverse statement holds true for antibonding MOs. Examples are given for all of these rules. The development of so-called orbital symmetry rules for chemical reactions has had a great impact on organic chemistry'. Corresponding rules for inorganic reactions have not been extensively presented or used up to now. The attemptin the literature2 have dealt only with the d orbitals of transition metal complexes. The conclusions have been neither definitive nor consistent. While d orbitals are of great importance in coordination chemistry, it is unlikely that these are the only important orbitals in chemical reactions. Also much of inorganic chemistry deals with the non-transition elements. It is necessary to include molecular orbitals made up of s and p atomic orbitals to have a complete understanding. In this article we will show in the most general way how symmetry rules for all chemical reactions can be derived3. The procedure used is to consider the variation of potential energy with