Overlap Determinant Method

Abstract

The basis of this method is a simple idea that chemical reaction is nothing but a specific transformation converting the reactant, characterized by the set of bonds µ_R into the product characterized by the set of bonds µ_P In classifying the character of the reaction, the key role is played by the mutual relation of corresponding sets. A similar situation is also encountered with the technique of correlation diagrams, where the question of the mutual relation between these sets is solved by looking for the mutual assignment between the molecular orbitals as the elements of individual sets. The overlap determinant method solves this problem globally by determining the value of the overlap integral of the approximate wave functions which, in a given reaction, characterize the reactant and the product. This approach, first proposed and practically applied by Trindle [33], arises from the simple intuitive idea that any changes in the structure of molecules, as far as allowed processes are concerned, should not change the nodal structure of the molecular orbitals so that the corresponding overlap integral should be nonzero. On the other hand, for forbidden reactions, which are intuitively connected with deeper changes of the nodal structure, the above criterion requires the zero value of the overlap integral. Although the correctness of this idea has already been proven in the original study by Trindle [33], the substantial numerical complexity of his method has so far prevented its practical exploitation. In the overlap determinant method this important conceptual shortcoming has been successfully eliminated. The result is a simple universal formalism, the great advantage of which is that its philosophy is close to the thinking of organic chemists. This circumstance finds its reflection in that the discrimination between allowed and forbidden processes is solved only on the basis of the knowledge of classical structural formulae of the reactant and the product. In order to demonstrate the principles on which the overlap determinant method is based, it is best to illustrate its practical use by concrete examples, taken first from the field of thermal pericyclic reactions.