P. B. Karadakov, D. L. Cooper, T. Thorsteinsson and J. Gerratt.
In: “Quantum Systems in Chemistry and Physics. Volume 1: Basic problems and models systems” ed. A. Hernández-Laguna, J. Maruani, R. McWeeny and S. Wilson (Kluwer, Dordrecht); 327-44 (2000).

Abstract

The combination of modern valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ring-opening of cyclohexadiene.
The SC descriptions of the electronic mechanisms of these three reactions are shown to substantiate the use of the long-established reaction schemes with full- and half-arrows, well-known from organic chemistry textbooks, in a context which is very meaningful, albeit slightly different from the classical interpretation. The half-arrows now indicate changes in the shapes of individual orbitals, accompanying the breaking of the bonds in which they participate in the reactant(s), and their re-engagement in new bonds within the product(s), rather than the movements of individual electrons. The full-arrows correspond to relocations of orbital, rather than electron pairs.
The SC results strongly suggest that the Diels-Alder reaction between butadiene and ethene and the 1,3-dipolar cycloaddition of fulminic acid to ethyne pass through aromatic conformations, while in the case of the 1,3-dipolar cycloaddition of fulminic acid to ethyne, the reacting system remains distinctly nonaromatic throughout the course of the reaction.

Key words: spin-coupled theory; pericyclic reactions; reaction mechanisms; modern valence bond; aromaticity; CASVB; VB.