SPIN-COUPLED DESCRIPTION OF ORGANIC-REACTION PATHWAYS - THE CYCLOADDITION REACTION OF 2 ETHENE MOLECULES

Spin-coupled (SC) theory is applied to the description of one of the simplest cycloaddition reactions: the orbital-symmetry-forbidden ground-state dimerization of two ethene molecules to cyclobutane: 2 C2H4 --> C4H8. The aim is to show that the easy-to-visualize and easy-to-interpret features of the SC wavefunction, namely, the form of the valence orbitals and the nature of the spin-coupling pattern within the active space, provide important guiding information, which helps make qualitative predictions about the reaction pathway without carrying out a detailed investigation of the related potential surface. It is demonstrated that the SC orbitals from a four-orbital active space, corresponding to the forbidden concerted face-to-face approach, bend outwards of the C4H8 ring, which suggests that optimum overlap can be achieved only through a non-concerted approach, passing either through a cis, or through a trans transition state. A re-examination of the size of the active space needed for the proper valence-bond (VB) type analysis of the reaction shows that eight valence orbitals are required in order to achieve correlated descriptions of the two carbon-carbon double bonds in the reacting ethenes, of the three carbon-carbon single bonds and of the two unpaired electrons in the tetramethylene biradical intermediates, as well as of the four equivalent carbon-carbon single bonds in the final product, cyclobutane. SC calculations for the model reaction pathways leading to the formation of cis and trans tetramethylene biradicals, performed within an eight-orbital active space indicate that the trans pathway has a lower potential barrier and leads to a biradical lower in energy; the minimum corresponding to the formation of a cis biradical is rather shallow. The electronic structure of the tetramethylene biradicals is rationalized in easily conceivable terms, such as orbital shapes and spin-coupling patterns.