Spin-coupled description of organic reaction pathways: the cycloaddition reaction of two ethene molecules

Abstract

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.