A vector-based representation of the chemical bond for predicting competitive and noncompetitive torquoselectivity of thermal ring-opening reactions

We present a new vector-based representation of the chemical bond referred to as the bond-path frame-work set B = {p, q, r}, where p, q, and r represent three paths with corresponding eigenvector-following paths with lengths H*, H, and the bond-path length from the quantum theory of atoms in molecules (QTAIM). We find that longer path lengths H of the ring-opening bonds predict the preference for the transition state inward (TSIC) or transition state outward (TSOC) of thermal ring opening reactions in agreement with experiment for all five reactions R1-R5. Competitiveness and noncompetitiveness have traditionally been considered using activation energies within transition state theory that is known to fail for thermal ring-opening reactions. Consequently, we find that the activation energy for R3 does not satisfactorily determine competitiveness or provide consistent agreement with experimental yields. We choose a selection of five competitive and noncompetitive reactions; methyl-cyclobutene (R1), ethyl-methyl-cyclobutene (R2), iso-propyl-methyl-cyclobutene (R3), ter-butyl-methyl-cyclobutene (R4), and phenyl-methyl-cyclobutene (R5). Therefore, in this investigation we provide a new criterion, within the QTAIM framework, to determine whether the reactions R1-R5 are competitive or noncompetitive. We that find R2, R3, and R5 are competitive and R1 and R4 are noncompetitive reactions in contrast to the results from the activation energies, calling into question the reliability of activation energies.