Predicting Competitive and Non-Competitive Torquoselectivity in Ring-Opening Reactions using QTAIM and the Stress Tensor

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