Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the stress tensor and QTAIM.

Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring-opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from quantum theory of atoms in molecules and the stress tensor to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring-opening reactions of 3-(trifluoromethyl)cyclobut-1-ene and 1-cyano-1-methylcyclobutene. We find the metallicity ξ(rb ) of the ring-opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector-based stress tensor response βσ was used to distinguish the effect of the CN, CH3 , and CF3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(rb ) and the stress tensor stiffness Sσ . We determine the directional properties of the TSIC and TSOC ring-opening reactions by constructing a stress tensor UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory-evaluated total energy barrier and hence will be more thermodynamically favored.