Analysis of Reaction Processes On the Basis of the Evolution of Dynamic Orbital Forces: Examples of Cycloadditions, S 2 Substitution, Nucleophilic Addition, and Hydrogen Transposition.

The derivative of the energy of a canonical molecular orbital (MO) [or dynamical orbital forces (DOFs)] with respect to a bond length provides a reliable index of the bonding/antibonding character of this MO on this bond. The DOFs of selected MOs as a function of the reaction coordinate were computed for a panel of model reaction mechanisms: [2+4] (Diels-Alder) cycloaddition, [2+2] cycloaddition, second-order nucleophilic substitution (S 2), nucleophilic addition to a carbonyl group, and [1,2] hydrogen transposition. The results highlight the nature of the reorganization of the main MOs and the stage of the reaction coordinate (RC) at which it occurs. For instance, in the Diels-Alder reaction, one can identify a part of the reaction that is dominated by repulsive four-electron interactions and another part dominated by attractive two-electron interactions. Also, the shape of the DOF as a function of the reaction coordinate reveals the existence of avoided MO crossings and their location on the RC. Even for spontaneous reactions with monotonic variation in the potential energy, extrema of the MO energy and sudden electron rearrangements can be put into evidence. This study provides quantitative support to classical MO analyses of reactivity such as correlation diagrams and frontier approximation.