Natural reaction orbitals for characterizing electron transfer responsive to nuclear coordinate displacement

The natural reaction orbital (NRO) is proposed as a new concept for analyzing chemical reactions from the viewpoint of the electronic theory. The pair of the occupied and virtual NROs that characterize electron transfer responsive to nuclear coordinate displacement along the reaction path is automatically extracted from the solution of the coupled-perturbed self-consistent-field (CPSCF) equation for the perturbation of the nuclear displacement. The NRO-based reaction analysis method is applied to several reactions. As a result, it is found that the sum of squares of the singular values, derived from the solution of the CPSCF equation, gives sharp peaks around the transition state structures and at the shoulders of the potential energy curve. The peaks around the transition states suggest a new physical meaning of transition state from the viewpoint of the electronic theory. Furthermore, the double peaks reveal the asynchronous processes of reactions, which are not always shown in potential energy analyses. Since the NRO-based reaction analysis method is universal and robust for describing reaction mechanisms from an electronic theory viewpoint, it is expected to lead to universal reaction analyses based on the electronic theory.