One-to-One Correspondence between Reaction Pathways and Reactive Orbitals

Abstract

The one-to-one correspondence between reaction pathways in the potential energy theory and reactive orbitals in the electronic theory for reactions is presented. In this study, the reactive orbital energy method is applied to the intrinsic reaction coordinates of the global reaction route map generated by an automated reaction path search method. The reactive orbital energy method specifies the pairs of occupied and unoccupied reactive orbitals driving chemical reactions and determines whether the reactions are electron transfer-driven or dynamics-driven. Surprisingly, it is found that the reactive orbital pairs are determined one by one for the electron transfer-driven reaction pathways from an identical molecule. The reactive orbital energy method is also found to provide the sophisticated interpretations of reactions for the electronic motions. This one-to-one correspondence is expected to trigger the unification of the potential energy theory and the electronic theory for reactions that have been independently developed.

Reactive orbital energy theory serving a theoretical foundation for the electronic theory of organic chemistry

“…The ROET analyses are performed using the calculated IRCs of the reaction paths and the MO energies at the geometries on the IRCs as follows 10,15 : Plotting the valence orbital energies for each IRC, the orbital energies are, first, traced along the IRCs for three reaction processes: reactant complex to product complex, reactant molecules to reactant complex, and product complex to product molecules. In our original orbital energy‐tracing program, the MO giving the maximum overlap between the succeeding points is automatically picked out, while if the picked orbital would be multiplicated, the orbital giving the minimum orbital energy gradients for the orbital energies at the anteroposterior steps is selected. The occupied and unoccupied valence orbitals giving the most stabilized (decreased) and most destabilized (increased) orbital energies are then chosen for the orbital energies traced along the IRC of the reaction process between the reactant and product complexes as the occupied and unoccupied reactive orbitals.…”

“…We have found no other orbital pairs, which are needed to represent the reactions in the present ROET analyses. Based on the above‐mentioned one‐to‐one correspondence between the reactive orbital pairs and reaction pathways, 15 we consider that the main occupied and unoccupied orbital pair drives each reaction pathway and that the orbitals of equivalent orbital energy variations are subject to the main orbital pair. We should also think of subsequent barrierless reaction processes that might connect to the main processes.…”

“…Since these subsequent processes cause wrong reaction‐driving CTs, they should be excluded from the ROET analysis. For more details of the ROET analyses, see our previous articles 10,15 …”

“…In this analysis, the occupied and unoccupied valence orbitals giving the most varied orbital energies through the reaction processes are defined as reaction‐driving orbitals called “reactive orbitals.” 9 This analysis also determines whether the reactions are charge transfer (CT)‐driven or structural deformation (dynamics)‐driven on the basis of the gradient of the orbital energy gaps between the occupied and unoccupied reactive orbitals through the reaction paths 9,14 . Based on the ROET analysis, it is recently found that there is the one‐to‐one correspondence between reaction pathways and reactive orbitals, implying the possibility of the unification of potential energy‐based theories and the electronic theories 15 . Applying the ROET analysis to reaction analyses can quantitatively reveal electronic movements for various types of reactions that have never been targeted in conventional reaction electronic theories.…”

An orbital-based representation for accurate Quantum Machine Learning

“…The FJK framework is general enough to be applicable to situations where magnitude of a complicated process can be estimated with a relatively simple orbitalbased descriptor. 69,70 Further applications were beyond the scope of this work and are part of future work. At the same time, we observed that for a poor choice of a Slater determinant pair representing the change of electronic structure FJK may be less accurate than conventional representations, as exemplified by QM7b's first excitation energies.…”