A new way of studying chemical reactions: a hand-in-hand URVA and QTAIM approach‡

Bond formation and bond cleavage processes are central to a chemical reaction. They can be investigated by monitoring changes in the potential energy surface (PES) or changes in the electron density (ED) distribution ρ(r) taking place during the reaction. However, it is not yet clear how the corresponding changes in the PES and ED are related, although the connection between energy and density has been postulated in the famous Hohenberg–Kohn theorem. Our unified reaction valley approach (URVA) identifies the locations of bond formation/cleavage events along the reaction path via the reaction path curvature peaks and their decomposition into the internal coordinate components associated with the bond to be formed or cleaved. One can also investigate bond formation/cleavage events using the quantum theory of atoms-in-molecule (QTAIM) analysis by monitoring changes in the topological properties of ρ(r) and the associated Laplacian ∇2ρ(r). By a systematic comparison of these two approaches for a series of ten representative chemical reactions ranging from hydrogen migration to cycloaddition reactions and gold(I) catalysis, we could for the first time unravel the PES–ED relationship. In the case of a bond formation, all changes in the ED occur shortly before or at the corresponding curvature peak, and in a bond cleavage, the ED changes occur at or shortly after the curvature peak. In any case, the ED changes always occurred in the vicinity of the curvature peak in accordance with the Hohenberg–Kohn theorem. Our findings provide a comprehensive view on bond formation/cleavage processes seen through the eyes of both the PES and ED and offer valuable guidelines on where to search for significant ED changes associated with bond formation or cleavage events.