On the Interplay between Nuclear-Nuclear Repulsion and the Electronic Components of the Reaction Force

The reaction force (RF) formalism has long been recognized as a useful method for analyzing energy changes occurring in a chemical reaction. In its original interpretation, the RF extrema are employed to divide the total energy along the reaction path into distinct regions associated with fundamental processes, such as changes in bonding and geometry reorganization. While effective, this decomposition of the total energy can lead to conceptual challenges and interpretations that lack intuitive clarity from a physical perspective. The central objective of this work is to further elucidate the distinct roles of electronic and nuclear repulsion energies in reaction barriers (i.e., forward and reverse directions) through a novel and alternative RF decomposition scheme. We achieve this by introducing an a priori separation of the total energy into these two fundamental contributions. In doing so, this strategy provides a uniquely transparent framework, enabling the reaction force to be partitioned into zones governed by electronic rearrangement and regions dominated by internuclear repulsion. Crucially, this approach reveals a key finding that confirms its physical insights; the nuclear-nuclear (V_nn) and electronic (E_e) energies exhibit contrasting and interpretable profiles (i.e., a double-maxima and a double-minima, respectively) along the reaction path. We support our conclusions by examining five simple reactions: (i) H_a^- + H_b-H_c → H_a-H_b + H_c^-, (ii) F_a^- + CH₃-F_b → F_a-CH₃ + F_b^-, (iii) F^- + CH₃-Cl → F-CH₃ + Cl^-, (iv) O=N-S-H → H-O-N=S, and (v) CO + HF → HCOF. By carefully scrutinizing these, we show that our force components behave in a general manner and confirm that the proposed method offers a more intuitive and reliable framework to distinguish between electronic reorganization and geometric changes throughout a reaction.