Spectral Decomposition of the Reaction Force Constant

Qualitative relationships between the reaction force constant κ(ξ), the second derivative of the potential energy V(ξ), and the reactive vibrational mode that drives the reaction in the transition state region have been used in the past to measure the synchronicity of key chemical events that lead a chemical reaction. In this work, we provide a formal demonstration that κ(ξ) can be expressed in terms of the frequencies of normal modes at each point of the reaction path. This produce a decomposition of κ(ξ) that is used to analyze few representatives chemical reactions, a series of intramolecular proton transfer on formic, thioformic and dithioformic acids, and an intermolecular double proton transfer in the HNS₂:H₂O complex. It has been found that this partitioning allows to identify unambigously the reactive mode that drives the reaction at each point along the reaction coordinate thus giving relevant and detailed information about the mechanism of the chemical reactions under study.