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 HNS
2:H
2
O 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.