  The description of chemical processes at the molecular level is often
facilitated by use of reaction coordinates, or collective variables (CVs). The
CV measures the progress of the reaction and allows the construction of
profiles that track the evolution of a specific property as the reaction
progresses. Whereas CVs are routinely used, especially alongside enhanced
sampling techniques, links between profiles and thermodynamic state functions
and reaction rate constants are not rigorously exploited. Here, we report a
unified treatment of such reaction profiles. Tractable expressions are derived
for the free-energy, internal-energy, and entropy profiles as functions of only
the CV.We demonstrate the ability of this treatment to extract quantitative
insight from the entropy and internal-energy profiles of various real-world
physicochemical processes, including intramolecular organic reactions, ionic
transport in superionic electrolytes, and molecular transport in nanoporous
materials.
