Quantum Free Energy Profiles for Molecular Proton Transfers

Although many molecular dynamics simulations treat the
atomic nuclei
as classical particles, an adequate description of nuclear quantum
effects (NQEs) is indispensable when studying proton transfer reactions.
Herein, quantum free energy profiles are constructed for three typical
proton transfers, which properly take NQEs into account using the
path integral formalism. The computational cost of the simulations
is kept tractable by deriving machine learning potentials. It is shown
that the classical and quasi-classical centroid free energy profiles
of the proton transfers deviate substantially from the exact quantum
free energy profile.