The variational polaron formalism for photoinduced proton-coupled electron transfer

The variational polaron formalism is employed to describe photoinduced proton-coupled electron transfer at a donor-acceptor site. The variational minimization criterion and the fluctuation decoupling make this a versatile approach that is applicable at all phonon bath reorganization energies, including at intermediate regimes where many of the perturbative approaches fail. Factors influencing the isotope effect such as energy bias, temperature, and initial wavepacket displacement are studied across reorganization energies. In some regimes, a transition from an inverse to a normal isotope effect is observed with an increase in electron-phonon coupling strength. The population decay rates show a complex dependency on the driving force for small to intermediate reorganization energies, exhibiting Marcus inverted region type behavior; this transitions to a normal region behavior at higher reorganization energies. The variational polaron results reduce to Redfield and to the full polaron in the weak and strong electron-phonon coupling limits, respectively. While the Fermi golden rule rate coincides with that of the variational polaron for large bath reorganization energies, it shows significant deviation at small-to-intermediate reorganization energies.