Theory of proton coupled electron transfer reactions: Assessing the Born-Oppenheimer approximation for the proton motion using an analytically solvable model

TL;DR

This paper evaluates the validity of the Born-Oppenheimer approximation in proton coupled electron transfer reactions using an analytically solvable model, highlighting its general applicability and the impact of vibrational tunneling on reaction rates.

Contribution

It introduces an analytically solvable model including Duschinsky rotation to assess the Born-Oppenheimer approximation in PCET reactions, revealing its general validity and limitations.

Findings

BO approximation is generally valid for proton motion

Vibrationally coherent tunneling significantly affects reaction rates

Some approximations may be inaccurate under certain parameters

Abstract

By employing an analytically solvable model including the Duschinsky rotation effect, we investigated the applicability of the commonly used Born-Oppenheimer (BO) approximation for separating the proton and proton donor-acceptor motions in theories of proton coupled electron transfer (PCET) reactions. Comparison with theories based on the BO approximation shows that, the BO approximation for the proton coordinate is generally valid while some further approximations may become inaccurate in certain range of parameters. We have also investigated the effect of vibrationally coherent tunneling in the case of small reorganization energy, and shown that it plays an important role on the rate constant and kinetic isotope effect.