Tutorial on computing nonadiabatic proton-coupled electron transfer rate constants

Proton-coupled electron transfer (PCET) is pervasive throughout chemistry, biology, and physics. Over the last few decades, we have developed a general theoretical formulation for PCET that includes the quantum mechanical effects of the electrons and transferring protons, including hydrogen tunneling, as well as the reorganization of the environment and the donor-acceptor fluctuations. Analytical rate constants have been derived in various well-defined regimes. This Tutorial focuses on the vibronically nonadiabatic regime, in which a golden rule rate constant expression is applicable. The goal is to provide detailed instructions on how to compute the input quantities to this rate constant expression for PCET in molecules, proteins, and electrochemical systems. The required input quantities are the inner-sphere and outer-sphere reorganization energies, the diabatic proton potential energy profiles, the electronic coupling, the reaction free energy, and the proton donor-acceptor distance distribution function. Instructions on how to determine the degree of electron-proton nonadiabaticity, which is important for determining the form of the vibronic coupling, are also provided. Detailed examples are given for thermal enzymatic PCET, homogeneous molecular electrochemical PCET, photochemical molecular PCET, and heterogeneous electrochemical PCET. A Python-based package, pyPCET, for computing nonadiabatic PCET rate constants, along with example scripts, input data, output files, and detailed documentation, is publicly available.