### Proton-Coupled Electron Transfer

- Proton-coupled electron transfer (PCET) reactions play a critical role in a variety of chemical and biological processes.
- We have developed a general theoretical formulation for PCET and have applied this theory to a wide range of experimentally studied reactions in solution, proteins, and electrochemistry.
- We have written several reviews on PCET.
^{43, 61, 106, 61, 132, 152} - This theory is relevant to energy conversion processes and solar cells.

**More Information**

**Tutorial (PDF)****/ (PPT)**

PCET Tutorial**webPCET:**

Web site providing general information about PCET, interactice Java applets allowing users to perform calculations on model PCET systems and visualize results, and programs that are relevant to PCET and can be downloaded.

**Our group is part of two energy centers:**

We have developed a general theoretical formulation for PCET reactions. This theory includes the quantum mechanical effects of the active electrons and transferring protons. The original formulation was based on a multistate continuum theory with fixed proton donor-acceptor distance.^{30, 35 }Subsequent extensions included the dynamical effects of an explicit molecular solvent or protein environment, as well as the proton donor-acceptor vibrational motion.^{69, 74, 77}

This theory has also been extended to electrochemical systems.^{102, 104, 115} We have derived nonadiabatic rate constant expressions in various well-defined regimes.^{35, 69, 115}

We have also developed the methodology for mixed quantum/classical molecular dynamics simulations with explicit solvent for PCET reactions.^{15, 18, 19, 27, 47}

In addition, we have developed methods for calculating the vibronic coupling and identified hydrogen atom transfer and PCET with electronically adiabatic and nonadiabatic proton transfer, respectively.^{90} We have developed diabatization schemes for generating charge-localized diabatic electron-proton vibronic states.^{136, 144}

Currently we are developing theoretical methods for describing the ultrafast nonequilibrium dynamics of photoinduced PCET reactions.^{119, 122, 130, 135, 147}

We have applied these theories to a wide range of chemical, biological, and electrochemical systems. In these applications, the theory provided explanations for the experimental trends in the rates and KIEs, and in some cases the temperature and pH dependences.

- Amidinium-carboxylate salt bridges
^{33, 45} - Iron bi-imidazoline complexes
^{44} - Ruthenium polypyridyl complexes
^{52} - DNA-acrylamide complexes
^{53} - Ruthenium-tyrosine complex
^{60} - Soybean lipoxygenase (SLO)
^{64, 93, 120} - Rhenium-tyrosine complex
^{97} - Quinol oxidation
^{114} - Osmium aquo complex/SAM/gold electrode
^{124} - Proton relays in electrochemical PCET
^{139}

We have derived expressions for the current densities, rate constants, and transfer coefficients for electrochemical PCET reactions.^{102, 104, 115}

The characteristics of electrochemical PCET are: pH dependence, non-Arrhenius behavior at high temperatures, asymmetric Tafel plots, and deviation of the transfer coefficients from the standard value of one-half.

We applied this theory to an osmium aquo complex attached to a self-assembled monolayer on a gold electrode.^{124} This work was motivated by experiments from the Finklea group. The calculated hydrogen/deuterium kinetic isotope effect for the standard rate constant, the cathodic transfer coefficient at zero overpotential, and the Tafel plot are in excellent agreement with experimental data. The theoretical calculations indicate that the asymmetry of the Tafel plot and the deviation of the transfer coefficient at zero overpotential from the standard value of one-half arise from the change in the equilibrium proton donor-acceptor distance upon electron transfer. The direction of the asymmetry and deviation from one-half is determined by the sign of this distance change, and the magnitude of these effects is determined by the magnitude of this distance change, as well as the reorganization energy and the distance dependence of the overlap between the initial and final proton vibrational wavefunctions.

We also applied this theory to proton relay systems studied by the Savéant group.^{139} Our calculations indicate that the standard PCET rate constant is lower for the double proton transfer system than for the analogous single proton transfer system because of the smaller overlap integral between the ground state reduced and oxidized proton vibrational wavefunctions, resulting in greater contributions from excited electron-proton vibronic states with higher free energy barriers.

We studied the mechanistic pathways for hydrogen evolution catalyzed by cobaloximes, cobalt complexes with supporting diglyoxime ligands.^{146, 148} We identified the most favorable mechanistic pathways and studied the substituent effects on these catalysts. Our calculations revealed a linear relation between the reduction potentials and p*K*_{a} values with respect to the Hammett constants, which quantify the electron donating or withdrawing character of the substituents.

We are studying the oxidation and production of H_{2} by nickel molecular electrocatalysts with pendant amines.^{151, 153} We have analyzed the sequential and concerted PCET mechanisms within the catalytic cycle. According to our calculations, the sequential ET-PT mechanism would require a moderate initial applied overpotential, followed by a PT reaction with a relatively low free energy barrier. Our calculations also indicate that the concerted electron-proton transfer standard rate constant will increase as the equilibrium distance between the nickel and nitrogen atoms decreases and as the pendant amines become more flexible to facilitate the contraction of this distance with a lower energy penalty.

We have developed an approach that combines integration of a Generalized Langevin equation for one or two collective solvent coordinates with surface hopping methods for electron-proton vibronic states.^{130, 135, 147} The results from this approach agree well with surface hopping calculations based on a four-state empirical valence bond model with explicit solvent molecules. This approach will enable us to study a wide range of photoinduced PCET processes.