▪ Abstract Proton-coupled electron transfer (PCET) is an important mechanism for charge transfer in a wide variety of systems including biology- and materials-oriented venues. We review several are...

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Proton-Coupled Electron Transfer

This is an overview of some of the important, challenging, and problematic issues in contemporary electron transfer research. After a qualitative discussion of electron transfer, its time and distance scales, energy curves, and basic parabolic energy models are introduced to define the electron transfer process. Application of transition state theory leads to the standard Marcus formulation of electron transfer rate constants. Electron transfer in solution is coupled to solvent polarization effects, and relaxation processes can contribute to and even control electron transfer. The inverted region, in which electron transfer rate constants decrease with increasing exoergicity, is one of the most striking phenomena in electron transfer chemistry. It is predicted by both semiclassical and quantum mechanical models, with the latter appropriate if there are coupled high- or medium-frequency vibrations. The intramolecular reorganizational energy has different contributions from different vibrational modes, whic...

Contemporary Issues in Electron Transfer Research

THE timescale of the response of solvent molecules to electronic rearrangement of solute molecules has a critical influence on the rates of chemical reactions in liquids1–10. In particular, if the solvent cannot adapt quickly enough to this rearrangement as the reactants pass through the transition state, the evolving products may recross the free-energy barrier, reducing the reaction rate. Computer simulations have shown11–18 that the response of a solvent to a change in solute charge distribution is strongly bimodal: there is an initial ultrafast response owing to inertial (mainly libra-tional) motions of the solvent molecules, followed by a slow component owing to diffusive motions. Water seems to be by far the 'fastest' solvent studied so far: simulations predict that well over half of the solvation response for atomic solutes is inertial, happening on a timescale of about 20 femtoseconds12,13. The presence of this ultrafast component implies that solvent friction plays an important role in many aqueous charge-transfer processes9,10,19–21. Experimental verification of this prediction has been lacking, however, in part because of the difficulty of obtaining sufficient time resolution. Here we present experimental measurements of the ultrafast solvation dynamics of a coumarin salt in water. When considered in conjunction with computer simulations, our results demonstrate that a solvent response on a timescale faster than 50 fs can dominate aqueous solvation dynamics.

Femtosecond solvation dynamics of water

An overview is provided on the development and status of potential energy functions that are used in atomic-level statistical mechanics and molecular dynamics simulations of water and of organic and biomolecular systems. Some topics that are considered are the form of force fields, their parameterization and performance, simulations of organic liquids, computation of free energies of hydration, universal extension for organic molecules, and choice of atomic charges. The discussion of water models covers some history, performance issues, and special topics such as nuclear quantum effects.

https://www.pnas.org/content/pnas/102/19/6665.full.pdf

Potential energy functions for atomic-level simulations of water and organic and biomolecular systems.

The radial distribution functions of water and ice from 220 to 673 K and at pressures up to 400 MPa

We present a molecular model for studying the prototypical ferric–ferrous electron transfer process in liquid water, and we discuss its structural implications. Treatment of the nonequilibrium dynamics will be the subject of future work. The elementary constituents in the model are classical water molecules, classical ferric ions (i.e., Fe3+ particles), and a quantal electron. Pair potentials and pseudopotentials describing the interactions between these constituents are presented. These interactions lead to ligand structures of the ferric and ferrous ions that are in good agreement with those observed in nature. The validity of the tight binding model is examined. With umbrella sampling, we have computed the diabatic free energy of activation for electron transfer. The number obtained, roughly 20 kcal/mol, is in reasonable accord with the aqueous ferric–ferrous transfer activation energy of about 15 to 20 kcal/mol estimated from experiment. The Marcus relation for intersecting parabolic diabatic free ene...

Molecular model for aqueous ferrous–ferric electron transfer

Path integral Monte Carlo methods are applied to the ST2 model of water to examine both the importance of quantum effects on the structure of liquid water and the differences in the structures of light and heavy water. Significant differences are apparent among the results for classical water, quantum H2O, and quantum D2O. For all quantities considered, the classical liquid is the most structured while quantum H2O is the least structured. The implications of these results for neutron and x‐ray diffraction experiments are examined; of the three atom–atom partial structure factors, the oxygen–oxygen function is found to be the most sensitive to quantum effects and the structural differences between light and heavy water appear to be large enough to be measured by x‐ray diffraction experiments.

A quantum mechanical study of structure in liquid H2O and D2O

By computer simulation and also by analytical methods we have computed the nuclear tunneling enhancement of the rate for ferrous–ferric exchange in water. The model we have examined is the one studied earlier where we treated water as a classical liquid [R. A. Kuharski, J. S. Bader, D. Chandler, M. Sprik, M. L. Klein, and R. W. Impey, J. Chem. Phys. 89, 3248 (1988)]. But now we treat water quantum mechanically and find that the tunneling enhancement is a factor of 60 in the rate constant. Further, as observed experimentally, we find that the isotope shift on the rate when changing from D2O to H2O is approximately a factor of 2. The computer simulation aspects of these calculations employ path integral methods and a novel partitioning of the free energy associated with electron transfer. Our results show that it is insufficient to quantize only the atoms composing the ligands. The quantum dynamics of water molecules beyond the first solvation shell prove quite significant.

Robert A. Kuharski

Papers

Molecular model for aqueous ferrous–ferric electron transfer

A quantum mechanical study of structure in liquid H2O and D2O

Role of nuclear tunneling in aqueous ferrous–ferric electron transfer

Molecular dynamics study of solvation in urea-water solution

Solvation of Hydrophobic Species in Aqueous Urea Solution: A Molecular Dynamics Study