Understanding molecular and electrochemical charge transfer: theory and computations

Electron, proton, and proton-coupled electron transfer (PCET) are crucial elementary processes in chemistry, electrochemistry, and biology. We provide here a gentle overview of retrospective and currently developing theoretical formalisms of chemical, electrochemical and biological molecular charge transfer processes, with examples of how to bridge electron, proton, and PCET theory with experimental data. We offer first a theoretical minimum of molecular electron, proton, and PCET processes in homogeneous solution and at electrochemical interfaces. We illustrate next the use of the theory both for simple electron transfer processes, and for processes that involve molecular reorganization beyond the simplest harmonic approximation, with dissociative electron transfer and inclusion of all charge transfer parameters. A core example is the electrochemical reduction of the S2O82- anion. This is followed by discussion of core elements of proton and PCET processes and the electrochemical dihydrogen evolution reaction on different metal, semiconductor, and semimetal (say graphene) electrode surfaces. Other further focus is on stochastic chemical rate theory, and how this concept can rationalize highly non-traditional behaviour of charge transfer processes in mixed solvents. As a second major area we address ("long-range") chemical and electrochemical electron transfer through molecular frameworks using notions of superexchange and hopping. Single-molecule and single-entity electrochemistry are based on electrochemical scanning probe microscopies. (In operando) scanning tunnelling microscopy (STM) and atomic force microscopy (AFM) are particularly emphasized, with theoretical notions and new molecular electrochemical phenomena in the confined tunnelling gap. Single-molecule surface structure and electron transfer dynamics are illustrated by self-assembled thiol molecular monolayers and by more complex redox target molecules. This discussion also extends single-molecule electrochemistry to bioelectrochemistry of complex redox metalloproteins and metalloenzymes. Our third major area involves computational overviews of molecular and electronic structure of the electrochemical interface, with new computational challenges. These relate to solvent dynamics in bulk and confined space (say carbon nanostructures), electrocatalysis, metallic and semiconductor nanoparticles, d-band metals, carbon nanostructures, spin catalysis and "spintronics", and "hot" electrons. Further perspectives relate to metal-organic frameworks, chiral surfaces, and spintronics.