Electron and Proton Transfer Mechanisms From Marcus to Supramolecular Constructions

Introduction

Since the middle of the last century, special attention has been devoted to the study of phenomenological and theoretical aspects of the elementary act of electron transfer. First significant breakthrough was Libby`s model (1952), according to which the products are in the wrong environment of solvent molecules when an electron is transferred from one reacting ion or molecule to another. Thus, spectroscopy into chemical kinetics was tacitly introduced the Frank-Condon principle. At the same time, the initially proposed model suffered from a clear violation of the law of energy conservation. The “way out” was found by R. A. Marcus, who assumed that energy levels can be adjusted via fluctuations in the environment surrounding the reagents.

With sufficiently large fluctuations corresponding to the intersection of the initial reagents' energy term with the reaction products' term, a transition with zero energy change is possible at the point of their intersection, and it could formally be considered as vertical. A little later, another scientist, in the future also a Nobel laureate, Henry Taube, joined the discussion about the mechanisms of reactions. He noted that the “simple” electron transfer is realized only in systems such as Ne/Ne⁺.

Taube noted that the charge transfer model between “solid balls” refers only to a relatively small class of redox reactions involving transition metal complexes with an inert and rigid coordination sphere. On the contrary, in the case of labile metal complexes, in which ligand substitution occurs rapidly, and especially in reactions involving non-metallic, molecular oxidants and reducing agents, we deal with the almost instantaneous penetration of one of the reagents into the coordination sphere of the other. In the transition state of inner sphere reactions, one or more ligands are part of the internal coordination sphere of both - oxidized or reduced species. Accordingly, the intermediate is a strong ion pair. Therefore, a single solvate shell is formed around the transient complex, which is weakly sensitive to how the electron density is distributed inside it.

During the discussion of Libby's concept, a third type of mechanism was also proposed, “involving the transfer of a hydrogen atom” from a reducing agent to an oxidizer. In fact, this is a synchronous transfer of an electron and a proton. An important consequence of the Frank-Condon principle is the quadratic dependence of the energy of the reorganization of the medium on the number of transferred electrons, which restricts the amount of simultaneously transferred electrons to one. And, nevertheless, the existence of synchronous two-electron processes, without intermediate formation of free radical products, is proved! Moreover, in enzymatic reactions, even electronic processes are the norm rather than the exception. An important class of compounds with unusual reactivity and the possibility of synchronous multi-electron transfers turned out to be complex with partial charge transfer: they are formed when a redox-active (i.e., capable of oxidation or reduction) ligand enters the coordination sphere of a transition metal ion that has the ability to change the degree of oxidation by more than unity.

Notable interest and, accordingly, a significant number of publications relating to multi-electrons (up to 8 electrons!) synchronous transfers in organized nanostructured systems used in electrochemical energy storage devices with high energy density, including multivalent batteries, since they can potentially provide high capacity. But the most interesting are supramolecular systems, in which rather act the laws of mechanics instead of statistical molecular physics. In this case, electron transfer reactions lead to mechanical work, similar to how it occurs in myoglobin during oxidative phosphorylation. Of course, for supramolecular “machines” models of the Markus type, as well as the application of the Frank-Condon principle, are inapplicable.

We emphasize that both in the Marcus model and in the Taube approach, as well as in all subsequent models, there is an attempt to use the transition state method (another name is the Theory of absolute reaction rates). For “molecular machines” the approach must be modified. The appropriate model includes a special kind of Markov random process. In physical literature, this model got named “ultrametric diffusion”. One of the most interesting demonstrations of redox processes in supramolecular systems became an international competition among supramolecular machines, called nanocar races. The first championship in this discipline took place in April 2017, the second one in March 2022, both in Toulouse.