How to read Robin-Day Classification?

Question

I am currently preparing for an exam and am stuck now with the Robin-Day classification. We had these three diagrams and also the explanations how the systems differ but we never talked about what the diagrams are supposed to show or how we have to read them.

The paper suggests that λ here is not (as one might suggest) the wavelenght required to excite an electron but the so called Marcus-reorganization energy and h(ab) is here the electronic coupling.

I understand that you have to treat the system a bit more complicated because you have a system that exchanges electrons without the formation or cleavage of bonds or any major geometric change. And there is also the concept of conductor and non conductive if we see class III compounds as being fully delocalized.

But why does the class I non conducting intervalence compound have these two energy curves, the class II a double well. I suppose because there is no λ in class three that, as there is no localization of the corresponding electrons, this reorganization is not important there. Still I'd be interested in how to actually understand the diagrams and what I can take from them.

Answer 1

Theses are potential energy diagrams, representing the 'stable' forms of both the reactant and the product of IVCT (and their immediate relationship with ligands and surrounding solvent). This is most easily seen in the class I case, where the curves are not merged at all, and instead represent the species as distinct (and the reaction unable to proceed). The reason the curves appear to merge is because the class II and class III cases are where electron transfer is able to occur, and thus the reactant has a reaction path with which to proceed to the product. There are in fact two reaction paths that a class II mixed-valence species can proceed to the product, one being optical (which is the IVCT transition, caused by absorption of light), and the other being thermal. The optical pathway occurs upon absorption of light at the bottom of the leftmost potential well, where it is excited to the top left of the upmost curve. This corresponds to lambda, which confusingly represents the energy of this optical transition (E=hv=\lambda). The position that the ion is now at on the potential energy curve is representative of a state where the electron has been exchanged, but the molecule is yet to rearrange bond lengths, and the surrounding solvent has not rearranged to accomodate the new distribution of charge. The molecule then relaxes down the adiabatic potential energy curve (not shown here, some diagrams have the same structure as class I in dotted lines, these lines being the adiabatic energy curves), to the rightmost potential energy well, where the molecule has completely rearranged the surrounding solvent and changed bond lengths to accomodate the new charge distribution. The thermal process is less relevant, except to note that the hump in the class II diagram is the thermal activation barrier, where an activation energy equivalent to or greater than this barrier is required for the reaction to proceed via this pathway.

A class III ion is one where there is full mixing of the two potential energy curves, such that they become the structure you see above. Clearly here there is no thermal activation barrier, as there is no hump, and the optical transition energy is actually equivalent to or smaller than 2Hab (twice the coupling constant). The result of the now missing thermal activation barrier is that the ion can freely transition between both states, equilibrating between them, resulting in partially charged ions, and a very delocalised system. Note that optical transitions still occur in class III ions, and are typically more intense than transitions in class II ions. There is just no good way of displaying where the transition occurs as it is in the same position as the 2Hab gap.

I realise this thread was created long ago, so this response likely won't be useful to the original poster, but hopefully anyone else who is interested will have a greater appreciation of how these diagrams work. I strongly recommend reading this paper https://onlinelibrary.wiley.com/doi/10.1002/9780470166314.ch1 if you can get access to it. It is by far the most understandable of all the papers on the subject, and very comprehensive.