Molecular Imaging. Markus Rudin

are familiar with in the form of proton transfer, in acid–base reactions such as

If we now focus on electron transfer, then probably the first one we meet in Physics is the transfer of the electron in a hydrogen atom from an atomic orbital in the ground state to another [2] in an excited state

      a process we might call photon induced intra-atomic ET.

The simplest molecule of Chemistry is, as we all know,

And the simplest ET reaction [3] is

      More in general we have gas phase interatomic ET reactions like

      The simplest ET reaction between neutral atoms giving a cation and an anion [4, p. 26] is

      In the last two reactions, the reactants and the products are different. Reaction (1.3) in which reactants and products are the same is the simplest example of an electron exchange reaction or self-exchange reaction.

A much more complicated kind of ET occurs when an ion dissolved in a polar solvent absorbs light. In this case, as in Eq. (1.2), the electron jumps to an excited state almost instantaneously, but a considerable longer time is required for the slower moving solvent dipoles to readjust to the new electronic configuration, electron density and associated electric field of the ion. Thus, for some time after the absorption act, the overall electrical polarization of the solvent medium in the neighborhood of the ion will not be in electrostatic equilibrium with the ion’s electric field, that is, the solvent polarization will not be the one dictated by the ion’s new charge distribution. This concept served as a basis of a theory of the absorption spectrum of various halide ions in solution [5].

      Even more complicated ET’s occur in the usual oxidation–reduction reactions. For instance, in:

      five electrons are altogether exchanged between

and Fe⁺², in successive elementary reaction steps, with an extensive rearrangement of chemical bonds among the atoms and of solvent molecules around the ions. In this case, the ET is nonradiative, that is, it doesn’t happen because of absorption or emission of light, but it is thermal: it happens because of suitable thermal fluctuations in nuclear configurations of reactants and solvation molecules. This last statement may sound obscure to the uninitiated but it will be made clear in the following.

      The simplest oxidation–reduction reactions in solution are those in which no bonds are broken or formed when the electron is transferred between reagents. Consider one such reaction:

      The symbol “aq” means that the ions in water solution are solvated, the number of water dipoles and/or their orientations around the ions being clearly dependent on the ionic charges. In this electron exchange or “self-exchange” reaction, two isotopes of iron are used—one of them, Fe^∗, radioactive—to follow the ET between the ions because without the use of isotopes the reagents and products systems look the same. It was “in this small corner of inorganic chemistry” (M.), that of isotopic exchange reactions, where from the story of ET in polar solvents began. In reactions such as these, in which reactants and products are the same, the standard free energy difference between final and initial states is zero and the thermodynamic control on the reaction is missing. They are very interesting because it is in such reactions that those “intrinsic factors” which control their chemical kinetics, that is, the structure of the transition state (TS) and the nature of the reaction coordinate, come to the fore.

      As for reactions in which reactants and products are the same, we may also remember the simplest of all bimolecular ones, the hydrogen atom exchange reaction:

the simplest reaction of Chemistry where a bond breaks while another bond forms [6, 7]. Here reactants and products are the same although a reaction really happens because a covalent bond breaks while another one forms. The Greek subscripts correspond here to the isotopic labels in (1.7).

If we now turn to Electrochemistry looking for examples of elementary reactions in which an electron is transferred from the electrode to the ion without formation or rupture of chemical bonds, we could consider for instance the reduction of permanganate to manganate [8]:

or of, say, protonated nitrogen oxide to NOH [9]:

      where M is the metal electrode.

Today, among the topics included in the field of ET, are: inorganic, organic and biological ET, charge transfer spectra, ET at interfaces other than metal electrode–liquid, like semiconductor–liquid, modified electrode–liquid, polymer–liquid and liquid–liquid, ET at colloids and micelles and many others, see Fig. 1, p. 51 in [10]. Among them a recent one is ET in quantum dots [11].

Electron transfer processes are also implicitly present when the cohesive energy is defined for ionic or metallic crystals in solid state physics [12].

       1.1.Description of Electron Transfer Reactions with Potential Energy Curves

       Adiabatic and Nonadiabatic Processes

      Before delving into the treatment of bimolecular ET reactions in polar solvents, we first consider—as a warm up and to introduce some fundamental concepts—the much simpler case of a diatomic ET in vacuo. Let us consider the reaction:

      Without in general being aware of it, we pass by this reaction when studying the formation of the ionic bond in alkali halides. Let us then consider the process of formation of the ionic bond in the molecule of NaCl starting with an atom of Na far apart from one of Cl and letting the two atoms slowly (adiabatically) approach each other