Weak electronic interactions

Here, n denotes a number operator, a creation operator, c an annihilation operator, and 8 an energy. The first term with the label a describes the reactant, the second term describes the metal electrons, which are labeled by their quasi-momentum k, and the last term accounts for electron exchange between the reactant and the metal Vk is the corresponding matrix element. This part of the Hamiltonian is similar to that of the Anderson-Newns model [Anderson, 1961 Newns, 1969], but without spin. The neglect of spin is common in theories of outer sphere reactions, and is justified by the comparatively weak electronic interaction, which ensures that only one electron is transferred at a time. We shall consider spin when we treat catalytic reactions. 

To place experimental studies in context, it is helpful to recall Marcus semiclassi-cal formulation of ET reaction rate theory. Briefly, for an ET reaction involving weak electronic interactions, the first-order rate constant can be written as [19,20]... 

Willig et al.39) measured the transient absorption of dye adsorbed TiOz film under ultrahigh-vacuum signal of the injected hot electrons on Ti02 with a rise time of < 25 fsec. The electron transfer reaction reported here did not involve redistribution of vibrational excitation energy and was thus completely different from the well-known Marcus-Levich-Jortner-Gerischer type of electron transfer at the weak electronic interaction. 

Nonadiabatic ET reactions are characterized by weak electronic interaction between the reactants and products at the transition-state nuclear configuration (/ ab bT). This coupling is directly related to the strength of the electronic interaction between the donor and acceptor [51]. When donors and acceptors are separated by long distances (>10A), direct overlap of their wavefunctions will be vanishingly small the material between the two redox sites must mediate the coupling. 

Similarly, the electronic absorption indicates only a weak electronic interaction between A and D [139-142]. Typically the UV-VIS absorption spectra of the molecules studied are a superposition of the bands attributed to the absorption of donor and acceptor subunits alone. In some cases a new band with a charge-transfer character appears [139,140]. This band can be separated if the parent bands (of both A and D subunits) are subtracted from the spectrum [143]. With the appropriate values of the absorption and emission maxima, the energies of the emitting species can be re-evaluated. 

When two identical activated alkene functions are included in the same molecule, inter-molecular coupling has to compete with intramolecular hydrocyclization. In most cases the intramolecular reaction, which corresponds to an overall two-electron process, takes precedence. Few mechanistic studies of intramolecular couplings have been reported. The main question is whether the coupling takes place at the mono-radical anion stage in an RS-type reaction (one unit reduced, the other not reduced), or at the bis(radical anion) stage in an RR-type reaction (both units reduced). The last case implies weak electronic interaction between the electrophores. 

Ferrocene is a very efficient triplet quencher, its quenching constants showing practically no difference for triplets between 66.6 (triphenylene) and 42.6 kcal/mole (anthracene) 185>. Two conclusions are possible either energy is transferred to ferrocene Ti (40.5 kcal/mole) or the quenching does not involve energy-transfer at all, and weak electronic interaction on contact between ferrocene and the triplet molecule effects rapid intersystem crossing of the latter by spin-orbit coupling. 

The importance of Marcus theoretical work on electron transfer reactions was recognized with a Nobel Prize in Chemistry in 1992, and its historical development is outlined in his Nobel Lecture.3 The aspects of his theoretical work most widely used by experimentalists concern outer-sphere electron transfer reactions. These are characterized by weak electronic interactions between electron donors and acceptors along the reaction coordinate and are distinct from inner-sphere electron transfer processes that proceed through the formation of chemical bonds between reacting species. Marcus theoretical work includes intermolecular (often bimolecular) reactions, intramolecular electron transfer, and heterogeneous (electrode) reactions. The background and models presented here are intended to serve as an introduction to bimolecular processes. 

Octanol-water partition coefficients were determined for indolizine and 2-phenylindolizine <82JPS614>. The tendency of pyridinium substituted indolizines to aggregate in aqueous and acetonitrile solution is dominated by solute-solvent interactions. It is proposed that 7t-stacking of the indolizine residues results in weak electronic interactions which are sufficient to result in the delocalization of bound excitonic states over the aggregate <93JPC1085>. 

The hyperpolarizability of adsorbed methylene blue in a methylene blue-smectite suspension is II times higher than that of methylene blue in a methanolic solution.This effect disappears with increasing loading. Thus, two effects play a role weak electronic interaction of the methylene blue molecule with the clay surface and organization of the dye molecules at the surface. 

There is a weak electronic interaction between the ic-systems of adjacent sheets and that, with van der Waals forces operating, holds the sheets together. The delocalization of the ic electrons within each sheet provides the stability of the structure, which is 190 J moh more stable than the other principal allotrope, diamond. In diamond, each carbon atom exerts its valency of four in a tetrahedral manner, and the carbon-carbon distance is 154 pm, Le. that expected for a single covalent bond. The enthalpy of atomization of carbon is significantly larger than that of boron, reflecting the effect of the extra valence electron. 

A weak electronic interaction between Pt and Mo was detected in flic XANES spectra of PtMo/C. This is indicated by an increase of the 5d orbital vacancy of Pt from 0.312 per Pt atom (for pure Pt) to about 0.337 with 70 at% of Mo in PtMo alloy (Figure 4.9) [75]. The different behavior of Ru is noteworthy in this respect. Up to 30 at% Ru the ul-band vacancy of Pt was fairly constant, followed by an exponential rise for higher Ru content (Figure 4.9), suggesting strong electronic interaction. 

One of the currently most promising approaches to a quantitative theory of electron transfer at an electrode is that of Marcus, whose fundamental assumption is that only a weak electronic interaction of the two reactants is required for a simple electron transfer process to occur. Interesting and significant deductions have been made quantum mechanically for simple electrode reaction in which no rupture or formation of chemical bonds occurs in the electron transfer step. The elaboration of the theory to include bond rupture is of obvious importance for the treatment of organic electrode processes. 

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