Potential energy surfaces electron transfer

Figure 1 Hush diagram for intervalence transfer within a class II mixed-valence ion. The dotted lines correspond to diabatic potential energy surfaces. The solid lines are adiabatic potential energy surfaces. Electron transfer can occur either optically (vertical transition with energy, Eop, equaling A) or thermally by moving along the lower adiabatic surface. In the diabatic limit, the barrier height for thermal electron...

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

The total Hamiltonian is the sum of the two terms H = H + //osc- The way in which the rate constant is obtained from this Hamiltonian depends on whether the reaction is adiabatic or nonadiabatic, concepts that are explained in Fig. 2.2, which shows a simplified, one-dimensional potential energy surface for the reaction. In the absence of an electronic interaction between the reactant and the metal (i.e., all Vk = 0), there are two parabolic surfaces one for the initial state labeled A, and one for the final state B. In the presence of an electronic interaction, the two surfaces split at their intersection point. When a thermal fluctuation takes the system to the intersection, electron transfer can occur in this case, the system follows the path... 

Figure 2.9 Model potential energy surface for combined electron and proton transfer. is the solvent coordinate for electron transfer and Q2 that for proton transfer. (See color insert.)...

Influence of surface oxidation, 12-28 Potential energy surface, 66-73 Reaction order, 21 -22 Tafel slope, 18-20, 276-277, 297 Oxygen tolerance, 618-620 Outer sphere electron transfer, 33-38... 

Figure 2.10 Potential energy surface for combined electron and proton transfer.

Conical intersections are involved in other types of chemistry in addition to photochemistry. Photochemical reactions are nonadiabatic because they involve at least two potential energy surfaces, and decay from the excited state to the ground state takes place as shown, for example, in Figure 9.2a. However, there are also other types of nonadiabatic chemistry, which start on the ground state, followed by an ex-cnrsion npward onto the excited state (Fig. 9.2b). Electron transfer problems belong to this class of nonadiabatic chemistry, and we have documented conical intersection... 

Figure 6. Diabatic potential energy surfaces for electron transfer reactions in the system AL/B.

The new potential energy surface has no minima. This means that the electron transfer leads to cleavage of the chemical bond. The possibility of the formation of a new chemical bond depends, in this case, on the location of the other PES (see below). 

Fig. 2 The molecular structure of I—III and the representation of the potential energy surfaces for adiabatic to nonadiabatic electron transfer reactions...

While a treatment of this unified model for electron- and ion-transfer reactions is beyond the scope of this book, we can gain some insight into the nature of electrochemical reactions by looking at some of its results. In particular, this model makes it possible to calculate the potential-energy surface of a reaction. To understand the meaning of... 

Equation (9.35) does not have a particularly useful form, since each electron-transfer reaction will have different equilibrium values y and j/2 of the solvent coordinate in the two charge states. The interpretation of the potential energy surfaces is much easier if we perform a linear transformation of the solvent coordinate q by introducing a new coordinate u ... 

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

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