Potential energy curves electron transfer

Figure C3.2.1. A slice tlirough tlie intersecting potential energy curves associated witli tlie K-l-Br2 electron transfer reaction. At tlie crossing point between tlie curves (Afy, electron transfer occurs, tlius Tiarjiooning tlie species,...

A semi-classical treatment171-175 of the model depicted in Fig. 15, based on the Morse curve theory of thermal dissociative electron transfer described earlier, allows the prediction of the quantum yield as a function of the electronic matrix coupling element, H.54 The various states to be considered in the region where the zero-order potential energy curves cross each other are shown in the insert of Fig. 15. The treatment of the whole kinetics leads to the expression of the complete quenching fragmentation quantum yield, oc, given in equation (61)... 

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 ... 

Further, the electron level of adsorbed particles differs from that of isolated adsorbate i>articles in vacuum as shown in Fig. 5-5, this electron level of the adsorbate particle shifts in the course of adsorption by a magnitude equivalent to the adsorption energy of the particles [Gomer-Swanson, 1963]. In the illustration of Fig. 5-5, the electron level of adsorbate particles is reduced in accordance with the potential energy curve of adsorption towards its lowest level at the plane of adsorption where the level width is broadened. In the case in which the allowed electron energy level of adsorbed particles, such as elumo and ehcmio, approaches the Fermi level, ep, of the adsorbent metal, an electron transfer occurs between... 

In Fig. 1, the energy bands are curved up near the surface to indicate this condition. The energy rise becomes greater as more oxygen is adsorbed. The Fermi level, of course, remains at the same energy, in equilibrium. When the bands are curved up near the surface, as in Fig. 1, it should be noted that there is a potential barrier to electron transfer between the interior and the surface states. This is what we have called the surface barrier. 

Figure 4. Schematic of the potential energy curves of the relevant electronic states The pump pulse prepares a coherent superposition of vibrational states in the electronic A 1 EJ state at the inner turning point. Around v = 13 this state is spin-orbit coupled with the dark b 3n state, causing perturbations. A two-photon probe process transfers the wavepacket motion into the ionization continuum via the (2) llg state [7].

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

Fig. 12. PET can be studied on the basis of intersecting harmonic potential-energy curves. In the approach of Marcus, the free energy of a reacting system is represented as a function of nuclear geometry on the horizontal axis. During excitation, there is a vertical transition (Franck-Condon) to a point on the excited-state surface, followed by vibrational relaxation. Electron transfer takes place at the crossing of the excited-state and ionic potential-energy curves. The transition-state energy, AGe, corresponds to the energy difference between the minimum on the excited-state surface and the point of intersection...

Figure 5 Potential energy curves for an electron-transfer reaction p(A+- -B) — s A- -B+), showing vibrational quantization, assuming the same vibrational frequency v in precursor and successor states. Some of the vibrational wavefunctions are indicated. The dotted arrows refer to electron transfer below the energy of the crossing of the two curves...

Figure 9 Potential energy curves for a mixed-valence iron(III,II) molecule, with various total spins S, and with coupling parameters such that the ordering of spin states is reversed in the electron-transfer transition state. (Reprinted with permission from Ref. 81, 1990 American Chemical Society)...

The principles of photoluminescence applied to solid oxide surfaces can be most easily understood by assuming some simplifications. For example, we can start by considering the Morse potential energy curves (Fig. 1) related to an ion pair such as M-+0-, taken as a harmonic oscillator to represent an oxide, typically an alkaline earth oxide. The absorption of light close to the fundamental absorption edge of this oxide leads to the excitation of an electron in the oxide ion followed by a charge-transfer process to create an exciton (an electron-hole pair), which is essentially... 

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