Nuclear configuration transfer

The reorganization of the nuclear configuration in exoergic electron-transfer reactions is usually considered in the same framework. A typical diagram of the terms is depicted in fig. 12. 

In the majority of cases of charge-transfer interaction in which reactants are free to change their nuclear configuration, the HO MO of the donor molecule and the LU MO of the acceptor molecule become most important, if the nuclear configuration change along the reaction pathway is taken into consideration, as has been made clear in Chap. 4. 

Equation (77) shows that if ph lp(R )/4 1 at an optimum distance R between the reactants, proton transfer occurs by means of tunneling between the unexcited states. However, the distance of the proton jump, 2r0(R ), is not equal to the distance between the points of minima of the potential wells of the proton in the equilibrium nuclear configuration. This case is a generalization of the results obtained in an earlier model by Dogonadze, Kuznetsov, and Levich36 (DKL model). 

Figure 1. Potential energy plot of the reactants (precursor complex) and products (successor complex) as a function of nuclear configuration Eth is the barrier for the thermal electron transfer, Eop is the energy for the light-induced electron transfer, and 2HAB is equal to the splitting at the intersection of the surfaces, where HAB is the electronic coupling matrix element. Note that HAB << Eth in the classical model. The circles indicate the relative nuclear configurations of the two reactants of charges +2 and +5 in the precursor complex, optically excited precursor complex, activated complex, and successor complex.

We first recall that the value pertinent in the electron transfer problem is that evaluated for the nuclear configuration Q Q, where the energy of the interseetion surface of (Q) and Hbb (Q) is a minimum. In some systems, it may happen that vl/ and 1]/ are closely related to stationary states of the Hamiltonian H, so that spectroscopic experiments performed on these states may provide useful information about the value of [47, 48]. To clarify this point, we expand the stationary states )/i (i= 1,2,. . . ) of H(r, Q) in the form ... 

The redox potentials may first be measured directly on the system in which the transfer takes place. This situation corresponds usually to intramolecular processes, but may also be encountered in bimolecular processes when the formation constant Kj is large enough for all the molecules to be complexed in the conditions of the experiment. The four possible redox states of the system are represented in Figure 6, each state being considered in its equilibrium nuclear configuration. The driving force AG° may be calculated either from Eq. (Al) or from Eq. (A2) ... 

Fig. 9.23. Square-well model for electronic mixing between two discrete states. The displacement toward resonance is derived from modulation of the energy levels by the coupling of the electronic levels to the nuclear motion of the surrounding medium. In configuration A, the electron is localized at the donor site B corresponds to the condition of quantum resonance between the two states C corresponds to the nuclear configuration in which the electron becomes localized on the acceptor site (Reprinted from R. J. D. Miller, G. McLendon, A. J. Nozik, W. Schmickler, and F. Willig, Surface Electron Transfer Processes, p. 4, copyright 1995 VCH-Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

To prove eqn (8-2.13), let us suppose that R, when it is applied to the nuclear framework, changes any general nuclear configuration from Znllo to X nuo, then if the base vectors are transferred as in 5-4(2) (see also Fig. 5-4.3), we have, in terms of coordinates rather than base vectors,... 

We can prove eqn (9-5.3) as follows. Let Q stand for a set of normal coordinates which reflect the displacements of the nuclei from their equilibrium positions in some general nuclear configuration XftUo and similarly let Q define these displacements after they have been transferred by It to other (but identical) nuclei. Then the relative positions of the nuclei are unchanged by /t and since V is a function solely of these relative positions (see the footnote to eqn (9-2.7)), we must have... 

The first step involves the formation of the precursor complex, where the reactants maintain their identity. In the second step there is, as we will see later, reorganization of the inner coordination shells as well as of the solvation spheres of the reactants so as to obtain a nuclear configuration appropriate to the activated complex through which the precursor complex is transformed into the successor complex. The electron transfer usually occurs during the latter stages of this reorganization process. The activated complex deactivates to form the successor complex if electron transfer has occurred or to reform the precursor complex if electron transfer has not occurred. The electron distribution in the successor complex corresponds to that of the products, so that the third step is simply the dissociation of the successor complex to form the separated products. 

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