Condonation theory based

In summary, it appears from this discussion that Franck-Condon energies can now be calculated for a diverse group of inorganic charge-transfer systems and that, although the accuracy of individual values is uncertain, it is possible qualitatively to rationalize the differences between analogous systems. Absolute predictions are much less satisfactory at the present time, and the electrostatic theory based on a dielectric continuum has only very limited applicability to the systems that have so far been studied. When inner-sphere reorganization... 

The Born and DW formalisms outlined in Section 2. 1 were the basis of many early theories of chemical reactions, see for example. Golden and Reiser [441. Golden [45.461. Micha [60-621. Suplinskas and Ross [951. Pirkle and McGee [67.681. Gelb and Suplinskas [391. Levich et al. [531. Brodskii et al. [121 and Eu et al. [381. However, in these early papers, it was necessary to introduce numerous simplifying approximations of uncertain validity in order to arrive at a tractable theory. This early work will not be reviewed here. More recent approximate theories based on the DW formalism, in particular Born and Franck-Condon theories of chemical reactions, are discussed in the general reviews mentioned above. 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

Besides charge transfer interactions, dipolar coupling between ttk transitions of bases may lead to delocalization of the excited states. In order to obtain some guidelines for our experimental studies, we have undertaken the calculation of excited Frank-Condon states within the framework of the exci-ton theory [26]. These studies were enriched by combining data from quantum chemistry and molecular dynamics calculations in collaboration with Krystyna Zakrzewska and Richard Lavery [26,27,27-29]. The general formalism is described in the Chapter by E. Bittner and A. Czader in the present volume. 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

The time-dependent perturbation theory of the rates of radiative ET is based on the Born-Oppenheimer approximation [59] and the Franck Condon principle (i.e. on the separation of electronic and nuclear motions). The theory predicts that the ET rate constant, k i, is given by a golden rule -type equation, i.e., it is proportional to the product of the square of the donor-acceptor electronic coupling (V) and a Franck Condon weighted density of states FC) ... 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

Ligand-field models serve the purpose of parameterizing experiments ). Their beauty and applicability stem from their derivation from the elementary theory of atomic spectra they are first-order perturbation models based upon a basis set of I functions (assumption 1, p. 71), and hence the interelectronic repulsion within the I shell may be accounted for in terms of Condon and Shortley parameters or Racah parameters. We obtain the expanded radial function model (25, 13,8). 

The Slater-Condon-Shortley theory is a first-order perturbation treatment based upon irreducible tensorial sets of 1-orbitals (2). 

Bayliss85 has made a quantitative approach to the study of solvent effects on the absorption spectra. Treating the solvent as a continuous dielectric medium, an expression has been developed for its effect on the Franck" Condon absorption of light, in terms of the polarization fprces of the solvent. The same result was obtained by employing methods based on quantum theory and classical dispersion theory. Bayliss85 has derived the following expression for the frequency shift, Av, caused by the solvent... 

A second important aspect of most microscopic theories of electron transfer is the assumption that the reactants and products do not change their configurations during the actual act of transfer. This idea is based essentially on the Franck-Condon principle, which says, in part, that nuclear momenta and positions do not change on the time scale of electronic transitions. Thus, the reactant and product, O and R, share a common nuclear configuration at the moment of transfer. 

The peiturbational estimate mentioned relies on the calculation of the weight of the determinant based on the first-order correction to the wave function in perturbation theory (p. 245). In such an estimate, the denominato- contains the excitation eneigy evaluated as the difference in rxbital eneigies between the Hartree-Fock determinant and the one in questirm. In the numeialor, there is a respective matrix elranent of the Hamiltonian calculated with the help of the known Slater-Condon rules (see Appendix M available at bottoite.elsevier.com/978-0-444-59436-5, p. el09>. 

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