Condonation theory

All experimental observations are quantitatively reproduced by the extended Franck-Condon theory outlined above this includes the rotational state distributions for all initial states as well as the population ratios of the two spin-orbit manifolds and the two A-doublet states. 

Clearly, the final results will depend on this. Physically, the projection should be made in the region where the free-rotor basis undergoes the most rapid change in character. (That is the prescription in the Franck-Condon theory of reactions.) It may be possible to eliminate this dependence to a large extent by a procedure which we now outline. This extension will also eliminate transitions to energetically closed channels. 

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. 

The Slater-Condon theory and Hartree-Fock method with relativistic corrections were combined In [6] for evaluating the ground configuration in Ru XXX, Slater and spin-orbit parameters and transition probabilities (E2 and Ml type). 

The Slater-Condon theory and Hartree-Fock method (with relativistic corrections) have been also applied to the energies and transition probabilities within the ground configuration of Ru XXXi and Pd XXXiii [8]. 

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

The Theory of Atomic Spectra, E. U. Condon and G. H. Shortley, Cambridge Univ. Press, Cambridge, England (1963)- Condon and Shortley. 

The amplitude for the so-ealled referenee CSF used in the SCF proeess is taken as unity and the other CSFs amplitudes are determined, relative to this one, by Rayleigh-Sehrodinger perturbation theory using the full N-eleetron Hamiltonian minus the sum of Foek operators H-H as the perturbation. The Slater-Condon rules are used for evaluating matrix elements of (H-H ) among these CSFs. The essential features of the MPPT/MBPT approaeh are deseribed in the following artieles J. A. Pople, R. Krishnan, H. B. Sehlegel, and J. S. Binkley, Int. J. Quantum Chem. 14, 545 (1978) R. J. Bartlett and D. M. Silver, J. Chem. Phys. 3258 (1975) R. Krishnan and J. A. Pople, Int. J. Quantum Chem. 

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... 

Note in passing that the common model in the theory of diffusion of impurities in 3D Debye crystals is the so-called deformational potential approximation with C a>)ccco,p co)ccco and J o ) oc co, which, for a strictly symmetric potential, displays weakly damped oscillations and does not have a well defined rate constant. If the system permits definition of the rate constant at T = 0, the latter is proportional to the square of the tunneling matrix element times the Franck-Condon factor, whereas accurate determination of the prefactor requires specifying the particular spectrum of the bath. 

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

Due to strong interaction of the reactants with the medium, the influence of the latter may not be reduced only to the widening of the vibrational levels of the proton in the molecules AH and BH. The theory takes into account the Franck-Condon factor determined by the reorganization of the medium during the course of the reaction. 

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

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