Electronic transition amplitudes

Franck-Condon and Herzberg-Teller Approximations of Electronic Transition Amplitudes... 

Electronic Transition Amplitudes We assume that a single-state approach is feasible, thus setting our discussion in the framework of the BO approximation. 

In the random phase approximation, the transition amplitude from state 0) to l) for any one electron operator O may be written as... 

The first-order Bom transition amplitude for the Coulomb scattering of a Volkov electron reads ... 

We have considered in particular the case of multiphoton transitions, to be observed with the help of intense high frequency fields as produced by X-ray Lasers or Free-Electron Lasers (FEL). As a result of our analysis, we have shown that two-photon bound-bound transition amplitudes in high-Z hydrogenic systems are significantly affected by relativistic corrections, even for low values of the charge of the nucleus. For instance at Z = 20, the corrections amount to about 10%, a value much higher than what is observed for standard one-photon transitions in X-ray spectroscopy measurements for which the non-relativistic dipole (NRD) approximation agrees with the exact result to within 99% at comparable frequencies. 

The electronic transition of a solute is a sudden phenomenon followed by other dynamical stages, with different exit channels. According to QM a sudden perturbation (due to a photon in this case) gives rise to nonzero amplitudes for a manifold of states. This also happens for molecules in solution. 

Fig. 4.1. Feynman diagrams corresponding to the transition amplitude (4.1), a without and b with electron-electron repulsion between the two electrons in the final state. The vertical wavy line and the dots in b indicate the Coulomb interaction, which is exactly accounted for by the two-electron Volkov solution. The dashed vertical line represents the electron-electron interaction Vi2 by which the second electron is set free...

The artificial intelligence-superexchange method in which the details of the electronic structure of the protein medium are taken into account was used for estimating the electronic coupling in the metalloproteins (Siddarth and Marcus, 1993a,b,c). Fig.2.11 demonstrates a correlation of experimental and calculated ET rate constants for cytochrome c derivatives, modified by Ru complexes. The influence of the special mutual orientation of the donor and acceptor orbitals in Ru(bpy)2im HisX-cytochrome c on the rate of electron transfer was analyzed by the transition amplitude methods (Stuchebrukhov and Marcus, 1995). In this reaction the transferring electron in the initial and the final states occupies the 3d shell of the Fe atom and the 4d shell of Ru, respectively. It was shown that the electron is localized on t2g subshells of the metal ions. Due to the near-... 

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