Franck-Condon transition probability

Theoretical distribution curves are synthesized from known potential curves (of the ground state, bound metastable, and repulsive excited states) of the molecular ion and from Franck-Condon transition probabilities. The necessity of including contributions from excited metastable states in the ion beam is indicated when a fit is obtained between the calculated... 

The ensemble of initial conditions can be characterized by the Franck-Condon transition probabilities and visualized in terms of the abundances of the vertical electron detachment energies (VDE s) between the Ag4 and Ag species. The histograms of the VDE s for three ensembles of different temperatures are shown in Fig. 7. For the ensemble generated for T=50 K,... 

Figure 8.5 Two-photon Franck-Condon transition probability spectra for the system of electronic surfaces with (a) = (6.0,8.0),...

Dissociation at a surface appears to be analogous to dissociation in the gas phase. The impinging electron causes a Franck-Condon transition to an electronic state which subsequently dissociates. This one-dimensional Franck-Condon excitation model is illustrated schematically in Fig. 31. The cross section for the electronic transition is probably comparable to gas phase excitation processes. After excitation the particle, which is now in a repulsive state, begins to move away from the surface. If it has sufficient energy it may escape from the surface. If not the fragments remain adsorbed. Moreover, radiationless de-excitation may occur... 

The second application is to the direct measurement of adsorption-desorption processes using the Auger peak height of the particular element as a monitor. The principal limitation is the possible influence of the electron beam on the adsorbate, which can result in beam-induced desorption, adsorption or dissociation. The basis of electron-stimulated desorption (ESD) was established some time ago independently be Menzel and Gomer [38] and Redhead [39]. Electron impact causes Franck—Condon transitions of bound electrons in the adsorbed species into excited states. There is, therefore, a probability of dissociation with subsequent desorption of the particular species involved. As an example of these effects on semiconductor surfaces, Joyce and Neave [40] have reported results on silicon, while Ranke and Jacobi [41] have discussed the electron-stimulated oxidation of GaAs. 

This nonradiative process violates the Laporte rule, which states that only Franck-Condon transitions occurring between states having the same spin multiphcity are allowed, the others being forbidden. It is important to note that in quantum physics forbidden transitions are not impossible, but this means that their probability is extremely low, i.e., with a longer duration or timehfe of the transition. Therefore, the radiative transition occurring between a singlet with no vibrational excitation to a triplet state has a mean timelife (t ) of several microseconds (i.e., 1 ps = 10 s) to milliseconds (i.e., 1 ms = 10 s) ... 

Figure 7.21 Franck-Condon principle applied to a case in which > r" and the 4-0 transition is the most probable...

The elementary act of an electrochemical redox reaction is the transition of an electron from the electrode to the electrolyte or conversely. Snch transitions obey the Franck-Condon principle, which says that the electron transition probability is highest when the energies of the electron in the initial and final states are identical. 

Thus, the inertia of the tunneling particle leads to two opposite effects a decrease of the transition probability due to the reorganization along the coordinate of the center of mass and an increase of the transition probability due to the increase of the Franck-Condon factor of the tunneling particle. Unlike the result in Ref. 66, it is found in Ref. 67 that for ordinary relationships between the physical parameters, the inertia leads to an increase of the transition probability. 

Radiative transitions may be considered as vertical transitions and may therefore be explained in terms of the Franck-Condon principle. The intensity of any vibrational fine structure associated with such transitions will, therefore, be related to the overlap between the square of the wavefunctions of the vibronic levels of the excited state and ground state. This overlap is maximised for the most probable electronic transition (the most intense band in the fluorescence spectrum). Figure... 

The variations in efficiency (rate) of radiationless transitions result from differences in the Franck-Condon factor, visualised by superimposing the vibrational wavefunctions, / (or /2 - the probability distributions), of the initial and final states. We will consider three cases illustrated in Figure 5.2. 

In the quantum mechanical description (in continuation of Box 2.2), the wavefunction can be described by the product of an electronic wavefunction VP and a vibrational wavefunction / (the rotational contribution can be neglected), so that the probability of transition between an initial state defined by ViXa and a final state defined by TQ/b is proportional to electron coordinates, this expression can be rewritten as the product of two terms < f i M vP2> 2 Franck-Condon factor. Qualitatively, the transition occurs from the lowest vibrational state of the ground state to the vibrational state of the excited state that it most resembles in terms of vibrational wavefunction. 

The probability of a particular vertical transition from the neutral to a certain vibrational level of the ion is expressed by its Franck-Condon factor. The distribution of Franck-Condon factors, /pc, describes the distribution of vibrational states for an excited ion. [33] The larger ri compared to ro, the more probable will be the generation of ions excited even well above dissociation energy. Photoelectron spectroscopy allows for both the determination of adiabatic ionization energies and of Franck-Condon factors (Chap. 2.10.1). 

The probability of a transition v" v is determined by the Franck-Condon factor, which is proportional to the squared overlap integral of both vibrational eigenfunctions in the upper and lower state. 

Thus, the absorption to the excited electronic state depends on the electronic transition dipole moment, the Franck-Condon (EC) overlap between the vibrational wavefunctions in both electronic states and the vibrational excitation probability. Indeed, as seen from the schematic representation in Eigure 2.1b, the absorption spectrum represents the reflection of the wavefunction, but it is also dependent on the EC factors that lead to intensity alterations in the observed features. 

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