Franck nuclear

There are cases where the variation of the electtonic ttansition moment with nuclear configuration caimot be neglected. Then it is necessary to work with equation (B 1.1.6) keeping the dependence of on Q and integrating it over the vibrational wavefiinctions. In most such cases it is adequate to use only the tenns up to first-order in equation (B 1.1.7). This results in modified Franck-Condon factors for the vibrational intensities [12]. 

A qualitatively different approach to probing multiple pathways is to interrogate the reaction intermediates directly, while they are following different pathways on the PES, using femtosecond time-resolved pump-probe spectroscopy [19]. In this case, the pump laser initiates the reaction, while the probe laser measures absorption, excites fluorescence, induces ionization, or creates some other observable that selectively probes each reaction pathway. For example, the ion states produced upon photoionization of a neutral species depend on the Franck-Condon overlap between the nuclear configuration of the neutral and the various ion states available. Photoelectron spectroscopy is a sensitive probe of the structural differences between neutrals and cations. If the structure and energetics of the ion states are well determined and sufficiently diverse in... 

Following Eq. (75), the rate constant for spin conversion may be expressed as a product of the electronic matrix element V and the nuclear Franck-Condon... 

The height of the potential barrier separating the initial and final states of the nuclear subsystem decreases and, hence, the Franck-Condon factor increases (Fig. 6). In the classical limit, this results in a decrease of the activation free energy. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

Nuclei move much more slowly than the much-lighter electrons, so when a transition occurs from one electronic state to another, it takes place so rapidly that the nuclei of the vibrating molecule can be assumed to be fixed during the transition. This is called the Franck-Condon principle, and a consequence of it is that an electronic transition is represented by a vertical arrow such as that shown in Figure 2.5 that is, an electronic transition occurs within a stationary nuclear framework. Thus the electronic transition accompanying the absorption of a photon is often referred to as a vertical transition or Franck-Condon transition. 

We next consider the expression for k in the classical formalism. According to the Franck-Condon principle, internuclear distances and nuclear velocities do not change during the actual electron transfer. This requirement is incorporated into the classical electron-transfer theories by postulating that the electron transfer occurs at the intersection of two potential energy surfaces, one for the reactants... 

The difference in the time-scales for electronic and nuclear motions is, of course, the basis of the Bom-Oppenheimer approximation (and the Franck-Condon principle). This... 

The function G in eq 1 is the Franck-Condon factor which accounts for the contribution of nuclear degrees of freedom and represents the thermal average of the overlap integrals between nuclear wavefunctions with respect to conservation of energy, and is given by (2, 3, 8, 9)... 

It is worthwhile to recognize that if the mechanism of the Auer mantle is indeed the theorem of Kirchhoff (opaque standard behaviour in the absorption bands strongly reduced emission outside the absorption bands) the principle of Franck and Condon applies to the thermal emission determined by the distribution of nuclear positions in the (hot) groundstates. In particular, one would not expect the slightest broadening of the emission bands relative to the absorption bands at the same T. The fluorescent or chemo-luminescent behaviour is entirely different in this respect. 

Dissociative electron attachment (DEA) occurs when the molecular transient anion state is dissociative in the Franck-Condon (FC) region, the localization time is of the order of or larger than the time required for dissociation along a particular nuclear coordinate, and one of the resulting fragments has positive electron affinity. In this case, a stable atomic or molecular anion is formed along with one or more neutral species. Dissociative electron attachment usually occurs via the formation of core-excited resonances since these possess sufficiently long lifetimes to allow for dissociation of the anion before autoionization. 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

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