Franck-Condon overlap

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... 

As we have reviewed here, the linear region is not fully repulsive, and transitions of the ground-state, linear conformer access vibrationally excited intermolecular levels that are delocalized in the angular coordinate. As depicted in Fig. 1, however, the internuclear distance is significantly longer in the excited state at the linear geometry. Consequently, there is favorable Franck-Condon overlap of the linear conformer with the inner-repulsive wall of the excited-state potential. It is therefore possible for the linear Rg XY conformers to be promoted to the continuum of states just above each Rg - - XY B,v ) dissociation limit. 

Flowever, there is a trade-off in using near-IR emissive lanthanides, in that luminescence lifetimes are shorter, and quantum yields lower, compared to complexes of Tb and Eu. This arises because the near-IR emissive lanthanides are quenched by lower harmonics of the O-H oscillator, increasing the Franck-Condon overlap with the metal excited state. For neodymium, matters are further complicated by the manifold of available metal-centered excited states, which leads to particularly effective quenching by C-H oscillators. Thus, complexes in which there are few C-H oscillators close to the metal are desirable if the luminescence lifetime is to be optimized (e.g. 44).76 97-101... 

An example of an application to actual spectroscopy is shown in Figure 6.9. This shows the states computed in the range of the 0 —> 3 CH spectral transition. The intensities were computed as a Franck-Condon overlap of the optically bright CH overtone state (Holme and Levine, 1989 Levine and Berry, 1989) with the relevant eigenstate. 

Franck-Condon overlap, which enhances the intensity of Q(0,0) band, and also prompts the S2 S internal conversion. The yields of S2... 

Adiabatic and Condon." Since the Condon approximation separates the electronic and the vibrational parts of the problem (see Section 10c), most of the papers using this approximation emphasize the latter aspect. Specifically, they analyze the so-called Franck-Condon overlap integrals [the (Xm X ) of Eq. (42)] and the occupancy factors of these vibrational levels. Such analyses include (1) the influence of mode type and/or number as well as... 

Figure 14.2 Schematic relationship between vertical absorption and emission energies and the adiabatic energy difference between the ground and excited states. [Note that a more rigorous treatment requires inclusion of ZPVE and thermal contiibutions in the adiabatic energy difference, and consideration of Franck-Condon overlap between quantized vibrational states for the vertical processes some of these points are discussed in Section 14.5.]...

Electronic transitions between two energy states are governed bytheFranck-Condon principle. In quantum mechanical terminology, the Franck-Condon overlap integral f xf x, dxv is important. xf and x" are, respectively, vibration wave functions for v in the final electronic state, and v" in the initial electronic state. 

In the theory of radiative transition, the dipole moment operator p. couples the two electronic energy states and the Franck-Condon overlap... 

Figure 5.2 Potential energy surface for So, S, and S2 and Franck-Condon overlap integral. Inset (A) Overlap integral between AJ 12 and SJ""° and (B) Sj and SJ ° states for horizontal transfer of energy.

The reaction Ne + (N2,Ne)N (Table III) is the only exoergic charge-transfer process for which the Cross section has been observed to increase with increasing vibrational quantum number of the neutral reactant.128 A probable rationale for this phenomenon is that both criteria of efficient charge transfer, namely, energy resonance and favorable Franck-Condon overlap, are satisfied if the reaction entails formation of a quartet N2+ state from the (v=2) vibrational level of N2 in the ground electronic state. 

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