Franck-Condon-transitions

Forster, Th 211, 278, 282, 285 Forster resonance energy transfer, 282 Forster singlet energy transfer, 378 Franck-Condon factors, 23 Franck-Condon principle, 5 Franck-Condon transition, 5 French, C. S., 555 Friedman, G., 353 Fritzsche, J., 37 Frosch, R. P 252, 267, 269 Fumaronitrile, photodimerization in solid state, 478... 

Figure 1.2. Diatomic potential energy curves and Franck-Condon transition.

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

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. 

Vibrational fine structure is absent from the excimer emission because the Franck-Condon transition is to the unstable dissociative state where the molecule dissociates before it is able to undergo a vibrational transition. In the case of the monomer emission, all electronic transitions are from the v = 0 vibrational level of M to the quantised vibrational levels of M, resulting in the appearance of vibrational fine structure. 

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. 

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... 

For all the polyacenes studied the first maximum in the kinetic spectrum always exceeds the work function by 0.8 e.v. This excess can be explained by the vertical Franck-Condon transition from the potential surface of the neutral molecule to that of the positive molecular ion, which possess different equilibrium interatomic distances. 

Adiabatic control of bond distance in selective non Franck-Condon transitions... 

Figure 1 (a) Singlet electronic states of Na2 between which the chosen non Franck-Condon transition takes place, (b) Potential curves displaced by the photon energies. 

In Fig.2 we show the evolution of the bond length of the molecule as the non Franck-Condon transition proceeds, both in STIRAP and in APLIP for intuitive and counterintuitive sequences. The calculations were obtained by solving the Schrodinger equation using sine square pulses with FWHM a = 5 ps. The results show that the dynamics... 

Here we report our exploration of the possibility of inducing an ultrafast non-Franck-Condon transition, which we defined to be the creation of a wave packet at the other turning point of the above-mentioned oscillation, see Fig. 1(b), faster than the time it takes the Franck-Condon packet to reach that turning point due to the natural (field-free) dynamics. We have explored two possible routes for inducing non-Franck-Condon transitions, namely phase-tailoring of a weak-field ultraviolet (UV) pulse [6] tmd a two-pulse scheme combining a transform limited weak-field UV pulse with a strong infrared (IR) field [7]. 

The above analysis shows that the IR+UV scheme could be a possible way to create ultrafast non-Franck-Condon transitions. In fact, we illustrated the case where the nuclear dynamics was sped up by the IR field only prior to UV excitation. A more efficient scheme would involve an IR-field induced acceleration of the nuclear motion in both electronic states. 

It was found earlier that a sudden frequency change during an electronic Franck-Condon transition leads to special quantum mechanical statistics, called squeezing [2-9], of the molecular vibrations [10-12], A state is termed squeezed if some of its characteristics have less noise than the corresponding quantum noise of the vacuum state. The concept of squeezing turned out to be very fruitful in basic research and implies a lot of promising practical possibilities. 

Figure 1. Uncertainty of the quadrature AX of the phonons (squeezing occurs if AX becomes less than unity) after a resonant Franck-Condon transition induced by a chirped pulse of moderate duration (u 0.0437a)) as a function of the chirp parameter tv, which is in the units of the phonon frequency at. The electron-lattice constant is supposed to beg = 5. The markers a-d refer to Fig. 2.

Here Fe(t) and Fg(t) are the time-dependent nonequilibrium Helmholtz free energies of the e and g states, respectively. The energy difference A U(t) can be replaced by a free energy difference due to the fact that the entropy is unchanged in a Franck-Condon transition [51]. Free energies in Eq. (3) can be represented [54] by a sum of an equilibrium value Fcq and an additional contribution related to nonequilibrium orientational polarization in the solvent. Thus for the free energy in the excited state Fe(t) we have... 

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... 

In the analysis of the data the authors applied a model that consisted of a Franck-Condon transition to three different surfaces. Once the molecule was on one of these surfaces it was allowed to undergo a classical trajectory to a final product. 

Although theoretical techniques for the characterization of resonance states advanced, the experimental search for reactive resonances has proven to be a much more difficult task [32-34], The extremely short lifetime of reactive resonances makes the direct observation of these species very challenging. In some reactions, transition state spectroscopy can be employed to study resonances through "half-collision experiments," where even very short-lived resonances may be detected as peaks in a Franck-Condon spectrum [35-38]. Neumark and coworkers [39] were able to assign peaks in the [IHI] photodetachment spectrum to resonance states for the neutral I+HI reaction. Unfortunately, transition state spectroscopy is not always feasible due to the absence of an appropriate Franck-Condon transition or due to practical limitations in the required level of energetic resolution. The direct study of reactive resonances in a full collision experiment, such as with a molecular beam apparatus, is the traditional and more usual environment to work. Unfortunately, observing resonance behavior in such experiments has proven to be exceedingly difficult. The heart of the problem is not a... 

If the electron solvent polarization is neglected, the study of electron transitions and the determination of the solvent shift do not require appreciable modifications in the basic scheme of ASEP/MD. During a Franck-Condon transition the solute and solvent nuclei remain fixed and hence the ASEP obtained for the initial state can be used for the rest of the states of interest. However, it is known that the electron degrees of freedom of the solvent can respond to the sudden change of the solute electron charge distribution. In fact, the polarization component can contribute appreciably to the final value of the solvent shift. The determination of this component requires additional calculations where the solute and solvent charge distributions are equilibrated. Each electronic state requires a separate calculation of the solvent polarization component. It is hence necessary to perform as many polarization calculations as electronic states being considered. 

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