Franck-Condon window

The pump and probe spectrum S(t) is then proportional to the overlap of the density pB(Qs, r,probe laser pulses, respectively ... 

Figure 2. Franck-Condon windows lVpc(Gi, r, v5) for the Na3(X) - N83(B) and for the Na3(B) Na3+ (X) + e transitions, X = 621 nm. The FC windows are evaluated as rather small areas of the lobes of vibrational wavefunctions that are transferred from one electronic state to the other. The vertical arrows indicate these regions in statu nascendi subsequently, the nascent lobes of the wavepackets move coherently to other domains of the potential-energy surfaces, yielding, e.g., the situation at t = 653 fs, which is illustrated in the figure. The snapshots of three-dimensional (3d) ab initio densities are superimposed on equicontours of the ab initio potential-energy surfaces of Na3(X), Na3(B), and Na3+ (X), adapted from Ref. 5 and projected in the pseudorotational coordinate space Qx r cos

Fig. 1. The principle of pumjvprobe spectroscopy by means of transient two-photon ionization A first fs-laser pulse electronically excites the particle into an ensemble of vibrational states creating a wave packet. Its temporal evolution is probed by a second probe pulse, which ionizes the excited particle as a function of the time-dependent Franck Condon-window (a) shows the principle for a bound-bound transition, where the oscillative behaviour of the wave packet will appear (b) shows it for a bound-free transition exhibiting the exponential decay of the fragmentizing particle, and (c) shows the process across a predissociated state, where the oscillating particle progressively leads into a fragmentation channel.

From Equation (15.1), it is clear that the kinetic energy of the departing atom can be controlled by tuning the laser frequency across the Franck-Condon window (i.e. the frequency range of the absorption continuum). Thus, by changing the laser frequency one can change the collision energy in bimolecular... 

Repulsive (real) intermediate states have also been used for multiple-photon excitation, despite their short lifetime. This approach allows the Franck-Condon window to be extended significantly and it has been used to study the Rydberg and ion-pair states of a number of molecules, including diatomic halogens and methyl iodide (see Section 18.2). 

When a molecule is excited to a continuum state, at least one of the bonds in the molecule will start to stretch. If the molecule is then further excited, before dissociation can occur, the effect is to widen the Franck-Condon window, compared with the ground state, in at least one coordinate. A good example of how this principle can be used to explore the higher excited states of molecules is provided by work on CH3I. 

Figure 18.2 Schematic diagram showing the potential curves for the ground state, the repulsive intermediate states and two of the Rydberg states of CH3I. The vertical arrows show the one-colour, non-resonant (dashed arrows), and the two-colour, resonant (solid arrows) routes for two-photon excitation to the Rydberg states. Note that resonance with the repulsive intermediate state (two-colour excitation) leads to stretching of the C-I bond and this changes the Franck-Condon window for excitation to the Rydberg state, favouring the C-I vibrational mode V3. Reproduced from Min etal, J. Photochem. Photobiol., 1996, 100 9, with permission of Elsevier...

Fig. 3.3. Excitation scheme for a one-color real-time (3P1) experiment on K2 (taken from [262]). A wave packet is prepared in the A by an ultrashort pump pulse. Its propagation on this PES is probed by a two-photon ionization process. The intermediate state (2) 77g acts as a Franck-Condon window. Excess energy is given to the electron e . The propagation of the wave packet is perturbed by the b 77u state (see Sect. 3.1.3). The data for the PES are taken from [322, 324-326]...

A resonant intermediate state ((2) acts as a spatially small Franck-Condon window. As is seen during the analysis of the real-time spectrum, this state with parity gerade acts under these special excitation conditions as a kind of filter, since only for a single internuclear separation R (Condon point) of the dimer can the transition take place from the A state to the ion state. This fact enables the explicit mapping of the wave packet s motion, i.e. the signal is expected to come and go periodically as the wave packet travels through this detection window. 

Fig. 3.10. Excitation scheme of 39,39K2 for the two-color experiment (a) and one-color experiment (b) (taken from [52]). In both cases a wave packet is prepared on the A state s PES by the pump pulse. In the two-color experiment the subsequent ionization by one photon is slightly favored at both the inner and at the outer turning points of the PES. In the one-color experiment the ionization is strongly enhanced by the (2) /7g state acting as a Franck-Condon window. Potential-energy curves are based on data given in [324, 325]...

Figure B3.1 (a) The potential energy curves of Hg + Hg and Hg + Hg [adapted from P. Gross and M. Dantus, J. Chem. Phys. 106, 8013 (1997)]. The long-range attraction and the well (depth 370 cm ) in the ground state potential, Vg R), are hardly noticeable on the energy scale shown. The vertical asymptotic separation of the two potential curves is the resonance excitation energy of a Hg atom, corresponding to the Sq- Pi transition. When the two Hg atoms are closer, the electronic energy gap (4.89 eV for an isolated atom) is lowered due to the stronger attraction in the excited state. At the relative separation / x the iaser frequency matches the potentiai gap. In other words, the Franck-Condon "window" is where the two atoms are at the separation Rx apart. A verticai transition at Rx prepares a bound vibrationai state of the excited eiectronic state. This is known as iaser-assisted recombination, Probiem O. (b) Panei (a) drawn in the dressed states picture.

Upper trace no phase difference between the two laser pulses. The wave-packet promoted by the first pulse and the newly promoted wave-packet can interfere constructively whenever the time delay between the pulses is a multiple of 300 fs so that the first wave-packet is back in the Franck-Condon window. Lower trace a jc phase difference between the two laser pulses. At intervals of 300 fs the returning wave-packet interferes destructively with the new wave-packet (adapted from N. F. Scherer eta/., J. Chem. Phys. 95, 1487 (1991). For other experiments showing interference between wave-packets excited by two pulses see Baumert eta . (1997). Even an electron can be so controlled during electron transfer (Barthel eta/., 2001 Martini eta ., 2001 Bardeen, 2001)]. 

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