Franck window

Spectroscopy provides a window to explain solvent effects. The solvent effects on spectroscopic properties, that is, electronic excitation, leading to absorption spectra in the nltraviolet and/or visible range, of solutes in solution are due to differences in the solvation of the gronnd and excited states of the solute. Such differences take place when there is an appreciable difference in the charge distribution in the two states, often accompanied by a profonnd change in the dipole moments. The excited state, in contrast with the transition state discussed above, is not in equilibrium with the surrounding solvent, since the time-scale for electronic excitation is too short for the readjustment of the positions of the atoms of the solute (the Franck-Condon principle) or of the orientation and position of the solvent shell around it. 

The pump and probe spectrum S(t) is then proportional to the overlap of the density pB(Qs, r,Franck-Condon window WFc(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

Figure 2. Bunch of the cation-neutral energy gaps of Ag2Au (right-hand side). Energies of 7.09 eV (dashed Une) and of 6.1 eV (full line) indicate the proximity of Franck-Condon region and of the minimum of neutral species, respectively, and are used for simulations of signals (compare probe window on the left-hand side).

A continuously operated stirred tank reactor (CSTR) for use up to 3 kbar and 300"C is shown in Fig. 4.10. The reactor is equipped with a fairly large sapphire window (visual observation and spectroscopic analysis. Spectroscopic studies may be conducted using a reflectance technique developed by Franck and Roth probing light enters the cell, passes through a sample layer with a precisely known thickness, and is reflected from a mirror which is positioned inside the fluid under investiga-... 

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.

Because the probabilities of absorption and emission depend on dipole moments in the same states, there exists a straightforward (linear) relationship between the molar absorption coefficient and the rate constant of the spontaneous emission (the higher the probability of absorption, the higher the emission) [7]. However, the observed fluorescence intensity is often much weaker than that expected, because the competitive nonradiative processes can deplete the excited state much faster than fluorescence. Hence, according to the Franck-Condon principle, the molecule finishes in a higher vibrational level of the ground state So- Then, a fast vibrational relaxation takes place that causes the intrinsic Stokes shift (the red shift of fluorescence with respect to absorption) [8]. One more fact is important and should be kept in mind for further discussion the absorption and emission of a photon by a particular molecule are two almost infinitely fast events, but they are separated by a time window of nanoseconds. 

A slightly more complicated apparatus has been described by Buback and Franck which only involves one sapphire window (Figure 18). The inner... 

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...

Effect of the detuning. The increase of the PA efficiency from to is mainly due to a larger density of atom pairs in the region of the PA window the ratio 0.0026/0.0003 in the probability density is comparable to the ratio 20/3.2 obtained for the PA probability P in Table 7.2. As illustrated in Figure 7.2, in the first case the PA window is located in the vicinity of a node of the initial stationary wavefunction (pg, , in the second case in the vicinity of a maximum, leading to a better Franck-Condon overlap. 

When a chirped laser pulse is used for the PA process, a coherent wavepacket is formed in the excited state, and has components in all the vibrational levels within the resonance window. After the pulse, this wavepacket propagates toward short distances. Because population transfer back to the initial state with a second (dump) pulse is a coherent process, it is convenient to use this property to optimize the formation of ultracold stable molecules. For instance, in the chosen example of Cs2 0 (65 -f 6P3/2), the time-dependent Franck-Condon overlap with the bound levels in the lower electronic state can be optimized by achieving a focused wavepacket. 

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