Franck-Condon points

The wavelength of the probe pulse is tuned around 400 nm. This pulse resonantly excites the WP in the B state to the upper E state. Subsequent laser-induced fluorescence (LIT) from the E state is detected with a photomultiplier. We have utilized two kinds of probe lasers an fs laser and a nanosecond (ns) laser. If we use an fs probe pulse, the overall WP is resonantly excited from B io E states. The excitation predominantly occurs around a specific internuclear distance called a Franck-Condon point [37]. The Franck-Condon point r c is defined as... 

Figure 7.5 Relation between the probe wavelength and the Franck—Condon point Taken from Ref. [37]. Reprinted with permission from American Association for the Advancement of Science.

Figure 4 Opening of a fast radiationless decay channel via conical intersection for (a) a barrier controlled reaction, (b) a barrierless path, and (c) an uphill path without transition state (sloped conical intersection). M" is an excited state intermediate and FC is a Franck-Condon point.

Nevertheless, this simple propagation method provides an intriguing picture of the evolution of the quantum mechanical wavepacket, at least for short times. It readily demonstrates that for short times the center of the wavepacket follows essentially a classical trajectory ( Ehrenfest s theorem, Cohen-Tannoudji, Diu, and Laloe 1977 ch.III). Figure 4.2 depicts an example the evolution of the two-dimensional wavepacket follows very closely the classical trajectory that starts initially with zero momenta at the Franck-Condon point. 

The Franck-Condon point in the transition from the ground state to the excited state potential is indicated in Fig. 27. The velocity distributions are calculated by transferring the wave packet after... 

Figure 27 Two-dimensional PES for the NO -like excited state as functions of the molecule surface distance R and the polar angle 4> in NO adsorbed on Ni(00 1) [19]. FC Franck-Condon point.

For instance Cr(CO)6+ is formed only during LI. The time-dependent behavior of the ion yields of Cr(CO)6+ is presented in Fig. 13. Deconvolution of the time-dependent ion yield with the instrument function derived from the Xe+ signal provides a measure of the time constant (ij) of 12.5 0.05 fs for the LI level (Table 2). This represents the time it takes for the excited Cr(CO)6 to cross to the repulsive surface through the conical intersection close to the Franck-Condon state. At the Franck-Condon point with Oh symmetry, the only coordinates with nonzero slope are the totally symmetric alg M-C stretch or the Jahn-Teller-active vibrations which have eg or t2g symmetry [32], The time taken for a wavepacket to travel from any... 

Fig. 9 Eigenvalues of the energy-difference Hessian computed at the Franck-Condon point of benzene in the 28-dimensional space orthogonal to the pseudo-branching plane. The labels refer to the most similar normal modes of So benzene (Wilson s convention). The dominant local motions are indicated in boxes (reprinted with permission from [31])...

Fig. 12.1. Left side Model intersecting the ground (Sq) and the hrst excited state (Sj) potential energy surfaces. The Franck-Condon point (A ) is geometrically identical to the minimum on the ground state, but it is located on the excited state surface. The arrows indicate the direction of the minimum energy path connecting the FC point (A ) to the conical intersection (Cl) and then to A and to the photoproduct B (adapted from Ref. [8]).

Figure 9.1 Motion of a wavepacket in coordinate space. Panels (a) - (f) depict six times in the evolution of an initially Gaussian wavepacket. The wavepacket is launched at the Franck-Condon point of a repulsive potential surface of a Y-X-Y triatomic molecule. The v coordinate (symmetric stretch) is bound and the u coordinate (antisymmetric stretch) is unbound. The wavepacket oscillates along v (the first partial recurrence is in frame e) and spreads along u (from Heller, 1978).

The existence of a conical intersection within or close to the Franck-Condon zone has very dramatic effects on the dynamics and hence on the spectra of polyatomic molecules. Usually, the density of spectral lines becomes very high and only the envelope, rather than the individual line, is of interest. This allows one to concentrate on short-time dynamics. For a reliable treatment of the dynamics it is important to describe the vicinity of the Franck-Condon point accmately. However, as only short-time d50iamics is required, the interaction potential away from the Franck-Condon point may be of lesser accuracy. 

Scheme 7.13 Cut through of the potential energy surfaces of benzene along the prefulvene mode—a vector from the Franck-Condon point to the Sj/Sq conical intersection— calculated using the MOLPRO program at the CASPT2 level with a (6,6) CAS space and a Roos ANO basis set truncated to 6-31G-quality Sj (black). So (red), Tj (green), and T2 (blue). Reprinted with permission from [28, 29]...

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