Wavepacket excited-state potential-energy surface

Figure Al.6.26. Stereoscopic view of ground- and excited-state potential energy surfaces for a model collinear ABC system with the masses of HHD. The ground-state surface has a minimum, corresponding to the stable ABC molecule. This minimum is separated by saddle points from two distmct exit chaimels, one leading to AB + C the other to A + BC. The object is to use optical excitation and stimulated emission between the two surfaces to steer the wavepacket selectively out of one of the exit chaimels (reprinted from [54]).

Eigure 4.1 shows a schematic of an excited-state potential energy surface and superimposed on it is a wavepacket, which is the initial wavepacket for a photodissociation process. An analysis line is drawn perpendicular to the contour lines in the asymptotic region of the surface, where there is no longer any substantial interaction between the separating fragments and the contour... 

Figure 4.1. Schematic diagram of an excited-state potential energy surface showing an initial wavepacket for a photodissociation calculation and indicatng its path toward the dissociation products. The line marked Roo is the analysis line. ...

Fig. 7.16. The ground- and the excited-state potential energy surfaces of NH3 as functions of one of the N-H bonds and the out-of-plane angle 0. They are based on the ab initio calculations of Rosmus et al. (1987). The arrow indicates the oscillatory motion along the -axis of the temporarily trapped wavepacket in the excited state. Reproduced from Dixon (1989).

Although, formally, the integral in Eq. (2.9) is over the range [0,00], the domain of integration may be shortened via three mechanisms.4 First, the effective lifetime of the wavepacket on the excited-state potential energy surface is limited by radiative decay rate and/or the collisional deactivation rate of the excited electronic state these effects can be represented by a phenomenological lifetime, T 1. Second has an intrinsic decay that... 

The quantum-mechanical description of the dynamics follows a very similar pattern. At the instant that the first photon is incident, the ground-state wavefunction makes a vertical (Franck-Condon) transition to the excited-state surface. The ground-state wavefunction is not a stationary state on the excited-state potential energy surface, so it must evolve as t increases. There are some interesting analytical properties of this time evolution if the excited-state surface is harmonic. In that case a gaussian wavepacket remains... 

The failure to achieve selectivity in this model system can be traced to the dynamics on the anharmonic excited-state surface, and, in particular, the wavepacket bifurcation. This observation motivated us to explore more systematically the features of the excited-state potential energy surface and excited-state wavepacket dynamics that are compatible with the proposed selectivity scheme. 

Figures 33a-33c show the swarm on the excited-state potential energy surface, for the same pulse sequence as Fig. 29 (second pulse at 610 a.u.). The swarm mimics closely the quantum wavepacket, including the sequence of contraction and spreading. Figures 33d-33/ shows the swarm on the ground-state potential energy surface, after the second pulse. Those trajectories that do exit do so from channel 2.

We have applied these ideas to the case described in Figs. 24 and 25, where wavepacket spreading on the broad, anharmonic, excited-state potential energy surface destroys the selectivity. A square pulse was used for... 

CN] —> I + CN. Wavepacket moves and spreads in time, with its centre evolving about 5 A in 200 fs. Wavepacket dynamics refers to motion on the intennediate potential energy surface B. Reprinted from Williams S O and lime D G 1988 J. Phys. Chem.. 92 6648. (c) Calculated FTS signal (total fluorescence from state C) as a fiinction of the time delay between the first excitation pulse (A B) and the second excitation pulse (B -> C). Reprinted from Williams S O and Imre D G, as above. 

Figure Al.6.20. (Left) Level scheme and nomenclature used in (a) single time-delay CARS, (b) Two-time delay CARS ((TD) CARS). The wavepacket is excited by cOp, then transferred back to the ground state by with Raman shift oij. Its evolution is then monitored by tOp (after [44])- (Right) Relevant potential energy surfaces for the iodine molecule. The creation of the wavepacket in the excited state is done by oip. The transfer to the final state is shown by the dashed arrows according to the state one wants to populate (after [44]).

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