Wavepacket localized state

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

The experiment is illustrated in figure B2.5.9. The initial pump pulse generates a localized wavepacket in the first excited state of Nal, which evolves with time. The potential well in the state is the result of an avoided crossing with the ground state. Every time the wavepacket passes this region, part of it crosses to the lower surface before the remainder is reflected at the outer wall of the potential. The crossing leads to... 

As in previous sections, the zeros of l (x, t) in the complex t plane at fixed x are of interest. This appears a hopeless task, but the situation is not that bleak. Thus, let us consider a wavepacket initially localized in the ground state in the sense that in Eq. (50), for some given x. 

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross-sections. Using the method of spectral quantization (SQ), it is possible to extract a Seigert state wavefunction from time-dependent quantum wavepackets using the Fourier relation Eq. (21). The state obtained in this way for J = 0 is shown in Fig. 7 this state is localized in the collinear F — H — D arrangement with 3-quanta of excitation in the asymmetric stretch mode, and 0-quanta of excitation in the bend and symmetric stretch modes. If the state pictured in Fig. 7 is used as an initial (prepared) state in a wavepacket calculation, one observes pure... 

Similar to the diatom-diatom reaction, the initial wavefunction is chosen as the direct product of a localized translational wavepacket for R and a specific (JMe) state for the atom-triatom system with a specific rovibrational eigenstate (z/o, Lo,Bo) f°r the triatom ABC ... 

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

We used short broadband pump pulses (spectral width 200 cm 1, pulse duration 130 fs FWHM) to excite impulsively the section of the NH absorption spectrum which includes the ffec-exciton peak and the first three satellite peaks [4], The transient absorbance change signal shows pronounced oscillations that persist up to about 15ps and contain two distinct frequency components whose temperature dependence and frequencies match perfectly with two phonon bands in the non-resonant electronic Raman spectrum of ACN [3] (Fig. 2a, b). Therefore the oscillations are assigned to the excitation of phonon wavepackets in the ground state. The corresponding excitation process is only possible if the phonon modes are coupled to the NH mode. Self trapping theory says that these are the phonon modes, which induce the self localization. 

The remainder of this paper is organized as follows In Sect. 5.2, we present the basic theory of the present control scheme. The validity of the theoretical method and the choice of optimal pulse parameters are discussed in Sect. 5.3. In Sect. 5.4 we provide several numerical examples i) complete electronic excitation of the wavepacket from a nonequilibrium displaced position, taking LiH and NaK as examples ii) pump-dump and creation of localized target wavepackets on the ground electronic state potential, using NaK as an example, and iii) bond-selective photodissociation in the two-dimensional model of H2O. A localized wavepacket is made to jump to the excited-state potential in a desirable force-selective region so that it can be dissociated into the desirable channel. Future perspectives from the author s point of view are summarized in Sect. 5.5. 

Transient absorption measurements have recently been recorded from the organometallic species chromium hexacarbonyl in ethanol solution [94], Absorption of a 65-fs, 310-nm excitation pulse was followed by measurement of excited-state absorption of a 65-fs, 480-nm probe pulse. The data shown in Figure 14 indicate a rapid nonexponential decay at short times followed by a gradual exponential rise. The slower feature was observed previously [95] and is known to correspond to the solvent complexation of Cr(CO)5 to yield Cr(CO)j(MeOH). The initial feature, which is observed at other probe wavelengths as well, is believed to correspond to the initial ligand loss reaction. Note that this case is different from ICN in that the initially excited wavepacket is not on the side of the Sj potential but rather (as is clear from the molecular symmetry) on a local potential maximum. The wavepacket must then spread that is, dissociation along either direction is equally likely. The rapid nonexponential decay was analyzed in terms of classical kinematics along a dissociative potential. 

These examples, although few and preliminary, nonetheless indicate the direction in which time-resolved spectroscopy of reactive species is headed. More detailed examinations of unstable structures between chemical reactants and products will certainly follow. A major goal in this area will be direct observation of coherent wavepacket propagation through local potential maxima (i.e., transition states). Experimental control over wavepacket momentum through potential maxima will be especially important in evaluating solvent effects, barrier recrossing probabilities, and so on. Methods that permit observation and control of transition state production may be anticipated. 

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