Wave packet dynamics, time-resolved

Molecular spectroscopy offers a fiindamental approach to intramolecular processes [18, 94]. The spectral analysis in temis of detailed quantum mechanical models in principle provides the complete infomiation about the wave-packet dynamics on a level of detail not easily accessible by time-resolved teclmiques. 

After the introduction of frequency resolved CARS by Maker and Terhune [1], time resolved experiments became possible with the invention of high power lasers with femtosecond resolution. Leonhardt [2] and for example Hayden [3] performed femtosecond CARS experiments in liquids. A first femtosecond time resolved CARS experiment in gas phase was performed by Motzkus et. al. [4] where the wave packet dynamics of the dissociation of Nal was monitored. The first observation of wave packet dynamics in gaseous iodine was reported by Schmitt et al. [5]. They were able to observe dynamics in both, the ground and excited state with the same experiment. A summary of high resolution spectroscopy in gas phase by nonlinear methods is given by Lang et al. [6]. 

In the time-resolved experiments described so far, the pump laser simply populates the intermediate excited state. The experiment, therefore, becomes a means to study that excited state. Dynamic processes like catalysis and theoretical studies, however, are often more concerned about the electronic ground state than about excited states. For this purpose, it is useful to investigate vibrational wave packet dynamics from that ground state. 

I. Fischer, D.M. Villeneuve, M.J.J. Vrakking, and A. Stolow, Femtosecond Wave-Packet Dynamics Studied by Time-Resolved Zero-Kinetic Energy Photoelectron Spectroscopy , J. Chem. Phys. 102, 5566 (1995). 

Kowalczyk, P., Radzewicz, C., Mostowski, J., Walmsley, I.A. Time-resolved luminescence from coherently excited molecules as a probe of molecular wave-packet dynamics. Phys. Rev. A 42, 5622-5626 (1990)... 

As a last example of a molecular system exhibiting nonadiabatic dynamics caused by a conical intersection, we consider a model that recently has been proposed by Seidner and Domcke to describe ultrafast cis-trans isomerization processes in unsaturated hydrocarbons [172]. Photochemical reactions of this type are known to involve large-amplitode motion on coupled potential-energy surfaces [169], thus representing another stringent test for a mixed quantum-classical description that is complementary to Models 1 and II. A number of theoretical investigations, including quantum wave-packet studies [163, 164, 172], time-resolved pump-probe spectra [164, 181], and various mixed... 

We turn now to a more detailed description of the photoionization probe step in order to clarify the ideas presented above. Time-resolved photoelectron spectroscopy probes the excited-state dynamics using a time-delayed probe laser pulse that brings about ionization of the excited-state wave packet, usually with a single photon... 

Figure 9. Time-resolved vibrational and electronic dynamics during internal conversion for DT pumped at = 287 nm and probed at Xpr0be — 352 nm. (a) Level scheme in DT for one- and two-photon probe ionization. The pump laser is identical to that in Fig. 8 and prepares the identical S2 state wave packet. The expected ionization propensity rules are 2 — Do + for 1-photon (u - g)...

As emphasized in this review, time-resolved X-ray diffraction of dynamical nonequilibrium structures involve, at any given time, the signal from a distribution of structures, as described by quantum mechanical wave-packets in the case of pure states. Thus, the interpretation of experimental data is nontrivial. For isolated molecules, direct inversion of diffraction data is possible in some cases as illustrated in this review. This approach might be useful also for reactions in the liquid phase - for the short-time dynamics before interaction with the solvent plays an important role. 

Figure 13 Comparison of the experimental and a quantum mechanically computed (by exact wave packet propagation using an ab initio computed potential energy) spectrum of a nonrotating Na, molecule pumped to its B electronic state. (Courtesy of Experiment by S. Rutz, E. Schreiber, and L. Woste Computations by B. Reischl, all of the Free University of Berlin) (a) The short time dynamics Shown is the population of the excited state vs. time as determined by a pump-probe experiment and by the computation (points connected by a straight-line segments). The periodicity (about 320 fs) is due to the symmetric stretch motion, (b) A frequency spectrum. The long time dynamics (as reflected in the well-resolved spectrum) show the contribution of a different set of vibrational modes. The dominant peaks can be identified as the radial pseudorotation motion of Na,(B) while the splittings are due to the angular pseudorotational motion. (Adapted from B. Reischl, Chem. Phys. Lett., 239 173 (1995) and V. Bonacic-Koutecky, J. Gaus, J. Manz, B. Reischl, and R. de Vivie-Riedle, to be published.)...

T.T. Nguyen-Dang, F. Chateauneuf, O. Atabek, X. He, Time-resolved dynamics (f two-channel molecular systems in cw laser fields Wave-packet construction in the Floquet formalism, Phys. Rev. A 51 (1995) 1387. 

It should be stressed that the wave-packet picture of photophysical relaxation and photochemical reaction dynamics described in this chapter is substantially different from the traditional concepts in this area. In contrast to the established picture of radiationless transitions in terms of interacting tiers of zero-order molecular eigenstates, the dynamics is rationalized in terms of local properties of PE surfaces such as slopes, barriers and surface intersections, a view which now becomes widely accepted in photochemistry. This picture is firmly based on ah initio electronic-structure theory, and the molecular relaxation d3mamics is described on the basis of quantum mechanics, replacing previously prevaUing kinetic models of electronic decay processes. Such a more detailed and rigorous description of elementary photochemical processes appears timely in view of the rich and specific information on ultrafast chemical processes which is provided by modern time-resolved spectroscopy. " ... 

In the second part of this chapter (Sect. 3.2), different wave packet propagation phenomena in excited alkali trimers are discussed. The time-resolved pseudorotation of the sodium trimer is presented in Sect. 3.2.2. Last but not least, applying laser pulses of the same wavelength but of different pulse width enables a mode-selective preparation of the trimer, hence controlling its dynamics (Sect. 3.2.4). Wave packet propagation on a repulsive PES (Sect. 3.2.5), studied on the potassium trimer, leads to the phenomena of ultrafast photodissociation, which then is the topic of the subsequent chapter. 

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