Femtosecond nuclear dynamics

The exploration of ultrafast molecular and cluster dynamics addressed herein unveiled novel facets of the analysis and control of ultrafast processes in clusters, which prevail on the femtosecond time scale of nuclear motion. Have we reached the temporal boarders of fundamental processes in chemical physics Ultrafast molecular and cluster dynamics is not limited on the time scale of the motion of nuclei, but is currently extended to the realm of electron dynamics [321]. Characteristic time scales for electron dynamics roughly involve the period of electron motion in atomic or molecular systems, which is characterized by x 1 a.u. (of time) = 24 attoseconds. Accordingly, the time scales for molecular and cluster dynamics are reduced (again ) by about three orders of magnitude from femtosecond nuclear dynamics to attosecond electron dynamics. Novel developments in the realm of electron dynamics of molecules in molecular clusters pertain to the coupling of clusters to ultraintense laser fields (peak intensity I = lO -lO W cm [322], where intracluster fragmentation and response of a nanoplasma occurs on the time scale of 100 attoseconds to femtoseconds [323]. 

THEORETICAL EXPLORATION OF SINGLE AND MULTI STATE FEMTOSECOND NUCLEAR DYNAMICS OF SMALL METALLIC CLUSTERS USING THE DF METHOD... 

Following a description of femtosecond lasers, the remainder of this chapter concentrates on the nuclear dynamics of molecules exposed to ultrafast laser radiation rather than electronic effects, in order to try to understand how molecules fragment and collide on a femtosecond time scale. Of special interest in molecular physics are the critical, intermediate stages of the overall time evolution, where the rapidly changing forces within ephemeral molecular configurations govern the flow of energy and matter. 

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization.

Recently, two basic questions of chemical dynamics have attracted much attention first, is it possible to detect ( film ) the nuclear dynamics directly on the femtosecond time scale and second, is it possible to direct (control) the nuclear dynamics directly as it unfolds These efforts of real-time detection and control of molecular dynamics are also known as femtosecond chemistry. Most of the work on the detection and control of chemical dynamics has focused on unimolecular reactions where the internuclear distances of the initial state are well defined within, of course, the quantum mechanical uncertainty of the initial vibrational state. The discussion in the following builds on Section 7.2.2, and we will in particular focus on the real-time control of chemical dynamics. It should be emphasized that the general concepts discussed in the present section are not limited to reactions in the gas phase. 

Femtosecond Biology Coherent Nuclear Dynamics Studied in Populations of Proteins... 

Until now we have discussed the dynamics in single electronic states, that is, translational and vibrational nuclear motion. We now extend the treatment and include the possibility of an electronic excitation. This is done within the Bom-Oppenheimer approximation where the nuclear dynamics in different electronic states is coupled exclusively by the external field. The system that serves as an example is the Na2 molecule, which has been studied extensively employing femtosecond spectroscopy [182-188]. 

Simulation of Nuclear Dynamics of Ceo From Vibrational Excitation by Near-IR Femtosecond Laser Pulses to Subsequent Nanosecond Rearrangement and Fragmentation... 

T. Laarmann et al. used temporally shaped femtosecond laser pulses with closed-loop, optimal control feedback (pulse shaping) to obtain detailed information on ulfrafast electronic and nuclear dynamics in Qo excited by near-IR pulses [9, 21]. They found that the branching ratios of fragments of Ceo, for example, /C, can be controlled by femtosecond laser pulses (A 800 nm) tailored by pulse shaping. The optimal pulses that maximized the yields of fragments were pulse trains at constant intervals the excitation by pulse trains of characteristic time intervals results in significant enhancement of C2-evaporation, a typical energy loss... 

Photoionization can create a coherent superposition of electronic states and therefore initiates electronic dynamics in atoms and molecules. Experiments on the latter are particularly difficult to interpret as change in the nuclear geometry is also expected. Indeed, the equilibrium geometry of the ionized and neutral species are unlikely to be the same. Therefore, the initial electron dynamics, that may last up to a few femtoseconds, is then followed by the onset of nuclear dynamics [ 1 ]. Theoretical methods are needed to help understand the effects seen in attosecond laser experiments (see, e.g., the reviews of Kling [2] and Ivanov [3]). 

The examples collected for this survey of femtosecond nonadiabatic dynamics at conical intersections illustrate the interesting interplay of coherent vibrational motion, vibrational energy relaxation and electronic transitions within a fully microscopic quantum mechanical description. It is remarkable that irreversible population and phase relaxation processes are so clearly developed in systems with just three or four nuclear degrees of freedom. 

When considering the femtosecond photoionization dynamics of complex systems, a completely exact evaluation of the time and energy resolved photoelectron spectrum is often not really necessary. Approximative schemes which require significantly lower computational effort are valuable in such cases. Within the nonperturbative formalism, Meier et al. have proposed an efficient computational scheme which incorporates the multi-configuration time-dependent Hartree method.An approximate method which is based on a classical-trajectory description of the nuclear dynamics has been elaborated by Hartmann, Heidenreich, Bonacic-Koutecky and coworkers and applied, among other systems,to the time-resolved photoionization spectroscopy of conical intersections in sodium fluoride clusters. 

The electronic energy thus computed at each molecular shape serves as a potential function working on nuclei, called (adiabatic) potential energy surface (PES), which drives nuclear wavepackets on it, and only in this stage time-variable is retrieved, to the time scale of nuclear dynamics mostly of the order of femtosecond. This is the standard theoretical framework for the study of the dynamics of molecules [59]. Very well structured and fast computer codes for quantum chemistry are now available, which can serve even as an alternative for experimental apparatus. 

We next study how the results of wavepacket dynamics can be tracked experimentally as a real-time history of chemical or physical events. Femtosecond time-resolved spectroscopy enables us to observe nuclear dynamics and to chart the path of chemical reactions in real time, and has been exploited in numerous applications ranging from fundamental studies of real-time motion in the photodissociation of diatomic molecules to stud-... 

In Chapter 5, we have studied some of the effects of laser fields on chemical dynamics. In particular, we have investigated how time-resolved photoelectron spectroscopy can be used as a very good means to monitor the femtosecond-scale nuclear dynamics such as the passage across nonadia-batic regions. The modulation of nonadiabatic interactions (both avoided crossing and conical intersection) is also among the main subjects from the view point of control of chemical reaction. Chapter 7, on the other hand, has treated nonadiabatic electron wavepacket dynamics relevant to chemical reactions. Here in this chapter, we therefore rise to the theory of electron dynamics in laser fields mainly associated with chemical dynamics. 

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