Localized wavepacket

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... 

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. 

In order to demonstrate the efficiency and robustness of the formulations presented in Sect. 5.2 and 5.3, three practical applications are considered here. In the first part of this section, we consider the complete excitation of a wavepacket from a nonequilibrium displaced position, which is directly related to the idea of bond-selective breaking, as explained in the Introduction . This is demonstrated numerically by taking diatomic molecules LiH and NaK as examples. In the second part, we consider the complete pump-dump control and creation of a localized wavepacket using quadratic chirping within the pump-dump mechanism. The bond-selective photodissociation of the H20 molecule is discussed in the third part of this subsection as an example of a multidimensional system. 

In this sense, the control of electronic transitions of wavepackets using short quadratically chirped laser pulses of moderate intensity is a very promising method, for two reasons. First, only information about the local properties of the potential energy surface and the dipole moment is required to calculate the laser pulse parameters. Second, this method has been demonstrated to be quite stable against variations in pulse parameters and wavepacket broadening. However, controlling of some types of excitation processes, such as bond-selective photodissociation and chemical reaction, requires the control of wavepacket motion on adiabatic potential surfaces before and/or after the localized wavepacket is made to jump between the two adiabatic potential energy surfaces. 

M. F. Herman and D. F. Coker (1999) Classical mechanics and the spreading of localized wavepackets in condensed phase molecular systems. J. Chem. Phys. Ill, p. 1801... 

The latter are displayed in Fig. 36. At first, the radial density is very compact and performs one vibrational oscillation. Then, at a time of about 1.5 ps, a bifurcation takes place where one part of the former localized wavepacket moves into the fragmentation channel (which is reached, by definition, for distances larger than... 

Does the formal definition of ho as a bound wavefunction have an optimal correspondence wifh fhe description of the resonance state in terms of an initially localized wavepacket ... 

Two pulses with a FWHM of 11 and 180 fs were selected for excitation. As expected from the previous S /So studies, the prepared excited wavepackets show different subsequent time evolutions. The longer pulse results in a broader wavepacket distribution on the surface, spreading over large areas of the reaction surface, whereas the short fs-pulse excitation results in a more localized wavepacket, dominantly accelerated and focused into the C 2-Coln. Following the relaxation transfer of this localized wavepacket reveals that nearly the complete transfer occurs through the symmetric conical intersection. Thus the influence of changing only one parameter, the pump-pulse duration, points to the possibility to control the molecular dynamics and thereby enhance the transfer through one of the conical intersections. 

Fig. 83 Preparation of an electronic wavepacket by a few-cycle pulse top, l ) and its free evolution bottom). The relative sign of the initial superposition is directly controllable by the Clip. A CEP of 0 r can introduce a positive sign and leads to a localization on the left, while a CEP of 1 introduces a negative sign and a localization of the wavepacket on the right or vice versa top, right). The localized wavepacket then starts to oscillate from one side to the other along the molecular bond...

Once we adopt the notion that a dynamic approach is strongly suggested by the uncertainty principle, we soon discover that nature often prepares well localized wavepackets with which to work. It is easy to show > that the electronic photoabsorption cross section is given in the usual weak field limit by... 

Not all molecules are cooperative in this effort, spectroscopically speaking. As an example, examine Fig. 6. It shows the second photoelectron band of carbon suboxide, 0=C=C=C=0. The nature of the 7T bonding in this molecule is such that all atoms experience some change of force constant and equilibrium distance in the excited state of the ion. In the configuration space of the molecule we have a localized wavepacket (j) on the upper ionic surface, but now the... 

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