Wave packages

Blaha, P., Schwarz, K., Dufek, P. et al. (1995) WIEN95 A Full Potential Linearized Augmented Plane Wave Package for Calculating Crystal Properties. Technical University, Vienna. 

Light consists of electromagnetic waves whose vibrations are transverse to the propagation direction. Such a wave package contains beams vibrating randomly in different manners. If the vibrations, however, exhibit some spatial preference then the light beam is said to be polarized. 

Snin-other-orbit interaction. 211 Trust radius, 319 Wave package, 389... 

The PAW all-electron implementation of ab initio molecular d)mamics has been developed by the Blochl group (Clausthal, Germany) and can be received from there but is licensed from IBM (Riischlikon, Switzerland). The PAW method is also part of other plane-wave packages such as VASP or ABINIT (see above). 

If the electrons would have their own motion on the valence band (VB), they should be characterized also by a velocity. However, since the electrons have a quantum nature depending on their occupancy on Bloch-Schrodinger crystalline orbitals (3.101) they should be represented by the associated wave package, further characterized by the group velocity correlated with the quantum eneigy as such (Putz, 2006) ... 

The wave function of the wave package can be found from the solution of the... 

Summation is performed over all stationary states (Fourier components) ftom which the wave package consists. The substantial peculiarity of the wave package is the fact that the square of the wave function, which characterizes the probability of finding the nuclei at certain distances, depends on time, unlike the stationary states. This implies that the dynamics of the nuclear motion is manifested in the time evolution of the wave package, which can formally be considered as the motion of the wave package over the PES. The high time resolution makes it possible to detect the dynamics of the nuclear motion in the real time. 

The concept of the wave package was introduced in 1926 by Shroedinger however, it was not virtually used in chemistry. The vibrational wave package has a special significance for chemistry, when immediately several vibrational states are coherently excited in the molecular system. In this case, the intramolecular dynamics of nuclei is described by the time evolution of vibration-rotational wave packages. Account for phase characteristics of the nuclear motion is a substantial specific feature of this description. 

This reaction is a non-adiabatic process. The potential curves for the Nal molecule are shown in Fig. 4.7. It is seen that there is a pseudo-crossing between the curves of the excited covalent state and ionic ground electronic state. The femtosecond light pulse forms the coherent nuclear wave package in the excited electronic state. We mentioned above that the intramolecular dynamics could be interpreted... 

In studying the kinetics of any process, we are interested in the time evolution of the concentration of the reactant or product. This implies that populations of the quantum states should be detected rather than the dynamics of wave packages (we are not interested in the phase characteristics of the nuclear motion). Here the high time resolution and high intensity become the main specific features of femtosecond pulses. Different classes of reactions were studied (Table 4.11). The time scale of the presented reactions is given in the last column of the table. 

The first experiments in this direction were performed in studying the dependence of the intramolecular dynamics of diatomic molecules in the absence of the chemical reaction. It was shown for the I2 molecule that the change in the sign of the chirp of the exciting femtosecond pulse substantially changes the intramolecular dynamics of the vibrational motion of atoms. Similar results were obtained by the study of the dynamics of rotational wave packages. 

Figure LI5.1. (a) Initial wave packet moves toward the barrier (b) strong interference effects appear when part of the wave packet enters the barrier, and therefore the wave function oscillates (for E

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