Time-dependent wavepacket method

Hankel, M. (2001) Time-Dependent Wavepacket Methods for the Calculation of Statc-to-Statc Molecular Reactive Cross Sections, Ph.D. thesis, University of Bristol, Bristol. 

Neuhauser, D., Baer, M., Judson, R.S. and Kouri, D.J. (1991) The application of time-dependent wavepacket methods to reactive scattering. Corny. Phys. Commuri. 63, 460-481. 

THE TIME DEPENDENT WAVEPACKET METHOD APPLICATION TO COLLISION INDUCED DISSOCIATION PROCESSES... 

ABSTRACT. After reviewing the time dependent wavepacket method as applied to collision induced dissociation processes,we report accurate quantum results for reactive and non reactive collinear A+BC systems. Both systems display a vibrational enhancement effect in the low energy region. While the non reactive systems exhibit a vibrational inhibition effect at higher energies,a more complex behavior is observed in the reactive case. Below the classical dissociation threshold,the non reactive systems display tunnelling tails which decrease with the initial vibrational excitation of the diatomic molecule. The reactive system displays important quantum effects at energies well above the classical dissociation threshold. 

In section 2,we review the time dependent wavepacket method,which is now well codified since the work of Me Cullough and Wyatt. Section 3 is devoted to a comparison of classical and quantum results for reactive and non reactive collinear calculations. Finally we discuss the possibility of extending these calculations to more realistic cases, such as approximate 3D quantum treatments. 

There are two classes in applications of quantum nuclear dynamics one is the stationary-state scattering theory to treat reactive scattering (chemical reactions), and the other is time-dependent wavepacket method. Here... 

The final solution to the quantum reactive scattering problem we shall consider is the time-dependent wavepacket method (see Wave Packets). This is one of the simplest ways to solve the Schrddinger equation for a chemical reaction, and it is also rapidly emerging as one of the most powerful. Moreover, it has the great advantage that its numerical implementation is only a small step away from its theoretical formulation, which makes the method especially easy to justify and explain. 

The time-dependent wavepacket method for state to state reactive scattering is based on the following remarkable expression for the reactive scattering matrix element 5cu,au( ) involving the Fourier transform of a correlation function Ccv. aaff) between an initial reactant wavepacket Xw and a... 

Figure 7 Schematic illustration of the time-dependent wavepacket method for state to state reactive scattering...

In order to clarify this point, and at the same time justify the time-dependent wavepacket method, we shall now describe how equation (58) can be obtained in a way that highlights the implications of its causal (f > 0) time integral. 

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