Licentiate thesis 2010-001

Absorbing Boundary Techniques for the Time-dependent Schrödinger Equation

Anna Nissen

11 February 2010


Chemical dissociation processes are important in quantum dynamics. Such processes can be investigated theoretically and numerically through the time-dependent Schrödinger equation, which gives a quantum mechanical description of molecular dynamics.

This thesis discusses the numerical simulation of chemical reactions involving dissociation. In particular, an accurate boundary treatment in terms of artificial, absorbing boundaries of the computational domain is considered. The approach taken here is based on the perfectly matched layer technique in a finite difference framework. The errors introduced due to the perfectly matched layer can be divided into two categories, the modeling error from the continuous model and numerical reflections that arise for the discretized problem. We analyze the different types of errors using plane wave analysis, and parameters of the perfectly matched layer are optimized so that the modeling error and the numerical reflections are of the same order. The level of accuracy is determined by estimating the order of the spatial error in the interior domain. Numerical calculations show that this procedure enables efficient calculations within a given accuracy. We apply our perfectly matched layer to a three-state system describing a one-dimensional IBr molecule subjected to a laser field and to a two-dimensional model problem treating dissociative adsorbtion and associative desorption of a H2 molecule on a solid surface. Comparisons made to standard absorbing layers in chemical physics prove our approach to be efficient, especially when high accuracy is of importance.

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