Wavepacket Propagation in the Determination of Microscopic Eigenenergies: II Back-Propagation in Imaginary Time

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 8 Issue 2 (2003) pp 107-111

Wavepacket Propagation in the Determination of Microscopic Eigenenergies: II Back-Propagation in Imaginary Time

Aletha M. Nowak and Larry Eno*

Department of Chemistry, Clarkson University, Potsdam, NY 13699-5810, ko00@clarkson.edu
Received June 25, 2002. Accepted December 18, 2002

Published online: 10 February 2003

Abstract. With the goal of enhancing undergraduate appreciation for the relationship between chemical structure and dynamics, we have taken wavepacket propagation, which is traditionally used in addressing dynamical problems, and made it the foundation for determining eigenenergies. In an earlier paper, a technique for determining eigenenergies that is founded on wavepacket propagation and called the spectral method was presented. A related technique is presented here, involving back-propagating a wavepacket in imaginary time. The propagation causes the wavepacket to approach its lowest energy component eigenstate, and hence a determination of the corresponding eigenenergy is made. Application is made to the electronic structure of the He atom for which calculations are undertaken first in the absence of the electron-electron interaction and then including the interaction; excellent agreement is obtained with known eigenenergies.

Key Words: In the Classroom; physical chemistry; quantum

(*) Corresponding author. (E-mail: ko00@clarkson.edu)

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