The adiabatic or Born-Oppenheimer approximation is often used in molecular calculations to simplify the solution to the Schrodinger equation. The basis of the approximation is the large difference in the relative motions of the nuclei and electrons in the molecule-the electrons are able to respond almost instantly to the movements of the nuclei. Thus, the nuclei may be regarded as being fixed in a certain position and the Schrodinger equation can then be solved using the potential obtained by solving the electronic problem at fixed nuclear configuration.
A similar argument can be used to decouple the angular and radial motions of many van der Waals complexes because, like nuclei in molecules, the radial motions in many van der Waals complexes are strongly localized. Fixing the radial separation between the atoms and molecules in the complex to a particular value results in a Schrodinger equation that is much simpler to solve because it is only dependent on angles. van der Waals complexes containing helium atoms, however, present a dilemma because the extremely weak interactions present also lead to large amplitude radial as well as angular motions. Because the basis of the adiabatic approximation is a large difference in time scale between the angular and radial motions, the validity of the adiabatic approximation for helium complexes is uncertain.
In this thesis, the adiabatic separation of angular and radial motion is shown to be accurate for extremely floppy complexes of helium by demonstrating its use on the van der Waals molecule He-HCN. A major application of this method is expected to be the quick calculation of approximate wave functions for Diffusion Monte Carlo studies of the rotation of impurity molecules inside ultra-cold droplets of helium. The method presented here is significantly faster than other methods (e.g., Variational Monte Carlo) that have been used to calculate approximate wave functions for Diffusion Monte Carlo.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8134 |
| Date | 01 May 2000 |
| Creators | Ward, P. Daniel |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
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