Using Quadrature and Collocation Methods to Calculate Spectra of Polyatomic Molecules with General Potential Energy Surfaces
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Authors
Simmons, Jesse
Date
Type
thesis
Language
eng
Keyword
Spectroscopy , Schroedinger Equation , Quadrature , Collocation , Potential Energy Surface , Iterative Methods
Alternative Title
Abstract
Calculating accurate rovibrational spectra of molecules composed of even just a few atoms is a difficult task due to the complexity of the quantum many-body problem. With few exceptions, theoretical efforts rely on the Born-Oppenheimer framework that introduces the concept of a nuclear potential energy surface. Although many very successful methods for finding rovibrational energies implement some form of approximation to the PES, in order to facilitate efficient calculation, to obtain the most accurate energies possible, it is necessary to employ methods that are usable with a general PES. The only methods compatible with such a PES are those that require evaluation only at certain nuclear geometries (points), such as quadrature or collocation. This thesis is composed of several studies that demonstrate the effectiveness of well-established quadrature-based methods and aim to improve the abilities of collocation methods. The first article included is a study of the low-lying rovibrational energy levels of the molecules CH2D+ and CHD2+ and is performed using a large quadrature-based calculation. The second article presents a collocation method whereby energy levels obtained using efficient routines based on approximate potential energy surfaces may be improved relative to the true potential with minimal computational effort. The last article introduces a method that incorporates many of the computational advantages currently realized by quadrature calculations into collocation for the first time. Results from all presented works should help facilitate future experimental and theoretical efforts.
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ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.