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Improving the Efficiency of Phase-Space Localized Basis Functions

Banff International Research Station for Mathematical Innovation and Discovery

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase-space localized (PSL) basis functions. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. Iterative methods are imperative if one wishes to avoid storing matrices which is important for larger molecules. Previously, we showed that it was possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. Here, we present a reformulation that improves the PSL basis functions themselves, and also a new method which more efficiently chooses the PSL functions. These methods are applied to the calculation of vibrational energies of $CH_2O$ and $CH_2NH$ using the iterative Arnoldi algorithm and PSL functions. We show that our PSL basis is competitive with other previously used basis sets for these molecules.

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Queen's University

2016-07-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58579

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/