Iterative Methods for Computing Vibrational Spectra

Tucker Carrington
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Tucker Carrington: Chemistry Department, Queen’s University, Kingston, ON K7L 3N6, Canada

Mathematics, 2018, vol. 6, issue 1, 1-14

Abstract: I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate ( F ) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

Keywords: vibrational spectroscopy; iterative eigensolvers; contracted basis functions; Smolyak grids; rank reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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