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Article

Iterative Methods for Computing Vibrational Spectra

Chemistry Department, Queen’s University, Kingston, ON K7L 3N6, Canada
Received: 21 December 2017 / Revised: 10 January 2018 / Accepted: 11 January 2018 / Published: 16 January 2018
(This article belongs to the Special Issue Computational Spectroscopy)
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. View Full-Text
Keywords: vibrational spectroscopy; iterative eigensolvers; contracted basis functions; Smolyak grids; rank reduction vibrational spectroscopy; iterative eigensolvers; contracted basis functions; Smolyak grids; rank reduction
MDPI and ACS Style

Carrington, T., Jr. Iterative Methods for Computing Vibrational Spectra. Mathematics 2018, 6, 13. https://0-doi-org.brum.beds.ac.uk/10.3390/math6010013

AMA Style

Carrington T Jr.. Iterative Methods for Computing Vibrational Spectra. Mathematics. 2018; 6(1):13. https://0-doi-org.brum.beds.ac.uk/10.3390/math6010013

Chicago/Turabian Style

Carrington, Tucker, Jr. 2018. "Iterative Methods for Computing Vibrational Spectra" Mathematics 6, no. 1: 13. https://0-doi-org.brum.beds.ac.uk/10.3390/math6010013

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