Iterative Methods for Computing Vibrational Spectra
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Authors
Carrington, Tucker Jr
Date
2017-12-21
Type
preprint
Language
en
Keyword
Vibrational Spectroscopy , Iterative Eigensolvers , Contracted Basis Functions , Smolyak Grids , Rank Reduction
Alternative Title
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. 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.