A Multi-Dimensional Smolyak Collocation Method in Curvilinear Coordinates for Computing Vibrational Spectra
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Authors
Avila, Gustavo
Carrington, Tucker Jr
Date
2015-12-02
Type
journal article
Language
en
Keyword
Computing Vibrational Spectra , Iterative Eigensolver , Energy Levels , Wavefunctions , Smolyak Grid , Kinetic Energy , Matrix Vector
Alternative Title
Abstract
In this paper, we improve the collocation method for computing vibrational spectra that was
presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative
eigensolver, energy levels and wavefunctions are determined from values of the potential on a
Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector
labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis
indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably.
Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate
integrals of coordinate dependent coefficients of differential operators. The ideas are tested by
computing energy levels of HONO using a KEO in bond coordinates