Using collocation to study the vibrational dynamics of molecules
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Authors
Carrington, Tucker Jr.
Date
2021-03-05
Type
journal article
Language
en
Keyword
Vibrational spectroscopy , Collocation , Computational method
Alternative Title
Abstract
In this paper, I review collocation methods for solving the time-independent and the time-dependent Schroedinger equation. Unlike traditional variational methods, collocation methods do not require integrals and quadrature. Either collocation or quadrature is necessary if the potential does not have a special form. If the basis is a direct product of univariate bases and the quadrature grid is also a direct product, there exist variational methods that do not require quadrature approximations for potential energy matrix elements. These methods, however, do require storing, in computer memory, vectors with as many components as there are quadrature points. For this reason direct-product variational methods are poor for problems with more than five atoms. There are well established ideas for reducing the size of the basis in a variational calculation. Three such ideas are: 1) prune the direct product basis; 2) use basis functions that are products of multivariate functions; 3) optimise the basis functions (e.g. Multiconfiguration time-dependent Hartree). Reducing the basis size, however, is not enough to the make variational methods tractable because, for all three of these ideas, quadrature rears its ugly head. Collocation is an attractive alternative to variational methods.
Description
© 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Citation
Carrington, T. (2021). Using collocation to study the vibrational dynamics of molecules. Spectrochimica Acta. Part A, Molecular and Biomolecular Spectroscopy, 248, 119158. https://doi.org/10.1016/j.saa.2020.119158
Publisher
Elsevier