Using collocation to study the vibrational dynamics of molecules

Spectrochimica Acta. Part A, Molecular and Biomolecular Spectroscopy
Tucker Carrington

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...Continue Reading

References

Jul 21, 2004·The Journal of Chemical Physics·Richard Dawes, Tucker Carrington
Aug 27, 2005·The Journal of Chemical Physics·Rob van Harrevelt, Uwe Manthe
Apr 10, 2009·The Journal of Chemical Physics·Edit MátyusAttila G Császár
Nov 10, 2009·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Feb 10, 2011·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Oct 15, 2011·Physical Chemistry Chemical Physics : PCCP·Attila G CsászárGábor Czakó
Jul 19, 2013·Spectrochimica Acta. Part A, Molecular and Biomolecular Spectroscopy·David Lauvergnat, André Nauts
Oct 15, 2013·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Dec 10, 2015·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Aug 1, 2016·The Journal of Chemical Physics·Robert Wodraszka, Tucker Carrington
Apr 8, 2017·The Journal of Chemical Physics·Tucker Carrington
Aug 16, 2017·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Oct 17, 2017·The Journal of Chemical Physics·Gustavo Avila, Tucker Carrington
Dec 7, 2018·The Journal of Chemical Physics·Sergei Manzhos, Tucker Carrington
May 3, 2020·The Journal of Chemical Physics·Robert Wodraszka, Tucker Carrington

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