Computing Vibrational Spectra Using a New Collocation Method With a Pruned Basis and More Points Than Basis Functions: Avoiding Quadrature
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Authors
Simmons, Jesse
Carrington, Tucker Jr.
Date
2023-04-13
Type
journal article
Language
en
Keyword
Alternative Title
Abstract
We present a new collocation method for computing the vibrational spectrum of a polyatomic molecule. Some form of quadrature or collocation is necessary when the potential energy surface does not have a simple form that simplifies the calculation of the potential matrix elements required to do a variational calculation. With quadrature, better accuracy is obtained by using more points than basis functions. To achieve the same advantage with collocation, we introduce a collocation method with more points than basis functions. Critically important, the method can be used with a large basis because it is incorporated into an iterative eigensolver. Previous collocation methods with more points than functions were incompatible with iterative eigensolvers. We test the new ideas by computing energy levels of molecules with as many as six atoms. We use pruned bases but expect the new method to be advantageous whenever one uses a basis for which it is not possible to find an accurate quadrature with about as many points as there are basis functions. For our test molecules, accurate energy levels are obtained even using non-optimal, simple, equally spaced points.
Description
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Jesse Simmons, Tucker Carrington; Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature. J. Chem. Phys. 14 April 2023; 158 (14): 144115, and may be found at https://doi.org/10.1063/5.0146703.
Citation
Jesse Simmons, Tucker Carrington; Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature. J. Chem. Phys. 14 April 2023; 158 (14): 144115. https://doi.org/10.1063/5.0146703
Publisher
AIP Publishing