Using collocation and a hierarchical basis to solve the vibrational Schrödinger equation
| Autor: | Tucker Carrington, Emil J. Zak |
|---|---|
| Přispěvatelé: | Department of Chemistry, Queen's University, Queen's University [Kingston, Canada] |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
[PHYS]Physics [physics]
Collocation 010304 chemical physics Basis (linear algebra) Schrödinger Equations Triangular matrix Vibrational Spectra General Physics and Astronomy Basis function 010402 general chemistry 01 natural sciences 0104 chemical sciences Matrix (mathematics) Tensor product Collocation method 0103 physical sciences Applied mathematics [CHIM]Chemical Sciences Physical and Theoretical Chemistry ComputingMilieux_MISCELLANEOUS Mathematics Interpolation |
| Zdroj: | Journal of Chemical Physics Journal of Chemical Physics, American Institute of Physics, 2019, 150 (20), pp.204108. ⟨10.1063/1.5096169⟩ |
| ISSN: | 0021-9606 1089-7690 |
| DOI: | 10.1063/1.5096169⟩ |
| Popis: | We show that it is possible to compute vibrational energy levels of polyatomic molecules with a collocation method and a basis of products of one-dimensional harmonic oscillator functions pruned so that it does not include functions for which the indices of many of the one-dimensional functions are nonzero. Functions with many nonzero indices are coupled only by terms that depend simultaneously on many coordinates, and they are typically small. The collocation equation is derived without invoking differences of interpolation operators, which simplifies implementation of the method. This, however, requires inverting a matrix whose elements are values of the pruned basis functions at the collocation points. The collocation points are the points on a Smolyak grid whose size is equal to the size of the pruned basis set. The Smolyak grid is built from symmetrized Leja points. Because both the basis and the grid are not tensor products, the inverse is not straightforward. It can be done by using so-called hierarchical 1-D basis functions. They are defined so that the matrix whose elements are the 1-D hierarchical basis functions evaluated at points is lower triangular. We test the method by applying it to compute 100 energy levels of CH2NH with an iterative eigensolver. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|