Two new methods for computing vibrational energy levels
I review two new ideas for coping with the size of large product basis sets and large product grids when one computes vibrational energy levels. The first is based on a tensor reduction scheme. It exploits advantages of a sum-of-products potential. The key idea is to use a basis each of whose functi...
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| Published in | Canadian journal of chemistry Vol. 93; no. 6; pp. 589 - 593 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Ottawa
NRC Research Press
01.06.2015
Canadian Science Publishing NRC Research Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0008-4042 1480-3291 |
| DOI | 10.1139/cjc-2014-0590 |
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| Abstract | I review two new ideas for coping with the size of large product basis sets and large product grids when one computes vibrational energy levels. The first is based on a tensor reduction scheme. It exploits advantages of a sum-of-products potential. The key idea is to use a basis each of whose function is a sum of optimized products and to compress the number of terms in each basis function. When the potential does not have the sum-of-products form, it is usually necessary to use quadrature. The second idea uses a nondirect product grid that has structure and is therefore compatible with efficient matrix–vector products. |
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| AbstractList | I review two new ideas for coping with the size of large product basis sets and large product grids when one computes vibrational energy levels. The first is based on a tensor reduction scheme. It exploits advantages of a sum-of-products potential. The key idea is to use a basis each of whose function is a sum of optimized products and to compress the number of terms in each basis function. When the potential does not have the sum-of-products form, it is usually necessary to use quadrature. The second idea uses a nondirect product grid that has structure and is therefore compatible with efficient matrix-vector products. Key words: theory, rovibrational spectroscopy, iterative methods, Lanczos algorithm. Cet article decrit deux nouvelles approches permettant l'utilisation d'une grande base de produits afin de calculer des niveaux vibrationnels. La premiere est fondee sur la reduction des tenseurs. Elle exploite les avantages d'un potentiel ayant la forme d'une somme de produits. L'idee clef est d'utiliser une base dont chacune des fonctions est une somme de produits optimises et de comprimer le nombre de termes dans chaque fonction de la base. Si le potentiel n'est pas une somme de produits, il faut utiliser une quadrature. La seconde approche consiste a utiliser une grille qui n'est pas un produit direct mais qui a assez de structure pour faciliter le calcul de produits matrice-vecteur. Mots-cles: theorie, spectroscopie rotationnelle-vibrationnelle, methodes iteratives, algorithme de Lanczos. I review two new ideas for coping with the size of large product basis sets and large product grids when one computes vibrational energy levels. The first is based on a tensor reduction scheme. It exploits advantages of a sum-of-products potential. The key idea is to use a basis each of whose function is a sum of optimized products and to compress the number of terms in each basis function. When the potential does not have the sum-of-products form, it is usually necessary to use quadrature. The second idea uses a nondirect product grid that has structure and is therefore compatible with efficient matrix-vector products. |
| Abstract_FL | Cet article décrit deux nouvelles approches permettant l’utilisation d’une grande base de produits afin de calculer des niveaux vibrationnels. La première est fondée sur la réduction des tenseurs. Elle exploite les avantages d’un potentiel ayant la forme d’une somme de produits. L’idée clef est d’utiliser une base dont chacune des fonctions est une somme de produits optimisés et de comprimer le nombre de termes dans chaque fonction de la base. Si le potentiel n’est pas une somme de produits, il faut utiliser une quadrature. La seconde approche consiste à utiliser une grille qui n’est pas un produit direct mais qui a assez de structure pour faciliter le calcul de produits matrice–vecteur. |
| Audience | Academic |
| Author | Carrington, Tucker |
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| SubjectTerms | algorithme de Lanczos Analysis Basis functions Binding energy Chemistry Energy levels iterative methods Lanczos algorithm Mathematical analysis Matrix Matrix algebra Matrix methods méthodes itératives Quadratures rovibrational spectroscopy spectroscopie rotationnelle–vibrationnelle Tensors theory théorie Vibrational spectra |
| Title | Two new methods for computing vibrational energy levels |
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