Quantum mechanical study of the Ã1A″→X̃1Σ+ sep spectrum for HCN

Bentley, J.; Brunet, Jean‐Philippe; Wyatt, Róbert E.; Friesner, Richard A.; Leforestier, Claude

doi:10.1016/0009-2614(89)85104-8

Cited by 76 publications

(10 citation statements)

References 36 publications

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“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24] An iterative method requires only the computation of matrix-vector products: the matrix is not modified or stored. 25 Hamiltonian matrixvector products can be computed without storing the Hamiltonian matrix and without even calculating its matrix elements.…”

Section: Introductionmentioning

confidence: 99%

A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions

Wang

Carrington

2003

The Journal of Chemical Physics

184

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Articles you may be interested inUsing a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4 J. Chem. Phys. 135, 064101 (2011); 10.1063/1.3617249Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12DA finite basis representation Lanczos calculation of the bend energy levels of methaneWe present a contracted basis-iterative method for calculating numerically exact vibrational energy levels of methane ͑a 9D calculation͒. The basis functions we use are products of eigenfunctions of bend and stretch Hamiltonians obtained by freezing coordinates at equilibrium. The basis functions represent the desired wavefunctions well, yet are simple enough that matrix-vector products may be evaluated efficiently. We use Radau polyspherical coordinates. The bend functions are computed in a nondirect product finite basis representation ͓J. Chem. Phys. 118, 6956 ͑2003͔͒ and the stretch functions are computed in a product potential optimized discrete variable ͑PODVR͒ basis. The memory required to store the bend basis is reduced by a factor of ten by storing it on a compacted grid. The stretch basis is optimized by discarding PODVR functions with high potential energies. The size of the primitive basis is 33 billion. The size of the product contracted basis is six orders of magnitude smaller. Parity symmetry and exchange symmetry between two of the H atoms are employed in the final product contracted basis. A large number of vibrational levels are well converged. These include almost all states up to 8000 cm Ϫ1 and some higher local mode stretch bands.

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Section: Introductionmentioning

confidence: 99%

A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions

Wang

Carrington

2003

The Journal of Chemical Physics

184

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“…2,24,[39][40][41][42] However, all previous studies were based on empirical PESs of some form for theÃ 1 A state and imposed the Condon approximation that assumes a constant transition dipole. These approximations lead to uncertainties that are not readily interpretable.…”

Section: Introductionmentioning

confidence: 99%

THEORETICAL STUDIES OF $\tilde{A}{}^1 A^{\prime\prime}\to\tilde{X}{}^1 A^\prime$ RESONANCE EMISSION SPECTRA OF HCN/DCN USING SINGLE LANCZOS PROPAGATION METHOD

Guo

Xie

2003

J. Theor. Comput. Chem.

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Using an efficient single Lanczos propagation method, we report theÃ 1 A →X 1 A resonance emission spectra of HCN and DCN from a number of low-lying vibrational levels of theÃ-state manifold. Our calculations represent the first such undertaking in which a high-quality ab initio based potential energy surface of the excited (Ã 1 A ) state and aÃ 1 A -X 1 A transition dipole surface were used. The results show a significant improvement over previous theoretical work in reproducing experimental stimulated emission pumping spectra of HCN. The improved theory-experiment agreement is attributed to the accurateÃ-state potential energy surface, while the impact of the transition dipole function was found to be relatively minor.

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“…For this reason, iterative methods are often used to calculate spectra. [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] They require only the computation of matrix-vector products and can be implemented without modifying or storing the matrix. When a direct product basis is used, the Hamiltonian matrix-vector products can be computed without storing the Hamiltonian matrix and without even calculating its matrix elements.…”

Section: Eigensolversmentioning

confidence: 99%

Two new methods for computing vibrational energy levels

Carrington

2015

Can. J. Chem.

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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.Résumé : 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.Mots-clés : théorie, spectroscopie rotationnelle-vibrationnelle, méthodes itératives, algorithme de Lanczos.

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Quantum mechanical study of the Ã1A″→X̃1Σ+ sep spectrum for HCN

Cited by 76 publications

References 36 publications

A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions

A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions

THEORETICAL STUDIES OF $\tilde{A}{}^1 A^{\prime\prime}\to\tilde{X}{}^1 A^\prime$ RESONANCE EMISSION SPECTRA OF HCN/DCN USING SINGLE LANCZOS PROPAGATION METHOD

Two new methods for computing vibrational energy levels

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