The Recursive Residue Generation Method

Wyatt, Róbert E.

doi:10.1002/9780470141229.ch5

Cited by 106 publications

(6 citation statements)

References 62 publications

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“…For very large systems, there are approximating algorithms based on variational methods, which effectively reduce the linear space of basis functions to "active spaces" (Wyatt 1989), or that make use of a multimode character of the wave functions (Carter et al 1998), as well as algorithms based on adiabatic solutions of the time-dependent Schrödinger equation (with typically more than 100 degrees of freedom, Jungwirth and Gerber 1995). Recently, an improved relaxation method has been applied to calculate vibrational eigenstates within the multiconfigurational timedependent Hartree method (Richter et al 2007, Vendrell et al 2007, Doriol et al 2008).…”

Section: Calculation Of Rovibrational Statesmentioning

confidence: 99%

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Marquardt¹,

Qüack²

2011

Handbook of High‐resolution Spectroscopy

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Analytical representations of potential energy hypersurfaces for the nuclear motion in polyatomic molecules from ab initio theory and experiment are discussed in a general way. The qualification of potential hypersurface representations from ab initio theory regarding the description of experimental data from rovibrational high-resolution spectroscopy and chemical reaction kinetics is analyzed in more detail for a restricted group of molecules including methane, CH 4 , ammonia, NH 3 , H 2 O 2 , and (HF) 2 . Current methods for the derivation of analytical representations of potential energy surfaces as well as some applications are reviewed.

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Section: Calculation Of Rovibrational Statesmentioning

confidence: 99%

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Marquardt¹,

Qüack²

2011

Handbook of High‐resolution Spectroscopy

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“…Although the Lanczos method has been in existence for more than half a century, its applications in molecular physics have been limited until quite recently. Wyatt was among the first to popularize the recursive approach, − which has flourished to become the method of choice today for studying highly excited vibrational spectra. , In particular, he promoted the approach of Cullum and Willoughby for identifying the so-called spurious eigenvalues that emerge in finite-precision arithmetic without the expensive orthogonalization, which renders the implementation of the Lanczos diagonalizer straightforward and very efficient. Our implementation of the Lanczos method has been reviewed in refs and , so no more detail is given here.…”

Section: Computational Detailsmentioning

confidence: 99%

Analysis of the HO₂ Vibrational Spectrum on an Accurate Ab Initio Potential Energy Surface

Jiang²,

Xie³

et al. 2007

J. Phys. Chem. A

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The complete vibrational spectrum of the HO2(X(2)A' ') radical, up to the H + O2 dissociation limit, has been determined quantum mechanically on an accurate potential energy surface (PES), based on approximately 15000 ab initio points at the icMRCI+Q/aug-cc-pVQZ level of theory. The vibrational states are found to be assignable at low energies but become more irregular as the energy approaches the dissociation limit. However, even at very high energies, regularity still exists, in sharp contrast to earlier results based on the double many-body expansion (DMBE) IV potential. Several Fermi resonances have been identified, and the spectrum is fit with a spectroscopic Hamiltonian. In addition, the vibrational dynamics is analyzed using a periodic orbit approach.

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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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The Recursive Residue Generation Method

Cited by 106 publications

References 62 publications

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Analysis of the HO₂ Vibrational Spectrum on an Accurate Ab Initio Potential Energy Surface

Two new methods for computing vibrational energy levels

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The Recursive Residue Generation Method

Cited by 106 publications

References 62 publications

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

Analysis of the HO2 Vibrational Spectrum on an Accurate Ab Initio Potential Energy Surface

Two new methods for computing vibrational energy levels

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About

Analysis of the HO₂ Vibrational Spectrum on an Accurate Ab Initio Potential Energy Surface