Getting started with Numerov’s method

González, Juan Luna; Thompson, Diane V

doi:10.1063/1.168593

Cited by 129 publications

(44 citation statements)

References 3 publications

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“…The e e , ␣ e , B e , and D 0 results also approve that the aug-cc-pV5Z basis set is the most suitable one for further calculations when compared with the experimental findings [24, 26 -28]. And finally, using the APEF obtained at the UCCSD(T)/aug-ccpV5Z level of theory, the radial Schrö dinger equation of nuclear motion is numerically solved with the Numerov method [23] to predict all the vibrational states. All the energy levels and corresponding classical turning points, R min and R max , and the inertial rotation and centrifugal distortion constants are determined when J ϭ 0.…”

Section: Methodsmentioning

confidence: 95%

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Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

Shi

Zhang

Sun

et al. 2009

Int. J. Quantum Chem.

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The coupled-cluster singles-doubles-approximate-triples [CCSD(T)]theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions (aug-cc-pV5Z) is used to investigate the spectroscopic properties of the HCl ϩ (X 2 ⌸) ion. The accurate potential energy curve is calculated over the internuclear separation range from 0.051 to 2.51 nm and is fitted to the analytic MurrellSorbie function, which is used to accurately determine the spectroscopic parameters such as D 0 , D e , e e , ␣ e , and B e .

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Section: Methodsmentioning

confidence: 95%

“…We use the Numerov method [23] with the automatic step-size selection to solve Eq. (10) numerically and have obtained a total of 26 vibrational states for the HCl ϩ (X 2 ⌸) ion when the rotational quantum number J is set equal to zero.…”

Section: Vibrational Manifoldsmentioning

confidence: 99%

Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

Shi

Zhang

Sun

et al. 2009

Int. J. Quantum Chem.

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“…In this paper, we solve the rovibrational Schrödinger equation by Numerov's method. 35 That is, the rovibrational constants are first determined in a direct forward manner from the analytic potential by solving the rovibrational Schrödinger equation and then the spectroscopic parameters are evaluated by fitting the vibrational levels obtained here.…”

Section: Theory and Methodsmentioning

confidence: 99%

A theoretical investigation of the S₂⁺ cation in the gas phase

et al. 2014

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The potential energy curves (PECs) of 18 lowest energy ⌳-S states of the S 2 + cation have been calculated using the complete active space self-consistent field method followed by the internally contracted multireference configuration interaction approach with the Davidson modification. When spin−orbit coupling is computed using the Breit−Pauli Hamiltonian with the cc-pCVTZ basis set, the 18 ⌳-S states split into 56 ⍀ components. To improve the quality of the PECs, core−valence correlation and scalar relativistic corrections are included. All PECs are extrapolated to the complete basis set limit. Based on the PECs obtained by the icMRCI+CV+DK+Q/(CBS-56) calculations, the spectroscopic parameters of 17 ⌳-S bound states and 50 ⍀ bound states are obtained. The transitions (including the Franck−Condon factors and radiative lifetimes) from two low-lying states to the ground state are calculated for several low vibrational levels. Analyses show that the spectroscopic parameters reported here can be expected to be reliably predicted. Résumé :Les courbes d'énergie potentielle (CEP) des 18 états ⌳-S de plus basse énergie du cation S 2 + ont été calculées à l'aide de la méthode du champ auto-cohérent de l'espace actif complet, suivie de l'approche d'interaction de configuration multiréférence à contraction interne avec correction de Davidson. Lorsque le couplage spin−orbite est calculé à l'aide de l'hamiltonien de Breit−Pauli avec la base cc-pCVTZ, les 18 états ⌳-S se scindent en 56 composants ⍀. Pour améliorer la qualité des CEP, la corrélation noyau−électron et les corrections relativistes scalaires sont prises en compte. Toutes les CEP sont extrapolées à la limite de la base complète. À partir des CEP générées par les calculs icMRCI+CV+DK+Q/(CBS-56), les paramètres spectroscopiques des 17 états liés ⌳-S et des 50 états liés ⍀ sont obtenus. Les transitions (notamment les facteurs de Franck−Condon et les durées de vie radiatives), des deux états de basse énergie jusqu'à l'état fondamental, sont calculées pour plusieurs niveaux vibrationnels bas. Les analyses montrent que les paramètres spectroscopiques fournis ici peuvent vraisemblablement être prédits de façon fiable. [Traduit par la Rédaction] Mots-clés : couplage spin−orbite, courbe d'énergie potentielle, paramètre spectroscopique, facteur de Franck−Condon, durée de vie radiative.

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“…The transmission coefficient is obtained by numerically solving the Schr€ odinger equation using the Numerov method. 53,54 This method is computationally efficient and accurate and does not require any simplifying assumptions about the shape of the barrier potential profile. The method is also numerically robust enabling the modeling of the steep current rises originating from resonance phenomena.…”

Section: A Tsu-esaki Methodsmentioning

confidence: 99%

Tsu-Esaki modeling of tunneling currents in ferroelectric tunnel junctions

Tuomisto

Dijken

Puska

2017

Journal of Applied Physics

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Getting started with Numerov’s method

Cited by 129 publications

References 3 publications

Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

A theoretical investigation of the S₂⁺ cation in the gas phase

Tsu-Esaki modeling of tunneling currents in ferroelectric tunnel junctions

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Getting started with Numerov’s method

Cited by 129 publications

References 3 publications

Spectroscopic investigations on the HCl(X2Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

Spectroscopic investigations on the HCl(X2Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

A theoretical investigation of the S2+ cation in the gas phase

Tsu-Esaki modeling of tunneling currents in ferroelectric tunnel junctions

Contact Info

Product

Resources

About

Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

Spectroscopic investigations on the HCl(X²Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

A theoretical investigation of the S₂⁺ cation in the gas phase