On testing difference equations for the diatomic eigenvalue problem

Kobeissi, Hafez; Kobeissi, Marwan; El‐Hajj, Ali

doi:10.1002/jcc.540090807

Cited by 46 publications

(12 citation statements)

References 17 publications

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“…For the study of the rovibrational problem there are many important theories and techniques in literature with computer programs as LEVEL [33][34][35][36] or the Duo program [37]. In order to obtain high order precision there is a need for large order centrifugal distortion constant as D v , H v , K Q v K [38][39][40][41][42][43][44]. By using the canonical function approach one can obtain these constants with the high values of vibrational levels even near dissociation by one single and simple routine.…”

Section: Dissociation Of Atomic Levels Be+hmentioning

confidence: 99%

Electronic structure with dipole moment calculations of the high-lying electronic states of BeH, MgH and SrH molecules

et al. 2018

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By using the complete active space self consistent field (CASSCF) with multi-reference configuration interaction MRCI+Q method including single and double excitations with Davidson correction, the 26, 27 and 25 low-lying doublet and quartet electronic states in the representation 2s+1 Λ (+/−) (without spin orbit interaction) of the molecules BeH, MgH and SrH have been investigated. The potential energy curves, the internuclear distance R e , the harmonic frequency ω e , the permanent dipole moment μ, the rotational constant B e and the electronic transition energy with respect to the ground state T e are calculated. Using the canonical approach the eigenvalue E v , the rotational constant B v and the abscissas of the turning points R min and R max have been calculated for the investigated electronic states. The comparison between the values of the present work and those available in the literature for several electronic states shows very good agreement.

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Section: Dissociation Of Atomic Levels Be+hmentioning

confidence: 99%

Electronic structure with dipole moment calculations of the high-lying electronic states of BeH, MgH and SrH molecules

et al. 2018

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“…17 The dipolemoment function is also taken to be the analytic form: 17 The dipolemoment function is also taken to be the analytic form:…”

Section: Not and Hadamard Gatesmentioning

confidence: 99%

Accuracy of gates in a quantum computer based on vibrational eigenstates

Babikov

2004

The Journal of Chemical Physics

107

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A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.

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“…Other inte-grators may improve the accuracy but not the consumption in computer time. 7 The comparison of the Cash and Raptis difference equation (CRDE)" and of ISDE12 with that of Numerov (NDE) shows that: (i) if E is the average error (for all the vibrational levels related to a standard diatomic potential U ) by using NDE, it is of 4~ x lo-* for CRDE, and E x for ISDF; (ii) if 7 is the computing time for NDE, it is of -37 for CRDE and -7 for ISDE. Other comparisons are given in ref.…”

Section: Numerical Applicationmentioning

confidence: 97%

Highly accurate diatomic centrifugal distortion constants for high orders and high levels

Korek

Kobeissi

1992

J Comput Chem

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The problem of the computation of the Centrifugal Distortion Constants (CDC) related to a diatomic potential is considered. The analytical expressions obtained from a reformulation of the Rayleigh-Schrodinger perturbation theory are used [Kobeissi et al., J. Mol. Spectrosc., 138, 1 (1989)l; these are -C t = l em(@o@n-m) where R = lh2, @o = $, is the vibrational wave function (corresponding to the given energy E, = eo) and @z, . . . , are the "rotational corrections" to a0, solutions of the rotational (nonhomogeneous) Schrodinger equations. These equations are integrated by using a recent integrator using a powerful local control allowing (for @, J a high accuracy.

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On testing difference equations for the diatomic eigenvalue problem

Cited by 46 publications

References 17 publications

Electronic structure with dipole moment calculations of the high-lying electronic states of BeH, MgH and SrH molecules

Electronic structure with dipole moment calculations of the high-lying electronic states of BeH, MgH and SrH molecules

Accuracy of gates in a quantum computer based on vibrational eigenstates

Highly accurate diatomic centrifugal distortion constants for high orders and high levels

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