On the computation of diatomic centrifugal distortion constants: Exact solutions for initial value problems

Kobeissi, Hafez; Korek, Mahmoud; Dagher, Mounzir

doi:10.1016/0022-2852(89)90092-1

Cited by 45 publications

(41 citation statements)

References 14 publications

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“…By making use of the well-known properties of cD,,(r) (continuity at any r, boundary conditions similar to those of the vibrational wavefunction $,, = Q0 (2-9)), one can derive the expressions [I] found by Hutson (2), or the expressions as presented in a recent work (6). a,, and 6,, are both solutions of eq.…”

Section: Theorymentioning

confidence: 99%

“…Other recent works presented improvements (3,4), or alternatives (5,6), over Hutson's method. In all these works, the computed CDC were limited to e, = Mu, i.e., to "low-order" distortion constants. The main reason for this limitation is the common belief that "there is little need for the higher order CDC" (3 However, in a recent publication (4), Coxon noticed for some diatomic hydrides that when the dissociation limit is approached by increasing v, constants beyond e5 = M,, appear to be needed, and that "the perturbation in the wavefunction needs to be calculated to approximately fourth order to provide agreement within the experimental uncertainties" (4).…”

Section: Introductionmentioning

confidence: 99%

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Diatomic centrifugal distortion constants for large orders at any level: application to the state

Korek¹,

Kobeissi²

1993

Can. J. Chem.

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MAHMOUD KOREK and HAFEZ KOBEISSI. Can. J. Chem. 71, 313 (1993).The determination of the centrifugal distortion constants (CDC) of a diatomic molecule is sought for high orders. When the vibrational energy e, = E, is known for a vibrational level u, the use of Rayleigh-Schrodinger perturbation theory gives the rotational constant el = B,, = (@,R@,) (with R = 1/r7), and the CDC e, = -D, = (@,R@,), e3 = H, = (@,R@,), . . . , e,, = (@,R@,,-,), . . . where @,,(r) is the solution of the nth rotational Schrodinger equation. The problem of the determination of a function @, , is solved by deriving exact analytical expressions for the initial values @,(r,) and @A(rO) at an arbitrary "origin" ro, the determination of any @,z(r) becoming as easy as that of @,(r) when eo is known; that of e,, becomes as easy as that of el = B, = (@,R@,). The application of the present formulation to the model LennardJones potential function allows the numerical computation of D,, H,,, L,,, Mu, N,,, 0,,, P,,, Q, for low and high u; the CDC beyond M,, are given for the first time; higher order CDC may be reached. The results for the four lowest order constants are in good agreement with those from previously confirmed methods. Appropriate tests for all orders show that the present method provides an elegant and competitive solution to the diatomic CDC problem even for large orders and high levels (near dissociation). (@,R@,), . . ., e,, = (@,R@,,-,), dans lesquelles @,,(r) est la solution de la n' ' " equation rotationnelle de Schrodinger. On a resolu le problkme de la determination d'une fonction @,, en derivant les expressions analytiques exactes pour les valeurs initiales @,,(ro) et @,',(ro) ?i une ccoriginen arbitraire, r,: la determination de chacune des @,,(r) devient aussi facile que celle de @,(r) lorsqu'on connait e, et celle de e,, devient aussi facile que celle de el = B, = (@,R@,). L'application de cette formulation ?i la fonction de potentiel modele de Lennard-Jones permet de faire des calculs numeriques de D,, H,,, L,,, M,,, N,,, Or,, P,, et Q, pour des valeurs tant tlevees que basses de u. On rapporte pour la premikre fois des valeurs des CDC au-dela de M,,; on pourrait atteindre des ordres plus tleves. Les resultats obtenus pour les quatre constantes les plus basses sont en bon accord avec celles obtenues antkrieurement avec des methodes confirmkes. Des essais appropries effectues pour tous les ordres demontrent que la methode rapportke ici prCsente une solution Clegante et competitive pour la solution du problkme des CDC de mol6cules diatorniques, m&me pour des ordres et des niveaux ClevCs (prks de la dissociation). On a aussi obtenu de bons resultats pour i n potentiel RKR d'un Ctat XOi-I, delimite par 109 niveaux.[Traduit par la redaction]

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diatomic centrifugal distortion constants for large orders at any level: application to the state

Korek¹,

Kobeissi²

1993

Can. J. Chem.

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“…The vibrational intervals in diatomic molecules are of interest in the context of such an enhancement. Within the Born-Oppenheimer approximation, the radial Schrödinger equation can be replaced, by using the canonical functions approach (Kobeissi, Korek, & Dagher 1989), and (Korek 1999) where the eigenvalues Ev, the rotational constants Bv, and the centrifugal distortion constants Dv have been calculated for the electronic state (1)…”

Section: Static Dipole Momentmentioning

confidence: 99%

Static Dipole Moments and Electronic Structure Calculations of the Low-Lying Electronic States of the Molecule Zinc Selinum ZnSe

Youssef¹,

Younes²,

Korek³

2017

MAS

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Zinc selenide is a compound that has many applications in optoelectrical systems. An understanding of its properties as an individual molecule can be of great help for its use at the nanoscale. Correspondingly, twenty two lowest electronic states of ZnSe have been studied in the 2s+1 Λ ± representation in this paper. The potential energy curves, the harmonic frequency ω e , the electronic energy T e , the static dipole moment and the internuclear distance r e have been investigated. These calculations have been performed by using the multi-reference configuration interaction (MRCI+Q) method with Davidson correction. A very good agreement is obtained by comparing the present results with those available in literature. New electronic states have studied in the present work for the first time.

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“…By using the canonical functions approach [24][25][26] and the cubic spline interpolation between each two consecutive points of the PECs obtained from the ab initio calculation of the SiO molecule, the eigenvalue E v , the rotational constant B v , the distortion constant D v , and the abscissas of the turning point r min and r max have been calculated up to the vibration level v = 52. These values for the state X ( …”

Section: The Vibration-rotation Calculationmentioning

confidence: 99%

“…In this work, we investigate the potential energy curves (PECs), the electric dipole moment and spectroscopic constants for the 20 2S+1 Λ ± lowlying electronic states of this molecule obtained by MRCI and RSPT2 calculations. Taking advantage of the electronic structure of the investigated electronic states of the SiO molecule and by using the canonical functions approach [24][25][26], the eigenvalues E v , the rotational constant B v and the abscissas of the turning points r min and r max have been calculated up to the vibrational level v = 52.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Study with Rovibrational and Dipole Moment Calculation of the SiO Molecule

Badreddine¹,

El-Kork²,

Korek³

2013

JMP

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Via CASSCF/MRCI and RSPT2 calculations (single and double excitation with Davidson correction) the potential energy curves of 20 electronic states in the representationof the molecule SiO have been calculated. By fitting these potential energy curves to a polynomial around the equilibrium internuclear distance r e , the harmonic frequency ω e , the rotational constant B e , and the electronic energy with respect to the ground state T e have been calculated. For the considered electronic states the permanent dipole moment μ have been plotted versus the internuclear distance r. Based on the canonical functions approach, the eigenvalues E v , the rotational constant B v and the abscissas of the turning points r min and r max have been calculated. The comparison of these values to the experimental and theoretical results available in the literature is presented. In the present work 8 higher electronic states have been studied theoretically for the first time.

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On the computation of diatomic centrifugal distortion constants: Exact solutions for initial value problems

Cited by 45 publications

References 14 publications

Diatomic centrifugal distortion constants for large orders at any level: application to the state

Diatomic centrifugal distortion constants for large orders at any level: application to the state

Static Dipole Moments and Electronic Structure Calculations of the Low-Lying Electronic States of the Molecule Zinc Selinum ZnSe

Theoretical Study with Rovibrational and Dipole Moment Calculation of the SiO Molecule

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