The rotating Morse potential model for diatomic molecules in the tridiagonalJ-matrix representation: I. Bound states

Nasser, Ibraheem; Abdelmonem, M. S.; Bahlouli, H.; Alhaidari, A. D.

doi:10.1088/0953-4075/40/21/011

Cited by 87 publications

(116 citation statements)

References 26 publications

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“…In the present work, the spectroscopic parameters for three diatomic molecules (LiH, H 2 , HF) are summarized in table1 [15,16,17], dissociation energy is obtained using (eq.4) compared with another energy. and potential energy curves for two functions began with Varshni potential function for ground 1 Σ + state (eq.…”

Section: Resultsmentioning

confidence: 99%

Theoretical Study for Potential Energy Curves, Dissociation Energy and Molecular Properties for (LiH, H2, HF) Molecules

Ayaash

2015

ILCPA

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ABSTRACT.A theoretical study has been carried out of calculating dissociation energies and potential energy curves (Deng-Fan potential and Varshni potential) and molecular parameters of of ground state of diatomic molecules (LiH, H 2 , HF). Dissociation energies and potential energy curves depended on spectroscopic constants (ω e , ω e x e , r e , α, µ, β , ) and our results has been compared with experimental results. Molecular and electronic properties as ε HOMO , ε LUMO, ionization potentials (IP), electron affinities (EA) and binding energy was performed by using B3P86/6-311++g** method and Gaussian program 03, the results is well in a agreement with that of other researchers. INTRODUCTIONA potential energy curve is a graphical representation of the change in potential energy of the molecule as a function of the distortion of the bond of the molecule from its equilibrium distance. The knowledge of potential energy curves is of prime importance in the study of diatomic molecular spectra [1]. In the calculations of Franck Condon factor, dissociation energy and thermodynamic quantities etc, the studies of potential energy carves are necessary. The empirical potential energy functions like Varshni [2] and Deng-Fan potential [3] are usually applied and the potential energy carves are drawn. Naturally to compute the turning points of various vibrational levels the accurate spectroscopic constants are required. The empirical potential energy functions also require these molecular constants.Lithium hydride, the simplest stable metallic hydride, and the subject of an extensive review in 1993, continues to generate intense theoretical and spectroscopic interest. In particular, it provides a testing ground for new techniques, permits validation of approximate methods, and the existence of various isotopes allows analysis of the breakdown of the Born-Oppenheimer (BO) approximation. Of additional interest are the mutual neutralization of Li + and H − ions.[4] Hydrogen fluoride is a chemical compound with the formula HF. This colorless gas is the principal industrial source of fluorine, often in the aqueous form as hydrofluoric acid, and thus is the precursor to many important compounds. HF is widely used in the petrochemical industry and is a component of many super acids. Hydrogen fluoride boils just below room temperature whereas the other hydrogen halides condense at much lower temperatures. Unlike the other hydrogen halides, HF is lighter than air and diffuses relatively quickly through porous substances. Hydrogen fluoride is a highly dangerous gas, forming corrosive and penetrating hydrofluoric acid upon contact with tissue. The gas can also cause blindness by rapid destruction of the corneas [5,6].Theoretical determination of the dissociation energy of the simplest, prototypical chemical bond in the hydrogen molecule has a long history. It started in 1927, very shortly after the discovery of quantum mechanics, by the work of Heitler and London [7] who approximately solved the Schrödinger equation for two electrons ...

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Section: Resultsmentioning

confidence: 99%

Theoretical Study for Potential Energy Curves, Dissociation Energy and Molecular Properties for (LiH, H2, HF) Molecules

Ayaash

2015

ILCPA

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“…(27), while the parameters D 0 , D 1 and D 2 depending on the first set or the second set, are given, respectively, by Eqs. (24) and (25).…”

Section: A Possible Mass Distributionmentioning

confidence: 99%

“…Several methods have been applied to solve the Schrö-dinger equation, among which are the factorization scheme [15,16], the path integral formulation [17], the supersymmetry approach [18], the algebraic way [19], the power series expansion [20,21], the two-point quasi-rational approximation method [22], the shifted large-N procedure [23], the transfer matrix method [24,25], the asymptotic iteration method [26][27][28], the NikiforovUvarov approach [29][30][31][32], the approximation of perturbation [33] and the auxiliary field method [34].…”

Section: Introductionmentioning

confidence: 99%

Solutions of Morse potential with position-dependent mass by Laplace transform

Miraboutalebi

2016

J Theor Appl Phys

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In the framework of the position-dependent mass quantum mechanics, the three dimensional Schrödinger equation is studied by applying the Laplace transforms combining with the point canonical transforms. For the potential analogues to Morse potential and via the Pekeris approximation, we introduce the general solutions appropriate for any kind of position dependent mass profile which obeys a key condition. For a specific position-dependent mass profile, the bound state solutions are obtained through an analytical form. The constant mass solutions are also relived.

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“…where the J-matrix kinematics quantities   The stability and accuracy of the theoretical scheme that we used are mainly dependent on two parameters, the length scale parameter  and the basis space dimension, N. It is important to choose the proper range of values of  where the bound and resonant energies are stable (i.e., independent of the value of  in this range) [17].…”

Section: 6mentioning

confidence: 99%

“…However, in our scheme we used the J-matrix approach to evaluate the resonances as being the poles of corresponding S-matrix. In fact, in order to find resonance and bound state energies we use the method based on the J-matrix calculation of the scattering S-matrix, ( ) S E , in the complex energy plane which is given by [15,16] where the J-matrix kinematics quantities   The stability and accuracy of the theoretical scheme that we used are mainly dependent on two parameters, the length scale parameter  and the basis space dimension, N. It is important to choose the proper range of values of  where the bound and resonant energies are stable (i.e., independent of the value of  in this range) [17].In summary, we have investigated the inverse square potential using the J-matrix machinery. Basically we have combined the inverse square singularity with the orbital term,…”

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confidence: 99%

J-matrix method of scattering for potentials with inverse square singularity: the real representation

Alhaidari¹,

Bahlouli²,

Al-Marzoug³

et al. 2015

Phys. Scr.

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Abstract:The J-matrix method was developed to handle regular short-range scattering potentials. Its accuracy, stability, and convergence properties compare favorably with other successful scattering methods. Recently, we extended the method to the treatment of potentials with 1 r  singularity. In this work, we do the same for 2 r  singular potentials. 03.65.Nk, 03.65.Ca, 03.65.Fd, 02.30.Gp Keywords: scattering, J-matrix method, tridiagonal physics, inverse square potential. PACS:The study of singular potentials of 2 1 r type in quantum and classical mechanics is a very old subject. Classically, particles subject to such a force fall to the origin with an infinite velocity [1]. In quantum theory, however, the wavefunction oscillates indefinitely while spiraling down to the origin, leading to indeterminacy of the boundary condition at the singularity [2]. This is due to the fact that for sufficiently singular potentials the conventional methods for finding the energy eigenvalues and associated eigen-functions fail. The strong divergence of the potential at the singular point governs the leading physical behavior of the system. Consequently, the standard methods of regular quantum mechanics are supplemented by regularization or renormalization schemes  a powerful tool for studying the behavior of physical theories at various length scales [3].Generally, the origin of the problem can be looked at from different angles and has, in fact, been tackled from different perspectives. The usual dominance of the kinetic energy term in the Hamiltonian is suppressed by the dominance of the singular interaction term near the singular point. In the case of strongly singular potentials, the wavefunction is ill behaved at the boundary leading to the lack of self-adjointness of the Hamiltonian. One way to resolve this problem is to consider the concept of self-adjoint extension of the Hamiltonian. However, such an extension is not unique and the spectrum and physical consequences depend on the chosen extension scheme (e.g., the extension parameter) [3]. A second way to resolve this problem is to use regularization and renormalization approaches. That is, the potential is regularized by introducing a short cutoff distance so that the wavefunction vanishes at this cutoff causing the removal of the undefined behavior at the singular point [4]. However, it has been found that the regularization scheme is very sensitive to the cut-off radius used to regularize the singular behavior of the potential at short distances. Physical quantities, such as scattering cross section, change dramatically with small variations in the cut-off radius and hence are not uniquely defined when this cutoff parameter is vanishingly small [5]. The issue of non-equivalence of renormalization and self-adjoint extensions for such singular interaction was also raised recently [6]. Thus, caution should be exercised while using self-adjoint extensions for the singular inverse square potential. 2Aside from the above approaches there was an alternative method ba...

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The rotating Morse potential model for diatomic molecules in the tridiagonalJ-matrix representation: I. Bound states

Cited by 87 publications

References 26 publications

Theoretical Study for Potential Energy Curves, Dissociation Energy and Molecular Properties for (LiH, H<sub>2</sub>, HF) Molecules

Theoretical Study for Potential Energy Curves, Dissociation Energy and Molecular Properties for (LiH, H<sub>2</sub>, HF) Molecules

Solutions of Morse potential with position-dependent mass by Laplace transform

J-matrix method of scattering for potentials with inverse square singularity: the real representation

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