Rotation-vibrational energies for some diatomic molecules with improved Rosen–Morse potential in D-dimensions

Udoh, M. E.; Okorie, U. S.; Ngwueke, M. I.; Ituen, Eno E.; Ikot, Akpan N.

doi:10.1007/s00894-019-4040-5

Cited by 25 publications

(11 citation statements)

References 32 publications

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“…Based on this manipulation, we can further represent the MPETP as the following improved form,

U ((), r) = D_{e} {(1 - \frac{e^{r_{e} / k} - q}{e^{r / k} - q})}^{2} .

This improved version tells us that the MPETP is entirely identical to the Tietz potential for diatomic molecules . The emergence of the improved Tietz potential and its special cases has attracted great attention in the physical and chemical community due to a combination of simple forms and effective applications, including relativistic and nonrelativistic treatments of molecular vibrational energies and predictions of thermochemical quantities for some diatomics . Through the introduction of the dissociation energy and equilibrium bond length as direct parameter identifications, we have overcome the fault that the potential parameters appearing in the original MPETP given in Equation lack explicit physical definitions.…”

Section: Improved Mpetpmentioning

confidence: 99%

Improved multiparameter exponential‐type potential for diatomic molecules

Xie¹,

Jia

2019

Int J of Quantum Chemistry

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We report an improved multiparameter exponential-type potential (MPETP) energy model for diatomic molecules. It is found that this potential is identical to the Tietz potential in the realm of diatomic molecules. The efficiency of the improved MPETP is clarified by simulating the internuclear interaction potential curve for the A ( 3 Π 1 ) state of the chlorine monofluoride molecule.chlorine monofluoride, improved multiparameter exponential-type potential, internuclear interaction potential

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“…Based on this manipulation, we can further represent the MPETP as the following improved form,

U ((), r) = D_{e} {(1 - \frac{e^{r_{e} / k} - q}{e^{r / k} - q})}^{2} .

Section: Improved Mpetpmentioning

confidence: 99%

Improved multiparameter exponential‐type potential for diatomic molecules

Xie¹,

Jia

2019

Int J of Quantum Chemistry

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“…One can compare Equation () with the following equation [21, 56–59],

\frac{d^{2} R}{{italicds}^{2}} + \frac{\overset{τ}{true} ((), s)}{σ ((), s)} \frac{dR}{ds} + \frac{\overset{σ}{true} ((), s)}{σ^{2} ((), s)} R = 0,

where

\begin{matrix} lefttrue \\ \overset{false˜}{τ} (s) & = 1 - s, σ (s) = s (1 - s), \overset{false˜}{σ} (s) = - A s^{2} + B s - C . \end{matrix}

Let us consider the solution of Equation () in following form,

R ((), s) = ϕ ((), s) y ((), s) .

Then one may obtain [56],

σ ((), s) y^{″} ((), s) + τ ((), s) y^{'} ((), s) + italicνy ((), s) = 0,

and

\begin{matrix} lefttrue \\ ϕ (s) = e^{\int \frac{π (s)}{σ (s)} ds}, \end{matrix}

where

\begin{matrix} lefttrue \\ π (s) & = \frac{σ^{'} (s) - \overset{false˜}{τ} (s)}{2} \pm \sqrt{((), σ^{'} (s) ...)} \end{matrix}

…”

Section: The Methodologymentioning

confidence: 99%

Ro‐vibrational energy and thermodynamic properties of molecules subjected to Deng–Fan potential through an improved approximation

Nath

Roy

2021

Int J of Quantum Chemistry

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Accurate solution of the Schrödinger equation with Deng-Fan potential is presented by means of Nikiforov-Uvarov method. A modified Pekeris-type approximation is proposed for the centrifugal term, from a linear combination of the r ! 0 and r ! r e limits. It can potentially offer a series of approximations (depending on an adjustable parameter λ). The existing approximations in the literature can then be recovered in certain special cases. Its efficiency and feasibility is demonstrated by a critical comparison of eigenvalues produced at various λ's for four molecules, namely, H 2 , LiH, HCl and CO. Analytical expressions are derived for energies, eigenfunctions and the thermodynamic properties such as vibrational mean free energy, vibrational free energy, vibrational entropy and vibrational specific heat. The effect of quantum correction on partition function and thermodynamic properties is discussed by including the correction up to 10th-order, for H 2 and LiH. The effect of λ parameter on these properties is also studied.

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“…quarks-fundammental constituents of hadrons and other areas of modern chemistry [22,23] and physics [24].…”

Section: The Trm Oscillatormentioning

confidence: 99%

“…In this work, we extend the research area to construct the minimum-uncertainty coherent states of the hyperbolic Rosen-Morse (HRM) [16] and trigonometric Rosen-Morse (TRM) oscillators [17]. Those models are widely used in many areas of exact sciences including quantum chromodynamics (quark interactions) [18], N-fold supersymmetries in Schrödinger, Pauli and Dirac equations [19], SUSYQM [17,20], the theory of molecular vibrations [16,21] and other fields of modern chemistry [22,23] and physics [24].…”

Section: Introductionmentioning

confidence: 99%

Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

Molski

2021

J Math Chem

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A mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.

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Rotation-vibrational energies for some diatomic molecules with improved Rosen–Morse potential in D-dimensions

Cited by 25 publications

References 32 publications

Improved multiparameter exponential‐type potential for diatomic molecules

Improved multiparameter exponential‐type potential for diatomic molecules

Ro‐vibrational energy and thermodynamic properties of molecules subjected to Deng–Fan potential through an improved approximation

Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

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