A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the p...

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Autores principales:	Redi Kristian Pingak, Albert Zicko Johannes, Fidelis Nitti, Meksianis Zadrak Ndii
Formato:	article
Lenguaje:	EN
Publicado:	Department of Chemistry, Universitas Gadjah Mada 2021
Materias:	semi-classical approximation classical potential functions hydrogen isotopes bohr-sommerfeld quantization Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/59e3fd702800449a8d50444a434b50a0
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id	oai:doaj.org-article:59e3fd702800449a8d50444a434b50a0
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spelling	oai:doaj.org-article:59e3fd702800449a8d50444a434b50a02021-12-02T15:56:44ZA Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation1411-94202460-157810.22146/ijc.63294https://doaj.org/article/59e3fd702800449a8d50444a434b50a02021-04-01T00:00:00Zhttps://jurnal.ugm.ac.id/ijc/article/view/63294https://doaj.org/toc/1411-9420https://doaj.org/toc/2460-1578This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.Redi Kristian PingakAlbert Zicko JohannesFidelis NittiMeksianis Zadrak NdiiDepartment of Chemistry, Universitas Gadjah Madaarticlesemi-classical approximationclassical potential functionshydrogen isotopesbohr-sommerfeld quantizationChemistryQD1-999ENIndonesian Journal of Chemistry, Vol 21, Iss 3, Pp 725-739 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	semi-classical approximation classical potential functions hydrogen isotopes bohr-sommerfeld quantization Chemistry QD1-999
spellingShingle	semi-classical approximation classical potential functions hydrogen isotopes bohr-sommerfeld quantization Chemistry QD1-999 Redi Kristian Pingak Albert Zicko Johannes Fidelis Nitti Meksianis Zadrak Ndii A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
description	This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.
format	article
author	Redi Kristian Pingak Albert Zicko Johannes Fidelis Nitti Meksianis Zadrak Ndii
author_facet	Redi Kristian Pingak Albert Zicko Johannes Fidelis Nitti Meksianis Zadrak Ndii
author_sort	Redi Kristian Pingak
title	A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
title_short	A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
title_full	A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
title_fullStr	A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
title_full_unstemmed	A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation
title_sort	theoretical study on vibrational energies of molecular hydrogen and its isotopes using a semi-classical approximation
publisher	Department of Chemistry, Universitas Gadjah Mada
publishDate	2021
url	https://doaj.org/article/59e3fd702800449a8d50444a434b50a0
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A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

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