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Rotational-Vibrational Energy Levels for the 𝑿𝟏𝚺+ State of 𝐑𝐛𝐇 Molecule

Yıl 2023, Cilt: 9 Sayı: 1, 99 - 106, 30.06.2023
https://doi.org/10.29132/ijpas.1274351

Öz

In this study, the more suitable potential energy function to model the experimental (observed) vibrational energy levels of the 𝑅𝑏𝐻(𝑋1Σ+) molecule has been determined by using the energy eigenvalue equations obtained for the general molecular potential (GMP) and the improved generalized Pöschl–Teller (IGPT) potential. In addition, by considering suitable potential energy function and the Pekeris-type approximation, which is the most appropriate approach to the centrifugal term in the discussion of bound states, the more accurate rotational-vibration energies of the 𝑅𝑏𝐻(𝑋1Σ+) molecule have been found.

Kaynakça

  • Du, J. F., Guo, P., & Jia, C. S. (2014). D-dimensional energies for scandium monoiodide. Journal of Mathematical Chemistry, 52, 2559-2569.
  • Eyube, E. S., Bitrus, B. M., & Jabil, Y. Y. (2021). Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules. Journal of Physics B: Atomic, Molecular and Optical Physics, 54(15), 155102.
  • Eyube, E. S., Notani, P. P., & Dikko, A. B. (2022). Modeling of diatomic molecules with modified hyperbolical-type potential. The European Physical Journal Plus, 137(3), 329.
  • Ezzine, M. M., Hachama, M., & Diaf, A. (2021). Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules. Physica Scripta, 96(12), 125260.
  • Frost, A. A., & Musulin, B. (1954). The Possible Existence of a Reduced Potential Energy Function for Diatomic Molecules1. Journal of the American Chemical Society, 76(8), 2045-2048.
  • Greene, R. L., & Aldrich, C. (1976). Variational wave functions for a screened Coulomb potential. Physical Review A, 14(6), 2363.
  • Hsieh, Y. K., Yang, S. C., Tam, A. C., Verma, K. K., & Stwalley, W. C. (1980). The RKR potential energy curves for the X1Σ+ and A1Σ+ states of RbH. Journal of Molecular Spectroscopy, 83(2), 311-316.
  • Jia, C. S., Diao, Y. F., Liu, X. J., Wang, P. Q., Liu, J. Y., & Zhang, G. D. (2012). Equivalence of the Wei potential model and Tietz potential model for diatomic molecules. The Journal of chemical physics, 137(1), 014101.
  • Kisoglu, H. F., Yanar, H., Aydogdu, O., & Salti, M. (2019). Relativistic spectral bounds for the general molecular potential: application to a diatomic molecule. Journal of molecular modeling, 25, 1-11.
  • Liu, J. Y., Zhang, G. D., & Jia, C. S. (2013). Calculation of the interaction potential energy curve and vibrational levels for the a3Σu+ state of Li27 molecule. Physics Letters A, 377(21-22), 1444-1447.
  • Morse, P. M. (1929). Diatomic molecules according to the wave mechanics. II. Vibrational levels. Physical review, 34(1), 57.
  • Mustafa, O. (2015a). On the ro–vibrational energies for the lithium dimer; maximum-possible rotational levels. Journal of Physics B: Atomic, Molecular and Optical Physics, 48(6), 065101.
  • Mustafa, O. (2015b). A new deformed Schiöberg-type potential and ro-vibrational energies for some diatomic molecules. Physica Scripta, 90(6), 065002.
  • Ocak, Z., Yanar, H., Salti, M., & Aydogdu, O. (2018). Relativistic spinless energies and thermodynamic properties of sodium dimer molecule. Chemical Physics, 513, 252-257.
  • Okorie, U. S., Ikot, A. N., & Chukwuocha, E. O. (2020). Approximate energy spectra of improved generalized Mobius square potential (IGMSP) for some diatomic hydride molecules. Journal of Molecular Modeling, 26, 1-9.
  • Pekeris, C. L. (1934). The rotation-vibration coupling in diatomic molecules. Physical Review, 45(2), 98.
  • Varshni, Y. P. (1957). Comparative study of potential energy functions for diatomic molecules. Reviews of Modern Physics, 29(4), 664.
  • Wang, P. Q., Liu, J. Y., Zhang, L. H., Cao, S. Y., & Jia, C. S. (2012). Improved expressions for the Schiöberg potential energy models for diatomic molecules. Journal of Molecular Spectroscopy, 278, 23-26.
  • Wang, P. Q., Zhang, L. H., Jia, C. S., & Liu, J. Y. (2012). Equivalence of the three empirical potential energy models for diatomic molecules. Journal of Molecular Spectroscopy, 274, 5-8.
  • Yanar, H. (2022a). More accurate ro-vibrational energies for SiF+(X 1Σ+) molecule. Physica Scripta, 97(4), 045404.
  • Yanar, H. (2022b). Comment on ‘Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules’. Journal of Physics B: Atomic, Molecular and Optical Physics, 55(17), 178001.
  • Yanar, H., Aydoğdu, O., & Saltı, M. (2016). Modelling of diatomic molecules. Molecular Physics, 114(21), 3134-3142.
  • Yanar, H., Taş, A., Salti, M., & Aydogdu, O. (2020). Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation. The European Physical Journal plus, 135(3), 292.
  • Zhang, G. D., Liu, J. Y., Zhang, L. H., Zhou, W., & Jia, C. S. (2012). Modified Rosen-Morse potential-energy model for diatomic molecules. Physical Review A, 86(6), 062510.

RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri

Yıl 2023, Cilt: 9 Sayı: 1, 99 - 106, 30.06.2023
https://doi.org/10.29132/ijpas.1274351

Öz

Bu çalışmada genel moleküler (GM) potansiyel ve geliştirilmiş genelleştirilmiş Pöschl–Teller (GGPT) potansiyeli için elde edilmiş enerji özdeğer denklemleri kullanılarak, RbH(X^1 Σ^+) molekülünün deneysel (gözlenen) titreşim enerji seviyelerini modelleyebilecek en iyi potansiyel enerji fonksiyonu belirlenmiştir. Ayrıca, bu potansiyel enerji fonksiyonu ve bağlı durumların tartışılmasında merkezcil terime uygulanabilecek en uygun yaklaşım olan Pekeris tipi yaklaşım ele alınarak RbH(X^1 Σ^+) molekülünün en olası dönme-titreşim enerjileri elde edilmiştir.

Kaynakça

  • Du, J. F., Guo, P., & Jia, C. S. (2014). D-dimensional energies for scandium monoiodide. Journal of Mathematical Chemistry, 52, 2559-2569.
  • Eyube, E. S., Bitrus, B. M., & Jabil, Y. Y. (2021). Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules. Journal of Physics B: Atomic, Molecular and Optical Physics, 54(15), 155102.
  • Eyube, E. S., Notani, P. P., & Dikko, A. B. (2022). Modeling of diatomic molecules with modified hyperbolical-type potential. The European Physical Journal Plus, 137(3), 329.
  • Ezzine, M. M., Hachama, M., & Diaf, A. (2021). Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules. Physica Scripta, 96(12), 125260.
  • Frost, A. A., & Musulin, B. (1954). The Possible Existence of a Reduced Potential Energy Function for Diatomic Molecules1. Journal of the American Chemical Society, 76(8), 2045-2048.
  • Greene, R. L., & Aldrich, C. (1976). Variational wave functions for a screened Coulomb potential. Physical Review A, 14(6), 2363.
  • Hsieh, Y. K., Yang, S. C., Tam, A. C., Verma, K. K., & Stwalley, W. C. (1980). The RKR potential energy curves for the X1Σ+ and A1Σ+ states of RbH. Journal of Molecular Spectroscopy, 83(2), 311-316.
  • Jia, C. S., Diao, Y. F., Liu, X. J., Wang, P. Q., Liu, J. Y., & Zhang, G. D. (2012). Equivalence of the Wei potential model and Tietz potential model for diatomic molecules. The Journal of chemical physics, 137(1), 014101.
  • Kisoglu, H. F., Yanar, H., Aydogdu, O., & Salti, M. (2019). Relativistic spectral bounds for the general molecular potential: application to a diatomic molecule. Journal of molecular modeling, 25, 1-11.
  • Liu, J. Y., Zhang, G. D., & Jia, C. S. (2013). Calculation of the interaction potential energy curve and vibrational levels for the a3Σu+ state of Li27 molecule. Physics Letters A, 377(21-22), 1444-1447.
  • Morse, P. M. (1929). Diatomic molecules according to the wave mechanics. II. Vibrational levels. Physical review, 34(1), 57.
  • Mustafa, O. (2015a). On the ro–vibrational energies for the lithium dimer; maximum-possible rotational levels. Journal of Physics B: Atomic, Molecular and Optical Physics, 48(6), 065101.
  • Mustafa, O. (2015b). A new deformed Schiöberg-type potential and ro-vibrational energies for some diatomic molecules. Physica Scripta, 90(6), 065002.
  • Ocak, Z., Yanar, H., Salti, M., & Aydogdu, O. (2018). Relativistic spinless energies and thermodynamic properties of sodium dimer molecule. Chemical Physics, 513, 252-257.
  • Okorie, U. S., Ikot, A. N., & Chukwuocha, E. O. (2020). Approximate energy spectra of improved generalized Mobius square potential (IGMSP) for some diatomic hydride molecules. Journal of Molecular Modeling, 26, 1-9.
  • Pekeris, C. L. (1934). The rotation-vibration coupling in diatomic molecules. Physical Review, 45(2), 98.
  • Varshni, Y. P. (1957). Comparative study of potential energy functions for diatomic molecules. Reviews of Modern Physics, 29(4), 664.
  • Wang, P. Q., Liu, J. Y., Zhang, L. H., Cao, S. Y., & Jia, C. S. (2012). Improved expressions for the Schiöberg potential energy models for diatomic molecules. Journal of Molecular Spectroscopy, 278, 23-26.
  • Wang, P. Q., Zhang, L. H., Jia, C. S., & Liu, J. Y. (2012). Equivalence of the three empirical potential energy models for diatomic molecules. Journal of Molecular Spectroscopy, 274, 5-8.
  • Yanar, H. (2022a). More accurate ro-vibrational energies for SiF+(X 1Σ+) molecule. Physica Scripta, 97(4), 045404.
  • Yanar, H. (2022b). Comment on ‘Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules’. Journal of Physics B: Atomic, Molecular and Optical Physics, 55(17), 178001.
  • Yanar, H., Aydoğdu, O., & Saltı, M. (2016). Modelling of diatomic molecules. Molecular Physics, 114(21), 3134-3142.
  • Yanar, H., Taş, A., Salti, M., & Aydogdu, O. (2020). Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation. The European Physical Journal plus, 135(3), 292.
  • Zhang, G. D., Liu, J. Y., Zhang, L. H., Zhou, W., & Jia, C. S. (2012). Modified Rosen-Morse potential-energy model for diatomic molecules. Physical Review A, 86(6), 062510.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Hilmi Yanar 0000-0002-6913-8441

Erken Görünüm Tarihi 23 Haziran 2023
Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 31 Mart 2023
Kabul Tarihi 4 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 9 Sayı: 1

Kaynak Göster

APA Yanar, H. (2023). RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri. International Journal of Pure and Applied Sciences, 9(1), 99-106. https://doi.org/10.29132/ijpas.1274351
AMA Yanar H. RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri. International Journal of Pure and Applied Sciences. Haziran 2023;9(1):99-106. doi:10.29132/ijpas.1274351
Chicago Yanar, Hilmi. “RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri”. International Journal of Pure and Applied Sciences 9, sy. 1 (Haziran 2023): 99-106. https://doi.org/10.29132/ijpas.1274351.
EndNote Yanar H (01 Haziran 2023) RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri. International Journal of Pure and Applied Sciences 9 1 99–106.
IEEE H. Yanar, “RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri”, International Journal of Pure and Applied Sciences, c. 9, sy. 1, ss. 99–106, 2023, doi: 10.29132/ijpas.1274351.
ISNAD Yanar, Hilmi. “RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri”. International Journal of Pure and Applied Sciences 9/1 (Haziran 2023), 99-106. https://doi.org/10.29132/ijpas.1274351.
JAMA Yanar H. RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri. International Journal of Pure and Applied Sciences. 2023;9:99–106.
MLA Yanar, Hilmi. “RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri”. International Journal of Pure and Applied Sciences, c. 9, sy. 1, 2023, ss. 99-106, doi:10.29132/ijpas.1274351.
Vancouver Yanar H. RbH Molekülünün X^1 Σ^+ Durumu için Dönme-Titreşim Enerji Seviyeleri. International Journal of Pure and Applied Sciences. 2023;9(1):99-106.

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