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Information theory and thermodynamic properties of diatomic molecules using molecular potential

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Abstract

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg’s uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

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References

  1. Heisenberg W (1927) Z Physik 43:172

    Article  Google Scholar 

  2. Mukherjee N, Roy AK (2018) Ann Phys 398:190

    Article  CAS  Google Scholar 

  3. Onate CA, Onyeaju MC, Ikot AN, Ebomwonyi O, Idiodi JOA (2019) Int J Quantum Chem E25991. https://doi.org/10.1992/qua.25991

  4. Onate CA, Onyeaju MC, Ikot AN, Ebomwonyi O (2017) Eur Phys J Plus 132:462

    Article  Google Scholar 

  5. Onate CA, Idiodi JOA (2016) Commun Theor Phys 66:275

    Article  Google Scholar 

  6. Torres-Arenas AJ, Dong Q, Sun GH, Dong SH (2018) Phys Lett A 382:1752

    Article  CAS  Google Scholar 

  7. Aygun A, Bayrak O, Boztosun I (2007) J Phys B At Mol Opt Phys 40:537

    Article  CAS  Google Scholar 

  8. Isonguyo CN, Oyewumi KJ, Oyun OS (2018) Int J Quant Chem 118:025620

    Article  Google Scholar 

  9. Romera E, Sánchez-Moreno P, Dehesa JS (2005) Chem Phys Lett 414:468

  10. Romera E, Sánchez-moreno P, Dehesa JS (2006) J Math Phys 47:103504

    Article  Google Scholar 

  11. Gonzalez-Ferez R, Dehesa JS (2005) Eur Phys J D 32:39

    Article  CAS  Google Scholar 

  12. Fisher RA (1925) Proc Cambridge Philos Soc 22:700

    Article  Google Scholar 

  13. Shannon CE (1948) Bell Syst Technol J 27:379

    Article  Google Scholar 

  14. Esquivel RO, Molina-Espıritu M, Angulo JC, Antolın J, Flores-Gallegos N, Dehesa JS (2011) Mole Phys 109:2353

    Article  CAS  Google Scholar 

  15. Esquivel RO, Flores-Gallegos N, Iuga C, Carrera EM, Angulo JC, Antolın J (2009) Theor Chem Acc 124:445

    Article  CAS  Google Scholar 

  16. Sañudo J, López-Ruiz R (2012) Phys Lett A 376:2288

    Article  Google Scholar 

  17. Rawlings ES, Barrera-Martinez JC, Rico-Ramirez V (2020) Ecol Modell 416:108845

    Article  Google Scholar 

  18. Fath BD, Cabezas H (2004) Ecol Modell 174:25

    Article  Google Scholar 

  19. Tang B, Wang YT, Peng XL, Zhang LH, Jia CS (2020) J Mol Strut 1199:126958

    Article  CAS  Google Scholar 

  20. Jia CS, Youa XT, Liua JY, Zhanga LH, Penga XL, Wanga YT, Wei LS (2019) Chem Phys Lett 717:16

    Article  CAS  Google Scholar 

  21. Jiang R, Jia C-S, Wang Y-Q, Peng X-L, Zhang LH (2019) Chem Phys Lett 726:83

    Article  CAS  Google Scholar 

  22. Jia CS, Wang YT, Wei LS, Wang CW, Peng XL, Zhang LH (2019) ACS Omega 4:20000

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Jia CS, Zeng R, Peng XL, Zhang LH, Zhao YL (2018) Chem Eng Sci 190:1

    Article  Google Scholar 

  24. Jia CS, Wang CW, Zhang LH, Peng XL, Tang HM, Zeng R (2018) Chem Eng Sci 183:26

    Article  CAS  Google Scholar 

  25. Peng XL, Jiang R, Jia CS, Zhang LH, Zhao YL (2018) Chem Eng Sci 190:122

    Article  CAS  Google Scholar 

  26. Jia CS, Zhang LH, Peng XL, Luo JX, Zhao YL, Liu JY, Guo JJ, Tang LD (2019) Chem Eng Sci 202:70

    Article  CAS  Google Scholar 

  27. Jiang R, Jia CS, Wang YQ, Peng XL, Zhang LH (2019) Chem Phys Lett 715:186

    Article  CAS  Google Scholar 

  28. Song XQ, Wang CW, Jia CS (2017) Chem Phys Lett 673:50

    Article  CAS  Google Scholar 

  29. Wang J, Jia CS, Li CJ, Peng XL, Zhang LH, Liu JY (2019) ACS Omega 4:19193

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Jia CS, Zhang LH, Wang CW (2017) Phys Lett 667:211

    CAS  Google Scholar 

  31. Chen XY, Li J, Jia CS (2019) ACS Omega 4:16121

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Ikot AN, Chukwuocha EO, Onyeaju MC, Onate CA, Ita BI, Udoh ME (2018) Pramana J Phys 90:22

    Article  Google Scholar 

  33. Onate CA, Ikot AN, Onyeaju MC, Ebomwonyi O, Idiodi JOA (2018) Karbala Int J Mod Sci 4:134

    Article  Google Scholar 

  34. Onate CA, Onyeaju MC, Bankole DT, Ikot AN (2020) J Mol Mod 26:311

    Article  CAS  Google Scholar 

  35. Solaimani M, Dong SH (2019) Int J Quant Chem 120:e26113

    Article  Google Scholar 

  36. Carrillo R, Gil-Barrera CA, Sun GH, Dong SH (2021) Eur Phys J Plus 136:1060

    Article  Google Scholar 

  37. Carrillo RS, Dong Q, Sun GH, Silva-Ortigoza R, Dong SH (2022) Results in Physics n22:105109

  38. Sun GH, Dong SH, Saad N (2013) Ann Phys 525:934

    Article  Google Scholar 

  39. Majumdar S, Mukherjee N, Roy AK (2019) Chem Phys Lett 716:257

    Article  CAS  Google Scholar 

  40. Onyeaju CA (2020) Onate. Few-Body Syst 61:21

    Article  Google Scholar 

  41. Onate CA, Onyeaju MC, Ikot AN, Idiodi JOA, Ojonubah JO (2017) JKPS 70:339

    Article  Google Scholar 

  42. Omugbe E (2020) Can J Chem 98:683

    Article  CAS  Google Scholar 

  43. Gordillo-Vázquez FJ, Kunc JA (1998) J Appl Phys 84:4693

    Article  Google Scholar 

  44. Ghanbari A, Khordad R (2021). Indian J Phys. https://doi.org/10.1007/s12348-021-02086-1

    Article  Google Scholar 

  45. Yanar H, Aydogdu O, Salti M (2016) Mol Phys 114:3134

    Article  CAS  Google Scholar 

  46. Al-Raeei M (2022) J Phys Condens Matter 34:284001

  47. De Oliveira D (2023). Can J Phys. https://doi.org/10.1139/cjp-2023-0146

    Article  Google Scholar 

  48. Pingak RK, Johannes AZ, Ngara ZS, Bukit M, Nitti F, Tambaru D, Ndii MZ (2021) Results Chem 3:100204

    Article  CAS  Google Scholar 

  49. Varshni YP (1957) Rev Mod Phys 29:664

    Article  CAS  Google Scholar 

  50. Ikhdair SM (2012) ISRN Math Phys 201525:1

  51. Tezcan C, Sever R (2009) Int J Theor Phys 48:337

    Article  Google Scholar 

  52. Omugbe E, Osafile OE, Okon IB, Enaibe EA, Onyeaju MC (2021) Mol Phys 119:e1909163

    Article  Google Scholar 

  53. Olendski O (2021) Int J Quant Chem 121:e26455

    Article  CAS  Google Scholar 

  54. Olendski O (2019) Eur J Phys 40:025402

    Article  Google Scholar 

  55. Sun GH, Avila AM, Dong SH (2013) Chin Phys B 22:050302

    Article  Google Scholar 

  56. Valencia-Torres R, Sun GH, Dong SH (2015) Phys Scr 90:035205

    Article  Google Scholar 

  57. Strekalov ML (2007) Chem Phys Lett 439:209

    Article  CAS  Google Scholar 

  58. Jia CS, Wang CW, Zhang LH, Peng XL, Zeng R, You XT (2017) Chem Phys Lett 676:150

    Article  CAS  Google Scholar 

  59. Stratt RM, Miller WH (1977) J Chem Phys 67:5894

    Article  CAS  Google Scholar 

  60. Guo J, Liu Y (2021) Commun Theor Phys 73:075002

    Article  Google Scholar 

  61. Eyube ES, Notani PP, Yabwa D, Omugbe E, Onate CA, Okon IB, Nyam GG, Jabil YY, Izam MM (2022) Int J Quantum Chem 123(5):e27040

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Acknowledgements

It is our pleasure for us to thank the kind referee for his many useful comments and suggestions, which greatly helped us in making improvements to this paper.

Author information

Authors and Affiliations

  1. Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Rivers State, Nigeria

    M. C. Onyeaju & A. N. Ikot

  2. Department of Physics, Faculty of Basic and Applied Science, University of Africa, Toru-Orua, Bayelsa State, Nigeria

    M. C. Onyeaju

  3. Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria

    E. Omugbe

  4. Department of Physics, Kogi State University, Anyigba, Kogi State, Nigeria

    C. A. Onate

  5. Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria

    I. B. Okon

  6. Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria

    E. S. Eyube

  7. Department of Physics, Akwa Ibom State University, P.M.B 1167, Ikot AkpodenUyo, Nigeria

    U. S. Okorie

  8. Department of Physics, Faculty of Science, University of Delta, Agbor, Delta State, Nigeria

    D. A. Ogwu & P. O. Osuhor

Authors
  1. M. C. Onyeaju
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  2. E. Omugbe
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  3. C. A. Onate
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  4. I. B. Okon
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  5. E. S. Eyube
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  6. U. S. Okorie
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  7. A. N. Ikot
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  8. D. A. Ogwu
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  9. P. O. Osuhor
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Contributions

MCO and ANI wrote the original draft. EO, USO and CAO carried out data curation and computations. EO, ESE and IBO validated the results. DAO and OPO carried out discussion of results.

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Correspondence to M. C. Onyeaju.

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Onyeaju, M.C., Omugbe, E., Onate, C.A. et al. Information theory and thermodynamic properties of diatomic molecules using molecular potential. J Mol Model 29, 311 (2023). https://doi.org/10.1007/s00894-023-05708-z

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