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The Heat Capacity of Triatomic Gases: An Analytical Approach

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Abstract

This paper reports an efficient closed-form representation of the heat capacity of linear triatomic molecules. An approximate method is proposed for factorizing the vibrational and rotational contributions to the ro-vibrational partition function using average vibrational quantum numbers. Single-valued analytical representations of the vibrational and rotational partition functions are also derived. The reliability of the proposed method for calculating heat capacity is verified by comparison with experimental data and theoretical calculations using the direct summation method with exact values of energy levels. The new approach is much more efficient than the explicit sum-over-states method.

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References

  1. X.-Q. Song, C.-W. Wang, C.-S. Jia, Thermodynamic properties for the sodium dimer. Chem. Phys. Lett. 673, 50 (2017). https://doi.org/10.1016/j.cplett.2017.02.010

    Article  ADS  CAS  Google Scholar 

  2. C.-J. Jia, L.-H. Zhang, C.-W. Wang, Thermodynamic properties for the lithium dimer. Chem. Phys. Lett. 667, 211 (2017). https://doi.org/10.1016/j.cplett.2016.11.059

    Article  ADS  CAS  Google Scholar 

  3. B. Tang, Y.-T. Wang, X.-L. Peng, L.-H. Zhang, C.-J. Jia, Efficient predictions of Gibbs free energy for the gases CO, BF, and gaseous BBr. J. Mol. Struct. 1199, 126958 (2020). https://doi.org/10.1016/j.molstruc.2019.126958

    Article  CAS  Google Scholar 

  4. H. Louis, B.I. Ita, N.I. Nzeata, Approximate solution of the Schrödinger equation with Manning-Rosen plus Hellmann potential and its thermodynamic properties using the proper quantization rule. Eur. Phys. J. Plus 134, 315 (2019). https://doi.org/10.1140/epjp/i2019-12835-3

    Article  Google Scholar 

  5. A. Diaf, M. Hachama, M.M. Ezzine, Thermodynamic properties for some diatomic molecules with the q-deformed hyperbolic barrier potential. Mol. Phys. 121, e2198045 (2023). https://doi.org/10.1080/00268976.2023.2198045

    Article  ADS  CAS  Google Scholar 

  6. C.A. Onate, M.C. Onyeaju, U.S. Okorie, A.N. Ikot, Thermodynamic functions for boron nitride with q-deformed exponential type potential. Results Phys. 16, 102959 (2020). https://doi.org/10.1016/j.rinp.2020.102959

    Article  Google Scholar 

  7. G.-H. Liu, Q.-C. Ding, C.-W. Wang, C.-S. Jia, Unified non-fitting explicit formulation of thermodynamic properties for five compounds. J. Mol. Struct. 1294, 136543 (2023). https://doi.org/10.1016/j.molstruc.2023.136543

    Article  CAS  Google Scholar 

  8. G.-H. Liu, Q.-C. Ding, C.-W. Wang, C.-S. Jia, Unified explicit formulations of thermodynamic properties for the gas NO2, and gaseous BF2 and AlCl2 radicals. Chem. Phys. Lett. 830, 140788 (2023). https://doi.org/10.1016/j.cplett.2023.140788

    Article  CAS  Google Scholar 

  9. C.-W. Wang, J. Wang, Y.-S. Liu, J. Li, X.-L. Peng, C.-S. Jia, L.-H. Zhang, L.-Z. Yi, J.-Y. Liu, C.-J. Li, X. Jia, Prediction of the ideal-gas thermodynamic properties for water. J. Mol. Liquids 321, 114912 (2021). https://doi.org/10.1016/j.molliq.2020.114912

    Article  CAS  Google Scholar 

  10. Q. Dong, H.I. GarsíaHernández, G.-H. Sun, M. Toutounji, S.-H. Dong, Exact solutions of the harmonic oscillator plus non-polynomial interaction. Proc. R. Soc. A 476, 20200050 (2020). https://doi.org/10.1098/rspa.2020.0050

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  11. M.L. Strekalov, On the partition function of Morse oscillators. Chem. Phys. Lett. 393, 192 (2004). https://doi.org/10.1016/j.cplett.2004.06.028

    Article  ADS  CAS  Google Scholar 

  12. M.L. Strekalov, An accurate closed-form expression for the rovibrational partition function of diatomic molecules. Chem. Phys. Lett. 764, 138262 (2021). https://doi.org/10.1016/j.cplett.2020.138262

    Article  CAS  Google Scholar 

  13. M.L. Strekalov, Rigorous factorization method of the vibrational and rotational contributions to the ro-vibrational partition function. Comput. Theor. Chem. 1202, 113337 (2021). https://doi.org/10.1016/j.comptc.2021.113337

    Article  CAS  Google Scholar 

  14. P.S. Dardy, J.S. Dahler, Equilibrium constants for the formation of van der Waals dimers: calculations for Ar-Ar and Mg-Mg. J. Chem. Phys. 93, 3562 (1990). https://doi.org/10.1063/1.458788

    Article  ADS  Google Scholar 

  15. F.V. Prudente, A. Riganelli, A.J.C. Varandas, Calculation of the rovibrational partition function using classical methods with quantum corrections. J. Phys. Chem. A 105, 5272 (2001). https://doi.org/10.1021/jp0043928

    Article  CAS  Google Scholar 

  16. L.V. Gurvich, I.V. Veyts, C.B. Alcock, Thermodynamic Properties of Individual Substances, vol. 1, 4th edn. (Hemisphere, New York, 1991)

    Google Scholar 

  17. Y. Babou, Ph. Rivière, M.-Y. Perrin, A. Soufiani, High-temperature and nonequilibrium partition function and thermodynamic data of diatomic molecules. Int. J. Thermophys. 30, 416 (2009). https://doi.org/10.1007/s10765-007-0288-6

    Article  ADS  CAS  Google Scholar 

  18. A.W. Irwin, Refined diatomic partition functions. I. Calculational methods and H2 and CO results. Astron. Astrophys. 182, 348 (1987)

    ADS  CAS  Google Scholar 

  19. Z. Qin, J.-M. Zhao, L.-H. Liu, High-temperature partition functions, specific heats and spectral radiative properties of diatomic molecules with an improved calculation of energy levels. JQSRT 210, 1 (2018). https://doi.org/10.1016/j.jqsrt.2018.02.004

    Article  ADS  CAS  Google Scholar 

  20. C.-S. Jia, C.-W. Wang, L.-H. Zhang, X.-L. Peng, R. Zeng, X.-T. You, Partition function of improved Tietz oscillators. Chem. Phys. Lett. 676, 150 (2017). https://doi.org/10.1016/j.cplett.2017.03.068

    Article  ADS  CAS  Google Scholar 

  21. C.O. Edet, U.S. Okorie, G. Osobonye, A.N. Ikot, G.J. Rampho, R. Sever, Thermal properties of Deng–Fan–Eckart potential model using Poisson summation approach. J. Math. Chem. 58, 989 (2020). https://doi.org/10.1007/s10910-020-01107-4

    Article  MathSciNet  CAS  Google Scholar 

  22. M.L. Strekalov, An accurate closed-form expression for the partition function of Morse oscillators. Chem. Phys. Lett. 439, 209 (2007). https://doi.org/10.1016/j.cplett.2007.03.052

    Article  ADS  CAS  Google Scholar 

  23. G.T. Osobonye, M. Adekanmbi, A.N. Ikot, U.S. Okorie, G.J. Rampho, Thermal properties of anharmonic Eckart potential model using Euler–MacLaurin formula. Pranama-J. Phys. 95, 98 (2021). https://doi.org/10.1007/s12043-021-02122-z

    Article  ADS  Google Scholar 

  24. H.J. Korsch, A new semiclassical expansion of the thermodynamic partition function. J. Phys. A 12, 1521 (1979). https://doi.org/10.1088/0305-4470/12/9/019

    Article  ADS  MathSciNet  Google Scholar 

  25. A.J. Thakkar, A technique for increasing the utility of the wigner-kirkwood expansion for the second virial coefficient. Mol. Phys. 36, 887 (1978). https://doi.org/10.1080/00268977800102011

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. H.H. Nielson, The vibration-rotation energies of molecules. Rev. Mod. Phys. 23, 90 (1951). https://doi.org/10.1103/RevModPhys.23.90

    Article  ADS  Google Scholar 

  27. R.H. Tipping, J.F. Ogilvie, The influence of the potential function on vibration-rotation wave functions and matrix elements of diatomic molecules. J. Mol. Struct. 35, 1 (1976). https://doi.org/10.1016/0022-2860(76)80100-7

    Article  ADS  CAS  Google Scholar 

  28. J. Goodsman, Diatomic Interaction Potential Theory (Academic Press, New York, 1973)

    Google Scholar 

  29. K.B. Wolf, Integral Transforms in Science and Engineering (Plenum Press, New York, 1979)

    Book  Google Scholar 

  30. R.S. McDowell, Rotational partition functions for linear molecules. J. Chem. Phys. 88, 356 (1988). https://doi.org/10.1063/1.454608

    Article  ADS  CAS  Google Scholar 

  31. J.E. Kilpatrick, R. Kayser, Direct partition function of the rigid diatomic rotor. J. Chem. Phys. 63, 5216 (1975). https://doi.org/10.1063/1.431305

    Article  ADS  CAS  Google Scholar 

  32. V.M. Osipov, Partition sums and dissociation energy for 12C16O2 at high temperatures. Mol. Phys. 102, 1785 (2004). https://doi.org/10.1080/00268970412331287016

    Article  ADS  CAS  Google Scholar 

  33. NIST Chemistry WebBook, NIST Standard Reference Database Number 69. https://doi.org/10.18434/T4D303

  34. M. Buchowiecki, Vibrational partition function for the multi-temperature theories of high-temperature flows of gases and plasmas. J. Phys. Chem. A 124, 4048 (2020). https://doi.org/10.1021/acs.jpca.0c01161

    Article  CAS  PubMed  Google Scholar 

  35. P. Sarkar, N. Poulin, T. Carrington, Calculating rovibrational energy levels of a triatomic molecule with a simple Lanczos method. J. Chem. Phys. 110, 10269 (1999). https://doi.org/10.1063/1.478960

    Article  ADS  CAS  Google Scholar 

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  1. Theoretical Chemistry Laboratory, Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, 3 Institutskaya Street, Novosibirsk, Russia, 630090

    Mikhail L. Strekalov

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MLS wrote the main manuscript text and prepared figures 1-5. Author reviewed the manuscript.

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Strekalov, M.L. The Heat Capacity of Triatomic Gases: An Analytical Approach. Int J Thermophys 45, 25 (2024). https://doi.org/10.1007/s10765-023-03315-x

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