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H2和HD分子宏观热力学性质

刘显洋 姚嘉薇 杨俊锋 樊群超 范志祥 田洪瑞

引用本文:
Citation:

H2和HD分子宏观热力学性质

刘显洋, 姚嘉薇, 杨俊锋, 樊群超, 范志祥, 田洪瑞
cstr: 32037.14.aps.74.20241793

Macroscopic thermodynamic properties of H2 and HD

LIU Xianyang, YAO Jiawei, YANG Junfeng, FAN Qunchao, FAN Zhixiang, TIAN Hongrui
cstr: 32037.14.aps.74.20241793
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  • 本文通过扩展的改进多参数指数型(the extended improved multiparameter exponential-type, EIMPET)势能模型, 结合实验光谱数据, 研究了H2和HD分子的热力学性质. 首先利用解析势能曲线计算得到分子的振转能级, 其次结合量子统计系综理论计算了分子在100—6000 K温度下的配分函数、摩尔热容、摩尔熵、摩尔焓以及约化摩尔吉布斯自由能. 计算结果与美国国家标准与技术研究所(National Institute of Standards and Technology, NIST)数据库中的数据具有良好的一致性. 本文的理论方法可用于预测某些气态物质的热力学性质.
    H2 molecule and their isotopes represent one of the modern clean energy sources. It is imperative to understand their thermodynamic properties for comprehending their behaviors under various conditions. Thereby promoting their more in-depth applications. In this paper, an extended improved multiparameter exponential-type potential (EIMPET) combined with the quantum statistical ensemble theory is used to investigate and analyze the thermodynamic properties of H2 and HD molecules. Firstly, reliable energy level data for molecules are obtained using the EIMPET potential. Subsequently, the one-dimensional Schrödinger equation is solved with the LEVEL program to determine the rovibrational energy levels of the molecules. Finally, the quantum statistical ensemble theory is integrated to determine the partition functions, molar heat capacity, molar entropy, molar enthalpy, and reduced molar Gibbs free energy of H2 and HD in a temperature range of 100–6000 K. The calculation results indicate that compared with IHH potential and IMPET potential, the EIMPET potential is closer to RKR data. A comparison of the calculated thermodynamic properties of the molecules reveals that the results from the EIMPET potential-based method accord well with those from the NIST database. Specifically, for H2, the root mean square (RMS) errors for $ {C_{\text{m}}}\left( T \right) $, $ {S_{\text{m}}}\left( T \right) $, $ {G_{\text{r}}}\left( T \right) $, and $ \Delta {H_{\text{r}}}\left( T \right) $are 0.6894 J·K–1·mol–1, 0.3824 J·K–1·mol–1, 0.1754 J·K–1·mol–1, and 0.9586 kJ·mol–1, respectively, while for HD, the RMS errors are 0.3431 J·K–1·mol–1, 0.1443 J·K–1·mol–1, 0.0495 J·K–1·mol–1, and 0.4863 kJ·mol–1, respectively. All of these results are superior to those obtained using IMPET potential, and to those obtained using IHH potential as a whole. These findings demonstrate the advantages and practical applications of the EIMPET potential in calculating the thermodynamic properties of diatomic gas molecules, providing a foundation for subsequently studying the thermodynamic properties of triatomic molecules.
      通信作者: 樊群超, fanqunchao@mail.xhu.edu.cn ; 范志祥, fanzhixiang@mail.xhu.edu.cn
    • 基金项目: 中央引导地方科技发展资金项目(批准号: 2024ZYD0167)和四川省自然科学基金青年科学基金(批准号: 2022NSFSC1857)资助的课题.
      Corresponding author: FAN Qunchao, fanqunchao@mail.xhu.edu.cn ; FAN Zhixiang, fanzhixiang@mail.xhu.edu.cn
    • Funds: Project supported by the Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province, China (Grant No. 2024ZYD0167) and the Fund for the Natural Science Foundation of Sichuan Province, China (Grant No. 2022NSFSC1857).
    [1]

    Wang C W, Peng X L, Liu J Y, et al. 2022 Int. J. Hydrogen Energy 47 27821Google Scholar

    [2]

    Fan X, Bañados E, Simcoe R A 2023 Annu. Rev. Astron. Astrophys. 61 373Google Scholar

    [3]

    Abramowitz S, Chase M W 1991 Pure Appl. Chem. 63 1449Google Scholar

    [4]

    Grein F 2023 Struct. Chem. 34 317Google Scholar

    [5]

    Yahiatène I, Hennig S, Huser T 2013 Chem. Phys. Lett. 587 1Google Scholar

    [6]

    Angelova M, Frank A 2005 Phys. At. Nucl. 68 1625Google Scholar

    [7]

    Halpern A M 2010 J. Chem. Educ. 87 174Google Scholar

    [8]

    Liu G Y, Sun W G, Liao B T 2015 Indian J. Phys. 89 1109Google Scholar

    [9]

    Jia C S, Zhang L H, Wang C W 2017 Chem. Phys. Lett. 667 211Google Scholar

    [10]

    Ding Q C, Jia C S, Liu J Z, Li J, Du R F, Liu J Y, Peng X L, Wang C W, Tang H X 2022 Chem. Phys. Lett. 803 139844Google Scholar

    [11]

    Jia C S, Wang C W, Zhang L H, Peng X L, Tang H M, Zeng R 2018 Chem. Eng. Sci. 183 26Google Scholar

    [12]

    Ikot A N, Chukwuocha E O, Onyeaju M C, Onate C A, Ita B I, Udoh M E 2018 Pramana-J. Phys. 90 22Google Scholar

    [13]

    Okorie U S, Ikot A N, Chukwuocha E O, Rampho G J 2020 Results Phys. 17 103078Google Scholar

    [14]

    Bakhti H, Diaf A, Hachama M 2020 Comput. Theor. Chem. 1185 112879Google Scholar

    [15]

    Oluwadare O J, Oyewumi K J, Abiola T O 2022 Indian J. Phys. 96 1921Google Scholar

    [16]

    Strekalov M L 2024 Chem. Phys. Impact 8 100444Google Scholar

    [17]

    Coveney P V, Wan S 2016 Phys. Chem. Chem. Phys. 18 30236Google Scholar

    [18]

    Fang Z, Vasiliu M, Peterson K A, Dixon D A 2017 J. Chem. Theory. Comput. 13 1057Google Scholar

    [19]

    Startsev A N 2019 J. Sulfur Chem. 40 435Google Scholar

    [20]

    van Speybroeck V, Gani R, Meier R J 2010 Chem. Soc. Rev. 39 1764Google Scholar

    [21]

    Kang D, Fan Q, Fan Z, Li H, Fu J 2024 Int. J. Quantum Chem. 124 e27373Google Scholar

    [22]

    National Institute of Standards and Technology (NIST), 2017 NIST Chemistry WebBook, NISTS Standard Reference Database Number 69. http://webbook.nist.gov/chemistry/

    [23]

    Xie B J, Jia C S 2020 Int. J. Quantum Chem. 120 e26058Google Scholar

    [24]

    Morse P M 1929 Phys. Rev. 34 57Google Scholar

    [25]

    Desai A M, Mesquita N, Fernandes V 2020 Phys. Scr. 95 085401Google Scholar

    [26]

    Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transfer 186 167Google Scholar

    [27]

    Ding Q C, Jia C S, Wang C W, Peng X L, Liu J Y, Zhang L H, Jiang R, Zhu S Y, Yuan H, Tang H X 2023 J. Mol. Liq. 371 121088Google Scholar

    [28]

    Hooydonk G V http://hdl.handle.net/1854/LU-1212652 [2024- 12-18]

    [29]

    Tobias I, Vanderslice J T 1961 J. Chem. Phys. 35 1852Google Scholar

    [30]

    Fink E H, Akins D L, Bradley Moore C 1969 Chem. Phys. Lett. 4 283Google Scholar

    [31]

    Wilkinson P G 1968 Can. J. Phys. 46 1225Google Scholar

    [32]

    Tian H, Fan Q, Fan Z, Fu J, Li H, Ma J, Xie F 2022 Int. J. Quantum Chem. 122 e26983Google Scholar

    [33]

    Leachman J W, Jacobsen R T, Penoncello S G, Lemmon E W 2009 J. Phys. Chem. Ref. Data 38 721Google Scholar

  • 图 1  H2和HD分子电子基态势能曲线 (a) H2分子不同势能曲线对比图; (b) HD分子不同势能曲线对比图

    Fig. 1.  Potential energy curves of the ground electronic states for H2 and HD molecules: (a) Comparison of different potential energy curves for the H2 molecule; (b) comparison of different potential energy curves for the HD molecule.

    图 2  (a) H2和(b) HD分子不同λ值的EIMPET势能曲线

    Fig. 2.  EIMPET potential energy curves for (a) H2 and (b) HD molecules with various λ values

    图 3  H2和HD分子的摩尔热容与NIST实验数据的比较图(AE为绝对误差) (a) H2分子的摩尔热容; (b) HD分子的摩尔热容

    Fig. 3.  Comparison of molar heat capacity of H2 and HD molecules with NIST experimental data (AE represents absolute error): (a) Molar heat capacity of H2 molecule; (b) molar heat capacity of HD molecule.

    图 4  H2分子(a)和HD分子(b)的摩尔熵与NIST实验数据的对比

    Fig. 4.  Comparison of the molar entropy of H2 (a) and HD molecules (b) with NIST experimental data.

    图 6  (a) H2分子的约化摩尔吉布斯自由能; (b) HD分子的约化摩尔吉布斯自由能

    Fig. 6.  (a) The reduced molar Gibbs free energy of the H2 molecule; (b) the reduced molar Gibbs free energy of the HD molecule.

    图 5  (a) H2分子的摩尔焓; (b) HD分子的摩尔焓

    Fig. 5.  (a) Molar enthalpy of the H2 molecule; (b) molar enthalpy of the HD molecule.

    表 1  H2和HD分子电子基态的实验光谱常数和可调参数$ \lambda $的值

    Table 1.  Experimental spectral constants and adjustable parameter $ \lambda $ of the ground electronic states of H2 and HD molecules.

    分子$ {D_{\text{e}}} $/cm–1$ {r_{\text{e}}} $/Å$ {\omega _{\text{e}}} $/cm–1$ {\alpha _{\text{e}}} $/cm–1$ \lambda $
    H238292.984[28]0.74144[28]4401.213[27]3.0622[27]–0.01
    HD38295.8[30]0.74141[30]3813.15[31]1.986[31]–0.04
    下载: 导出CSV

    表 2  H2分子不同温度下的摩尔热容以及绝对误差

    Table 2.  Molar heat capacity of H2 molecule at different temperatures and absolute errors.

    T/K $ {C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}} $
    /(J·K–1·mol–1)
    $ {C}_{{\mathrm{m}}}^{{\mathrm{I}}{\mathrm{H}}{\mathrm{H}}} $
    /(J·K–1·mol–1)
    $ {C}_{{\mathrm{m}}}^{{\mathrm{I}}{\mathrm{M}}{\mathrm{P}}{\mathrm{E}}{\mathrm{T}}} $
    /(J·K–1·mol–1)
    $ {C}_{{\mathrm{m}}}^{{\mathrm{E}}{\mathrm{I}}{\mathrm{M}}{\mathrm{P}}{\mathrm{E}}{\mathrm{T}}} $
    /(J·K–1·mol–1)
    $ \Delta {C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}\text{-}{\mathrm{I}}{\mathrm{H}}{\mathrm{H}}} $
    /(J·K–1·mol–1)
    $ \Delta {C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}\text{-}{\mathrm{I}}{\mathrm{M}}{\mathrm{P}}{\mathrm{E}}{\mathrm{T}}} $
    /(J·K–1·mol–1)
    $ \Delta {C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}\text{-}{\mathrm{E}}{\mathrm{I}}{\mathrm{M}}{\mathrm{P}}{\mathrm{E}}{\mathrm{T}}} $
    /(J·K–1·mol–1)
    100 28.154 29.521 29.520 29.520 1.367 1.366 1.366
    300 28.849 29.210 29.212 29.212 0.361 0.363 0.363
    500 29.260 29.265 29.270 29.270 0.005 0.010 0.010
    700 29.441 29.432 29.452 29.452 0.009 0.011 0.011
    900 29.881 29.857 29.910 29.908 0.024 0.029 0.027
    1100 30.581 30.535 30.629 30.626 0.046 0.048 0.045
    1300 31.423 31.354 31.491 31.487 0.069 0.068 0.064
    1500 32.298 32.204 32.384 32.378 0.094 0.086 0.080
    1700 33.139 33.017 33.243 33.236 0.122 0.104 0.097
    1900 33.917 33.763 34.040 34.031 0.154 0.123 0.114
    2100 34.624 34.432 34.768 34.757 0.192 0.144 0.133
    2300 35.263 35.029 35.430 35.416 0.234 0.167 0.153
    2500 35.842 35.560 36.036 36.018 0.282 0.194 0.176
    2700 36.370 36.036 36.595 36.573 0.334 0.225 0.203
    2900 36.856 36.464 37.119 37.091 0.392 0.263 0.235
    3100 37.311 36.856 37.616 37.581 0.455 0.305 0.270
    3300 37.740 37.218 38.096 38.051 0.522 0.356 0.311
    3500 38.149 37.558 38.565 38.508 0.591 0.416 0.359
    3700 38.544 37.882 39.029 38.958 0.662 0.485 0.414
    3900 38.928 38.196 39.491 39.405 0.732 0.563 0.477
    4100 39.301 38.502 39.952 39.849 0.799 0.651 0.548
    4300 39.665 38.803 40.412 40.292 0.862 0.747 0.627
    4500 40.017 39.099 40.868 40.732 0.918 0.851 0.715
    4700 40.355 39.388 41.316 41.164 0.967 0.961 0.809
    4900 40.676 39.671 41.750 41.585 1.005 1.074 0.909
    5100 40.976 39.942 42.163 41.988 1.034 1.187 1.012
    5300 41.252 40.199 42.548 42.369 1.053 1.296 1.117
    5500 41.498 40.439 42.900 42.721 1.059 1.402 1.223
    5700 41.712 40.656 43.211 43.038 1.056 1.499 1.326
    5900 41.890 40.849 43.476 43.315 1.041 1.586 1.425
    6000 41.965 40.934 43.590 43.436 1.031 1.625 1.471
    MAE 0.564 0.587 0.519
    *$ \Delta {C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}\text{-}{\mathrm{m}}{\mathrm{o}}{\mathrm{d}}{\mathrm{e}}{\mathrm{l}}}=|{C}_{{\mathrm{m}}}^{{\mathrm{N}}{\mathrm{I}}{\mathrm{S}}{\mathrm{T}}}-{C}_{{\mathrm{m}}}^{{\mathrm{m}}{\mathrm{o}}{\mathrm{d}}{\mathrm{e}}{\mathrm{l}}}| $; MAE: mean absolute error
    下载: 导出CSV

    表 3  H2和HD分子不同势能模型下的预测数据与NIST数据的方均根误差

    Table 3.  Root mean square error of predicted data for H2 and HD molecules under different potential energy models compared to NIST data.

    热力学量 H2EIMPET H2IMPET H2IHH HDEIMPET HDIMPET HDIHH
    Cm/(J·K–1·mol–1) 0.6894 0.7750 0.7019 0.3431 0.6338 0.4055
    Sm/(J·K–1·mol–1) 0.3824 0.4096 0.4591 0.1443 0.2732 0.1575
    ΔHr/(kJ·mol–1) 0.9586 1.1052 1.2110 0.4863 0.9749 0.5946
    Gr/(J·K–1·mol–1) 0.1754 0.1805 0.2005 0.0495 0.0859 0.0452
    下载: 导出CSV
  • [1]

    Wang C W, Peng X L, Liu J Y, et al. 2022 Int. J. Hydrogen Energy 47 27821Google Scholar

    [2]

    Fan X, Bañados E, Simcoe R A 2023 Annu. Rev. Astron. Astrophys. 61 373Google Scholar

    [3]

    Abramowitz S, Chase M W 1991 Pure Appl. Chem. 63 1449Google Scholar

    [4]

    Grein F 2023 Struct. Chem. 34 317Google Scholar

    [5]

    Yahiatène I, Hennig S, Huser T 2013 Chem. Phys. Lett. 587 1Google Scholar

    [6]

    Angelova M, Frank A 2005 Phys. At. Nucl. 68 1625Google Scholar

    [7]

    Halpern A M 2010 J. Chem. Educ. 87 174Google Scholar

    [8]

    Liu G Y, Sun W G, Liao B T 2015 Indian J. Phys. 89 1109Google Scholar

    [9]

    Jia C S, Zhang L H, Wang C W 2017 Chem. Phys. Lett. 667 211Google Scholar

    [10]

    Ding Q C, Jia C S, Liu J Z, Li J, Du R F, Liu J Y, Peng X L, Wang C W, Tang H X 2022 Chem. Phys. Lett. 803 139844Google Scholar

    [11]

    Jia C S, Wang C W, Zhang L H, Peng X L, Tang H M, Zeng R 2018 Chem. Eng. Sci. 183 26Google Scholar

    [12]

    Ikot A N, Chukwuocha E O, Onyeaju M C, Onate C A, Ita B I, Udoh M E 2018 Pramana-J. Phys. 90 22Google Scholar

    [13]

    Okorie U S, Ikot A N, Chukwuocha E O, Rampho G J 2020 Results Phys. 17 103078Google Scholar

    [14]

    Bakhti H, Diaf A, Hachama M 2020 Comput. Theor. Chem. 1185 112879Google Scholar

    [15]

    Oluwadare O J, Oyewumi K J, Abiola T O 2022 Indian J. Phys. 96 1921Google Scholar

    [16]

    Strekalov M L 2024 Chem. Phys. Impact 8 100444Google Scholar

    [17]

    Coveney P V, Wan S 2016 Phys. Chem. Chem. Phys. 18 30236Google Scholar

    [18]

    Fang Z, Vasiliu M, Peterson K A, Dixon D A 2017 J. Chem. Theory. Comput. 13 1057Google Scholar

    [19]

    Startsev A N 2019 J. Sulfur Chem. 40 435Google Scholar

    [20]

    van Speybroeck V, Gani R, Meier R J 2010 Chem. Soc. Rev. 39 1764Google Scholar

    [21]

    Kang D, Fan Q, Fan Z, Li H, Fu J 2024 Int. J. Quantum Chem. 124 e27373Google Scholar

    [22]

    National Institute of Standards and Technology (NIST), 2017 NIST Chemistry WebBook, NISTS Standard Reference Database Number 69. http://webbook.nist.gov/chemistry/

    [23]

    Xie B J, Jia C S 2020 Int. J. Quantum Chem. 120 e26058Google Scholar

    [24]

    Morse P M 1929 Phys. Rev. 34 57Google Scholar

    [25]

    Desai A M, Mesquita N, Fernandes V 2020 Phys. Scr. 95 085401Google Scholar

    [26]

    Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transfer 186 167Google Scholar

    [27]

    Ding Q C, Jia C S, Wang C W, Peng X L, Liu J Y, Zhang L H, Jiang R, Zhu S Y, Yuan H, Tang H X 2023 J. Mol. Liq. 371 121088Google Scholar

    [28]

    Hooydonk G V http://hdl.handle.net/1854/LU-1212652 [2024- 12-18]

    [29]

    Tobias I, Vanderslice J T 1961 J. Chem. Phys. 35 1852Google Scholar

    [30]

    Fink E H, Akins D L, Bradley Moore C 1969 Chem. Phys. Lett. 4 283Google Scholar

    [31]

    Wilkinson P G 1968 Can. J. Phys. 46 1225Google Scholar

    [32]

    Tian H, Fan Q, Fan Z, Fu J, Li H, Ma J, Xie F 2022 Int. J. Quantum Chem. 122 e26983Google Scholar

    [33]

    Leachman J W, Jacobsen R T, Penoncello S G, Lemmon E W 2009 J. Phys. Chem. Ref. Data 38 721Google Scholar

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出版历程
  • 收稿日期:  2024-12-30
  • 修回日期:  2025-03-24
  • 上网日期:  2025-04-01

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