• Acta Physica Sinica
  • Vol. 69, Issue 5, 053301-1 (2020)
Jun Jian1, Jiao Lei1, Qun-Chao Fan1、*, Zhi-Xiang Fan1、*, Jie Ma2, Jia Fu1, Hui-Dong Li1, and Yong-Gen Xu1
Author Affiliations
  • 1Key Laboratory of High Performance Scientific Computation, School of Science, Xihua University, Chengdu 610039, China
  • 2State Key Laboratory of Quantum Optics and Quantum Optics Devices, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, China
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    DOI: 10.7498/aps.69.20191723 Cite this Article
    Jun Jian, Jiao Lei, Qun-Chao Fan, Zhi-Xiang Fan, Jie Ma, Jia Fu, Hui-Dong Li, Yong-Gen Xu. Theoretical study on thermodynamic properties of NO gas[J]. Acta Physica Sinica, 2020, 69(5): 053301-1 Copy Citation Text show less
    Comparison between the VAM full vibrational energies and experimental ones
    Fig. 1. Comparison between the VAM full vibrational energies and experimental ones
    Comparison of the relative errors of different heat capacities
    Fig. 2. Comparison of the relative errors of different heat capacities
    $\upsilon $$E_{\rm{\upsilon }}^{{\rm{exp}}}$[17]$E_{\rm{\upsilon }}^{{\rm{MCSCF}}}$[16]$E_{\rm{\upsilon }}^{{\rm{VAM}}}$$E_{\rm{\upsilon }}^{{\rm{exp}}} - E_{\rm{\upsilon }}^{{\rm{MCSCF}}}$$E_{\rm{\upsilon }}^{{\rm{exp}}} - E_{\rm{\upsilon }}^{{\rm{VAM}}}$υ$E_{\rm{\upsilon }}^{{\rm{VAM}}}$
    注:$E_{\rm{\upsilon }}^{{\rm{VAM}}}$中表示VAM计算所需的已知实验振动能级用黑体标出.
    0948.50948.60948.50–0.1002640240.70
    12824.502824.602824.50–0.1002741310.84
    24627.304672.404672.27–45.10–44.972842340.94
    36491.906492.106491.90–0.2002943329.70
    48283.508283.908283.43–0.400.073044275.74
    510046.9010047.8010046.90–0.9003145177.59
    611782.3011783.7011782.30–1.4003246033.69
    713489.4013491.7013489.60–2.30–0.203346842.41
    815171.8015168.733447602.00
    916823.9016819.603548310.62
    1018448.0018442.063648966.35
    1120044.0020035.933749567.15
    1221611.8021600.993850110.90
    1323151.3023136.973950595.35
    1424662.4024643.564051018.15
    1526144.8026120.384151376.86
    1627598.5027567.044251668.92
    1729023.2028983.044351891.64
    1830367.884452042.23
    1931720.95
    2033041.62
    2134329.18
    2235582.84
    2336801.78
    2437985.07
    2539131.73
    $D_{\rm{e}}^{{\rm{exp}}}$52155.68$D_{\rm{e}}^{{\rm{cal}}}$52155.68
    Table 1. Comparison of different vibrational levels of NO in the ground state (in cm–1).
    T/K $U_{{\rm{RKR}}}^{{\rm{cal}}}$$U_{{\rm{MCSCF}}}^{{\rm{cal}}}$$U_{{\rm{SHO}}}^{{\rm{cal}}}$$U_{{\rm{VAM}}}^{{\rm{cal}}}$
    100021.2821.2821.2721.28
    110022.6122.6122.5922.61
    120023.9823.9923.9523.98
    130025.3925.4025.3425.39
    140026.8426.8426.7726.84
    150028.3128.3128.2328.31
    160029.8029.8029.7029.80
    170031.3131.3131.2031.31
    180032.8432.8432.7132.84
    190034.3834.3934.2434.38
    200035.9435.9435.7735.94
    210037.5137.5137.3237.51
    220039.0939.0938.8839.09
    230040.6840.6840.4540.68
    240042.2842.2842.0342.28
    250043.8943.8943.6143.89
    260045.5045.5045.1945.50
    270047.1247.1246.7947.12
    280048.7548.7548.3848.75
    290050.3850.3849.9950.38
    300052.0152.0151.5952.01
    310053.6653.6553.2053.66
    320055.3055.3054.8155.30
    330056.9556.9556.4356.95
    340058.6058.6058.0558.60
    350060.2660.2659.6760.26
    360061.9261.9261.2961.92
    370063.5863.5862.9163.59
    380065.2565.2464.5465.25
    390066.9166.9166.1766.92
    400068.5868.5867.8068.60
    410070.2670.2569.4370.27
    420071.9371.9371.0771.95
    430073.6173.6172.7073.63
    440075.2975.2874.3475.32
    450076.9776.9675.9777.01
    460078.6578.6477.6178.69
    470080.3380.3279.2580.39
    480082.0182.0180.8982.08
    490083.6983.6982.5383.78
    500085.3885.3784.1785.48
    Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).
    T/K $S_{{\rm{RKR}}}^{{\rm{cal}}}$$S_{{\rm{MCSCF}}}^{{\rm{cal}}}$$S_{{\rm{SHO}}}^{{\rm{cal}}}$$S_{{\rm{VAM}}}^{{\rm{cal}}}$
    100060.5060.5060.4260.50
    110061.7661.7661.6761.76
    120062.9662.9662.8662.96
    130064.0964.0963.9764.09
    140065.1665.1665.0365.16
    150066.1766.1766.0366.17
    160067.1367.1366.9967.13
    170068.0568.0567.8968.05
    180068.9268.9268.7668.92
    190069.7669.7669.5869.76
    200070.5670.5670.3770.56
    210071.3271.3271.1371.32
    220072.0672.0671.8572.06
    230072.7772.7772.5572.77
    240073.4573.4573.2273.45
    250074.1074.1073.8774.10
    260074.7374.7374.4974.73
    270075.3575.3575.0975.35
    280075.9475.9475.6775.94
    290076.5176.5176.2376.51
    300077.0677.0676.7877.06
    310077.6077.6077.3077.60
    320078.1278.1277.8278.12
    330078.6378.6378.3178.63
    340079.1279.1278.8079.13
    350079.6079.6079.2779.61
    360080.0780.0779.7280.07
    370080.5380.5380.1780.53
    380080.9780.9780.6080.97
    390081.4181.4081.0381.41
    400081.8381.8381.4481.83
    410082.2482.2481.8482.25
    420082.6582.6482.2482.65
    430083.0483.0482.6283.05
    440083.4383.4283.0083.43
    450083.8083.8083.3683.81
    460084.1784.1783.7284.18
    470084.5384.5384.0884.55
    480084.8984.8984.4284.90
    490085.2485.2384.7685.25
    500085.5885.5785.0985.60
    Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).
    T/K ${C_{{\rm{exp}}}}$$C_{{\rm{RKR}}}^{{\rm{cal}}}$$C_{{\rm{MCSCF}}}^{{\rm{cal}}}$$C_{{\rm{SHO}}}^{{\rm{cal}}}$$C_{{\rm{VAM}}}^{{\rm{cal}}}$${\delta _{{\rm{RKR}}}}$a${\delta _{{\rm{MCSCF}}}}$b${\delta _{{\rm{SHO}}}}$c${\delta _{{\rm{VAM}}}}$d
    注: a, ${\delta _{{\rm{RKR}}}} = \left| {C_{{\rm{exp}}}^{} - C_{{\rm{RKR}}}^{{\rm{cal}}}} \right|/C_{{\rm{exp}}}^{} \times 100\% $; b, ${\delta _{{\rm{MCSCF}}}} = \left| {C_{{\rm{exp}}}^{} - C_{{\rm{MCSCF}}}^{{\rm{cal}}}} \right|/C_{{\rm{exp}}}^{} \times 100\% $; c, $ {\delta _{{\rm{SHO}}}} = \left| {C_{{\rm{exp}}} - C_{{\rm{SHO}}}^{{\rm{cal}}}} \right|/C_{{\rm{exp}}} \times 100\% $; d, $ {\delta _{{\rm{VAM}}}} = \left| {C_{{\rm{exp}}} - C_{{\rm{VAM}}}^{{\rm{cal}}}} \right|/C_{{\rm{exp}}} \times 100\% .$
    100013.2013.0413.0410.7213.041.22%1.22%18.82%1.22%
    110013.6813.5213.5211.2413.521.18%1.18%17.85%1.18%
    120014.0913.9313.9311.7313.931.16%1.16%16.77%1.16%
    130014.4414.2714.2712.1714.271.17%1.17%15.69%1.17%
    140014.7414.5614.5612.5814.561.19%1.19%14.66%1.19%
    150014.9914.8114.8112.9414.811.21%1.21%13.70%1.21%
    160015.2215.0315.0313.2615.031.23%1.23%12.83%1.23%
    170015.4115.2215.2113.5515.221.26%1.26%12.04%1.26%
    180015.5815.3815.3813.8115.381.29%1.29%11.35%1.29%
    190015.7315.5215.5214.0415.521.33%1.33%10.73%1.33%
    200015.8615.6515.6414.2515.651.36%1.37%10.18%1.36%
    210015.9815.7615.7614.4315.761.41%1.41%9.71%1.41%
    220016.0915.8615.8614.5915.861.45%1.45%9.29%1.45%
    230016.1815.9515.9414.7415.951.48%1.49%8.92%1.48%
    240016.2716.0316.0314.8816.031.52%1.53%8.59%1.52%
    250016.3516.1016.1015.0016.101.56%1.57%8.31%1.56%
    260016.4316.1716.1715.1016.171.61%1.61%8.07%1.61%
    270016.5016.2316.2315.2016.231.65%1.65%7.85%1.65%
    280016.5616.2816.2815.2916.281.69%1.70%7.67%1.69%
    290016.6216.3416.3315.3816.341.74%1.74%7.51%1.73%
    300016.6816.3816.3815.4516.391.77%1.78%7.37%1.77%
    310016.7316.4316.4315.5216.431.82%1.83%7.25%1.80%
    320016.7816.4716.4715.5816.471.87%1.88%7.16%1.85%
    330016.8316.5116.5115.6416.511.91%1.92%7.08%1.88%
    340016.8816.5516.5415.6916.551.96%1.97%7.01%1.92%
    350016.9216.5816.5815.7416.592.01%2.02%6.96%1.95%
    360016.9616.6116.6115.7916.622.06%2.07%6.91%1.99%
    370017.0016.6416.6415.8316.662.12%2.13%6.89%2.03%
    380017.0416.6716.6715.8716.692.18%2.19%6.86%2.06%
    390017.0816.6916.6915.9116.722.24%2.25%6.85%2.09%
    400017.1116.7216.7115.9416.752.31%2.32%6.85%2.13%
    410017.1516.7416.7415.9716.782.38%2.40%6.86%2.16%
    420017.1816.7616.7516.0016.812.46%2.48%6.86%2.18%
    430017.2116.7716.7716.0316.832.55%2.57%6.88%2.21%
    440017.2416.7916.7916.0516.862.64%2.66%6.90%2.24%
    450017.2816.8016.8016.0816.892.74%2.76%6.93%2.26%
    460017.3116.8116.8116.1016.912.85%2.86%6.96%2.29%
    470017.3416.8216.8216.1216.942.96%2.99%7.00%2.31%
    480017.3616.8316.8316.1416.963.09%3.11%7.04%2.32%
    490017.3916.8316.8316.1616.993.22%3.25%7.08%2.35%
    500017.4216.8416.8316.1817.013.37%3.38%7.13%2.36%
    Table 4. Comparisons of different molar capacities with observed experimental (in J·K–1·mol–1).
    Jun Jian, Jiao Lei, Qun-Chao Fan, Zhi-Xiang Fan, Jie Ma, Jia Fu, Hui-Dong Li, Yong-Gen Xu. Theoretical study on thermodynamic properties of NO gas[J]. Acta Physica Sinica, 2020, 69(5): 053301-1
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