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氮气分子${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}} \text{和} { b}^1\Pi_{\rm u} $电子态的不透明度

陈晨 赵国鹏 祁月盈 吴勇 王建国

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氮气分子${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}} \text{和} { b}^1\Pi_{\rm u} $电子态的不透明度

陈晨, 赵国鹏, 祁月盈, 吴勇, 王建国

Opacities of ${ X}^1\Sigma^+_{\rm g}, a'{}^1\Sigma^-_{\rm u}, a{}^1\Pi_{\rm g} \text{ and } { b}^1\Pi_{\rm u}$ electronic states for nitrogen molecule

Chen Chen, Zhao Guo-Peng, Qi Yue-Ying, Wu Yong, Wang Jian-Guo
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  • 采用考虑Davidson修正的多参考组态相互作用(MRCI+Q)方法, 计算了氮气分子${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$b1Пu电子态的势能曲线、偶极跃迁矩阵元、光谱常数和振动能级, 计算结果与其他实验和理论数据符合较好. 基于分子结构数据, 研究了氮气分子在100 atm (1 atm = 1.01×105 Pa)压强下, 295—20000 K温度范围内的不透明度. 结果表明, 在波长分布范围内, 不透明度随着温度的升高而变大; 当温度小于5000 K时, 不透明度主要分布在紫外区域, 当温度大于10000 K时, 激发态的贡献使得不透明度在红外区域也开始有明显的布居. 本文探明了温度效应对氮气分子不透明度的影响, 可以为天体物理和核武器领域提供理论和数据支持.
    Multi-reference configuration interaction (MRCI) approach with Davison size-extensivity correction (+Q) is employed to calculate the potential curves and dipole moments of ${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$ and $b{}^1{\Pi _{\rm u}}$ electronic states of N2. The spectroscopic constants and vibrational level spaceings are calculated and in excellent agreement with the available theoretical results and experimental data. Based on the calculated molecular structure parameters, the opacities of N2 in a temperature range of 295–20000 K under a pressure of 100 atm (1 atm = 1.01×105 Pa) are presented. The results demonstrate that the wavelength range of absorption cross sections are enlarged with the temperature increasing. Moreover, the cross sections are mainly dominated in the range of ultraviolet for the cases with temperature T < 5000 K, while the obvious population can be found in the infrared ranges for the cases with temperature T > 10000 K due to the contribution of the excited states. The influence of temperature on the opacities of nitrogen molecule are investigated in the present work, which can provide theoretical and data support for researches of astrophysics and nuclear weapons.
      通信作者: 赵国鹏, guopengzhao@zjxu.edu.cn ; 吴勇, wu_yong@iapcm.ac.cn
    • 基金项目: 国家重点研发计划 (批准号: 2017YFA0403200)和国家自然科学基金 (批准号: 12105119)资助的课题.
      Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Wu Yong, wu_yong@iapcm.ac.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0403200) and the National Natural Science Foundation of China (Grant No. 12105119)
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    Liang M C, Heays A N, Lewis B R, Gibson S T, Yung Y L 2007 Astrophys. J. Lett. 664 L115Google Scholar

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    Stark G, Huber K P, Yoshino K, Smith P L, Ito K 2005 J. Chem. Phys. 123 214303Google Scholar

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  • 图 1  氮气分子${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$b1Пu电子态的势能曲线

    Fig. 1.  Potential energy curves for the ${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$ and b1Пu states of nitrogen molecular.

    图 2  氮气分子的偶极跃迁矩阵元随核间距的变化

    Fig. 2.  Transition dipole moments for different states of nitrogen molecular as a function of internuclear distance R.

    图 3  氮气分子的配分函数

    Fig. 3.  The partition functions of nitrogen molecular.

    图 4  压强为100 atm时, 不同温度下氮气分子的不透明度 (a) 295 K; (b) 500 K; (c) 1000 K; (d) 2000 K

    Fig. 4.  Opacities of nitrogen molecule at different temperatures under the pressure of 100 atm: (a) 295 K; (b) 500 K; (c) 1000 K; (d) 2000 K.

    图 5  压强为100 atm时, 不同温度下氮气分子的不透明度 (a) 2500 K; (b) 5000 K; (c) 10000 K; (d) 20000 K

    Fig. 5.  Opacities of nitrogen molecule at different temperatures under the pressure of 100 atm: (a) 2500 K; (b) 5000 K; (c) 10000 K; (d) 20000 K.

    表 1  氮气分子的光谱常数

    Table 1.  Spectral constants of nitrogen molecular.

    StateMethod Te/cm–1ωe/cm–1ωexe/cm–1Be/cm–1ReDe/eV
    ${X^1}\Sigma _{\rm{g}}^ + $Present02357.116814.38831.99681.09859.8396
    MR-AQCC[48]023371.10199.6426
    MR-CISD[48]023421.10169.6468
    MR-CISD+Q[48]023351.10199.6489
    DFT(et-QZ3P-2D)[49]0235614.31.9861.1012
    DFT(ATZP) [49]0234613.31.9741.1045
    CCSD(T)[50]02342.814.0911.9831.1014
    CCSD[50]02356.113.9721.9871.1003
    CASSCF[30]023581.0929.82
    Expt. [20]02358.5714.3241.998241.097689.7593
    $a'{}^1\Sigma _{\rm u}^ -$Present68344.0981528.454411.44791.47941.27556.1725
    MR-AQCC[48]6776215141.28076.1230
    MR-CISD[48]6848015171.28046.0915
    MR-CISD+Q[48]6753115131.28086.1254
    DFT(et-QZ3P-2D) [49]64968.914689.711.4501.2887
    DFT(ATZP) [49]64578.2147111.11.4461.2906
    MRCI[28]690321523.611.911.47251.278
    CASSCF[30]15721.2775.81
    Expt. [20]677391530.2712.11.48011.27546.1278
    a1ПgPresent69486.4251691.401713.60991.61351.22156.04016
    MR-AQCC[48]6908616761.22665.9587
    MR-CISD[48]6956616911.22615.9568
    MR-CISD+Q[48]6895116701.22685.9617
    DFT(et-QZ3P-2D) [49]69078.0168412.41.6091.2236
    DFT(ATZP) [49]68910.6164714.01.6011.2264
    MRCI[28]699711687.513.911.60341.225
    CASSCF[30]16761.2306.30
    Expt. [20]68951.21694.213.91.61701.22035.9775
    b1ПuPresent102357.2682.0947–5.95311.39291.3191.9599
    MR-AQCC[48]1012446071.34561.9742
    MR-CISD[48]1023336321.34821.8942
    MR-CISD+Q[48]1010186001.34891.9859
    MRCI[26]101703.8681.1–8.81.437
    Expt.[20]100817.52.0265
     Expt.[51]101675634.8 1.4481.284 
    下载: 导出CSV

    表 2  氮气分子${X^1}\Sigma _{\rm{g}}^ + $态的振动能级间隔(EvEv–1)(单位: cm–1)

    Table 2.  Vibrational level spaceings (EvEv–1) (in cm–1) for ${X^1}\Sigma _{\rm{g}}^ + $ state of nitrogen molecular.

    vPresent8R RMR CCSD[52]MR-AQCC[52]MR-ACPF[53]Expt.[54]Expt.[55]
    12327.52336.52330.412328.542329.92329.9
    22299.42308.42301.812299.892301.32301.2
    32270.52279.82273.142271.182272.52272.6
    42242.02251.42244.472242.452243.82243.8
    52213.12222.52215.742213.692215.12215.0
    62184.42193.72186.982184.872186.22186.2
    72155.62164.72158.172156.012157.42157.4
    82126.62135.32129.312127.102128.42128.4
    92097.62106.02100.402098.132099.52099.5
    102068.72076.42071.432069.092070.42070.4
    112039.62046.72042.392040.022041.42041.4
    122010.32016.82013.292010.842012.12012.1
    131981.11987.01984.101981.581982.91983.0
    141951.71956.91954.831952.261953.61953.5
    151922.21927.01925.431922.791924.11924.2
    161892.71896.91895.961893.251894.61894.7
    171863.11866.71866.311863.531864.91865.1
    181833.61836.61836.551833.691835.01835.4
    191803.81806.31806.601803.681805.01805.6
    201773.61775.91774.61775.6
    211743.31745.51744.11745.7
    221712.71714.81713.31715.5
    231681.81684.01682.11685.0
    241650.51652.81650.51655.0
    251618.81621.61618.41624.0
    261586.51585.9
    271553.81552.8
    281520.81519.0
    291487.31484.7
    301453.2
    下载: 导出CSV

    表 3  氮气分子$ a'{}^1\Sigma _{\rm u}^ - $, $ a{}^1{\Pi _{\rm g}} $$ b{}^1{\Pi _{\rm u}} $态的振动能级间隔(Ev Ev–1)(单位: cm–1)

    Table 3.  Vibrational level spaceings (Ev Ev–1) (in cm–1) for $a'{}^1\Sigma _{\rm u}^ -$, $ a{}^1{\Pi _{\rm g}} $ and$ b{}^1{\Pi _{\rm u}} $ states of nitrogen molecular.

    v$ { {a} }'{}^1\Sigma _{ {\rm u} }^ - $a1Пgb1Пu
    PresentExpt.[20]PresentExpt.[20]PresentExpt.[20]
    11506.71506.241664.61666.34645.2645.4
    21482.81482.451637.61638.51710.9705.3
    31459.31458.901609.61610.77745.2747.6
    41436.01435.571581.81583.07763.7774.8
    51412.81412.471554.51555.46772.9789.6
    61389.81389.581527.31527.93776.4794.4
    71367.41366.881500.11500.49774.8791.4
    81345.01344.411473.31473.15770.5782.8
    91322.81322.101446.41445.91762.7770.2
    101300.71300.001419.71418.77752.4754.8
    111278.81278.061393.11391.77740.2737.9
    121257.11256.311366.61364.87725.2719.8
    131235.81234.701340.31338.12708.4701.0
    141214.51213.271314.21311.50689.0681.4
    151193.11191.981288.21285.03667.1660.5
    161172.01170.841262.1642.1637.9
    171151.21149.831236.4613.4612.6
    181130.41128.951210.9580.3584.0
    191109.61108.191185.3541.8551.0
    201088.81159.7
    211068.11134.0
    221047.51108.4
    231026.91082.8
    241006.21057.1
    25985.41031.2
    26964.51005.0
    27943.4978.4
    28922.3951.4
    下载: 导出CSV
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    Vuitton V, Yelle R V, Anicich V G 2006 Astrophys. J. Lett. 647 L175Google Scholar

    [12]

    Liang M C, Heays A N, Lewis B R, Gibson S T, Yung Y L 2007 Astrophys. J. Lett. 664 L115Google Scholar

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    Knauth D C, Andersson B G, McCandliss S R, Moos H W 2004 Nature 429 636Google Scholar

    [14]

    Stark G, Huber K P, Yoshino K, Smith P L, Ito K 2005 J. Chem. Phys. 123 214303Google Scholar

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    Rothman L S, Jacquemart D, Barbe A, et al. 2005 J. Quant. Spectrosc. Radiat. Transfer 96 139Google Scholar

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    Rothman L S, Gordon I E, Barbe A, et al. 2009 J. Quant. Spectrosc. Radiat. Transfer 110 533Google Scholar

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    Gordon I E, Rothman L S, Hill C, et al. 2017 J. Quant. Spectrosc. Radiat. Transfer 203 3Google Scholar

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    Rothman L S, Gordon I E, Barber R J, Dothe H, Gamache R R, Goldman A, Perevalov V I, Tashkun S A and Tennyson J 2010 J. Quant. Spectrosc. Radiat. Transfer 111 2139Google Scholar

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    Niu M L, Heays A N, Jones S, Salumbides E J, van Dishoeck E F, De Oliveira N, Nahon L, Ubachs W 2015 J. Mol. Spectrosc. 315 137Google Scholar

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    Heays A N, Lewis B R, De Oliveira N, Ubachs W 2019 J. Chem. Phys. 151 224305Google Scholar

    [26]

    Spelsberg D, Meyer W 2001 J. Chem. Phys. 115 6438Google Scholar

    [27]

    San-Fabián E, Pastor-Abia L 2003 Theor. Chem. Acc. 110 276Google Scholar

    [28]

    Hochlaf M, Ndome H, Hammoutène D, Vervloet M 2010 J. Phys. B: At. Mol. Opt. Phys. 43 245101Google Scholar

    [29]

    Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2012 Int. J. Quantum Chem. 112 1323Google Scholar

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    Xin Y, Ding H B 2014 Plasma Sci. Technol. 16 104Google Scholar

    [31]

    Lavín C, Velasco A M, Martín I 2010 Chem. Phys. Lett. 487 38Google Scholar

    [32]

    Lavín C, Velasco A M 2011 Astrophys. J. 739 16Google Scholar

    [33]

    Lavín C, Velasco A M 2016 Astrophys. J. 816 58Google Scholar

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    Lavín C, Velasco A M 2017 Astrophys. J. Suppl. Ser. 229 19Google Scholar

    [35]

    Velasco A M, Lavín C 2020 Astrophys. J. 899 57Google Scholar

    [36]

    Velasco A M, Alonso J L, Redondo P, Lavín C 2021 Astrophys. J. 922 100Google Scholar

    [37]

    Qin Z, Zhao J, Liu L 2019 Mol. Phys. 117 1Google Scholar

    [38]

    Liang R H, Liu Y M, Li F Y 2021 Phys. Scr. 96 125402Google Scholar

    [39]

    Weck P F, Schweitzer A, Kirby K, Hauschildt P H, Stancil P C 2004 Astrophys. J. 613 567Google Scholar

    [40]

    Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO: a Package of ab initio Programs

    [41]

    Le Roy R J 2002 LEVEL 7.5: a Computer Program for Solving the Radial Schrodinger Equation for Bound and Quasibound Levels (University of Waterloo, Chemical Physics Research Report CP-655)

    [42]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum. Chem. 8 61Google Scholar

    [43]

    Werner H J, Knowles P J 1985 J. Chem. Phys. 82 5053Google Scholar

    [44]

    Woon D E, Dunning T H 1995 J. Chem. Phys. 103 4572Google Scholar

    [45]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [46]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

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    Moore C E 1975 Natl. Stand. Ref. Data Ser. (U.S. Natl. Bur. Stand) doc. 3 Sect. 5

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    Müller T, Dallos M, Lischka H, Dubrovay Z, Szalay P G 2001 Theor. Chem. Acc. 105 227Google Scholar

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    Falzon C T, Chong D P, Wang F 2006 J. Comput. Chem. 27 163Google Scholar

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出版历程
  • 收稿日期:  2022-01-07
  • 修回日期:  2022-03-17
  • 上网日期:  2022-07-09
  • 刊出日期:  2022-07-20

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