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中国物理学会期刊
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Molecular opacities of $ {{\text{X}}^{2}}{\Sigma}_{\text{g}}^{+} $, A2Πu and $ {{\text{B}}^{2}}{\Sigma}_{\text{u}}^{+} $ states of nitrogen cation

Chen Chen ,  Zhao Guo-Peng ,  Qi Yue-Ying ,  Wu Yong ,  Wang Jian-Guo

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Molecular opacities of $ {{\text{X}}^{2}}{\Sigma}_{\text{g}}^{+} $, A2Πu and $ {{\text{B}}^{2}}{\Sigma}_{\text{u}}^{+} $ states of nitrogen cation

Chen Chen, Zhao Guo-Peng, Qi Yue-Ying, Wu Yong, Wang Jian-Guo
Acta Phys. Sin., 2022, 71(19): 193101.
doi: 10.7498/aps.71.20220734
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  • Abstract

    The potential curves, spectroscopic constants and dipole moments for $ {{\text{X}}^{2}}{\Sigma}_{\text{g}}^{+} $, A2Πu and $ {{\text{B}}^{2}}{\Sigma}_{\text{u}}^{+} $ state of $ {\text{N}}_{2}^{+} $ are calculated by the internal contraction multi reference configuration interaction (icMRCI) method, with Davidson correction taken into consideration. According to the results of molecular structures, we present the partition function in a temperature range of 100–40000 K and the opacities at different temperatures (295, 500, 1000, 2000, 2500, 5000 and 10000 K) under a fixed pressure of 100 atm. It is found that the populations of excited states increase with temperature increasing, as a result, the wavelength range of opacity also increases and band boundaries for different transitions gradually become obscure. In comparison with the cases of N2 with the same pressure and temperature, significant discrepancies are found in the wavelength ranges and structures of opacity of $ {\text{N}}_{2}^{+} $ for the present work. The influence of temperature on the opacity of $ {\text{N}}_{2}^{+} $ is studied systematically in the present work, which is expected to provide theoretical and data support for astrophysics.

    Authors and contacts

    • 1.

      Institute of Modern Physics, Fudan University, Shanghai 200433, China

    • 2.

      College of Data Science, Jiaxing University, Jiaxing 314001, China

    • 3.

      National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

    • 4.

      HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China

      • Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Qi Yue-Ying, yying_qi@zjxu.edu.cn ; Wu Yong, wu_yong@iapcm.ac.cn ; 
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403200) and the National Natural Science Foundation of China (Grant No. 12105119).

    References

    [1]

    Cravens T E, Robertson I P, Waite J H, Yelle R V, Kasprzak W T, Keller C N, Ledvina S A, Niemann H B, Luhmann J G, McNutt R L, Ip W H, Haya V D L, Wodarg M, Wahlund J E, Anicich V G, Vuitton V 2006 Geophys. Res. Lett. 33 L07105Google Scholar

    [2]

    Dutuit O, Carrasco N, Thissen R, Vuitton V, Alcaraz C, Pernot P, Lavvas P 2013 Astrophys. J. Suppl. Ser. 204 20Google Scholar

    [3]

    Scherf M, Lammer H, Erkaev N V, Mandt K E, Thaller S E, Marty B 2020 Space Sci. Rev. 216 1Google Scholar

    [4]

    Bruna P J, Grein F 2008 J. Mol. Spectrosc. 250 75Google Scholar

    [5]

    Erkaev N V, Scherf M, Thaller S E, Lammer H, Mezentsev A V, Ivanov V A, Mandt K E 2021 Mon. Not. R. Astron. Soc. 500 2020Google Scholar

    [6]

    Opitom C, Hutsemékers D, Jehin E, Rousselot P, Pozuelos F J, Manfroid J, Moulane Y, Gillon M, Benkhaldoun Z 2019 Astron. Astrophys. 624 A64Google Scholar

    [7]

    Jenniskens P, Laux C O, Schaller E L 2004 Astrobiology 4 109Google Scholar

    [8]

    Abe S, Ebizuka N, Yano H, Watanabe J I, Borovička J 2005 Astrophys. J. 618 L141Google Scholar

    [9]

    Ho W C, Jäger W, Cramb D C, Ozier I, Gerry M C L 1992 J. Mol. Spectrosc. 153 692Google Scholar

    [10]

    Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2011 Comput. Theor. Chem. 966 44Google Scholar

    [11]

    Huffman R E, Larrabee J C, Tanaka Y 1964 Disc. Faraday Soc. 37 159Google Scholar

    [12]

    Bruna P J, Grein F 2004 J. Mol. Spectrosc. 227 67Google Scholar

    [13]

    Sinhal M 2021 Ph. D. Dissertation (Basel: University of Basel)
    [14]

    Fassbender M 1924 Z. Phys. 30 73
    [15]

    Childs W H J 1932 Proc. Roy. Soc. 137 641Google Scholar

    [16]

    Meinel A B 1950 Astrophys. J. 112 562Google Scholar

    [17]

    Dalby F W, Douglas A E 1951 Phys. Rev. 84 843Google Scholar

    [18]

    Lofthus A, Krupenie P H 1977 J. Phys. Chem Ref. Data 6 113Google Scholar

    [19]

    Dick K A, Benesch W, Crosswhite H M, Tilford S G, Gottscho R A, Field R W 1978 J. Mol. Spectrosc. 69 95Google Scholar

    [20]

    Gudeman C S, Saykally R J 1984 Annu. Rev. Phys. Chem. 35 387Google Scholar

    [21]

    Miller T A, Suzuki T, Hirota E 1984 J. Chem. Phys. 80 4671Google Scholar

    [22]

    Wu S H, Chen Y Q, Zhuang H, Yang X H, Bi Z Y, Ma L S, L Y Y 2001 J. Mol. Spectrosc. 209 133Google Scholar

    [23]

    Moon S Y, Choe W 2003 Spectrochim. Acta Part B 58 249Google Scholar

    [24]

    Zhang Y P, Deng L H, Zhang J, Chen Y Q 2015 Chin. J. Chem. Phys. 28 134Google Scholar

    [25]

    Nishiyama T, Taguchi M, Suzuki H, Dalin P, Ogawa Y, Brandstron U, Sakanoi T 2021 Earth Planets Space 73 30Google Scholar

    [26]

    Chauveau S, Perrin M Y, Riviere P, Soufiani A 2002 J. Quant. Spectrosc. Radiat. Transfer 72 503Google Scholar

    [27]

    Yan B, Feng W 2010 Chin. Phys. B 19 033303Google Scholar

    [28]

    Peyrou B, Chemartin L, Lalande P, Chéron B G, Riviere P, Perrin M Y, Soufiani A 2012 J. Phys. D:Appl. Phys. 45 455203Google Scholar

    [29]

    Liu H, Shi D H, Wang S, Sun J F, Zhu Z L 2014 J. Quant. Spectrosc. Radiat. Transfer 147 207Google Scholar

    [30]

    Qin Z, Zhao J M, Liu L H 2017 J. Quant. Spectrosc. Radiat. Transfer 202 2Google Scholar

    [31]

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

    [32]

    Liang R H, Liu Y M, Li F Y 2021 Contrib. Plasma Phys. 61 e2021000366Google Scholar

    [33]

    Liang R H, Liu Y M, Li F Y 2021 J. Appl. Phys. 130 063303Google Scholar

    [34]

    马文, 靳奉涛, 袁建民 2007 物理学报 56 5709Google Scholar

    Ma W, Jin F T, Yuan J M 2007 Acta Phys. Sin. 56 5709Google Scholar

    [35]

    Lin X H, Liang G Y, Wang J G, Peng Y G, Shao B, Li R, Wu Y 2019 Chin. Phys. B 28 053101Google Scholar

    [36]

    Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 023101Google Scholar

    [37]

    Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. Lett. 37 123101Google Scholar

    [38]

    Li R, Liang G Y, Lin X H, Zhu Y H, Zhao S T, Wu Y 2019 Chin. Phys. B 28 043102Google Scholar

    [39]

    Xu X S, Dai A Q, Peng Y G, Wu Y, Wang J G 2018 J. Quant. Spectrosc. Radiat. Transfer 206 172Google Scholar

    [40]

    Slipher V M 1933 Mon. Not. R. Astron. Soc. 93 657Google Scholar

    [41]

    Feldman P D 1973 J. Geophys. Res. 78 2010Google Scholar

    [42]

    Langhoff S R, Bauschlicher C W 1988 J. Chem. Phys. 88 329Google Scholar

    [43]

    Langhoff S R, Bauschlicher C W, Partridge H 1987 J. Chem. Phys. 87 4716Google Scholar

    [44]

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

    [45]

    陈晨,赵国鹏,祁月盈,吴勇,王建国 2022 物理学报 71 143102Google Scholar

    Chen C, Zhao G P, Qi Y Y, Wu Y, Wang J G 2022 Acta Phys. Sin. 71 143102Google Scholar

    [46]

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

    [47]

    Werner H J and Meyer W 1980 J. Chem. Phys. 73 2342Google Scholar

    [48]

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

    [49]

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

    [50]

    Werner H J, Knowles P J, Manby F R, Schütz M, Celani P, Knizia G, Korona T, Lindh R, Mitrushenkov A, Rauhut G 2010 MOLPRO: a Package of ab initio Programs
    [51]

    Thulstrup E W, Andersen A 1975 J. Phys. B:Atom. Mol. Phys. 8 965Google Scholar

    [52]

    Zhang Y, Hanson D M 1986 Chem. Phys. Lett. 127 33Google Scholar

    [53]

    Berning A, Werner H J 1994 J. Chem. Phys. 100 1953Google Scholar

    [54]

    Li X Z, Paldus J 2000 Mol. Phys. 98 1185Google Scholar

    [55]

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

    [56]

    Bruna P J, Grein F 2008 J. Molecular Spectroscopy 250 75
    [57]

    Li X Z, Paldus J 2009 Phys. Chem. Chem. Phys. 11 5281Google Scholar

    [58]

    Langhoff S R, Bauschlicher Jr C W 1988 J. Chemical Physics 88 329
    [59]

    Bernath P F, Dalgarno A 1996 Phys. Today 49 94

  • 图 1  $ {\rm{N}}_{2}^{+} $ 的$ {{\rm{X}}^{2}}{\Sigma}_{\rm{g}}^{+} $, $ {{\rm{A}}^{2}}{{{\Pi }}_{\rm{u}}} $和$ {{\rm{B}}^{2}}{\Sigma}_{\rm{u}}^{+} $态的势能曲线

    Figure 1.  Potential energy curves for the $ {{\rm{X}}^{2}}{\Sigma}_{\rm{g}}^{+} $, $ {{\rm{A}}^{2}}{{{\Pi }}_{\rm{u}}} $ and $ {{\rm{B}}^{2}}{\Sigma}_{\rm{u}}^{+} $ states of $ {\rm{N}}_{2}^{+} $.

    DownLoad: Full-Size Img PowerPoint

    图 2  $ {\text{N}}_{\text{2}}^{\text{ + }} $的偶极跃迁矩阵元随核间距的变化关系

    Figure 2.  Transition dipole moments of $ {\text{N}}_{\text{2}}^{\text{ + }} $ as a function of internuclear distance R.

    DownLoad: Full-Size Img PowerPoint

    图 3  $ {\text{N}}_{\text{2}}^{\text{ + }} $的配分函数

    Figure 3.  The partition functions of $ {\text{N}}_{\text{2}}^{\text{ + }} $.

    DownLoad: Full-Size Img PowerPoint

    图 4  压强为100 atm时, $ {\text{N}}_{\text{2}}^{\text{ + }} $(黑线)和$ {{\text{N}}_2} $(红线)[45] 在不同温度下的不透明度　(a) 295 K, (b) 500 K, (c) 1000 K, (d) 2000 K.

    Figure 4.  Opacities of $ {\text{N}}_{\text{2}}^{\text{ + }} $ (black line) and $ {{\text{N}}_2} $ (red line) [45] at different temperatures under pressure of 100 atm, (a) 295 K, (b) 500 K, (c) 1000 K, (d) 2000 K.

    DownLoad: Full-Size Img PowerPoint

    图 5  压强为100 atm时, $ {\text{N}}_{\text{2}}^{\text{ + }} $(黑线)和$ {{\text{N}}_2} $(红线)[45] 在不同温度下的不透明度　(a) 2500 K, (b) 5000 K, (c) 10000 K.

    Figure 5.  Opacities of $ {\text{N}}_{\text{2}}^{\text{ + }} $ (black line) and $ {{\text{N}}_2} $ (red line) [45] at different temperatures under pressure of 100 atm, (a) 2500 K, (b) 5000 K, (c) 10000 K.

    DownLoad: Full-Size Img PowerPoint

    表 1  $ {\rm{N}}_{{2}}^{{+}} $分子离子$ {{\rm{X}}^{{2}}}{\Sigma}_{\rm{g}}^{{+}} $, $ {{\rm{A}}^{{2}}}{{\Pi}_{\rm{u}}} $和$ {{\rm{B}}^{{2}}}{\Sigma}_{\rm{u}}^{{+}} $的振动能级间隔(单位: cm–1).

    Table 1.  Vibration energy level intervals for $ {{\text{X}}^{2}}{\Sigma}_{\text{g}}^{+} $, $ {{\text{A}}^{2}}{{\Pi}_{\text{u}}} $ and $ {{\text{B}}^{2}}{\Sigma}_{\text{u}}^{+} $ state of $ {\text{N}}_{2}^{+} $ (in cm–1).

    $ \nu $$ {{\rm{X}}^{2}}{\Sigma}_{\rm{g}}^{+} $$ {{\rm{A}}^{2}}{{\Pi}_{\rm{u}}} $$ {{\rm{B}}^{2}}{\Sigma}_{\rm{u}}^{+} $
    This workExperiment[18]This workExperiment[18]This workExperiment[18]
    12160.202186.31860.801873.12350.812371.5
    22127.692131.81830.131843.22296.852318.8
    32095.202118.81800.421813.32236.542260.4
    42062.182054.01770.501783.72169.602196.4
    52028.652057.71740.202095.352122.8
    61994.382003.61710.162008.012041.0
    71960.151977.91680.471904.721951.1
    81926.841940.71650.761790.501838.2
    91893.061903.81621.041671.731726.9
    101856.931870.91591.271553.841596.7
    111818.041835.81561.571441.301479.9
    121776.201800.61531.561339.771371.4
    131733.591764.71501.571251.041276.3
    141693.161733.51471.761175.431196.3
    151657.081684.31442.161111.181126.6
    161625.931655.81412.801053.801067.1
    171597.901616.31383.511002.491015.5
    181570.431576.81354.06955.83966.0
    191541.511537.31324.26913.25922.0
    201510.091497.81294.02873.37882.0
    DownLoad: CSV

    表 2  ${\text{N}}_2^+$的光谱常数.

    Table 2.  Spectroscopic constants of $\rm N_2^+$.

    StateSource　${R_{\rm{e}}}$/Å${T_{\rm{e}}}$/$ {{\rm c}}{{{\rm m}}^{{{ - }}1}} $${\omega _{\rm{e}}}$/$ {{\rm c}}{{{\rm m}}^{{{ - }}1}} $${B_{\rm{e}}}$/$ {{\rm c}}{{{\rm m}}^{{{ - }}1}} $${D_{\rm{e}}}$/eV
    ${ { {\rm X} }^{2} }{{\Sigma}}_{ {\rm g} }^{+}$This work1.119102196.23241.92278.7145
    Expt.[18]1.11602207.001.93198.7128
    Theory[51]1.17020758.4
    Theory[52]1.10601.97
    Theory[53]1.12012193.41.919
    Theory[54]1.120321951.917
    Theory[55]1.11892204.51.924
    Theory[56]1.126102140
    Theory[57]1.122185
    ${ { {\rm A} }^{2} }{ { {\Pi } }_{ {\rm u} } }$This work1.17778911.19351890.34121.73587.6096
    Expt.[18]1.1779016.41903.531.7487.5948
    Theory[51]1.2614517.9716936.7
    Theory[52]1.16590161.773
    Theory[53]1.17811898.01.735
    Theory[54]1.176219181.739
    Theory[55]1.17721900.11.737
    Theory[56]1.18758872.101850
    Theory[57]1.1771911
    ${ { \rm {B} }^{2} }{\Sigma}_{ {\rm u} }^{+}$This work1.077225861.7412398.85912.07525.5273
    Expt.[18]1.07725566.02419.842.0735.5428
    Theory[51]1.1630649.0618054.6
    Theory[52]1.075255662.084
    Theory[58]1.0832258232441.8
    Theory[54]1.077624252.072
    　Theory[56]1.083825325.802370
    DownLoad: CSV
  • [1]

    Cravens T E, Robertson I P, Waite J H, Yelle R V, Kasprzak W T, Keller C N, Ledvina S A, Niemann H B, Luhmann J G, McNutt R L, Ip W H, Haya V D L, Wodarg M, Wahlund J E, Anicich V G, Vuitton V 2006 Geophys. Res. Lett. 33 L07105Google Scholar

    [2]

    Dutuit O, Carrasco N, Thissen R, Vuitton V, Alcaraz C, Pernot P, Lavvas P 2013 Astrophys. J. Suppl. Ser. 204 20Google Scholar

    [3]

    Scherf M, Lammer H, Erkaev N V, Mandt K E, Thaller S E, Marty B 2020 Space Sci. Rev. 216 1Google Scholar

    [4]

    Bruna P J, Grein F 2008 J. Mol. Spectrosc. 250 75Google Scholar

    [5]

    Erkaev N V, Scherf M, Thaller S E, Lammer H, Mezentsev A V, Ivanov V A, Mandt K E 2021 Mon. Not. R. Astron. Soc. 500 2020Google Scholar

    [6]

    Opitom C, Hutsemékers D, Jehin E, Rousselot P, Pozuelos F J, Manfroid J, Moulane Y, Gillon M, Benkhaldoun Z 2019 Astron. Astrophys. 624 A64Google Scholar

    [7]

    Jenniskens P, Laux C O, Schaller E L 2004 Astrobiology 4 109Google Scholar

    [8]

    Abe S, Ebizuka N, Yano H, Watanabe J I, Borovička J 2005 Astrophys. J. 618 L141Google Scholar

    [9]

    Ho W C, Jäger W, Cramb D C, Ozier I, Gerry M C L 1992 J. Mol. Spectrosc. 153 692Google Scholar

    [10]

    Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2011 Comput. Theor. Chem. 966 44Google Scholar

    [11]

    Huffman R E, Larrabee J C, Tanaka Y 1964 Disc. Faraday Soc. 37 159Google Scholar

    [12]

    Bruna P J, Grein F 2004 J. Mol. Spectrosc. 227 67Google Scholar

    [13]

    Sinhal M 2021 Ph. D. Dissertation (Basel: University of Basel)
    [14]

    Fassbender M 1924 Z. Phys. 30 73
    [15]

    Childs W H J 1932 Proc. Roy. Soc. 137 641Google Scholar

    [16]

    Meinel A B 1950 Astrophys. J. 112 562Google Scholar

    [17]

    Dalby F W, Douglas A E 1951 Phys. Rev. 84 843Google Scholar

    [18]

    Lofthus A, Krupenie P H 1977 J. Phys. Chem Ref. Data 6 113Google Scholar

    [19]

    Dick K A, Benesch W, Crosswhite H M, Tilford S G, Gottscho R A, Field R W 1978 J. Mol. Spectrosc. 69 95Google Scholar

    [20]

    Gudeman C S, Saykally R J 1984 Annu. Rev. Phys. Chem. 35 387Google Scholar

    [21]

    Miller T A, Suzuki T, Hirota E 1984 J. Chem. Phys. 80 4671Google Scholar

    [22]

    Wu S H, Chen Y Q, Zhuang H, Yang X H, Bi Z Y, Ma L S, L Y Y 2001 J. Mol. Spectrosc. 209 133Google Scholar

    [23]

    Moon S Y, Choe W 2003 Spectrochim. Acta Part B 58 249Google Scholar

    [24]

    Zhang Y P, Deng L H, Zhang J, Chen Y Q 2015 Chin. J. Chem. Phys. 28 134Google Scholar

    [25]

    Nishiyama T, Taguchi M, Suzuki H, Dalin P, Ogawa Y, Brandstron U, Sakanoi T 2021 Earth Planets Space 73 30Google Scholar

    [26]

    Chauveau S, Perrin M Y, Riviere P, Soufiani A 2002 J. Quant. Spectrosc. Radiat. Transfer 72 503Google Scholar

    [27]

    Yan B, Feng W 2010 Chin. Phys. B 19 033303Google Scholar

    [28]

    Peyrou B, Chemartin L, Lalande P, Chéron B G, Riviere P, Perrin M Y, Soufiani A 2012 J. Phys. D:Appl. Phys. 45 455203Google Scholar

    [29]

    Liu H, Shi D H, Wang S, Sun J F, Zhu Z L 2014 J. Quant. Spectrosc. Radiat. Transfer 147 207Google Scholar

    [30]

    Qin Z, Zhao J M, Liu L H 2017 J. Quant. Spectrosc. Radiat. Transfer 202 2Google Scholar

    [31]

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

    [32]

    Liang R H, Liu Y M, Li F Y 2021 Contrib. Plasma Phys. 61 e2021000366Google Scholar

    [33]

    Liang R H, Liu Y M, Li F Y 2021 J. Appl. Phys. 130 063303Google Scholar

    [34]

    马文, 靳奉涛, 袁建民 2007 物理学报 56 5709Google Scholar

    Ma W, Jin F T, Yuan J M 2007 Acta Phys. Sin. 56 5709Google Scholar

    [35]

    Lin X H, Liang G Y, Wang J G, Peng Y G, Shao B, Li R, Wu Y 2019 Chin. Phys. B 28 053101Google Scholar

    [36]

    Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 023101Google Scholar

    [37]

    Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. Lett. 37 123101Google Scholar

    [38]

    Li R, Liang G Y, Lin X H, Zhu Y H, Zhao S T, Wu Y 2019 Chin. Phys. B 28 043102Google Scholar

    [39]

    Xu X S, Dai A Q, Peng Y G, Wu Y, Wang J G 2018 J. Quant. Spectrosc. Radiat. Transfer 206 172Google Scholar

    [40]

    Slipher V M 1933 Mon. Not. R. Astron. Soc. 93 657Google Scholar

    [41]

    Feldman P D 1973 J. Geophys. Res. 78 2010Google Scholar

    [42]

    Langhoff S R, Bauschlicher C W 1988 J. Chem. Phys. 88 329Google Scholar

    [43]

    Langhoff S R, Bauschlicher C W, Partridge H 1987 J. Chem. Phys. 87 4716Google Scholar

    [44]

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

    [45]

    陈晨,赵国鹏,祁月盈,吴勇,王建国 2022 物理学报 71 143102Google Scholar

    Chen C, Zhao G P, Qi Y Y, Wu Y, Wang J G 2022 Acta Phys. Sin. 71 143102Google Scholar

    [46]

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

    [47]

    Werner H J and Meyer W 1980 J. Chem. Phys. 73 2342Google Scholar

    [48]

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

    [49]

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

    [50]

    Werner H J, Knowles P J, Manby F R, Schütz M, Celani P, Knizia G, Korona T, Lindh R, Mitrushenkov A, Rauhut G 2010 MOLPRO: a Package of ab initio Programs
    [51]

    Thulstrup E W, Andersen A 1975 J. Phys. B:Atom. Mol. Phys. 8 965Google Scholar

    [52]

    Zhang Y, Hanson D M 1986 Chem. Phys. Lett. 127 33Google Scholar

    [53]

    Berning A, Werner H J 1994 J. Chem. Phys. 100 1953Google Scholar

    [54]

    Li X Z, Paldus J 2000 Mol. Phys. 98 1185Google Scholar

    [55]

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

    [56]

    Bruna P J, Grein F 2008 J. Molecular Spectroscopy 250 75
    [57]

    Li X Z, Paldus J 2009 Phys. Chem. Chem. Phys. 11 5281Google Scholar

    [58]

    Langhoff S R, Bauschlicher Jr C W 1988 J. Chemical Physics 88 329
    [59]

    Bernath P F, Dalgarno A 1996 Phys. Today 49 94
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Publishing process
  • Received Date:  18 April 2022
  • Accepted Date:  18 May 2022
  • Available Online:  03 October 2022
  • Published Online:  05 October 2022

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