-
本文采用考虑了Davidson修正的内收缩多参考组态相互作用(icMRCI)方法, 计算了
$ {\text{N}}_{2}^{+} $ 体系的$ {{\text{X}}^{2}}{\Sigma}_{\text{g}}^{+} $ ,$ {{\rm{A}}^{2}}{\Pi }_{\rm{u}}$ 和$ {{\text{B}}^{2}}{\Sigma}_{\text{u}}^{+} $ 电子态的势能曲线、光谱常数和偶极跃迁矩阵元. 根据计算的分子结构数据, 给出了配分函数, 并模拟了压强在100 atm (1 atm=1×105 Pa)的条件下, 温度分别为295, 500, 1000, 2000, 2500, 5000和10000 K的不透明度. 结果表明, 由于激发态的布居数随着温度的升高逐渐增多, 不透明度分布的波长范围逐渐增大, 并且不同谱带的分界线也逐渐变得模糊. 本工作中计算的$ {\text{N}}_{2}^{+} $ 分子离子不透明度, 还在相同压强和温度条件下与其中性分子不透明度进行了对比,发现无论是波长分布范围还是峰值结构都存在显著差异. 本工作系统分析了温度效应对氮气分子离子不透明度的影响, 可以为天体物理领域提供理论和数据支持.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.-
Keywords:
- nitrogen cation /
- spectroscopic constants /
- opacities
[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 L07105
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Google Scholar
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[10] Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2011 Comput. Theor. Chem. 966 44
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[11] Huffman R E, Larrabee J C, Tanaka Y 1964 Disc. Faraday Soc. 37 159
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[13] Sinhal M 2021 Ph. D. Dissertation (Basel: University of Basel)
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Chen C, Zhao G P, Qi Y Y, Wu Y, Wang J G 2022 Acta Phys. Sin. 71 143102
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[46] Woon D E, Dunning T H. 1995 J. Chem. Phys. 103 4572
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[48] Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61
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[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
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[52] Zhang Y, Hanson D M 1986 Chem. Phys. Lett. 127 33
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Google Scholar
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-
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Fig. 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}^{+} $ .
图 2
$ {\text{N}}_{\text{2}}^{\text{ + }} $ 的偶极跃迁矩阵元随核间距的变化关系Fig. 2. Transition dipole moments of
$ {\text{N}}_{\text{2}}^{\text{ + }} $ as a function of internuclear distance R.
图 3
$ {\text{N}}_{\text{2}}^{\text{ + }} $ 的配分函数Fig. 3. The partition functions of
$ {\text{N}}_{\text{2}}^{\text{ + }} $ .
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.Fig. 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.
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.Fig. 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.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 work Experiment[18] This work Experiment[18] This work Experiment[18] 1 2160.20 2186.3 1860.80 1873.1 2350.81 2371.5 2 2127.69 2131.8 1830.13 1843.2 2296.85 2318.8 3 2095.20 2118.8 1800.42 1813.3 2236.54 2260.4 4 2062.18 2054.0 1770.50 1783.7 2169.60 2196.4 5 2028.65 2057.7 1740.20 2095.35 2122.8 6 1994.38 2003.6 1710.16 2008.01 2041.0 7 1960.15 1977.9 1680.47 1904.72 1951.1 8 1926.84 1940.7 1650.76 1790.50 1838.2 9 1893.06 1903.8 1621.04 1671.73 1726.9 10 1856.93 1870.9 1591.27 1553.84 1596.7 11 1818.04 1835.8 1561.57 1441.30 1479.9 12 1776.20 1800.6 1531.56 1339.77 1371.4 13 1733.59 1764.7 1501.57 1251.04 1276.3 14 1693.16 1733.5 1471.76 1175.43 1196.3 15 1657.08 1684.3 1442.16 1111.18 1126.6 16 1625.93 1655.8 1412.80 1053.80 1067.1 17 1597.90 1616.3 1383.51 1002.49 1015.5 18 1570.43 1576.8 1354.06 955.83 966.0 19 1541.51 1537.3 1324.26 913.25 922.0 20 1510.09 1497.8 1294.02 873.37 882.0 
下载: 导出CSV
表 2
${\text{N}}_2^+$ 的光谱常数.Table 2. Spectroscopic constants of
$\rm N_2^+$ .State Source ${R_{\rm{e}}}$/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 work 1.1191 0 2196.2324 1.9227 8.7145 Expt.[18] 1.116 0 2207.00 1.9319 8.7128 Theory[51] 1.17 0 2075 8.4 Theory[52] 1.106 0 1.97 Theory[53] 1.1201 2193.4 1.919 Theory[54] 1.1203 2195 1.917 Theory[55] 1.1189 2204.5 1.924 Theory[56] 1.1261 0 2140 Theory[57] 1.12 2185 ${ { {\rm A} }^{2} }{ { {\Pi } }_{ {\rm u} } }$ This work 1.1777 8911.1935 1890.3412 1.7358 7.6096 Expt.[18] 1.177 9016.4 1903.53 1.748 7.5948 Theory[51] 1.26 14517.97 1693 6.7 Theory[52] 1.165 9016 1.773 Theory[53] 1.1781 1898.0 1.735 Theory[54] 1.1762 1918 1.739 Theory[55] 1.1772 1900.1 1.737 Theory[56] 1.1875 8872.10 1850 Theory[57] 1.177 1911 ${ { \rm {B} }^{2} }{\Sigma}_{ {\rm u} }^{+}$ This work 1.0772 25861.741 2398.8591 2.0752 5.5273 Expt.[18] 1.077 25566.0 2419.84 2.073 5.5428 Theory[51] 1.16 30649.06 1805 4.6 Theory[52] 1.075 25566 2.084 Theory[58] 1.0832 25823 2441.8 Theory[54] 1.0776 2425 2.072 Theory[56] 1.0838 25325.80 2370
下载: 导出CSV
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[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 L07105
Google Scholar
[2] Dutuit O, Carrasco N, Thissen R, Vuitton V, Alcaraz C, Pernot P, Lavvas P 2013 Astrophys. J. Suppl. Ser. 204 20
Google Scholar
[3] Scherf M, Lammer H, Erkaev N V, Mandt K E, Thaller S E, Marty B 2020 Space Sci. Rev. 216 1
Google Scholar
[4] Bruna P J, Grein F 2008 J. Mol. Spectrosc. 250 75
Google 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 2020
Google 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 A64
Google Scholar
[7] Jenniskens P, Laux C O, Schaller E L 2004 Astrobiology 4 109
Google Scholar
[8] Abe S, Ebizuka N, Yano H, Watanabe J I, Borovička J 2005 Astrophys. J. 618 L141
Google Scholar
[9] Ho W C, Jäger W, Cramb D C, Ozier I, Gerry M C L 1992 J. Mol. Spectrosc. 153 692
Google Scholar
[10] Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2011 Comput. Theor. Chem. 966 44
Google Scholar
[11] Huffman R E, Larrabee J C, Tanaka Y 1964 Disc. Faraday Soc. 37 159
Google Scholar
[12] Bruna P J, Grein F 2004 J. Mol. Spectrosc. 227 67
Google 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. 137 641
Google Scholar
[16] Meinel A B 1950 Astrophys. J. 112 562
Google Scholar
[17] Dalby F W, Douglas A E 1951 Phys. Rev. 84 843
Google Scholar
[18] Lofthus A, Krupenie P H 1977 J. Phys. Chem Ref. Data 6 113
Google Scholar
[19] Dick K A, Benesch W, Crosswhite H M, Tilford S G, Gottscho R A, Field R W 1978 J. Mol. Spectrosc. 69 95
Google Scholar
[20] Gudeman C S, Saykally R J 1984 Annu. Rev. Phys. Chem. 35 387
Google Scholar
[21] Miller T A, Suzuki T, Hirota E 1984 J. Chem. Phys. 80 4671
Google 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. 209 133
Google Scholar
[23] Moon S Y, Choe W 2003 Spectrochim. Acta Part B 58 249
Google Scholar
[24] Zhang Y P, Deng L H, Zhang J, Chen Y Q 2015 Chin. J. Chem. Phys. 28 134
Google Scholar
[25] Nishiyama T, Taguchi M, Suzuki H, Dalin P, Ogawa Y, Brandstron U, Sakanoi T 2021 Earth Planets Space 73 30
Google Scholar
[26] Chauveau S, Perrin M Y, Riviere P, Soufiani A 2002 J. Quant. Spectrosc. Radiat. Transfer 72 503
Google Scholar
[27] Yan B, Feng W 2010 Chin. Phys. B 19 033303
Google 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 455203
Google Scholar
[29] Liu H, Shi D H, Wang S, Sun J F, Zhu Z L 2014 J. Quant. Spectrosc. Radiat. Transfer 147 207
Google Scholar
[30] Qin Z, Zhao J M, Liu L H 2017 J. Quant. Spectrosc. Radiat. Transfer 202 2
Google Scholar
[31] Liang R H, Liu Y M, Li F Y 2021 Phys. Scr. 96 125402
Google Scholar
[32] Liang R H, Liu Y M, Li F Y 2021 Contrib. Plasma Phys. 61 e2021000366
Google Scholar
[33] Liang R H, Liu Y M, Li F Y 2021 J. Appl. Phys. 130 063303
Google Scholar
[34] 马文, 靳奉涛, 袁建民 2007 物理学报 56 5709
Google Scholar
Ma W, Jin F T, Yuan J M 2007 Acta Phys. Sin. 56 5709
Google 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 053101
Google Scholar
[36] Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 023101
Google Scholar
[37] Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. Lett. 37 123101
Google Scholar
[38] Li R, Liang G Y, Lin X H, Zhu Y H, Zhao S T, Wu Y 2019 Chin. Phys. B 28 043102
Google Scholar
[39] Xu X S, Dai A Q, Peng Y G, Wu Y, Wang J G 2018 J. Quant. Spectrosc. Radiat. Transfer 206 172
Google Scholar
[40] Slipher V M 1933 Mon. Not. R. Astron. Soc. 93 657
Google Scholar
[41] Feldman P D 1973 J. Geophys. Res. 78 2010
Google Scholar
[42] Langhoff S R, Bauschlicher C W 1988 J. Chem. Phys. 88 329
Google Scholar
[43] Langhoff S R, Bauschlicher C W, Partridge H 1987 J. Chem. Phys. 87 4716
Google Scholar
[44] Weck P F, Schweitzer A, Kirby K, Hauschildt P H, Stancil P C 2004 Astrophys J. 613 567
Google Scholar
[45] 陈晨,赵国鹏,祁月盈,吴勇,王建国 2022 物理学报 71 143102
Google Scholar
Chen C, Zhao G P, Qi Y Y, Wu Y, Wang J G 2022 Acta Phys. Sin. 71 143102
Google Scholar
[46] Woon D E, Dunning T H. 1995 J. Chem. Phys. 103 4572
Google Scholar
[47] Werner H J and Meyer W 1980 J. Chem. Phys. 73 2342
Google Scholar
[48] Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61
Google Scholar
[49] Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803
Google 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. 8 965
Google Scholar
[52] Zhang Y, Hanson D M 1986 Chem. Phys. Lett. 127 33
Google Scholar
[53] Berning A, Werner H J 1994 J. Chem. Phys. 100 1953
Google Scholar
[54] Li X Z, Paldus J 2000 Mol. Phys. 98 1185
Google Scholar
[55] Spelsberg D, Meyer W 2001 J. Chem. Phys. 115 6438
Google 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 5281
Google 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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