CO+分子离子X2Σ+, A2Π和B2Σ+态的不透明度

安斯腰力吐; 王佟; 肖利丹; 刘迪; 张夏; 闫冰

doi:10.7498/aps.74.20250380

摘要

一氧化碳分子离子(CO⁺)在大气及天体物理环境中起着关键作用, 其不透明度的理论研究对辐射输运建模具有重要意义. 本文基于实验观测数据, 采用Modified-Morse (MMorse)势函数改进并构建了CO⁺分子离子X²Σ⁺, A²Π和B²Σ⁺电子态的势能曲线, 进一步提取了振动能级和光谱常数. 同时, 利用考虑Davidson修正的多参考组态相互作用(MRCI+Q)方法计算了势能曲线和电偶极跃迁矩. 改进获得的MMorse势与计算得到的势能曲线非常吻合, 且光谱常数和振动能级与其他理论和实验数据符合较好. 结合MMorse势函数和从头计算获得的电偶极跃迁矩, 计算了CO⁺分子离子在100 atm (1 atm=1.01×10⁵ Pa)压强下, 298—15000 K温度范围内的不透明度, 并探究了不同温度对高温谱的影响. 研究结果表明, 高温环境(T > 5000 K)会导致不同能带系统的谱线展宽与边界模糊, 这种混合效应在T > 10000 K时尤为突出, 揭示了高温下分子离子光谱退化的微观机制. 本研究可以为天体物理领域提供一些理论依据和数据支持. 本文数据集可在https://doi.org/10.57760/sciencedb.j00213.00136中访问获取.

关键词:

Abstract

Carbon monoxide cation (CO⁺) plays a dominant role in some astrophysical atmosphere environments, and theoretical research on its opacity is crucial for modeling radiative transport. In this work, based on experimentally observed vibrational energy levels of the X²Σ⁺, A²Π, and B²Σ⁺ electronic states of CO⁺, the potential energy curves are improved and constructed using a modified Morse (MMorse) potential function, then the vibrational energy levels and spectroscopic constants are extracted. In the meantime, the internally contracted multireference configuration interaction (MRCI) method with Davison size-extensivity correction (+Q) is used to calculate the potential energy curves and transition dipole moments. The refined MMorse potential shows excellent agreement with the computed potential energy curves, while the spectroscopic constants and vibrational levels indicate strong consistency with existing theoretical and experimental data. The opacities of the CO⁺ molecule is computed at different temperatures under the pressure of 100 atm. The result shows that as temperature rises, the opacities of transitions in the long-wavelength range increases because of the larger population on excited electronic states at higher temperatures. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00136.

Keywords:

作者及机构信息

吉林大学原子与分子物理研究所, 长春　130012

通信作者: 张夏, xiazhang@jlu.edu.cn ; 闫冰, yanbing@jlu.edu.cn

基金项目: 国家自然科学基金(批准号: 12274178, 12374230)资助的课题.

Authors and contacts

Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Corresponding author: ZHANG Xia, xiazhang@jlu.edu.cn ; YAN Bing, yanbing@jlu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12274178, 12374230).

文章全文

参考文献

[1]	Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 23101 Google Scholar
[2]	Li R, Sang J Q, Lin X H, Li J J, Liang G Y, Wu Y 2022 Chin. Phys. B 31 103101 Google Scholar
[3]	Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. Lett. 37 123101 Google Scholar
[4]	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
[5]	Xiao L, An S, Liu D, Minaev B F, Ågren H, Yan B 2025 Spectrochim. Acta, Part A 330 125704 Google Scholar
[6]	Herzberg G 1950 Molecular Spectra and Molecular Structure: I (New York: Van Nostrand Reinhold Company) pp240–491
[7]	Davies P B, Rothwell W J 1985 J. Chem. Phys. 83 5450 Google Scholar
[8]	Krishna Swamy K S 1986 Earth Moon Planets 34 281 Google Scholar
[9]	Haridass C, Prasad C V V, Reddy S P 2000 J. Mol. Spectrosc. 199 180 Google Scholar
[10]	Krupenie P H 1966 The Band Spectrum of Carbon Monoxide (Gaithersburg, MD: National Institute of Standards and Technology) pp1–37
[11]	Huebner W F 1990 Physics and Chemistry of Comets (Berlin Heidelberg: Springer) pp245–303
[12]	Haridass C, Prasad C V V, Reddy S P 1992 ApJ 388 669 Google Scholar
[13]	Bembenek Z, Domin U, Kepa R, Porada K, Rytel M, Zachwieja M, Jakubek Z, Janjic J D 1994 J. Mol. Spectrosc. 165 205 Google Scholar
[14]	Zhuang H, Yang X H, Wu S H, Bi Z Y, Ma L S, Liu Y Y, Chen Y Q 2001 Mol. Phys. 99 1447 Google Scholar
[15]	Yang X H, Wu Y D, Chen Y Q 2007 J. Mol. Spectrosc. 245 84 Google Scholar
[16]	Baltzer P, Lundqvist M, Wannberg B, Karlsson L, Larsson M, Hayes M A, West J B, Siggel M R F, Parr A C, Dehmer J L 1994 J. Phys. B: At. Mol. Opt. Phys. 27 4915 Google Scholar
[17]	Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure 4: Constants of Diatomic Molecules (New York: van Nostrand Reinhold Comp
[18]	Reddy R R, Viswanath R 1990 J. Astrophys. Astron. 11 67 Google Scholar
[19]	Kępa R, Malak Z, Szajna W, Zachwieja M 2003 J. Mol. Spectrosc. 220 58 Google Scholar
[20]	Wu Y D, Yang X H, Guo Y C, Chen Y Q 2008 J. Mol. Spectrosc. 248 81 Google Scholar
[21]	Coxon J A, Kępa R, Piotrowska I 2010 J. Mol. Spectrosc. 262 107 Google Scholar
[22]	Hamilton P A, Hughes A N, Sales K D 1993 J. Chem. Phys. 99 436 Google Scholar
[23]	Araújo J P, Ballester M Y, Lugão I G, Silva R P, Martins M P 2024 J. Mol. Model 30 352 Google Scholar
[24]	Tobias I, Fallon R J, Vanderslice J T 1960 J. Chem. Phys. 33 1638 Google Scholar
[25]	Krupenie P H, Weissman S 1965 J. Chem. Phys. 43 1529 Google Scholar
[26]	Singh R B, Rai D K 1966 J. Mol. Spectrosc. 19 424 Google Scholar
[27]	Locht R 1977 Chem. Phys. 22 13 Google Scholar
[28]	Honjou N, Sasaki F 1979 Mol. Phys. 37 1593 Google Scholar
[29]	Rosmus P, Werner H J 1982 Mol. Phys. 47 661 Google Scholar
[30]	Okada K, Iwata S 2000 J. Chem. Phys. 112 1804 Google Scholar
[31]	Mezei J Z, Backodissa-Kiminou R D, Tudorache D E, Morel V, Chakrabarti K, Motapon O, Dulieu O, Robert J, Tchang-Brillet W Ü L, Bultel A, Urbain X, Tennyson J, Hassouni K, Schneider I F 2015 Plasma Sources Sci. Technol. 24 035005 Google Scholar
[32]	Weck P F, Schweitzer A, Kirby K, Hauschildt P H, Stancil P C 2004 Astrophys. J. 613 567 Google Scholar
[33]	Mourik T V, Wilson A K, Dunning Jr T H 1999 Mol. Phys. 99 529 Google Scholar
[34]	Werner H, Knowles P J, Knizia G, Manby F R, Schütz M 2012 WIREs Comput. Mol. Sci. 2 242 Google Scholar
[35]	Le Roy R J 2017 J. Quant. Spectrosc. Ra. Transfer 186 167 Google Scholar
[36]	Yurchenko S N, Lodi L, Tennyson J, Stolyarov A V 2016 Comput. Phys. Commun. 202 262 Google Scholar
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[41]	Szajna W, Kepa R, Zachwieja M 2004 Eur. Phys. J. D 30 49 Google Scholar
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施引文献

图 1 CO⁺的X²Σ⁺, A²Π和B²Σ⁺态的势能曲线

Fig. 1. Potential energy curves for the X²Σ⁺, A²Π and B²Σ⁺ states of CO⁺.

下载: 全尺寸图片幻灯片

图 2 CO⁺分子离子X²Σ⁺, A²Π和B²Σ⁺态的改进与实验的振动能级之间误差的绝对值

Fig. 2. Absolute value of errors of the vibrational energy levels between our refined results and those given by experiment for the X²Σ⁺, A²Π and B²Σ⁺ electronic states.

下载: 全尺寸图片幻灯片

图 3 一氧化碳阳离子的电偶极跃迁矩随核间距R的变化

Fig. 3. Transition dipole moments for different states of CO⁺ cation as a function of internuclear distance R.

下载: 全尺寸图片幻灯片

图 4 CO⁺分子离子的配分函数

Fig. 4. Partition functions of CO⁺.

下载: 全尺寸图片幻灯片

图 5 在100 atm压强时, CO⁺分子离子在不同温度下, 各个电子态之间的跃迁对整体不透明度的贡献　(a) 298 K; (b) 2000 K

Fig. 5. Contributions of electronic state transitions to the total opacity of CO⁺ cation at different temperatures under pressure of 100 atm: (a) 298 K; (b) 2000 K.

下载: 全尺寸图片幻灯片

图 6 在100 atm 压强下, CO⁺分子离子X²Σ⁺, A²Π和B²Σ⁺态的不透明度随温度的变化(T = 298, 2000, 5000, 10000, 15000 K)

Fig. 6. Opacities of CO⁺ cation for temperatures of 298 K, 2000 K, 5000 K, 10000 K and 15000 K at a pressure of 100 atm including transitions of B²Σ⁺-X²Σ⁺, B²Σ⁺-A²Π and A²Π-X²Σ⁺.

下载: 全尺寸图片幻灯片

表 1 CO⁺分子离子X²Σ⁺, A²Π和B²Σ⁺态的振动能级间隔(单位cm^–1)

Table 1. Vibrational energy level intervals for X²Σ⁺, A²Π和B²Σ⁺ state of CO⁺ (in cm^–1).

v	X²Σ⁺		A²Π		B²Σ⁺
v	Refined	Exp^[21]	Refined	Exp^[21]	Refined	Exp^[39]
1	2183.96	2183.89	1535.08	1535.05	1679.49	1679.55
2	2153.53	2153.56	1508.02	1508.03	1626.18	1626.61
3	2123.18	2123.24	1481.08	1481.11	1575.66	1575.77
4	2092.87	2092.92	1454.26	1454.29	1527.62	1527.02
5	2062.56	2062.58	1427.55	1427.56	1481.78	1480.36
6	2032.21	2032.20	1400.93	1400.92	1437.90	1435.78
7	2001.79	2001.79	1374.40	1374.40	1395.74
8	1971.26	1971.33	1347.94	1347.95	1355.11
9	1940.61	1940.82	1321.56	1321.32	1315.81
10	1909.80	1910.26	1295.25	1295.09	1277.70
11	1878.80	1879.68	1269.00	1268.82	1240.61
12	1847.60	1849.06	1242.80	1242.60	1204.42
13	1816.18	1818.42	1216.65	1217.00	1169.02
14	1784.50	1787.79	1190.54	1190.00	1134.28
15	1752.56	1757.19	1164.47		1100.11
16	1720.33	1726.60	1138.43		1066.44
17	1687.79	1695.30	1112.43		1033.17
18	1654.93	1666.00	1086.45		1000.24
19	1621.72	1632.00	1060.50		967.57
20	1588.14	1601.00	1034.56		935.11

下载: 导出CSV

表 2 CO⁺分子离子的光谱常数

Table 2. Spectroscopic constants of the doublet Λ-S states for CO⁺.

Λ-S states		T_e/cm^–1	R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/cm^–1
X²Σ⁺	Refined	0	1.1152	2214.72	15.2312	1.9767	67533.4167
	Theory^[30]	0	1.119	2214.6	14.75		66731
	Theory^[39]			2212.05	17.74	1.980561	67813.483
	Theory^[40]	0	1.1153	2214.15	15.15	1.9769
	Exp^[30]	0	1.1151	2215.1	15.27		67535
	Exp^[39]			2214.3904(10)	15.1304(31)	1.976964(12)
	Exp^[41]			2214.2219(79)	15.1509(31)	1.976949(26)
A²Π	Refined	20733.0015	1.2437	1561.17	13.3236	1.5895	46186.90
	Theory^[30]	20594	1.246	1570.0	12.86		46473
	Theory^[40]	19628.2	1.2438	1562.79	13.93	1.5894
	Exp^[30]	20733.3	1.2437	1562.0	13.53		47128
B²Σ⁺	Refined	45876.6989	1.1689	1712.84	22.3220	1.7989	37988.4876
	Theory^[30]	45979	1.170	1742.7	25.99		37123
	Theory^[39]	45868.20		1742.94	19.61	1.805184	37854.825
	Exp^[30]	45876.7	1.1687	1734.1	27.92		37692
	Exp^[39]	45878.204(95)		1734.480(98)	28.033(90)	1.799491(21)
	Exp^[41]	45876.724(48)		1734.626(86)	28.272(38)	1.799526(20)

下载: 导出CSV

[1]	Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 23101 Google Scholar
[2]	Li R, Sang J Q, Lin X H, Li J J, Liang G Y, Wu Y 2022 Chin. Phys. B 31 103101 Google Scholar
[3]	Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. Lett. 37 123101 Google Scholar
[4]	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
[5]	Xiao L, An S, Liu D, Minaev B F, Ågren H, Yan B 2025 Spectrochim. Acta, Part A 330 125704 Google Scholar
[6]	Herzberg G 1950 Molecular Spectra and Molecular Structure: I (New York: Van Nostrand Reinhold Company) pp240–491
[7]	Davies P B, Rothwell W J 1985 J. Chem. Phys. 83 5450 Google Scholar
[8]	Krishna Swamy K S 1986 Earth Moon Planets 34 281 Google Scholar
[9]	Haridass C, Prasad C V V, Reddy S P 2000 J. Mol. Spectrosc. 199 180 Google Scholar
[10]	Krupenie P H 1966 The Band Spectrum of Carbon Monoxide (Gaithersburg, MD: National Institute of Standards and Technology) pp1–37
[11]	Huebner W F 1990 Physics and Chemistry of Comets (Berlin Heidelberg: Springer) pp245–303
[12]	Haridass C, Prasad C V V, Reddy S P 1992 ApJ 388 669 Google Scholar
[13]	Bembenek Z, Domin U, Kepa R, Porada K, Rytel M, Zachwieja M, Jakubek Z, Janjic J D 1994 J. Mol. Spectrosc. 165 205 Google Scholar
[14]	Zhuang H, Yang X H, Wu S H, Bi Z Y, Ma L S, Liu Y Y, Chen Y Q 2001 Mol. Phys. 99 1447 Google Scholar
[15]	Yang X H, Wu Y D, Chen Y Q 2007 J. Mol. Spectrosc. 245 84 Google Scholar
[16]	Baltzer P, Lundqvist M, Wannberg B, Karlsson L, Larsson M, Hayes M A, West J B, Siggel M R F, Parr A C, Dehmer J L 1994 J. Phys. B: At. Mol. Opt. Phys. 27 4915 Google Scholar
[17]	Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure 4: Constants of Diatomic Molecules (New York: van Nostrand Reinhold Comp
[18]	Reddy R R, Viswanath R 1990 J. Astrophys. Astron. 11 67 Google Scholar
[19]	Kępa R, Malak Z, Szajna W, Zachwieja M 2003 J. Mol. Spectrosc. 220 58 Google Scholar
[20]	Wu Y D, Yang X H, Guo Y C, Chen Y Q 2008 J. Mol. Spectrosc. 248 81 Google Scholar
[21]	Coxon J A, Kępa R, Piotrowska I 2010 J. Mol. Spectrosc. 262 107 Google Scholar
[22]	Hamilton P A, Hughes A N, Sales K D 1993 J. Chem. Phys. 99 436 Google Scholar
[23]	Araújo J P, Ballester M Y, Lugão I G, Silva R P, Martins M P 2024 J. Mol. Model 30 352 Google Scholar
[24]	Tobias I, Fallon R J, Vanderslice J T 1960 J. Chem. Phys. 33 1638 Google Scholar
[25]	Krupenie P H, Weissman S 1965 J. Chem. Phys. 43 1529 Google Scholar
[26]	Singh R B, Rai D K 1966 J. Mol. Spectrosc. 19 424 Google Scholar
[27]	Locht R 1977 Chem. Phys. 22 13 Google Scholar
[28]	Honjou N, Sasaki F 1979 Mol. Phys. 37 1593 Google Scholar
[29]	Rosmus P, Werner H J 1982 Mol. Phys. 47 661 Google Scholar
[30]	Okada K, Iwata S 2000 J. Chem. Phys. 112 1804 Google Scholar
[31]	Mezei J Z, Backodissa-Kiminou R D, Tudorache D E, Morel V, Chakrabarti K, Motapon O, Dulieu O, Robert J, Tchang-Brillet W Ü L, Bultel A, Urbain X, Tennyson J, Hassouni K, Schneider I F 2015 Plasma Sources Sci. Technol. 24 035005 Google Scholar
[32]	Weck P F, Schweitzer A, Kirby K, Hauschildt P H, Stancil P C 2004 Astrophys. J. 613 567 Google Scholar
[33]	Mourik T V, Wilson A K, Dunning Jr T H 1999 Mol. Phys. 99 529 Google Scholar
[34]	Werner H, Knowles P J, Knizia G, Manby F R, Schütz M 2012 WIREs Comput. Mol. Sci. 2 242 Google Scholar
[35]	Le Roy R J 2017 J. Quant. Spectrosc. Ra. Transfer 186 167 Google Scholar
[36]	Yurchenko S N, Lodi L, Tennyson J, Stolyarov A V 2016 Comput. Phys. Commun. 202 262 Google Scholar
[37]	Yurchenko S N, Al-Refaie A F, Tennyson J 2018 Astron. Astrophys. 614 A131 Google Scholar
[38]	https://physics.nist.gov/cgi-bin/ASD/levels_pt.pl [2025-3-11]
[39]	Ventura L R, Da Silva R S, Ballester M Y, Fellows C E 2020 J. Quant. Spectrosc. Ra. Transfer 256 107312 Google Scholar
[40]	Reddy R R, Nazeer Ahammed Y, Rama Gopal K, Baba Basha D 2004 J. Quant. Spectrosc. Ra. Transfer 85 105 Google Scholar
[41]	Szajna W, Kepa R, Zachwieja M 2004 Eur. Phys. J. D 30 49 Google Scholar
[42]	Hakalla R, Szajna W, Piotrowska I, Malicka M I, Zachwieja M, Kępa R 2019 J. Quant. Spectrosc. Ra. Transfer 234 159 Google Scholar
[43]	Szajna W, Kȩpa R, Field R W, Hakalla R 2024 J. Quant. Spectrosc. Ra. Transfer 324 109059 Google Scholar

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CO⁺分子离子X²Σ⁺, A²Π和B²Σ⁺态的不透明度

Opacities of X²Σ⁺, A²Π, and B²Σ⁺ states of CO⁺molecule ion

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吉林大学原子与分子物理研究所, 长春　130012

通信作者: 张夏, xiazhang@jlu.edu.cn ; 闫冰, yanbing@jlu.edu.cn

Authors and contacts

Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Corresponding author: ZHANG Xia, xiazhang@jlu.edu.cn ; YAN Bing, yanbing@jlu.edu.cn

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