氮气分子<inline-formula><tex-math id="Z-20220715032739-1">\begin{document}${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}} \text{和} { b}^1\Pi_{\rm u} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20220043_Z-20220715032739-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20220043_Z-20220715032739-1.png"/></alternatives></inline-formula>电子态的不透明度

陈晨; 赵国鹏; 祁月盈; 吴勇; 王建国

doi:10.7498/aps.71.20220043

摘要

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${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$和b¹П_u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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
复旦大学, 现代物理研究所, 上海　200433

2.
嘉兴学院数据科学学院, 嘉兴　314001

3.
北京应用物理与计算数学研究所, 计算物理重点实验室, 北京　100088

4.
北京大学工学院, 应用物理与技术研究中心, 北京　100871

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.

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

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)

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 氮气分子${X^1}\Sigma _{\rm{g}}^ + ,{a^\prime }^1\Sigma _{\rm{u}}^ - ,{a^1}{\Pi _{\rm{g}}}$和b¹П_u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 b¹П_u states of nitrogen molecular.

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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.

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图 3 氮气分子的配分函数

Fig. 3. The partition functions of nitrogen molecular.

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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.

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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.

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表 1 氮气分子的光谱常数

Table 1. Spectral constants of nitrogen molecular.

State	Method	T_e/cm^–1	ω_e/cm^–1	ω_ex_e/cm^–1	B_e/cm^–1	R_e/Å	D_e/eV
${X^1}\Sigma _{\rm{g}}^ + $	Present	0	2357.1168	14.3883	1.9968	1.0985	9.8396
	MR-AQCC^[48]	0	2337			1.1019	9.6426
	MR-CISD^[48]	0	2342			1.1016	9.6468
	MR-CISD+Q^[48]	0	2335			1.1019	9.6489
	DFT(et-QZ3P-2D)^[49]	0	2356	14.3	1.986	1.1012
	DFT(ATZP)^[49]	0	2346	13.3	1.974	1.1045
	CCSD(T)^[50]	0	2342.8	14.091	1.983	1.1014
	CCSD^[50]	0	2356.1	13.972	1.987	1.1003
	CASSCF^[30]	0	2358			1.092	9.82
	Expt.^[20]	0	2358.57	14.324	1.99824	1.09768	9.7593
$a'{}^1\Sigma _{\rm u}^ -$	Present	68344.098	1528.4544	11.4479	1.4794	1.2755	6.1725
	MR-AQCC^[48]	67762	1514			1.2807	6.1230
	MR-CISD^[48]	68480	1517			1.2804	6.0915
	MR-CISD+Q^[48]	67531	1513			1.2808	6.1254
	DFT(et-QZ3P-2D)^[49]	64968.9	1468	9.71	1.450	1.2887
	DFT(ATZP)^[49]	64578.2	1471	11.1	1.446	1.2906
	MRCI^[28]	69032	1523.6	11.91	1.4725	1.278
	CASSCF^[30]		1572			1.277	5.81
	Expt.^[20]	67739	1530.27	12.1	1.4801	1.2754	6.1278
a¹П_g	Present	69486.425	1691.4017	13.6099	1.6135	1.2215	6.04016
	MR-AQCC^[48]	69086	1676			1.2266	5.9587
	MR-CISD^[48]	69566	1691			1.2261	5.9568
	MR-CISD+Q^[48]	68951	1670			1.2268	5.9617
	DFT(et-QZ3P-2D)^[49]	69078.0	1684	12.4	1.609	1.2236
	DFT(ATZP)^[49]	68910.6	1647	14.0	1.601	1.2264
	MRCI^[28]	69971	1687.5	13.91	1.6034	1.225
	CASSCF^[30]		1676			1.230	6.30
	Expt.^[20]	68951.2	1694.2	13.9	1.6170	1.2203	5.9775
b¹П_u	Present	102357.2	682.0947	–5.9531	1.3929	1.319	1.9599
	MR-AQCC^[48]	101244	607			1.3456	1.9742
	MR-CISD^[48]	102333	632			1.3482	1.8942
	MR-CISD+Q^[48]	101018	600			1.3489	1.9859
	MRCI^[26]	101703.8	681.1	–8.8	1.437
	Expt.^[20]	100817.5					2.0265
	Expt.^[51]	101675	634.8		1.448	1.284

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

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

v	Present	8R RMR CCSD^[52]	MR-AQCC^[52]	MR-ACPF^[53]	Expt.^[54]	Expt.^[55]
1	2327.5	2336.5	2330.41	2328.54	2329.9	2329.9
2	2299.4	2308.4	2301.81	2299.89	2301.3	2301.2
3	2270.5	2279.8	2273.14	2271.18	2272.5	2272.6
4	2242.0	2251.4	2244.47	2242.45	2243.8	2243.8
5	2213.1	2222.5	2215.74	2213.69	2215.1	2215.0
6	2184.4	2193.7	2186.98	2184.87	2186.2	2186.2
7	2155.6	2164.7	2158.17	2156.01	2157.4	2157.4
8	2126.6	2135.3	2129.31	2127.10	2128.4	2128.4
9	2097.6	2106.0	2100.40	2098.13	2099.5	2099.5
10	2068.7	2076.4	2071.43	2069.09	2070.4	2070.4
11	2039.6	2046.7	2042.39	2040.02	2041.4	2041.4
12	2010.3	2016.8	2013.29	2010.84	2012.1	2012.1
13	1981.1	1987.0	1984.10	1981.58	1982.9	1983.0
14	1951.7	1956.9	1954.83	1952.26	1953.6	1953.5
15	1922.2	1927.0	1925.43	1922.79	1924.1	1924.2
16	1892.7	1896.9	1895.96	1893.25	1894.6	1894.7
17	1863.1	1866.7	1866.31	1863.53	1864.9	1865.1
18	1833.6	1836.6	1836.55	1833.69	1835.0	1835.4
19	1803.8	1806.3	1806.60	1803.68	1805.0	1805.6
20	1773.6	1775.9			1774.6	1775.6
21	1743.3	1745.5			1744.1	1745.7
22	1712.7	1714.8			1713.3	1715.5
23	1681.8	1684.0			1682.1	1685.0
24	1650.5	1652.8			1650.5	1655.0
25	1618.8	1621.6			1618.4	1624.0
26	1586.5				1585.9
27	1553.8				1552.8
28	1520.8				1519.0
29	1487.3				1484.7
30	1453.2

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

Table 3. Vibrational level spaceings (E_v– E_v–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} }^ - $		a¹П_g		b¹П_u
v	Present	Expt.^[20]	Present	Expt.^[20]	Present	Expt.^[20]
1	1506.7	1506.24	1664.6	1666.34	645.2	645.4
2	1482.8	1482.45	1637.6	1638.51	710.9	705.3
3	1459.3	1458.90	1609.6	1610.77	745.2	747.6
4	1436.0	1435.57	1581.8	1583.07	763.7	774.8
5	1412.8	1412.47	1554.5	1555.46	772.9	789.6
6	1389.8	1389.58	1527.3	1527.93	776.4	794.4
7	1367.4	1366.88	1500.1	1500.49	774.8	791.4
8	1345.0	1344.41	1473.3	1473.15	770.5	782.8
9	1322.8	1322.10	1446.4	1445.91	762.7	770.2
10	1300.7	1300.00	1419.7	1418.77	752.4	754.8
11	1278.8	1278.06	1393.1	1391.77	740.2	737.9
12	1257.1	1256.31	1366.6	1364.87	725.2	719.8
13	1235.8	1234.70	1340.3	1338.12	708.4	701.0
14	1214.5	1213.27	1314.2	1311.50	689.0	681.4
15	1193.1	1191.98	1288.2	1285.03	667.1	660.5
16	1172.0	1170.84	1262.1		642.1	637.9
17	1151.2	1149.83	1236.4		613.4	612.6
18	1130.4	1128.95	1210.9		580.3	584.0
19	1109.6	1108.19	1185.3		541.8	551.0
20	1088.8		1159.7
21	1068.1		1134.0
22	1047.5		1108.4
23	1026.9		1082.8
24	1006.2		1057.1
25	985.4		1031.2
26	964.5		1005.0
27	943.4		978.4
28	922.3		951.4

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[1]	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
[2]	Liang G Y, Peng Y G, Li R, Wu Y, Wang J G 2020 Chin. Phys. B 29 023101 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]	Li R, Liang G Y, Lin X H, Zhu Y H, Zhao S T, Wu Y 2019 Chin. Phys. B 28 043102 Google Scholar
[5]	Xu X S, Dai A Q, Peng Y G, Wu Y, Wang J G 2018 J. Quant. Spectrosc. Radiat. Transfer 206 172 Google Scholar
[6]	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
[7]	Liu X M, Donald E S 2006 Astrophys. J. 645 1560 Google Scholar
[8]	Bishop J, Feldman P D 2003 J. Geophys. Res. 108 1243 Google Scholar
[9]	Strobel D F, Shemansky D E 1982 J. Geophys. Res. 87 1361 Google Scholar
[10]	Stevens M H 2001 J. Geophys. Res. 106 3685 Google Scholar
[11]	Vuitton V, Yelle R V, Anicich V G 2006 Astrophys. J. Lett. 647 L175 Google Scholar
[12]	Liang M C, Heays A N, Lewis B R, Gibson S T, Yung Y L 2007 Astrophys. J. Lett. 664 L115 Google Scholar
[13]	Knauth D C, Andersson B G, McCandliss S R, Moos H W 2004 Nature 429 636 Google Scholar
[14]	Stark G, Huber K P, Yoshino K, Smith P L, Ito K 2005 J. Chem. Phys. 123 214303 Google Scholar
[15]	Rothman L S, Jacquemart D, Barbe A, et al. 2005 J. Quant. Spectrosc. Radiat. Transfer 96 139 Google Scholar
[16]	Rothman L S, Gordon I E, Barbe A, et al. 2009 J. Quant. Spectrosc. Radiat. Transfer 110 533 Google Scholar
[17]	Gordon I E, Rothman L S, Hill C, et al. 2017 J. Quant. Spectrosc. Radiat. Transfer 203 3 Google Scholar
[18]	Rothman L S, Wattson R B, Gamache R, Schroeder J W, McCann A 1995 Proc. Soc. 2471 105 Google Scholar
[19]	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 2139 Google Scholar
[20]	Lofthus A, Krupenie P H 1977 J. Phys. Chem. Ref. Data 6 113 Google Scholar
[21]	Stark G, Smith P L, Huber K P, Yoshino K, Ito K 1992 J. Chem. Phys. 97 4809 Google Scholar
[22]	Haverd V E, Lewis B R, Gibson S T, Stark G 2005 J. Chem. Phys. 123 214304 Google Scholar
[23]	Robert Wu C Y, Judge D L, Matsui T 2006 J. Geophys. Res. 111 A5 Google Scholar
[24]	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. 315 137 Google Scholar
[25]	Heays A N, Lewis B R, De Oliveira N, Ubachs W 2019 J. Chem. Phys. 151 224305 Google Scholar
[26]	Spelsberg D, Meyer W 2001 J. Chem. Phys. 115 6438 Google Scholar
[27]	San-Fabián E, Pastor-Abia L 2003 Theor. Chem. Acc. 110 276 Google Scholar
[28]	Hochlaf M, Ndome H, Hammoutène D, Vervloet M 2010 J. Phys. B: At. Mol. Opt. Phys. 43 245101 Google Scholar
[29]	Shi D H, Xing W, Sun J F, Zhu Z L, Liu Y F 2012 Int. J. Quantum Chem. 112 1323 Google Scholar
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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

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

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1.
复旦大学, 现代物理研究所, 上海　200433

2.
嘉兴学院数据科学学院, 嘉兴　314001

3.
北京应用物理与计算数学研究所, 计算物理重点实验室, 北京　100088

4.
北京大学工学院, 应用物理与技术研究中心, 北京　100871

通信作者: 赵国鹏, guopengzhao@zjxu.edu.cn ; 吴勇, wu_yong@iapcm.ac.cn ;

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Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Wu Yong, wu_yong@iapcm.ac.cn ;

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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

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

摘要

Abstract

作者及机构信息

1. 复旦大学, 现代物理研究所, 上海 200433 2. 嘉兴学院数据科学学院, 嘉兴 314001 3. 北京应用物理与计算数学研究所, 计算物理重点实验室, 北京 100088 4. 北京大学工学院, 应用物理与技术研究中心, 北京 100871

通信作者: 赵国鹏, guopengzhao@zjxu.edu.cn ; 吴勇, wu_yong@iapcm.ac.cn ;

Authors and contacts

Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Wu Yong, wu_yong@iapcm.ac.cn ;

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1.
复旦大学, 现代物理研究所, 上海　200433

2.
嘉兴学院数据科学学院, 嘉兴　314001

3.
北京应用物理与计算数学研究所, 计算物理重点实验室, 北京　100088

4.
北京大学工学院, 应用物理与技术研究中心, 北京　100871