ICl<sup>+</sup>分子离子激发态的包含自旋-轨道耦合效应的理论研究

李瑞; 窦荣龙; 高婷; 李奇楠; 宋超群

doi:10.7498/aps.74.20250510

摘要

采用高精度的多参考组态相互作用方法研究了ICl⁺分子离子的电子结构. 在计算过程中, 通过考虑Davidson修正、自旋-轨道耦合效应和芯-价电子关联提高计算结果的准确性. 获得了两条能量最低的解离极限相关的21个Λ-S态和42个Ω态势能曲线. 在计算的势能曲线基础上, 拟合了束缚态的光谱常数, 这些理论光谱常数与已知的实验结果吻合较好. 研究了ICl⁺分子离子的偶极矩, 并通过相同对称性电子态2²Σ⁺/3²Σ⁺和2²Π/3²Π在交叉区域中主要电子组态成分的变化阐明了偶极矩的变化规律. 计算了与2²Π, 3²Π, 1²Δ, 2²Δ态相关的自旋-轨道耦合矩阵元. 借助于2²Π, 3²Π, 1²Δ, 2²Δ态及邻近电子态的势能曲线, 讨论了相应的预解离通道. 最后对ICl⁺分子离子激发态至基态的跃迁性质展开了研究. 基于计算所得的跃迁偶极矩和Franck-Condon因子, 给出了激发态较低振动能级的自发辐射寿命. 本文数据集可在https://doi.org/10.57760/sciencedb.j00213.00140中访问获取.

关键词:

Abstract

The electronic structure of the ICl⁺ molecular ion is investigated by using high-level multireference configuration interaction (MRCI) method. To improve computational accuracy, Davidson corrections, spin-orbit coupling (SOC), and core-valence electron correlations effects are incorporated into the calculations. The potential energy curves (PECs) of 21 Λ-S states associated with the two lowest dissociation limits I⁺(¹D_g)+Cl(²P_u) and I⁺(³P_g)+Cl(²P_u) are obtained. The dipole moments (DMs) of the 21 Λ-S states of ICl⁺ are systematically studied, and the variations of DMs of the identical symmetry state (2²Σ⁺/3²Σ⁺ and 2²Π/3²Π) in the avoided crossing regions are elucidated by analyzing the dominant electronic configuration. When considering the SOC effect, the Λ-S states with the same Ω components may form new avoided crossing point, making the PECs more complex. With the help of calculated SOC matrix element, the interaction between crossing states can be elucidated. Spin-orbit coupling matrix elements involving the 2²Π, 3²Π, 1²Δ and 2²Δ states are calculated. By analyzing potential energy curves of these states and the nearby electronic states, the possible predissociation channels for 2²Π, 3²Π, 1²Δ and 2²Δ states are provided. Based on the computed PECs, the spectroscopic constants of bound Λ-S and Ω states are determined. The comparison of the spectroscopic constants between Λ-S and Ω states indicates that the SOC effect has an obvious correction to the spectroscopic properties of low-lying states. Finally, the transition properties between excited states and the ground state are studied. Based on the computed transition dipole moments and Franck-Condon factors, radiative lifetimes for the low-lying vibrational levels of excited states are evaluated. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j 00213.00140.

Keywords:

作者及机构信息

齐齐哈尔大学理学院物理系, 齐齐哈尔　161006

通信作者: 李瑞, ruili06@mails.jlu.edu.cn

基金项目: 黑龙江省自然科学基金(批准号: LH2022A026)、黑龙江省省属高等学校基本科研业务费科研项目(批准号: 145409330, 145309621)和国家自然科学基金(批准号: 42371113)资助的课题.

Authors and contacts

Department of Physics, College of Science, Qiqihar University, Qiqihar 161006, China

Corresponding author: LI Rui, ruili06@mails.jlu.edu.cn

Funds: Project supported by the Natural Science Foundation of Heilongjiang Province, China (Grant No. LH2022A026), the Fundamental Research Funds in Heilongjiang Province Universities, China (Grant Nos. 145409330, 145309621), and the National Natural Science Foundation of China (Grant No. 42371113).

文章全文

参考文献

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施引文献

图 1 ICl⁺分子离子的Λ-S态势能曲线

Fig. 1. Potential energy curves of the Λ-S states of ICl⁺ molecular ion.

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图 2 ICl⁺分子离子的Λ-S态偶极矩曲线　(a)双重态的偶极矩; (b)四重态的偶极矩

Fig. 2. Dipole moments curves of the Λ-S states of ICl⁺ molecular ion: (a) Dipole moment of the doublet state; (b) dipole moment of the quartet state.

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图 3 2²Π/3²Π (a)和2²Σ⁺/3²Σ⁺ (b)的组态权重 (c²)

Fig. 3. The R-dependent weights (c²) of the electronic configurations of 2²Π/3²Π (a) and 2²Σ⁺/3²Σ⁺ (b) states.

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图 4 交叉区域振动能级的放大视图

Fig. 4. An amplified view of crossing region with the corresponding vibrational levels.

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图 5 包含2²Π, 1²Δ态(a)和2²Δ, 3²Π态(b)的自旋-轨道耦合矩阵元随核间距的变化

Fig. 5. Variation curves of spin-orbit coupling matrix elements of 2²Π, 1²Δ states (a) and 2²Δ, 3²Π states (b) with internuclear distance.

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图 6 ICl⁺分子离子的Ω态势能曲线

Fig. 6. Potential energy curves of the Ω states of ICl⁺ molecular ion.

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图 7 ICl⁺分子离子跃迁偶极矩曲线

Fig. 7. Transition dipole moments curves of ICl⁺ molecular ion.

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表 1 ICl⁺分子离子R_e附近的组态权重和垂直激发能

Table 1. Electronic configuration and vertical excitation energies of ICl⁺ molecular ion at R_e.

Λ-S 态	R_e 附近的组态权重/%	T/cm^–1
Χ²Π	7σ²8σ²9σ²10σ²11σ⁰3π⁴4π⁴5π³(91)	0
$ {1^4}{\Sigma ^ - } $	7σ²8σ²9σ²10σ²11σ¹3π⁴4π⁴5π²(77) 7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(20)	18885.3
2²Π	7σ²8σ²9σ²10σ²11σ⁰3π⁴4π³5π⁴(87) 7σ²8σ²9σ²10σ¹11σ¹3π⁴4π⁴5π³(6)	23660.8
1²Δ	7σ²8σ²9σ²10σ²11σ¹3π⁴4π⁴5π²(67) 7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(29)	25549.0
1²Σ⁺	7σ²8σ²9σ²10σ²11σ¹3π⁴4π⁴5π²(59) 7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(34)	28700.8
2²Σ⁺	7σ²8σ²9σ²10σ¹11σ⁰3π⁴4π⁴5π⁴(94)	33963.0
1⁴Δ	7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(99)	35589.7
2²Δ	7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(96)	43617.4
3²Σ⁺	7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(95)	44332.0
$ {3^2}{\Sigma ^ - } $	7σ²8σ²9σ²10σ²11σ¹3π⁴4π³5π³(67) 7σ²8σ²9σ²10σ¹11σ²3π⁴4π⁴5π²(22) 7σ²8σ²9σ²10σ²11σ¹3π⁴4π⁴5π²(9)	52169.3
3²Π	7σ²8σ²9σ²10σ²11σ²3π⁴4π⁴5π¹(48) 7σ²8σ²9σ²10σ²11σ²3π⁴4π³5π²(48)	53534.0

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表 2 ICl⁺分子离子Λ-S态的光谱常数

Table 2. Spectroscopic constants of the Λ-S states of ICl⁺ molecular ion.

Λ-S态		T_e/cm^–1	D₀/eV	B_e/cm^–1	ω_e/cm^–1	R_e/Å
Χ²Π	本文	0	2.50	0.1221	432	2.24
Χ²Π	实验^a)	0	2.52
2²Π	本文	18218	0.27	0.0915	259	2.59
	实验^b)	19551
	理论^c)	14352			207	2.78
1²Δ	本文	17516	0.35	0.0737	109	2.89
1⁴Σ^–	本文	13617	0.83	0.0889	218	2.63
1⁴Δ	本文	17183	0.39	0.0670	138	3.03
1²Σ⁺	本文	18015	0.28	0.0654	153	3.05
3²Π	本文	22122	0.80	0.0628	526	3.14
3²Π	实验^a)	22420
2²Δ	本文	24768	0.52	0.0696	171	2.97
2²Σ⁺	本文	25192	0.47	0.0687	164	2.99
3²Σ^–	本文	25241	0.46	0.0630	181	3.13
注: ^a)文献[33]; ^b)文献[12]; ^c)文献[16].

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表 3 ICl⁺分子离子Ω态的解离关系

Table 3. Dissociation relationships of Ω states of ICl⁺ molecular ion.

原子态 (I⁺+Cl)	Ω态	能量/cm^–1
原子态 (I⁺+Cl)	Ω态	本文	实验^a)
I⁺(³Pg₂)+Cl(²Pu_3/2)	7/2, 5/2(2), 3/2(3), 1/2(4)	0	0
I⁺(³Pg₂)+Cl(²Pu_1/2)	5/2, 3/2(2), 1/2(2)	821	882
I⁺(³Pg₀)+Cl(²Pu_3/2)	3/2, 1/2	6433	6448
I⁺(³Pg₁)+Cl(²Pu_3/2)	5/2, 3/2(2), 1/2(3)	6901	7087
I⁺(³Pg₀)+Cl(²Pu_1/2)	1/2	7254	7330
I⁺(³Pg₁)+Cl(²Pu_1/2)	3/2, 1/2(2)	7722	7969
I⁺(¹Dg₂)+Cl(²Pu_3/2)	7/2, 5/2(2), 3/2(3), 1/2(4)	13950	13727
I⁺(¹Dg₂)+Cl(²Pu_1/2)	5/2, 3/2(2), 1/2(2)	14771	14610
注: ^a)文献[34].

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表 4 ICl⁺分子离子Ω态的光谱常数

Table 4. Spectroscopic constants of Ω states of ICl⁺ molecular ion.

Ω态		T_e/cm^–1	D₀/eV	B_e/cm^–1	ω_e/cm^–1	R_e/Å	R_e处主要的Λ-S成分/%
X²Π_3/2	本文	0	2.31	0.1216	419	2.250	X²Π (98.1)
	实验^a)				390
	实验^b)				429	2.240±0.01
	理论^c)				311	2.470
X²Π_1/2	本文	4501	1.75	0.1217	426	2.248	X²Π (97.7)
	实验^d)	4680
	实验^b)	4670±16			437	2.224±0.001
	理论^c)	5424			314	2.460
1/2(II)	本文	14808	0.50	0.0864	244	2.666	$ {1^4}{\Sigma ^ - } $ (79.7) 1²Σ⁺ (12.5)
1/2(III)	本文	17191	0.21	0.0656	78	3.063	$ {1^2}{\Sigma ^ - } $ (38.3) 1⁴Σ⁺ (25.7) 3²Π (10.8) 1²Π (5.8)
3/2(II)	本文	15202	0.44	0.0831	156	1.518	$ {1^4}{\Sigma ^ - } $ (80.7) 1⁴Σ⁺ (6.7)
3/2(III)	本文	16795	0.21	0.0649	107	3.003	1⁴Δ (58.3) 1²Δ (34.8)
注: ^a)文献[6]; ^b)文献[12]; ^c)文献[16]; ^d)文献[33].

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表 5 ICl⁺分子离子跃迁的Frank-Condon因子

Table 5. Frank-Condon factors for the transition of ICl⁺ molecular ion.

		ν" = 0	ν" = 1	ν" = 2	ν" = 3	ν" = 4
1²Δ-Χ²Π
ν' = 0	本文	1.888×10^–17	8.612×10^–16	1.956×10^–14	2.919×10^–13	3.193×10^–12
ν' = 1	本文	3.271×10^–16	1.436×10^–14	3.138×10^–13	4.501×10^–12	4.724×10^–11
ν' = 2	本文	2.958×10^–15	1.252×10^–13	2.635×10^–12	3.635×10^–11	3.662×10^–10
2²Δ-Χ²Π
ν' = 0	本文	4.361×10^–27	5.255×10^–25	2.996×10^–23	1.085×10^–21	2.796×10^–20
ν' = 1	本文	1.373×10^–25	1.547×10^–23	8.325×10^–22	2.864×10^–20	7.046×10^–19
ν' = 2	本文	2.081×10^–24	2.230×10^–22	1.149×10^–20	3.797×10^–19	8.989×10^–18
2²Σ⁺-X²Π
ν' = 0	本文	5.553×10^–27	5.602×10^–25	2.715×10^–23	8.439×10^–22	1.889×10^–20
ν' = 1	本文	2.304×10^–25	2.065×10^–23	9.017×10^–22	2.559×10^–20	5.290×10^–19
3²Σ⁺-X²Π
ν' = 0	本文	4.161×10^–18	2.943×10^–16	1.010×10^–14	2.216×10^–13	3.456×10^–12
ν' = 1	本文	4.071×10^–17	2.814×10^–15	9.431×10^–14	2.019×10^–12	3.067×10^–11
ν' = 2	本文	2.033×10^–16	1.374×10^–14	4.503×10^–13	9.412×10^–12	1.394×10^–10
1/2(II)-Χ²Π_3/2
ν' = 0	本文	1.226×10^–9	3.102×10^–8	3.870×10^–7	3.155×10^–6	1.872×10^–5
ν' = 1	本文	1.923×10^–8	4.431×10^–7	4.996×10^–6	3.649×10^–5	1.921×10^–4
ν' = 2	本文	1.679×10^–7	3.501×10^–6	3.541×10^–5	2.296×10^–4	1.060×10^–3
1/2(III)-Χ²Π_3/2
ν' = 0	本文	1.314×10^–22	9.703×10^–21	3.517×10^–19	8.368×10^–18	1.457×10^–16
ν' = 1	本文	5.532×10^–21	3.879×10^–19	1.346×10^–17	3.083×10^–16	5.184×10^–15
ν' = 2	本文	2.944×10^–20	1.987×10^–18	6.647×10^–17	1.468×10^–15	2.379×10^–14
3/2(III)-Χ²Π_3/2
ν' = 0	本文	1.106×10^–22	5.929×10^–21	1.542×10^–19	2.607×10^–18	3.216×10^–17
ν' = 1	本文	3.736×10^–21	1.836×10^–19	4.435×10^–18	7.052×10^–17	8.256×10^–16

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表 6 ICl⁺分子离子的辐射寿命

Table 6. Radiative lifetimes of ICl⁺ molecular ion.

跃迁		辐射寿命/s
跃迁		ν' = 0	ν' = 1	ν' = 2
1²Δ-Χ²Π	本文	5.69×10^–3	4.92×10^–3	4.40×10^–3
2²Δ-Χ²Π	本文	5.83×10^–5	6.18×10^–5	6.99×10^–5
2²Σ⁺-X²Π	本文	2.91×10^–5	3.28×10^–5
3²Σ⁺-X²Π	本文	1.58×10^–5	1.66×10^–5	1.83×10^–5
1/2(II)-Χ²Π_3/2	本文	3.73×10^–2	3.42×10^–2	3.09×10^–2
1/2(III)-Χ²Π_3/2	本文	1.38×10^–2	5.43×10^–3	7.61×10^–3
3/2(III)-Χ²Π_3/2	本文	3.28×10^–2	2.06×10^–2

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[1]	Sherwen T, Schmidt J A, Evans M J, Carpenter L J, Großmann K, Eastham S D, Jacob D J, Dix B, Koenig T K, Sinreich R, Ortega I, Volkamer R, Saiz-Lopez A, Prados-Roman C, Mahajan A S, Ordóñez C 2016 Atmos. Chem. Phys. 16 12239 Google Scholar
[2]	Vogt R, Sander R, Glasow R V, Crutzen P J 1999 J. Atmos. Chem. 32 375 Google Scholar
[3]	Calvert J G, Lindberg S E 2004 Atmos. Environ. 38 5087 Google Scholar
[4]	Küpper F C, Feiters M C, Olofsson B, Kaiho T, Yanagida S, Zimmermann M B, Carpenter L J, Luther G W, Lu Z, Jonsson M, Kloo L 2011 Angew. Chem. Int. Ed. 50 11598 Google Scholar
[5]	Evans S, Orchard A F 1971 Inorg. Chim. Acta. 5 81 Google Scholar
[6]	Potts A W, Price W C 1971 Trans. Faraday Soc. 67 1242 Google Scholar
[7]	Eland J H D 1979 J. Chem. Phys. 70 2926 Google Scholar
[8]	Dibeler V H, Walker J A, McCulloh K E, Rosenstock H M 1971 Int. J. Mass Spectro. Ion Phys. 7 209 Google Scholar
[9]	Venkateswarlu P 1975 Can. J. Phys. 53 812 Google Scholar
[10]	Tuckett R P, Castellucci E, Bonneau M 1985 Chem. Phys. 92 43 Google Scholar
[11]	Kaur D, Yencha A J, Donovan R J, Kvaran A, Hopkirk A 1993 Org. Mass Spectrom. 28 327 Google Scholar
[12]	Yencha A J, Lopes M C A, King G C 2000 Chem. Phys. Lett. 325 559 Google Scholar
[13]	Ridley T, Beattie D A, Cockett M C R, Lawley K P, Donovan R J 2002 Phys. Chem. Chem. Phys. 4 1398 Google Scholar
[14]	Straub P A, McLean A D 1974 Theoret. Chim. Acta 32 227 Google Scholar
[15]	Dyke J M, Josland G D, Snijders J G, Boerrigter P M 1984 Chem. Phys. 91 419.Google Scholar
[16]	Balasubramanian K 1985 Chem. Phys. 95 225 Google Scholar
[17]	Werner H, Knowles P J, Knizia G, Manby F R, Schütz M 2012 Wires Comput. Mol. Sci. 2 242 Google Scholar
[18]	Peterson K A, Yousaf K E 2010 J. Chem. Phys. 133 174116 Google Scholar
[19]	Peterson K A, Dunning Jr T H 2002 J. Chem. Phys. 117 10548 Google Scholar
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ICl⁺分子离子激发态的包含自旋-轨道耦合效应的理论研究

Theoretical study on excited states of ICl⁺ molecular ion considering spin-orbit coupling

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齐齐哈尔大学理学院物理系, 齐齐哈尔　161006

通信作者: 李瑞, ruili06@mails.jlu.edu.cn

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Department of Physics, College of Science, Qiqihar University, Qiqihar 161006, China

Corresponding author: LI Rui, ruili06@mails.jlu.edu.cn

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ICl+分子离子激发态的包含自旋-轨道耦合效应的理论研究

Theoretical study on excited states of ICl+ molecular ion considering spin-orbit coupling

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Abstract

作者及机构信息

齐齐哈尔大学理学院物理系, 齐齐哈尔 161006

通信作者: 李瑞, ruili06@mails.jlu.edu.cn

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Department of Physics, College of Science, Qiqihar University, Qiqihar 161006, China

Corresponding author: LI Rui, ruili06@mails.jlu.edu.cn

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ICl⁺分子离子激发态的包含自旋-轨道耦合效应的理论研究

Theoretical study on excited states of ICl⁺ molecular ion considering spin-orbit coupling

齐齐哈尔大学理学院物理系, 齐齐哈尔　161006