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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.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+(1Dg)+Cl(2Pu) and I+(3Pg)+Cl(2Pu) 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 athttps://doi.org/10.57760/sciencedb.j 00213.00140 .
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Keywords:
- ICl+ /
- MRCI+Q method /
- spectroscopic constants /
- spin-orbit coupling /
- radiative lifetimes
[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
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[3] Calvert J G, Lindberg S E 2004 Atmos. Environ. 38 5087
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[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
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[6] Potts A W, Price W C 1971 Trans. Faraday Soc. 67 1242
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[7] Eland J H D 1979 J. Chem. Phys. 70 2926
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[8] Dibeler V H, Walker J A, McCulloh K E, Rosenstock H M 1971 Int. J. Mass Spectro. Ion Phys. 7 209
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[9] Venkateswarlu P 1975 Can. J. Phys. 53 812
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[10] Tuckett R P, Castellucci E, Bonneau M 1985 Chem. Phys. 92 43
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[11] Kaur D, Yencha A J, Donovan R J, Kvaran A, Hopkirk A 1993 Org. Mass Spectrom. 28 327
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[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
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[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
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[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
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[20] Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259
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[25] Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823
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[26] Le Roy R J 2017 J. Quant. Spectrosc. Ra. 186 167
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Google Scholar
Zhu Y H, Li R 2024 Acta Phys. Sin. 73 053101
Google Scholar
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Google Scholar
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Wu D L, Guo Z Y, Zhou J J, Ruan W, Zeng X F, Xie A D 2022 Acta Phys. Sin. 71 223101
Google Scholar
[32] 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
[33] Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure (Vol. IV) (New York: Van Nostrand Reinhold) p342
[34] Moore C E 1971 Atomic Energy Levels (Washington (DC): National Bureau of Standards Publications
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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.
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.
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.
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.
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.
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.
表 1 ICl+分子离子Re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 Re.
Λ-S 态 Re 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 Te/cm–1 D0/eV Be/cm–1 ωe/cm–1 Re/Å Χ2Π 本文 0 2.50 0.1221 432 2.24 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 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 本文 实验a) I+(3Pg2)+Cl(2Pu3/2) 7/2, 5/2(2), 3/2(3), 1/2(4) 0 0 I+(3Pg2)+Cl(2Pu1/2) 5/2, 3/2(2), 1/2(2) 821 882 I+(3Pg0)+Cl(2Pu3/2) 3/2, 1/2 6433 6448 I+(3Pg1)+Cl(2Pu3/2) 5/2, 3/2(2), 1/2(3) 6901 7087 I+(3Pg0)+Cl(2Pu1/2) 1/2 7254 7330 I+(3Pg1)+Cl(2Pu1/2) 3/2, 1/2(2) 7722 7969 I+(1Dg2)+Cl(2Pu3/2) 7/2, 5/2(2), 3/2(3), 1/2(4) 13950 13727 I+(1Dg2)+Cl(2Pu1/2) 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 Te/cm–1 D0/eV Be/cm–1 ωe/cm–1 Re/Å Re处主要的Λ-S成分/% X2Π3/2 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 X2Π1/2 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)-Χ2Π3/2 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)-Χ2Π3/2 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)-Χ2Π3/2 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 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)-Χ2Π3/2 本文 3.73×10–2 3.42×10–2 3.09×10–2 1/2(III)-Χ2Π3/2 本文 1.38×10–2 5.43×10–3 7.61×10–3 3/2(III)-Χ2Π3/2 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
[20] Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259
Google Scholar
[21] Werner H J, Knowles P J 1985 J. Chem. Phys. 82 5053
Google Scholar
[22] Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514
Google Scholar
[23] Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803
Google Scholar
[24] Langhoff S R, Davidson E R 1974 Int. J. Quantum. Chem. 8 61
Google Scholar
[25] Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823
Google Scholar
[26] Le Roy R J 2017 J. Quant. Spectrosc. Ra. 186 167
Google Scholar
[27] Wu D L, Liu B K, Zhou W T, Chen J Y, Lai Z L, Liu B, Yan B 2025 Chin. Phys. B 34 043101
Google Scholar
[28] 刘铭婕, 田亚莉, 王瑜, 李晓筱, 和小虎, 宫廷, 孙小聪, 郭古青, 邱选兵, 李传亮 2025 物理学报 74 023101
Google Scholar
Liu M J, Tian Y L, Wang Y, Li X X, He X H, Gong T, Sun X C, Guo G Q, Qiu X B, Li C L 2025 Acta Phys. Sin. 74 023101
Google Scholar
[29] 朱宇豪, 李瑞 2024 物理学报 73 053101
Google Scholar
Zhu Y H, Li R 2024 Acta Phys. Sin. 73 053101
Google Scholar
[30] Li R, Lv H N, Sang J Q, Liu X H, Liang G Y 2024 Chin. Phys. B 33 053101
Google Scholar
[31] 伍冬兰, 郭自依, 周俊杰, 阮文, 曾学锋, 谢安东 2022 物理学报 71 223101
Google Scholar
Wu D L, Guo Z Y, Zhou J J, Ruan W, Zeng X F, Xie A D 2022 Acta Phys. Sin. 71 223101
Google Scholar
[32] 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
[33] Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure (Vol. IV) (New York: Van Nostrand Reinhold) p342
[34] Moore C E 1971 Atomic Energy Levels (Washington (DC): National Bureau of Standards Publications
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