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AsH+离子的电子结构和跃迁性质

侯秋宇 关皓益 黄雨露 陈世林 杨明 万明杰

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AsH+离子的电子结构和跃迁性质

侯秋宇, 关皓益, 黄雨露, 陈世林, 杨明, 万明杰

Electronic structures and transition properties of AsH+ cation

Hou Qiu-Yu, Guan Hao-Yi, Huang Yu-Lu, Chen Shi-Lin, Yang Ming, Wan Ming-Jie
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  • 采用多参考组态相互作用方法计算了AsH+离子前3个离解极限所对应的8个电子态 (X2Π, a4Σ, A2Σ, b4Π, B2Δ, C2Σ+, D2Π, 22Σ+) 的电子结构. As原子选择了aug-cc-pwCV5Z-PP相对论赝势基组. 在计算中考虑了Davidson修正, 芯-价电子关联和自旋-轨道耦合效应. 拟合得到了所有态的光谱常数, 离解能越大的电子态, 其谐振频率越大, 平衡核间距越小. 考虑自旋-轨道耦合效应后, 由于避免交叉, B2Δ3/2和B2Δ5/2变为双势阱结构. 最后预测了$ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $, $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $$ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $跃迁的弗兰克-康登因子、自发辐射速率和自发辐射寿命, 计算结果表明$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $阻禁跃迁的强度很小. 本文的计算结果为以后AsH+离子的光谱实验研究提供理论基础.
    Potential energy curves (PECs), dipole moments (DMs) and transition dipole moments (TDMs) of the X2Π, a4Σ, A2Σ, b4Π, B2Δ, C2Σ+, D2Π, 22Σ+ states correlating with the three lowest dissociation channels of AsH+ cation are calculated by using the multireference configuration interaction (MRCI) method. The Davidson correction, core-valence (CV) correlation, and spin-orbit coupling (SOC) effect are all considered. The aug-cc-pV5Z all-electron basis set of H atom and the aug-cc-pwCV5Z-PP pseudopotential basis set of As atom are both selected in the calculation.In the complete active space self-consistent field (CASSCF) calculation, H (1s) and As (4s4p) shell are selected as active orbitals, As (3p3d) shells are selected as closed orbitals, which keeps doubly occupation, the remaining electrons are in the frozen orbitals. In the MRCI calculation, As (3p3d) shells are used for CV correlation, and the calculation accuracy can be improved. The SOC effects are considered with Breit-Pauli operators.All calculated states are bound states. The X2Π is the ground state, which is a deep potential well, the dissociation energy is 3.100 eV. The b4Π, C2Σ+ and D2Π are weakly bound states. The spectroscopic parameters are obtained by solving radial Schrodinger equation. To the best of our knowledge, there has been no study of the spectroscopy of AsH+ cation so far. Comparing with Ⅴ-hydride cations MH+ (M = N, P, As), the orders of the energy levels of the low-lying states for three ions are identical. The dissociation energy and harmonic frequency both decrease with the increase of the atomic weight of M.At spin-free level, the PEC of b4Π state and the PEC of B2Δ state cross at about 1.70 Å. When SOC effects are taken into account, according to the rule of avoid-crossing, the $ {{{\rm{B}}^2}}{\Delta _{3/2}} $state and $ {{{\rm{B}}^2}}{\Delta _{5/2}} $state change to the double potential wells, and the avoided crossing between the $ {{{\rm{B}}^2}}{\Delta _{3/2}} $ ($ {{{\rm{B}}^2}}{\Delta _{3/2}} $) state and ${{\rm{b}}^4}{\Pi _{3/2}}$ (${{\rm{b}}^4}{\Pi _{5/2}}$) state is observed. The transition dipole moment (TDM) of the $ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $, $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ and $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ transition are also calculated. The TDM at the equilibrium distance of the $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ spin-forbidden reaches 0.036 Debye, therefore, the SOC effect plays an important role. Based on the accurate PECs and PDMs, the Franck-Condon factors, spontaneous radiative coefficients, and spontaneous radiative lifetimes of the $ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $, $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $, and $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ transition are also calculated.
      通信作者: 万明杰, wanmingjie1983@sina.com
    • 基金项目: 宜宾学院预研项目(批准号: 2019YY06)、宜宾学院计算物理四川省高等学校重点实验室开放基金(批准号: YBXYJSWL-ZD-2020-001)和宜宾学院培育项目(批准号: 2021PY71)资助的课题.
      Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com
    • Funds: Project supported by the Pre-Research Project of Yibin University, China (Grant No. 2019YY06), the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University, China (Grant No. YBXYJSWL-ZD-2020-001), and the Cultivation Project of Yibin University, China (Grant No. 2021PY71).
    [1]

    Dixon R N, Duxbury G, Lamberton H M 1968 Proc. R. Soc. London, Ser. A. 305 271Google Scholar

    [2]

    Arens M, Richter W 1990 J. Chem. Phys. 93 7094Google Scholar

    [3]

    Beutel M, Setzer K D, Shestakov O, Fink E H 1996 J. Mol. Spectrosc. 178 165Google Scholar

    [4]

    Pettersson L G, Langhoff S R 1986 J. Chem. Phys. 85 3130Google Scholar

    [5]

    Matsushita T, Marian C M, Klotz R, Peyerimho S D 1987 Can. J. Phys. 65 155Google Scholar

    [6]

    Balasubramanian K, Nannegari V 1989 J. Mol. Spectrosc. 138 482Google Scholar

    [7]

    Shi D H, Liu H, Sun J F, Zhang J P, Liu Y F, Zhu Z L 2009 J. Mol. Struct. 911 8Google Scholar

    [8]

    Bian W S, Li D H, Cao J W, Ma H T 2022 Phys. Chem. Chem. Phys. 24 10114Google Scholar

    [9]

    赵东锋, 秦成兵, 张群, 陈旸 2009 科学通报 54 3190Google Scholar

    Zhao D F, Qin C B, Zhang Q, Chen Y 2009 Chin. Sci. Bull. 54 3190Google Scholar

    [10]

    Wan M J, Zhang Y G, Song C Q, Gao Tao 2008 J. Phys. B:At. Mol. Opt. Phys. 41 215102Google Scholar

    [11]

    Yang C L, You Y, Wang M S, Ma X G, Liu W W 2015 Phys. Rev. A 92 032502Google Scholar

    [12]

    Bruna P J, Hirsch G, Peyerimhoff S D, Buenker R J 1981 Mol. Phys. 42 875Google Scholar

    [13]

    Li G X, Gao T, Zhang Y G 2008 Chin. Phys. B 17 2040Google Scholar

    [14]

    Yan B, Zhang X, Li X 2015 Spectrochim. Acta, Part A 142 1Google Scholar

    [15]

    邢伟, 孙金锋, 施德恒, 朱遵略 2018 物理学报 67 193101Google Scholar

    Xing W, Sun J F, Shi D H, Zhu Z L 2018 Acta Phys. Sin. 67 193101Google Scholar

    [16]

    滑亚文, 刘以良, 万明杰 2020 物理学报 69 153101Google Scholar

    Hua Y W, Liu Y L, Wan M J 2020 Acta Phys. Sin. 69 153101Google Scholar

    [17]

    高峰, 张红, 张常哲, 赵文丽, 孟庆田 2021 物理学报 70 153301Google Scholar

    Gao F, Zhang H, Zhang C Z, Zhao W L, Meng Q T 2021 Acta Phys. Sin. 70 153301Google Scholar

    [18]

    Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010.1)

    [19]

    Dunning Jr. T H 1989 J. Chem. Phys. 90 1007Google Scholar

    [20]

    Peterson K A, Yousaf K E 2010 J. Chem. Phys. 133 174116Google Scholar

    [21]

    Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053Google Scholar

    [22]

    Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259Google Scholar

    [23]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [24]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [25]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61Google Scholar

    [26]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823Google Scholar

    [27]

    Le Roy R J 2007 LEVEL 8.0: a Computer Program for Solving the Radial Schröinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663

    [28]

    Moore C E 1971 Atomic Energy Levels vol. Ⅱ (Washington, DC: US Govt Printing Office) p144

    [29]

    Huber K, Herzberg G 1979 Molecular Spectra and Molecular Structure Vol. 4. Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) p460

    [30]

    Tarroni R, Palmieri P, Mitrushenkov A, Tosi P, Bassi D 1997 J. Chem. Phys. 106 10265Google Scholar

    [31]

    Colin R 1989 J. Mol. Spectrosc. 136 387Google Scholar

    [32]

    Li R, Zhai Z, Zhang X M, Jin M X, Xu H F, Yan B 2015 J. Quant. Spectrosc. Radiat. Transfer 157 42Google Scholar

    [33]

    Xiao L D, Liu Y, Li R, Xiao Z Y, Yan B 2021 J. Quant. Spectrosc. Radiat. Transfer 266 107593Google Scholar

  • 图 1  AsH+离子X2Π, a4Σ, A2Σ, b4Π, B2Δ, C2Σ+, D2Π和22Σ+态的势能曲线

    Fig. 1.  Potential energy curves of the X2Π, a4Σ, A2Σ, b4Π, B2Δ, C2Σ+, D2Π and 22Σ+ states of AsH+ cation.

    图 2  电子态之间的自旋-轨道矩阵元.

    Fig. 2.  Spin-orbit matrix elements of the AsH+ anion.

    图 3  Ω态的势能曲线

    Fig. 3.  Potential energy curves of the Ω states of AsH+ cation.

    图 4  Ω态的偶极矩

    Fig. 4.  Dipole moments of the Ω states of AsH+ cation.

    图 5  AsH+离子的跃迁偶极矩

    Fig. 5.  Transition dipole moments of AsH+ cation.

    表 1  AsH+离子Λ-S态的离解关系

    Table 1.  Dissociation relationships of Λ-S states of AsH+

    原子态Λ-S态ΔE/cm–1
    本文工作实验值[28]
    As+(3Pg)+H(2Sg)X2Π, a4Σ,
    A2Σ, b4Π
    00
    As+(1Dg)+H(2Sg)B2Δ, C2Σ+, D2Π8222.188752
    As+(1Sg)+H(2Sg)22Σ+20400.6921252
    下载: 导出CSV

    表 2  Λ-S的光谱常数

    Table 2.  Spectroscopic parameters of the Λ-S states.

    Λ-S statesReωe/cm–1ωeχe/cm–1Be/cm–1De/eVTe/cm–1
    X21.51312222.5842.087.36323.1000
    a4Σ1.62111433.4252.396.45281.20815260.18
    A2Σ2.0523598.0335.704.02570.31322481.02
    b43.9651111.8927.811.10240.01524885.54
    B2Δ1.72601139.5249.115.68470.82126654.73
    C2Σ+3.2885140.5422.861.61010.02832911.82
    D23.3767172.3229.151.50050.03532993.70
    22Σ+2.4140532.5447.362.92630.18843887.70
    下载: 导出CSV

    表 3  第五主族氢化物离子的光谱常数对比

    Table 3.  Comparison of the spectroscopy parameters of the Ⅴ-group hydride cations.

    分子离子Λ-S态Reωe/cm–1De/eVTe/cm–1
    NH+X21.080a2810.6a4.40a0
    a4Σ~1.105b~2520b3.66c509d
    A2Σ1.206a1578.2a1.76a22161.27a
    B2Δ1.161a2011.2a3.25a23331a
    PH+X21.4226e2412.79e3.525e0
    a4Σ1.4816e1832.51e1.790e13998e
    A2Σ1.7914e823.68e0.490e24476e
    B2Δ1.5454e1512.20e1.277e26322e
    AsH+X21.5131f2222.58f3.100f0
    a4Σ1.6211f1433.42f1.208f15260.18f
    A2Σ2.0523f598.03f0.313f22481.02f
    B2Δ1.7260f1139.52f0.188f43887.70f
    注: a文献[10] , b文献[29] , c文献[30] , d文献[31] , e文献[14], e本文计算值.
    下载: 导出CSV

    表 4  AsH+离子Ω态的离解关系

    Table 4.  Dissociation relationships of Ω states of AsH+.

    原子态Ω态ΔE/cm–1
    本文工作实验值[28]
    As+(3P0)+H(2S1/2)1/200
    As+(3P1)+H(2S1/2)3/2, 1/2, 1/21090.351061
    As+(3P2)+H(2S1/2)5/2, 3/2, 3/2, 1/2, 1/22721.662540
    As+(1D2)+H(2S1/2)5/2, 3/2, 3/2, 1/2, 1/211252.9410093
    As+(1S0)+H(2S1/2)1/224909.8822593
    下载: 导出CSV

    表 5  Ω的光谱常数

    Table 5.  Spectroscopic parameters of the Ω states.

    Ω statesReωe /cm–1ωeχe /cm–1Be /cm–1De /eVTe /cm–1
    $ {{{\rm{X}}^2}}{\Pi _{1/2}} $1.51462339.1441.997.35923.3140
    $ {{{\rm{X}}^2}}{\Pi _{3/2}} $1.51212344.1142.997.36473.2161696.92
    $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - $1.62221535.8858.516.44471.24817777.19
    $ {{{\rm{a}}^4}}\Sigma _{3/2}^ - $1.62101688.2169.696.45541.24917910.08
    $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - $2.0581685.6435.993.99760.40025773.03
    $ {{{\rm{B}}^2}}{\Delta _{3/2}} $第一势阱1.72851175.3458.145.68570.32130513.22
    第二势阱3.2405333.2649.991.72150.07628497.77
    $ {{{\rm{B}}^2}}{\Delta _{5/2}} $第一势阱1.72591186.5251.975.69230.35630548.89
    第二势阱3.3318283.6049.291.56540.05529071.95
    下载: 导出CSV

    表 6  AsH+离子的弗兰克-康登因子(单位: s-1)、总自发辐射速率和自发辐射寿命(单位: μs)

    Table 6.  Franck-Condon Factors, spontaneous emission rates (unit of s-1) and spontaneous radiative lifetimes τ (unit of μs) of the AsH+ cation.

    跃迁ν′ν″ = 0ν″ = 1ν″ = 2ν″ = 3ν″ = 4ν″ = 5ΣAτ = 1/ΣA
    A2Σ ↔ X2Π00.00560.02800.07220.12750.17150.1843
    2295.525374.756276.274791.312627.481065.8722838.7643.75
    $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $00.68170.24470.06130.01070.00140.0001
    1545.42319.7260.848.080.740.041934.85517
    $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $00.00410.02160.05880.10980.15650.1789
    3036.677910.0910373.68987.85672.572703.6740012.7624.99
    下载: 导出CSV
  • [1]

    Dixon R N, Duxbury G, Lamberton H M 1968 Proc. R. Soc. London, Ser. A. 305 271Google Scholar

    [2]

    Arens M, Richter W 1990 J. Chem. Phys. 93 7094Google Scholar

    [3]

    Beutel M, Setzer K D, Shestakov O, Fink E H 1996 J. Mol. Spectrosc. 178 165Google Scholar

    [4]

    Pettersson L G, Langhoff S R 1986 J. Chem. Phys. 85 3130Google Scholar

    [5]

    Matsushita T, Marian C M, Klotz R, Peyerimho S D 1987 Can. J. Phys. 65 155Google Scholar

    [6]

    Balasubramanian K, Nannegari V 1989 J. Mol. Spectrosc. 138 482Google Scholar

    [7]

    Shi D H, Liu H, Sun J F, Zhang J P, Liu Y F, Zhu Z L 2009 J. Mol. Struct. 911 8Google Scholar

    [8]

    Bian W S, Li D H, Cao J W, Ma H T 2022 Phys. Chem. Chem. Phys. 24 10114Google Scholar

    [9]

    赵东锋, 秦成兵, 张群, 陈旸 2009 科学通报 54 3190Google Scholar

    Zhao D F, Qin C B, Zhang Q, Chen Y 2009 Chin. Sci. Bull. 54 3190Google Scholar

    [10]

    Wan M J, Zhang Y G, Song C Q, Gao Tao 2008 J. Phys. B:At. Mol. Opt. Phys. 41 215102Google Scholar

    [11]

    Yang C L, You Y, Wang M S, Ma X G, Liu W W 2015 Phys. Rev. A 92 032502Google Scholar

    [12]

    Bruna P J, Hirsch G, Peyerimhoff S D, Buenker R J 1981 Mol. Phys. 42 875Google Scholar

    [13]

    Li G X, Gao T, Zhang Y G 2008 Chin. Phys. B 17 2040Google Scholar

    [14]

    Yan B, Zhang X, Li X 2015 Spectrochim. Acta, Part A 142 1Google Scholar

    [15]

    邢伟, 孙金锋, 施德恒, 朱遵略 2018 物理学报 67 193101Google Scholar

    Xing W, Sun J F, Shi D H, Zhu Z L 2018 Acta Phys. Sin. 67 193101Google Scholar

    [16]

    滑亚文, 刘以良, 万明杰 2020 物理学报 69 153101Google Scholar

    Hua Y W, Liu Y L, Wan M J 2020 Acta Phys. Sin. 69 153101Google Scholar

    [17]

    高峰, 张红, 张常哲, 赵文丽, 孟庆田 2021 物理学报 70 153301Google Scholar

    Gao F, Zhang H, Zhang C Z, Zhao W L, Meng Q T 2021 Acta Phys. Sin. 70 153301Google Scholar

    [18]

    Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010.1)

    [19]

    Dunning Jr. T H 1989 J. Chem. Phys. 90 1007Google Scholar

    [20]

    Peterson K A, Yousaf K E 2010 J. Chem. Phys. 133 174116Google Scholar

    [21]

    Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053Google Scholar

    [22]

    Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259Google Scholar

    [23]

    Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803Google Scholar

    [24]

    Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514Google Scholar

    [25]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61Google Scholar

    [26]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823Google Scholar

    [27]

    Le Roy R J 2007 LEVEL 8.0: a Computer Program for Solving the Radial Schröinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663

    [28]

    Moore C E 1971 Atomic Energy Levels vol. Ⅱ (Washington, DC: US Govt Printing Office) p144

    [29]

    Huber K, Herzberg G 1979 Molecular Spectra and Molecular Structure Vol. 4. Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) p460

    [30]

    Tarroni R, Palmieri P, Mitrushenkov A, Tosi P, Bassi D 1997 J. Chem. Phys. 106 10265Google Scholar

    [31]

    Colin R 1989 J. Mol. Spectrosc. 136 387Google Scholar

    [32]

    Li R, Zhai Z, Zhang X M, Jin M X, Xu H F, Yan B 2015 J. Quant. Spectrosc. Radiat. Transfer 157 42Google Scholar

    [33]

    Xiao L D, Liu Y, Li R, Xiao Z Y, Yan B 2021 J. Quant. Spectrosc. Radiat. Transfer 266 107593Google Scholar

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出版历程
  • 收稿日期:  2022-06-02
  • 修回日期:  2022-07-13
  • 上网日期:  2022-10-27
  • 刊出日期:  2022-11-05

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