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LiCl阴离子的光谱性质和跃迁性质

郭芮 谭涵 袁沁玥 张庆 万明杰

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LiCl阴离子的光谱性质和跃迁性质

郭芮, 谭涵, 袁沁玥, 张庆, 万明杰

Spectroscopic and transition properties of LiCl anion

Guo Rui, Tan Han, Yuan Qin-Yue, Zhang Qing, Wan Ming-Jie
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  • 采用多参考组态相互作用方法结合全电子基组计算了LiCl- 阴离子5个电子态 (X2Σ+, A2∏, B2Σ+, 32Σ+, 22∏) 的电子结构. 为了得到精确的光谱常数, 计算中考虑了Davidson 修正、芯-价电子关联效应和自旋-轨道耦合效应. 拟合得到各电子态的光谱常数、分子常数、自发辐射速率和自发辐射寿命. 基态的光谱常数与实验值和其他理论值符合较好, 同时报道了LiCl 阴离子激发态的光谱常数以及其到基态的跃迁性质. 计算结果表明A2$\leftrightarrow $X2Σ+跃迁具有高对角分布的弗兰克-康登因子f00, 第一激发态A2∏有较短的自发辐射寿命. 构造A2∏ (ν′) $\leftrightarrow $ X2Σ+ ($\nu''$)准循环跃迁进行激光冷却LiCl 阴离子需要一束主激光和两束抽运激光. 以上结果预测了激光冷却LiCl阴离子是可行的.
    The electronic structure of the X2Σ+, A2Π, B2Σ+, 32Σ+, and 22Π state of LiCl anion are performed at an MRCI+Q level. Davison correction, core-valence correction and spin-orbit coupling effect are also considered. The ground state X2Σ+ of LiCl anion correlates with the lowest dissociation channel Li(2Sg) + Cl(1Sg); the A2∏ state and B2Σ+ state correlate with the second dissociation channel Li(2Pu) + Cl(1Sg); the 32Σ+ state and 22Π state correlate with the third dissociation channel Li(1Sg) + Cl(2Pu).Spectroscopic parameters are calculated by solving the radial Schröedinger equation. The equilibrium internuclear distance Re of the ground state X2Σ+ is 2.1352 Å, which is a little bigger than the experimental datum, with an error being 0.5%. It is a deep potential well, and the dissociation energy De is 1.886 eV. These values are in good agreement with experimental data. The A2∏ state is at 13431.93 cm–1 above the X2Σ+ state. The Re is 2.1198 Å, which is only 0.0154 Å smaller than that of the X2Σ+ state. The values of energy level Gν and rotational constant Bν of five Λ-S states are also calculated. The values are in good agreement with available theoretical ones. The electronic structures of the excited states are also reported. The SOC effect weakly influences the spectroscopic parameters for the $ {\text{X}}{}^2\Sigma _{1/2}^ + $, $ {\text{A}}{}^2{\Pi _{1/2}} $, $ {\text{A}}{}^2{\Pi _{3/2}} $, and $ {\text{B}}{}^2\Sigma _{1/2}^ + $ state. From the analysis of the SO matrix, it can be seen that the SOC effect plays a little role in realizing the A2Π $\leftrightarrow $ X2Σ+ transition, so, it can be ignored.The scheme of laser cooling of LiCl anion has constructed at a spin – free level. The A2∏(ν) $\leftrightarrow $ X2Σ+($v'' $) transition has a highly diagonally distributed Franck-Condon factor f00 = 0.9898, the calculated branching ratio of the diagonal term R00 is 0.9893, and spontaneous radiative lifetime of A2∏ is 35.45 ns. A main pump laser and two repumping lasers for driving the A2∏(ν) $\leftrightarrow $ X2Σ+($v'' $) transitions are required. The laser wavelengths are 744.10, 774.30 and 772.42 nm, respectively. Owing to the summation of R00, R01, and R02 being closer to 1, the A2∏(ν) $\leftrightarrow $ X2Σ+($v'' $) transition is a quasicycling transition. These results imply that the LiCl anion is a candidate for laser cooling.
      通信作者: 万明杰, wanmingjie1983@sina.com
    • 基金项目: 宜宾学院国家级大学生创新创业训练计划项目(批准号: 202110641022),宜宾学院预研项目(批准号: 2019YY06)和宜宾学院计算物理四川省高等学校重点实验室开放基金(YBXYJSWL-ZD-2020-001)资助的课题
      Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com
    • Funds: Project supported by the National Undergraduate Training Program for Innovation, Entrepreneurship of Yibin University (Grant No. 202110641022) and the Pre-Research Project of Yibin University, China (Grant No. 2019YY06) and the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University (Grant No. YBXYJSWL-ZD-2020-001)
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  • 图 1  X2Σ+, A2∏, B2Σ+, 32Σ+和22∏电子态的势能曲线

    Fig. 1.  Potential energy curves of the X2Σ+, A2∏, B2Σ+, 32Σ+ and 22∏ states.

    图 2  Ω态的势能曲线

    Fig. 2.  Potential energy curves of the Ω states.

    图 3  LiCl阴离子的自旋-轨道矩阵元. SOi的表示见表5

    Fig. 3.  Spin-orbit matrix elements of the of the LiCl anion. The explanations of the SOi symbols are presented in Table 6.

    图 4  (a) Λ-S态的电偶极矩; (b) Λ-S态的跃迁偶极矩

    Fig. 4.  (a) The permanent dipole moments of the Λ-states; (b) the transition dipole moments of the Λ-states.

    图 5  驱动A2$\leftrightarrow $ X2Σ+跃迁进行激光冷却的途径

    Fig. 5.  Proposed laser cooling scheme via A2$\leftrightarrow $ X2Σ+ transition.

    表 1  LiCl阴离子Λ-S态的离解关系

    Table 1.  Calculated dissociation relationships of the Λ-S states of LiCl anion.

    ΔE/cm–1
    原子态分子态本文工作实验值[3638]
    Li(2Sg)+Cl(1Sg)X2Σ+00
    Li(2Pu)+ Cl(1Sg)A2Π, B2Σ+14903.7914253.13
    Li(1Sg)+Cl(2Pu)32Σ+, 22Π23703.6124594.67
    下载: 导出CSV

    表 2  LiCl阴离子Λ-S态的光谱常数

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

    电子态Reωe/cm–1ωeχe/cm–1Be/cm–1De/eVD0/eVTe/cm–1
    X2Σ+2.1352535.335.81730.72051.88861.8560
    实验值[20]2.18(4)0
    实验值[21]2.123(15)1.75(2)0
    理论值[22]2.12a0
    理论值[23]2.1354537.7b6.34b0.7203b1.810
    A22.1198554.655.71570.73101.99021.955913431.93
    B2Σ+2.0282652.796.12520.79851.66531.625017491.75
    32Σ+5.859430.190.84830.09630.03620.035338607.64
    227.141139.080.56160.06380.01360.011238855.32
    a采用HF方法计算得到基态的核间距.
    下载: 导出CSV

    表 3  X2Σ+, A2∏, B2Σ+, 32Σ+和22∏态的振动能级和转动常数

    Table 3.  Vibrational energy levels, rotational constants of the X2Σ+, A2∏, B2Σ+, 32Σ+ and 22∏ states.

    νX2Σ+ A2 B2Σ+ 32Σ+ 22
    Gν BνGνBνGνBνGνBνGνBν
    本文工作文献[23]本文工作文献[23]本文工作本文工作本文工作本文工作本文工作本文工作本文工作本文工作
    0266.72264.07 0.71460.7143 276.480.7252 325.330.7927 14.960.0940 6.120.0631
    1790.93791.770.70290.7023820.210.7136966.070.781143.020.089318.150.0618
    21303.271307.010.69110.69031352.130.70211594.230.769768.840.085728.920.0572
    31803.711809.920.67940.67841872.340.69072210.020.758493.220.082629.300.0095
    42292.312300.650.66770.66662380.970.67932813.560.7471116.240.079631.320.0112
    52769.152779.340.65600.65482878.130.66803404.890.7359138.170.076533.190.0125
    63234.293246.110.64440.64303363.870.65673984.090.7247158.980.072535.070.0140
    73687.833701.100.63280.63133838.290.64554551.200.7135178.260.067836.530.0310
    84129.884144.450.62120.61974301.420.63435106.170.7023195.600.062637.330.0257
    94560.614576.290.60970.60814753.370.62315648.950.6911210.770.057139.110.0188
    下载: 导出CSV

    表 4  LiCl阴离子Ω态的离解关系

    Table 4.  Calculated dissociation relationships of the Ω states of LiCl anion.

    ΔE/cm–1
    原子态分子态 Ω本文工作实验值[3638]
    Li(2S1/2)+Cl(1S0)1/200
    Li(2P1/2)+ Cl(1S0)1/214252.7714903.62
    Li(2P3/2)+ Cl(1S0)1/2, 3/214253.5014903.96
    Li(1S0)+Cl(2P3/2)1/2, 3/223415.4124153.49
    Li(1S0)+Cl(2P1/2)1/224288.4825035.84
    下载: 导出CSV

    表 5  LiCl阴离子Ω态的光谱常数

    Table 5.  Spectroscopic parameters of the Ω states of LiCl anion at icMRCI+Q level.

    Ω态Reωe/cm–1ωeχe /cm–1 Be/cm–1De/eVTe/cm–1
    $ {\text{X}}{}^2\Sigma _{1/2}^ + $2.1352535.325.81720.72051.88860
    $ {\text{A}}{}^2{\Pi _{1/2}} $2.1196554.875.71530.73112.009413419.77
    $ {\text{A}}{}^2{\Pi _{3/2}} $2.1200554.415.71600.73082.005913444.07
    $ {\text{B}}{}^2\Sigma _{1/2}^ + $2.0282652.796.12530.79851.667917491.75
    下载: 导出CSV

    表 6  LiCl阴离子的自旋-轨道矩阵元

    Table 6.  Notation of spin-orbit matrix element.

    SO矩阵元
    $ {\text{S}}{{\text{O}}_1} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_2} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _x}} \right\rangle $$ {\text{S}}{{\text{O}}_3} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_4} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _x}} \right\rangle $
    $ {\text{S}}{{\text{O}}_5} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_6} = \left\langle {{3^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _x}} \right\rangle $$ {\text{S}}{{\text{O}}_7} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_8} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _x}} \right\rangle $
    $ {\text{S}}{{\text{O}}_9} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_{10}} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _x}} \right\rangle $$ {\text{S}}{{\text{O}}_{11}} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_{12}} = \left\langle {{3^2}{\Sigma ^ + }} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _x}} \right\rangle $
    $ {\text{S}}{{\text{O}}_{13}} = {\text{i}}\left\langle {{{\text{A}}^2}{\Pi _x}} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_{14}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _y}} \right\rangle $$ {\text{S}}{{\text{O}}_{15}} = {\text{i}}\left\langle {{2^2}{\Pi _y}} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{{\text{A}}^2}{\Pi _x}} \right\rangle $$ {\text{S}}{{\text{O}}_{16}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right|\hat H_{{\text{SO}}}^{{\text{BP}}}\left| {{2^2}{\Pi _y}} \right\rangle $
    下载: 导出CSV

    表 7  A2$\leftrightarrow $ X2Σ+和B2Σ+ $\leftrightarrow $ X2Σ+跃迁的弗兰克-康登因子fν'ν'', 爱因斯坦系数Aν'ν''和自发辐射寿命 (单位: ns)

    Table 7.  Franck-Condon Factors fν'ν'', Einstein coefficients Aν'ν'', and radiative lifetimes τ of the A2$\leftrightarrow $ X2Σ+ and B2Σ+ $\leftrightarrow $ X2Σ+ transitions of LiCl anion(in ns).

    跃迁f00f01f02f03
    A00A01A02A03τ = 1/ΣA
    f10f11f12f13
    A10A11A12A13
    A2∏ $\leftrightarrow $ X2Σ+0.98980.01010.00018.70(–7)
    279042002983133848.8544.6035.45
    0.01020.96860.02090.0004
    269660273366006073351233235.43
    B2Σ+ $\leftrightarrow $ X2Σ+0.59080.29090.08940.0225
    183168007658290203873045221034.99
    0.32660.12860.28880.1671
    1227960042617807988480397939033.00
    下载: 导出CSV
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    [20]

    Carlsten J L, Peterson J R. Lineberger W C 1976 Chem. Phys. Lett. 37 5Google Scholar

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    Miller T M, Leopold D G, Murray K K, Lineberger W C 1986 J. Chem. Phys. 85 2368Google Scholar

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    Jordan K D, Luken W 1976 J Chem. Phys. 64 2760Google Scholar

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    Li S, Zheng R, Chen S J, Fan Q C 2015 Mol. Phys. 113 1433Google Scholar

    [24]

    Weck P F, Kirby K, Stancil P C 2004 J. Chem. Phys. 120 4216Google Scholar

    [25]

    Kurosaki Y, Yokoyama K 2012 J. Chem. Phys. 137 064305Google Scholar

    [26]

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

    [27]

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

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

    [29]

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

    [30]

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

    [31]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1283

    [32]

    Xiao K L, Yang C L, Wang M S, Ma X G, Liu W W 2013 J. Chem. Phys. 139 074305Google Scholar

    [33]

    Weigend F 2008 J. Comput. Chem. 29 167Google Scholar

    [34]

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出版历程
  • 收稿日期:  2021-09-10
  • 修回日期:  2021-10-09
  • 上网日期:  2022-02-20
  • 刊出日期:  2022-02-20

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