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考虑自旋-轨道耦合效应下SeH阴离子的光谱和跃迁性质

万明杰 柳福提 黄多辉

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考虑自旋-轨道耦合效应下SeH阴离子的光谱和跃迁性质

万明杰, 柳福提, 黄多辉

Spectroscopic and transition properties of SeH anion including spin-orbit coupling

Wan Ming-Jie, Liu Fu-Ti, Huang Duo-Hui
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  • 采用高精度的从头算方法研究了SeH阴离子的基态(X1Σ+)和低激发(a3Π, A1Π, b3Σ+, 21Σ+)的势能曲线、偶极矩和跃迁偶极矩. 在计算中考虑了价-芯(CV)电子关联、Davidson修正、标量相对论修正和自旋-轨道耦合效应(SOC). 考虑了SOC效应后, $ {{\rm{b}}^3}\Sigma _{{0^ - }}^ + $$ {{\rm{b}}^3}\Sigma _{{1}}^ + $态变为了弱束缚态. 计算得到$ {{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow $${{\rm{X}}^1}\Sigma _{{0^ + }}^ +$$ {{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁具有很大的跃迁偶极矩. 这三种跃迁都同时具有高对角分布的弗兰克-康登因子f00及振动分支比R00. 计算得到了$ {{\rm{a}}^3}{\Pi _{{1}}}$, $ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$$ {{\rm{A}}^1}{\Pi _{{1}}}$激发态的自发辐射寿命都很短, 能够实现对SeH阴离子的快速激光冷却. $ {{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁为三能级跃迁, 中间态的存在对构建准闭合的循环能级的影响可以忽略. 驱动$ {{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, $ {{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $$ {{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁进行激光冷却SeH阴离子的激光波长都在可见光范围内. 本文的结果为以后激光冷却SeH阴离子的实验提供了部分理论参考.
    Potential energy curves (PECs), permanent dipole moments (PDMs) and transition dipole moments (TMDs) of five Λ-S states of SeH anion are calculated by the MRCI + Q method with ACVQZ-DK basis set. The core-valence corrections, Davidson corrections, scalar relativistic corrections, and spin-orbit coupling (SOC) effects are also considered. In the CASSCF step, Se(1s2s2p3s3p) shells are put into the frozen orbitals, which are not optimized. Six molecular orbitals are chosen as active space, including H(1s) and Se(4s4p5s) shells, and eight electrons are distributed in a (4, 1, 1, 0) active space, which is referred to as CAS (8, 6), and the Se(3d) shell is selected as a closed-shell, which keeps doubly occupation. In the MRCI step, the remaining Se(3d) shell is used for core-valence calculations of SeH anion. The SOC effects are taken into account in the one- and two- electron Breit-Pauli operators.The b3Σ+ state is a repulsive state. Other excited states are bound, and all states possess two potential wells. The $ {{\rm{b}}^{{3}}}\Sigma _{{0^ - }}^ + $ and $ {{\rm{b}}^3}\Sigma _{{1}}^ + $ both turn into bound states when the SOC effect is considered. All spectroscopic parameters of Λ-S states and Ω states are reported for the first time. The TDMs of the $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $, $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, $ {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{1}}}$, and $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$ transitions are also calculated. The TDMs of the $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ and $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ transitions are large in the Franck-Condon region, which are about –2.05 Debye (D) and 1.45 D at Re. Notably, the TDMs of the $ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition cannot be ignored. The value of TDM at Re equals –0.15 D.Based on the accurately PECs and PDMs, the values of Franck-Condon factor fυυ, vibrational branching ratio Rυυ and radiative coefficient of the $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $, $ {{\rm{a}}^{{3}}}{{{\Pi }}_{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^{{1}}}{{\Sigma }}_{{0^ + }}^ + $, and $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ transitions are also calculated. Highly diagonally distributed Franck-Condon factor f00 and the values of vibrational branching ratio R00 of the $ {{\rm{a}}^{{3}}}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$, $ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$, and $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transitions are obtained, respectively. Spontaneous radiation lifetimes of the $ {{\rm{a}}^3}{\Pi _{{1}}}$, $ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$, and $ {{\rm{A}}^1}{\Pi _{{1}}}$ excited states are all short for rapid laser cooling. The influences of intervening states of the $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transition can be ignored. The proposed cooling wavelengths using the $ {{\rm{a}}^3}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + (\upsilon '')$, $ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$, and $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transitions are all in the visible region.
      通信作者: 黄多辉, hdhzhy912@163.com
    • 基金项目: 宜宾学院预研项目(批准号: 2019YY06)和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) 资助的课题
      Corresponding author: Huang Duo-Hui, hdhzhy912@163.com
    • Funds: Project supported by 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, China (Grant No. YBXYJSWL-ZD-2020-001)
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  • 图 1  X1Σ+, a3Π, A1Π, b3Σ+和21Σ+电子态的势能曲线

    Fig. 1.  Potential energy curves of the X1Σ+, a3Π, A1Π, b3Σ+, and 21Σ+ states.

    图 2  9个Ω电子态的势能曲线

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

    图 3  ${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _1}$${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$跃迁的跃迁偶极矩

    Fig. 3.  Transition dipole moments of the ${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $, ${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _1}$, and ${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$ transition.

    图 4  激光冷却SeH阴离子的方案 (a)${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁; (b) ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁

    Fig. 4.  Proposed laser cooling scheme: (a) Using the ${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition; (b) using the ${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition.

    图 5  采用${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $跃迁进行激光冷却SeH阴离子的方案

    Fig. 5.  Proposed laser cooling scheme by using the ${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition.

    表 1  Λ-S的光谱常数

    Table 1.  Spectroscopic parameters of the Λ-S states.

    Λ-S态来源Reωe/cm–1ωeχe/cm–1Be/cm–1De/eVTe/cm–1
    X1Σ+ACVQZ-DK1.46942300.7746.107.85073.4870
    AVQZ-DK1.46142380.3245.577.93263.711
    实验[17]1.4696 a7.7289 c
    1.4806 b
    a3Π本文工作第一势阱1.47782206.52123.457.84280.51920642.90
    第二势阱2.1787839.8749.663.440160.45024549.11
    A1Π本文工作第一势阱1.47262373.65127.147.83910.73421240.75
    第二势阱2.2780437.6244.073.09320.14726997.57
    b3Σ+本文工作repulsive
    21Σ+本文工作第一势阱1.61881336.456.19550.22851684.73
    第二势阱4.0808198.909.961.01900.13546349.30
    注: a 为SeH分子基态的平衡核间距的实验值来源于文献[18]; b为SeH分子基态的平衡核间距的实验值来源于文献[33], 结果不准确;
    c 为采用最小二乘法得到转动惯量B.
    下载: 导出CSV

    表 2  第VI主簇氢化物阴离子基态的光谱常数

    Table 2.  Spectroscopic parameters of the ground state X1Σ+ of the Group VI-hydride anions.

    阴离子来源Reωe/cm–1ωeχe/cm–1Be/cm–1De/eV
    OH文献[14]0.96453722.1087.9319.11114.9857
    SH文献[15]1.34352622.0446.669.55903.8793
    SeH本文工作1.46942300.7746.107.85073.487
    TeH文献[16]1.66311973.7336.82726.09963.0568
    下载: 导出CSV

    表 3  Ω态的离解关系

    Table 3.  Calculated dissociation relationships of the Ω states.

    离解通道分子态(Ω)相对能量/cm–1
    ACVQZ-DKAVQZ-DK实验[34-36]
    Se(2P3/2) + H(2S1/2)2, 1, 1, 0+, 0000
    Se(2P1/2) + H(2S1/2)1, 0+, 02303.772192.98
    Se(1D2) + H(1S0)0+20032.2419047.4519790.88
    下载: 导出CSV

    表 4  Ω电子态的光谱常数

    Table 4.  Spectroscopic parameters of the Ω states.

    Ω态Reωe/cm–1ωeχe/cm–1Be/cm–1De/eVTe/cm–1
    ${{\rm{X}}^1}\Sigma _{{0^ + }}^ + $1.46942301.3147.017.84993.3950
    ${{\rm{a}}^3}{\Pi _2}$第一势阱1.47772207.22122.397.84160.52319787.17
    第二势阱2.1739861.0252.103.40810.45423751.54
    ${{\rm{a}}^3}{\Pi _{{1}}}$第一势阱1.47592232.16111.707.84340.56020036.27
    第二势阱2.1822818.1155.643.39290.38624301.10
    ${{\rm{a}}^3}{\Pi _{{{{0}}^ - }}}$第一势阱1.47782205.83124.977.84850.51321472.52
    第二势阱2.1986778.2873.703.40480.26725261.96
    ${{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$第一势阱1.47772208.03122.907.84220.52221477.12
    第二势阱2.1619904.1549.023.43550.52725454.22
    ${{\rm{A}}^1}{\Pi _{{1}}}$第一势阱1.47442368.50144.227.82620.68621821.04
    第二势阱排斥态
    ${{\rm{b}}^3}\Sigma _{{0^ - }}^ + $第一势阱3.1807318.8935.641.69880.09628945.41
    ${{\rm{b}}^3}\Sigma _{{1}}^ + $第二势阱3.2046239.1330.941.66620.06629184.63
    ${2^1}\Sigma _{{0^ + }}^ + $第一势阱1.61901332.506.18950.22551714.58
    第二势阱4.0800190.578.841.01900.13546351.94
    下载: 导出CSV

    表 5  ${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^{{3}}}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $${{\rm{A}}^1}{\Pi _1} \leftrightarrow $${{\rm{X}}^1}\Sigma _{{0^ + }}^ +$跃迁的辐射系数${A_{\upsilon '\upsilon ''}}$、弗兰克-康登因子${f_{\upsilon '\upsilon ''}}$和振动分支比${R_{\upsilon '\upsilon ''}}$

    Table 5.  Emission rates ${A_{\upsilon '\upsilon ''}}$, Franck-Condon Factors ${f_{\upsilon '\upsilon ''}}$, branching ratios ${R_{\upsilon '\upsilon ''}}$ of the ${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $, ${{\rm{a}}^{{3}}}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $, and ${{\rm{A}}^1}{\Pi _1} \leftrightarrow $ ${{\rm{X}}^1}\Sigma _{{0^ + }}^ +$ transitions.

    Index${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow $
    ${{\rm{X}}^1}\Sigma _{{0^ + }}^ + $
    ${{\rm{a}}^{{3}}}{\Pi _{{0^ + }}} \leftrightarrow $
    ${{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $
    ${{\rm{A}}^1}{\Pi _1} \leftrightarrow$
    $ {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $
    ${f_{\upsilon '\upsilon ''}}$f000.99490.99220.9974
    f010.00470.00720.0025
    f020.00040.00060.0001
    f100.00510.00790.0026
    f110.95410.93240.9792
    f120.03370.04860.0159
    ${A_{\upsilon '\upsilon ''}}\rm /s$A005.02×1068.02×1041.36×107
    A011.88×1024.28×1031.87×104
    A022.81×1017.48×1012.00×103
    A101.10×1056.50×1025.79×104
    A114.13×1069.13×1041.32×107
    A121.32×1041.57×1041.45×105
    ${R_{\upsilon '\upsilon ''}}$R000.999960.94840.9985
    R013.7×10–50.05060.0014
    R025.6×10–60.00090.0001
    R100.025920.00600.0043
    R110.97070.83940.9836
    R120.00310.14460.0108
    下载: 导出CSV
  • [1]

    Shuman E S, Barry J F, DeMille D 2010 Nature 467 820Google Scholar

    [2]

    Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001Google Scholar

    [3]

    Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E A, Tarbutt M R, Sauer B E 2014 Phys. Rev. A 89 053416Google Scholar

    [4]

    Gao Y, Gao T 2014 Phys. Rev. A 90 052506Google Scholar

    [5]

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

    [6]

    Cui J, Xu J G, Qi J X, Dou G, Zhang Y G 2018 Chin. Phys. B 27 103101Google Scholar

    [7]

    Wan M J, Yuan D, Jin C G, Wang F H, Yang Y J, Yu Y, Shao J X 2016 J. Chem. Phys. 145 024309Google Scholar

    [8]

    张云光, 张华, 窦戈, 徐建刚 2017 物理学报 66 233101Google Scholar

    Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101Google Scholar

    [9]

    Xu L, Wei W, Xia Y, Deng L Z, Yin J P 2017 Chin. Phys. B 26 033702Google Scholar

    [10]

    Yzombard P, Hamamda M, Gerber S, Doser M, Comparat D 2015 Phys. Rev. Lett. 114 213001Google Scholar

    [11]

    Zhang Q Q, Yang C L, Wang M S, Ma X G, Liu W W 2017 Spectrochim. Acta. Part A 185 365Google Scholar

    [12]

    Zhang Q Q, Yang C L, Wang M S, Ma X G, Liu W W 2017 Spectrochim. Acta. Part A 182 130Google Scholar

    [13]

    Zeid I, Abdallah R A, El Kork N, Korek M 2020 Spectrochim. Acta. Part A 224 117461Google Scholar

    [14]

    Wan M J, Huang D H, Yu Y, Zhang Y G 2017 Phys. Chem. Chem. Phys. 19 27360Google Scholar

    [15]

    万明杰, 李松, 金成国, 罗华锋 2019 物理学报 68 063103Google Scholar

    Wan M J, Li S, Jin C G, Luo H F 2019 Acta. Phys. Sin. 68 063103Google Scholar

    [16]

    Deng B L, Wan M J, Zhao X F, Tang K, Zhang X Q 2020 Spectrochim. Acta. Part A 227 117684Google Scholar

    [17]

    Stoneman R C, Larson D J 1987 Phys. Rev. A 35 2928Google Scholar

    [18]

    Brown J M, Fackerell A D 1982 Physica. Scripta. 25 351Google Scholar

    [19]

    Balasubramanian K, Liao M Z, Han M 1987 Chem. Phys. Lett. 139 551Google Scholar

    [20]

    Binning Jr R C, Curtiss L A 1990 J. Chem. Phys. 92 1860Google Scholar

    [21]

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

    [22]

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

    [23]

    Werner H J, Meyer W 1980 J. Chem. Phys. 73 2342Google Scholar

    [24]

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

    [25]

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

    [26]

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

    [27]

    Douglas N, Kroll N M 1974 Ann. Phys. 82 89Google Scholar

    [28]

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出版历程
  • 收稿日期:  2020-08-26
  • 修回日期:  2020-09-21
  • 上网日期:  2021-01-26
  • 刊出日期:  2021-02-05

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