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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^ - }}^ + $ 和$ {{\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 $ ${{\rm{X}}^1}\Sigma _{{0^ + }}^ +$ 和$ {{\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}}^{{ + }}}}}$ 和$ {{\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^ + }}^ + $ 和$ {{\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 fυ′υ″, vibrational branching ratio Rυ′υ″ 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.-
Keywords:
- spin-orbit coupling effects /
- vibrational branching ratios /
- spontaneous radiative lifetimes /
- laser cooling
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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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 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^ + }}^ + $ ,${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _1}$ 和${{\rm{A}}^{{1}}}{\Pi _1} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$ 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 Re/Å ωe/cm–1 ωeχe/cm–1 Be/cm–1 De/eV Te/cm–1 X1Σ+ ACVQZ-DK 1.4694 2300.77 46.10 7.8507 3.487 0 AVQZ-DK 1.4614 2380.32 45.57 7.9326 3.711 实验[17] 1.4696 a 7.7289 c 1.4806 b a3Π 本文工作 第一势阱 1.4778 2206.52 123.45 7.8428 0.519 20642.90 第二势阱 2.1787 839.87 49.66 3.44016 0.450 24549.11 A1Π 本文工作 第一势阱 1.4726 2373.65 127.14 7.8391 0.734 21240.75 第二势阱 2.2780 437.62 44.07 3.0932 0.147 26997.57 b3Σ+ 本文工作 repulsive 21Σ+ 本文工作 第一势阱 1.6188 1336.45 — 6.1955 0.228 51684.73 第二势阱 4.0808 198.90 9.96 1.0190 0.135 46349.30 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.
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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.
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表 4 Ω电子态的光谱常数
Table 4. Spectroscopic parameters of the Ω states.
Ω态 Re/Å ωe/cm–1 ωeχe/cm–1 Be/cm–1 De/eV Te/cm–1 ${{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ 1.4694 2301.31 47.01 7.8499 3.395 0 ${{\rm{a}}^3}{\Pi _2}$ 第一势阱 1.4777 2207.22 122.39 7.8416 0.523 19787.17 第二势阱 2.1739 861.02 52.10 3.4081 0.454 23751.54 ${{\rm{a}}^3}{\Pi _{{1}}}$ 第一势阱 1.4759 2232.16 111.70 7.8434 0.560 20036.27 第二势阱 2.1822 818.11 55.64 3.3929 0.386 24301.10 ${{\rm{a}}^3}{\Pi _{{{{0}}^ - }}}$ 第一势阱 1.4778 2205.83 124.97 7.8485 0.513 21472.52 第二势阱 2.1986 778.28 73.70 3.4048 0.267 25261.96 ${{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$ 第一势阱 1.4777 2208.03 122.90 7.8422 0.522 21477.12 第二势阱 2.1619 904.15 49.02 3.4355 0.527 25454.22 ${{\rm{A}}^1}{\Pi _{{1}}}$ 第一势阱 1.4744 2368.50 144.22 7.8262 0.686 21821.04 第二势阱 排斥态 ${{\rm{b}}^3}\Sigma _{{0^ - }}^ + $ 第一势阱 3.1807 318.89 35.64 1.6988 0.096 28945.41 ${{\rm{b}}^3}\Sigma _{{1}}^ + $ 第二势阱 3.2046 239.13 30.94 1.6662 0.066 29184.63 ${2^1}\Sigma _{{0^ + }}^ + $ 第一势阱 1.6190 1332.50 — 6.1895 0.225 51714.58 第二势阱 4.0800 190.57 8.84 1.0190 0.135 46351.94
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表 5
${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ ,${{\rm{a}}^{{3}}}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ 和${{\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 ''}}$ f00 0.9949 0.9922 0.9974 f01 0.0047 0.0072 0.0025 f02 0.0004 0.0006 0.0001 f10 0.0051 0.0079 0.0026 f11 0.9541 0.9324 0.9792 f12 0.0337 0.0486 0.0159 ${A_{\upsilon '\upsilon ''}}\rm /s$ A00 5.02×106 8.02×104 1.36×107 A01 1.88×102 4.28×103 1.87×104 A02 2.81×101 7.48×101 2.00×103 A10 1.10×105 6.50×102 5.79×104 A11 4.13×106 9.13×104 1.32×107 A12 1.32×104 1.57×104 1.45×105 ${R_{\upsilon '\upsilon ''}}$ R00 0.99996 0.9484 0.9985 R01 3.7×10–5 0.0506 0.0014 R02 5.6×10–6 0.0009 0.0001 R10 0.02592 0.0060 0.0043 R11 0.9707 0.8394 0.9836 R12 0.0031 0.1446 0.0108
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[1] Shuman E S, Barry J F, DeMille D 2010 Nature 467 820
Google Scholar
[2] Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001
Google 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 053416
Google Scholar
[4] Gao Y, Gao T 2014 Phys. Rev. A 90 052506
Google Scholar
[5] You Y, Yang C L, Wang M S, Ma X G, Liu W W 2015 Phys. Rev. A 92 032502
Google Scholar
[6] Cui J, Xu J G, Qi J X, Dou G, Zhang Y G 2018 Chin. Phys. B 27 103101
Google 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 024309
Google Scholar
[8] 张云光, 张华, 窦戈, 徐建刚 2017 66 233101
Google Scholar
Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101
Google Scholar
[9] Xu L, Wei W, Xia Y, Deng L Z, Yin J P 2017 Chin. Phys. B 26 033702
Google Scholar
[10] Yzombard P, Hamamda M, Gerber S, Doser M, Comparat D 2015 Phys. Rev. Lett. 114 213001
Google Scholar
[11] Zhang Q Q, Yang C L, Wang M S, Ma X G, Liu W W 2017 Spectrochim. Acta. Part A 185 365
Google Scholar
[12] Zhang Q Q, Yang C L, Wang M S, Ma X G, Liu W W 2017 Spectrochim. Acta. Part A 182 130
Google Scholar
[13] Zeid I, Abdallah R A, El Kork N, Korek M 2020 Spectrochim. Acta. Part A 224 117461
Google Scholar
[14] Wan M J, Huang D H, Yu Y, Zhang Y G 2017 Phys. Chem. Chem. Phys. 19 27360
Google Scholar
[15] 万明杰, 李松, 金成国, 罗华锋 2019 68 063103
Google Scholar
Wan M J, Li S, Jin C G, Luo H F 2019 Acta. Phys. Sin. 68 063103
Google Scholar
[16] Deng B L, Wan M J, Zhao X F, Tang K, Zhang X Q 2020 Spectrochim. Acta. Part A 227 117684
Google Scholar
[17] Stoneman R C, Larson D J 1987 Phys. Rev. A 35 2928
Google Scholar
[18] Brown J M, Fackerell A D 1982 Physica. Scripta. 25 351
Google Scholar
[19] Balasubramanian K, Liao M Z, Han M 1987 Chem. Phys. Lett. 139 551
Google Scholar
[20] Binning Jr R C, Curtiss L A 1990 J. Chem. Phys. 92 1860
Google 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 5053
Google Scholar
[23] Werner H J, Meyer W 1980 J. Chem. Phys. 73 2342
Google Scholar
[24] Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803
Google Scholar
[25] Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514
Google Scholar
[26] Laughoff S R, Davidson E R 1974 Int. J Quantum. Chem. 8 61
Google Scholar
[27] Douglas N, Kroll N M 1974 Ann. Phys. 82 89
Google Scholar
[28] Hess B A 1986 Phys. Rev. A 33 3742
Google Scholar
[29] Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823
Google Scholar
[30] DeYonker N J, Peterson K A, Wilson A K 2007 J. Phys Chem A 111 11383
Google Scholar
[31] Dunning Jr T H 1989 J. Chem. Phys. 90 1007
Google Scholar
[32] 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
[33] Huber K, Herzberg G 1979 Molecular Spectra and Molecular Structure Vol. 4. Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) p586
[34] Moore C E 1971 Atomic Energy Levels (Vol. 1) (Washington, DC: US Govt Printing Office) pp2, 150
[35] Lykke K R, Murray K K, Lineberger W C 1991 Rhys. Rev. A 43 6104
Google Scholar
[36] Hotop H, Lineberger W C 1985 J. Phys. Chem. Ref. Data 14 731
Google Scholar
[37] Lane I C 2015 Phys. Rev. A 92 022511
Google Scholar
[38] You Y, Yang C L, Zhang Q Q, Wang M S, Ma X G, Wang W W 2016 Phys. Chem. Chem. Phys. 18 19838
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