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含自旋-轨道耦合的$ {{\bf{O}}}_{2}^{ - } $光谱常数计算

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

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含自旋-轨道耦合的$ {{\bf{O}}}_{2}^{ - } $光谱常数计算

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
物理学报,
doi: 10.7498/aps.74.20241435
cstr: 32037.14.aps.74.20241435

Calculation of $ {\mathrm{O}}^ -_2 $ spectroscopic constants with spin-orbit coupling

LIU Mingjie, TIAN Yali, WANG Yu, LI Xiaoxiao, HE Xiaohu, GONG Ting, SUN Xiaocong, GUO Guqing, QIU Xuanbing, LI Chuanliang
Acta Phys. Sin.,
doi: 10.7498/aps.74.20241435
cstr: 32037.14.aps.74.20241435
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  • 摘要

    本文采用完全活性空间自洽场(complete active space self-consistent field, CASSCF)和加戴维森校正的多参考组态相互作用(multireference configuration interaction with Davidson correction, MRCI+Q)方法, 研究了超氧阴离子(${\text{O}}_{2}^{{ - }}$)的低激发电子态及自旋-轨道耦合(spin-orbit coupling, SOC)效应对电子态的影响. 使用aug-cc-pV5Z-dk基组, 计算了${\text{O}}_{2}^{{ - }}$第一和第二解离极限对应的42个Λ-S态的势能曲线(potential energy curves, PECs)以及束缚态的光谱常数. 同时考虑SOC效应, 计算了这42个Λ-S态分裂形成的84个Ω态的PECs和部分束缚态的光谱常数. 其中第一解离极限结果与已有文献高度一致, 第二解离极限结果为本文首次计算提供. 这些结果为研究${\text{O}}_{2}^{{ - }}$的电子结构和光谱性质提供了重要的理论依据. 针对${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$态的双势阱现象, 本文通过比较不同基组下的计算结果, 证实了${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$态的双势阱形成源于与${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$态的避免交叉影响. 此外, 研究发现基组大小直接影响${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$态的首个势阱深度, 这进一步表明基组选择对光谱常数计算的精确性至关重要. 本文数据集可在科学数据银行https://doi.org/10.57760/sciencedb.j00213.00076中访问获取.

    Abstract

    A comprehensive theoretical study on the low-energy electronic states of superoxide anion (${\text{O}}_{2}^{{ - }}$) is carried out, focusing on the influence of spin-orbit coupling (SOC) on these states. Utilizing the complete active space self-consistent field (CASSCF) method combined with the multireference configuration interaction method with Davidson correction (MRCI+Q) and employing the aug-cc-pV5Z-dk basis set that includes Douglas-Kroll relativistic corrections, the electron correlation and relativistic effects are accurately considered in this work. This work concentrates on the first and second dissociation limits of ${\text{O}}_{2}^{{ - }}$, calculating the potential energy curves (PECs) and spectroscopic constants of 42 Λ-S states. After introducing SOC, 84 Ω states are obtained through splitting, and their PECs and spectroscopic constants are calculated. Detailed data of the electronic states related to the second dissociation limit are provided. The results show excellent agreement with those in the existing literature, thus validating the reliability of the method. This work confirms through calculations with different basis sets that the double-well structure of the ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ state originates from avoiding crossing with the ${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ state, and finds that the size of the basis set can significantly affect the depth of its potential well. After considering SOC, the total energy of the system decreases, especially for the states with high orbital angular momentum (such as the ${{1}^{2}}{{\Phi }}_{\text{u}}$ and ${{1}^{4}}{{{\Delta }}_{\text{g}}}$ states), leading to energy level splitting and energy reduction, while other spectroscopic constants remain essentially unchanged. These findings provide valuable theoretical insights into the electronic structure and spectroscopic properties of ${\text{O}}_{2}^{{ - }}$, present important reference data for future research in fields such as atmospheric chemistry, plasma physics, and molecular spectroscopy. The datasets provided in this work are available from https://doi.org/10.57760/sciencedb.j00213.00076.

  • 图 1  ${\text{O}}_{2}^{{ - }}$ Λ-S态PECs　(a) 42个Λ-S态的PECs; (b)第一解离极限二重态的PECs; (c)第二解离极限二重态的PECs; (d) 第一解离极限四重态的PECs

    Fig. 1.  Λ-S states Potential energy curves for ${\text{O}}_{2}^{{ - }}$: (a) Potential energy curves of 42 Λ-S states; (b) potential energy curves for the first dissociation limit doublet state; (c) potential energy curves for the second dissociation limit doublet state; (d) potential energy curves for the first dissociation limit quartet state.

    下载: 全尺寸图片 幻灯片

    图 2  ${\text{O}}_{2}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $与 ${{2}^{2}}{{\Sigma }}_{\text{g}}^ + $态PECs

    Fig. 2.  ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $ and ${{2}^{2}}{{\Sigma }}_{\text{g}}^ + $ potential energy curves of ${\text{O}}_{2}^{{ - }}$.

    下载: 全尺寸图片 幻灯片

    图 3  不同基组及冻结电子情况下的下${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$和${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ PECs的比较

    Fig. 3.  Comparison of the potential energy curves of ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ and ${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ for different basis sets and frozen electrons.

    下载: 全尺寸图片 幻灯片

    图 4  由42个Λ-S态产生的84个Ω态PECs　(a) Ω = 7/2; (b) Ω = 5/2; (c) Ω = 3/2; (d) Ω = 1/2

    Fig. 4.  Potential energy curves for 84 Ω states generated by 42 Λ-S states: (a) Ω = 7/2; (b) Ω = 5/2; (c) Ω = 3/2; (d) Ω = 1/2.

    下载: 全尺寸图片 幻灯片

    图 5  由4重Π态产生的4个Ω态的PECs (Ω = –1/2)

    Fig. 5.  Potential energy curves for 4 Ω states generated by quadruple Π state (Ω = –1/2).

    下载: 全尺寸图片 幻灯片

    表 1  ${\text{O}}_{2}^{{ - }}$第一和第二解离极限对应的Λ-S态和Ω态

    Table 1.  Λ-S and Ω states corresponding to the first and second dissociation limits of ${\text{O}}_{2}^{{ - }}$.

    原子态 能级/cm–1 Λ-S态 Ω态
    本文 NIST[32]
    O(2s22p4 3Pg)+O–(2s22p5 2Pu) 0 0 ${\text{X}}{}^{2}{{{\Pi }}_{\text{g}}}$ ${\text{X}}{}^{2}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${\text{X}}{}^{2}{{{\Pi }}_{{\text{g, 1/2}}}}$
    ${2}{}^{2}{{{\Pi }}_{\text{g}}}$ ${2}{}^{2}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${2}{}^{2}{{{\Pi }}_{{\text{g, 1/2}}}}$
    ${1}{}^{2}{{{\Delta }}_{\text{g}}}$ ${1}{}^{2}{{{\Delta }}_{{\text{g, 5/2}}}}$ , ${1}{}^{2}{{{\Delta }}_{{\text{g, 3/2}}}}$
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{\text{g, 1/2}}}^{+}$
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{{\text{g, 1/2}}}^{{ - }}$
    ${{2}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{\text{g, 1/2}}}^{{ - }}$
    ${\text{A}}{}^{2}{{{\Pi }}_{\text{u}}}$ ${\text{A}}{}^{2}{{{\Pi }}_{{\text{u, 1/2}}}}$ , ${\text{A}}{}^{2}{{{\Pi }}_{{\text{u, 3/2}}}}$
    ${2}{}^{2}{{{\Pi }}_{\text{u}}}$ ${2}{}^{2}{{{\Pi }}_{{\text{u, 1/2}}}}$ , ${2}{}^{2}{{{\Pi }}_{{\text{u, 3/2}}}}$
    ${1}{}^{2}{\Delta _{\text{u}}}$ ${1}{}^{2}{\Delta _{{\text{u, 5/2}}}}$ , ${1}{}^{2}{\Delta _{{\text{u, 3/2}}}}$
    ${{1}^{2}}{{\Sigma }}_{\text{u}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{\text{u, 1/2}}}^{+}$
    ${{1}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{{\text{u, 1/2}}}^{{ - }}$
    ${{2}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{\text{u, 1/2}}}^{{ - }}$
    ${1}{}^{4}{{{\Pi }}_{\text{g}}}$ ${1}{}^{4}{{{\Pi }}_{{\text{g, 5/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{g, 1/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{g, - 1/2}}}}$
    ${2}{}^{4}{{{\Pi }}_{\text{g}}}$ ${2}{}^{4}{{{\Pi }}_{{\text{g, 5/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{g, 1/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{g, - 1/2}}}}$
    ${1}{}^{4}{{{\Delta }}_{\text{g}}}$ ${1}{}^{4}{{{\Delta }}_{{\text{g, 7/2}}}}$ , ${1}{}^{4}{{{\Delta }}_{{\text{g, 5/2}}}}$ , ${1}{}^{4}{{{\Delta }}_{{\text{g, 3/2}}}}$ , ${1}{}^{4}{{{\Delta }}_{{\text{g, 1/2}}}}$
    $ {{1}^{4}}{{\Sigma }}_{\text{g}}^{+} $ $ {{1}^{4}}{{\Sigma }}_{{\text{g, 1/2}}}^{+} $ , $ {{1}^{4}}{{\Sigma }}_{{\text{g, 3/2}}}^{+} $
    $ {{1}^{4}}{{\Sigma }}_{\text{g}}^{{ - }} $ $ {{1}^{4}}{{\Sigma }}_{{\text{g, 1/2}}}^{{ - }} $ , $ {{1}^{4}}{{\Sigma }}_{{\text{g, 3/2}}}^{{ - }} $
    $ {{2}^{4}}{{\Sigma }}_{\text{g}}^{{ - }} $ $ {{2}^{4}}{{\Sigma }}_{{\text{g, 1/2}}}^{{ - }} $ , $ {{2}^{4}}{{\Sigma }}_{{\text{g, 3/2}}}^{{ - }} $
    ${1}{}^{4}{{{\Pi }}_{\text{u}}}$ ${1}{}^{4}{{{\Pi }}_{{\text{u, 5/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{u, 3/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{u, 1/2}}}}$ , ${1}{}^{4}{{{\Pi }}_{{\text{u, - 1/2}}}}$
    ${2}{}^{4}{{{\Pi }}_{\text{u}}}$ ${2}{}^{4}{{{\Pi }}_{{\text{u, 5/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{u, 3/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{u, 1/2}}}}$ , ${2}{}^{4}{{{\Pi }}_{{\text{u, - 1/2}}}}$
    ${1}{}^{4}{{{\Delta }}_{\text{u}}}$ 14Δu, 7/2 , 14Δu, 5/2 , 14Δu, 3/2 , 14Δu, 1/2
    $ {{1}^{4}}{{\Sigma }}_{\text{u}}^{+} $ $ {1}^{4}{\text{Σ}}_{\text{u}, \text{1/2}}^{+} $ , $ {1}^{4}{\text{Σ}}_{\text{u}, \text{3/2}}^{+} $
    ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ $ {\text{a}}^{4}{\text{Σ}}_{\text{u}, \text{1/2}}^{-} $ , $ {\text{a}}^{4}{\text{Σ}}_{\text{u}, \text{3/2}}^{-} $
    ${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ $ {2}^{4}{\text{Σ}}_{\text{u}, \text{1/2}}^{-} $ , $ {2}^{4}{\text{Σ}}_{\text{u}, \text{3/2}}^{-} $
    O(2s22p4 1Dg)+O–(2s22p5 2Pu) 15878.24 15867.86 ${3}{}^{2}{{{\Pi }}_{\text{g}}}$ ${3}{}^{2}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${3}{}^{2}{{{\Pi }}_{{\text{g, 1/2}}}}$
    ${4}{}^{2}{{{\Pi }}_{\text{g}}}$ ${4}{}^{2}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${4}{}^{2}{{{\Pi }}_{{\text{g, 1/2}}}}$
    ${5}{}^{2}{{{\Pi }}_{\text{g}}}$ $5{}^{2}{{{\Pi }}_{{\text{g, 3/2}}}}$ , ${5}{}^{2}{{{\Pi }}_{{\text{g, 1/2}}}}$
    ${1}{}^{2}{{\Phi }}_{\text{g}}$ ${1}{}^{2}{{\Phi }}_{{\text{g, 7/2}}}$ , ${1}{}^{2}{{\Phi }}_{{\text{g, 5/2}}}$
    ${2}{}^{2}{{{\Delta }}_{\text{g}}}$ ${2}{}^{2}{{{\Delta }}_{{\text{g, 5/2}}}}$ , ${2}{}^{2}{{{\Delta }}_{{\text{g, 3/2}}}}$
    ${3}{}^{2}{{{\Delta }}_{\text{g}}}$ ${3}{}^{2}{{{\Delta }}_{{\text{g, 5/2}}}}$ , ${3}{}^{2}{{{\Delta }}_{{\text{g, 3/2}}}}$
    ${{2}^{2}}{{\Sigma }}_{\text{g}}^{+}$ $ {2}^{2}{\text{Σ}}_{\text{g}, \text{1/2}}^{+} $
    ${{3}^{2}}{{\Sigma }}_{\text{g}}^{+}$ $ {3}^{2}{\text{Σ}}_{\text{g}, \text{1/2}}^{+} $
    ${{3}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$ $ {3}^{2}{\text{Σ}}_{\text{g}, \text{1/2}}^{-} $
    ${3}{}^{2}{{{\Pi }}_{\text{u}}}$ ${3}{}^{2}{{{\Pi }}_{{\text{u, 3/2}}}}$ , ${3}{}^{2}{{{\Pi }}_{{\text{u, 1/2}}}}$
    ${4}{}^{2}{{{\Pi }}_{\text{u}}}$ ${4}{}^{2}{{{\Pi }}_{{\text{u, 3/2}}}}$ , ${4}{}^{2}{{{\Pi }}_{{\text{u, 1/2}}}}$
    ${5}{}^{2}{{{\Pi }}_{\text{u}}}$ ${5}{}^{2}{{{\Pi }}_{{\text{u, 3/2}}}}$ , ${5}{}^{2}{{{\Pi }}_{{\text{u, 1/2}}}}$
    ${1}{}^{2}{{\Phi }}_{\text{u}}$ ${1}{}^{2}{{\Phi }}_{{\text{u, 7/2}}}$ , ${1}{}^{2}{{\Phi }}_{{\text{u, 5/2}}}$
    ${2}{}^{2}{{{\Delta }}_{\text{u}}}$ ${2}{}^{2}{{{\Delta }}_{{\text{u, 5/2}}}}$ , ${2}{}^{2}{{{\Delta }}_{{\text{u, 3/2}}}}$
    ${3}{}^{2}{{{\Delta }}_{\text{u}}}$ ${3}{}^{2}{{{\Delta }}_{{\text{u, 5/2}}}}$ , ${3}{}^{2}{{{\Delta }}_{{\text{u, 3/2}}}}$
    ${{2}^{2}}{{\Sigma }}_{\text{u}}^{+}$ $ {2}^{2}{\text{Σ}}_{\text{u}, \text{1/2}}^{+} $
    ${{3}^{2}}{{\Sigma }}_{\text{u}}^{+}$ $ {3}^{2}{\text{Σ}}_{\text{u}, \text{1/2}}^{+} $
    ${{3}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$ $ {3}^{2}{\text{Σ}}_{\text{u}, \text{1/2}}^{-} $
    下载: 导出CSV

    表 2  第一和第二解离极限束缚Λ-S态在其Re处的主要电子组态

    Table 2.  Main electronic configurations of bound Λ-S states at Re in the first and second dissociation limits.

    Λ-S态 Λ-S态在Re处的主要组态
    ${\text{X}}{}^{2}{{{\Pi }}_{\text{g}}}$ 3σg21πu41πg33σu0 (98.05%)
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^{+}$ 3σg11πu41πg43σu0 (96.32%)
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$ 3σg21πu31πg33σu1 (97.30%)
    ${\text{A}}{}^{2}{{{\Pi }}_{\text{u}}}$ 3σg21πu41πg33σu0 (92.88%)
    ${1}{}^{2}{\Delta _{\text{u}}}$ 3σg21πu41πg23σu1 (60.17%) 3σg21πu21πg43σu1 (34.59%)
    ${{1}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$ 3σg21πu41πg23σu1 (73.86%)
    ${1}{}^{4}{{{\Pi }}_{\text{g}}}$ 3σg11πu31πg43σu1 (99.97%)
    ${1}{}^{4}{\Delta _{\text{g}}}$ 3σg21πu31πg33σu1 (70.71%)
    ${{1}^{4}}{{\Sigma }}_{\text{g}}^{+}$ 3σg21πu31πg33σu1 (70.71%)
    ${{1}^{4}}{{\Sigma }}_{\text{g}}^{{ - }}$ 3σg11πu41πg23σu2 (69.48%) 3σg21πu31πg33σu1 (48.39%)
    ${1}{}^{4}{{{\Pi }}_{\text{u}}}$ 3σg11πu41πg33σu1 (99.85%)
    ${2}{}^{4}{{{\Pi }}_{\text{u}}}$ 3σg21πu31πg23σu2 (99.87%)
    ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$(1st well) 3σg21πu41πg23σu1 (97.21%)
    (2 nd well) 3σg21πu41πg23σu1 (61.53%) 3σg21πu31πg43σu1 (32.34%)
    ${3}{}^{2}{{{\Pi }}_{\text{g}}}$ 3σg11πu31πg43σu1 (63.92%)
    ${2}{}^{2}{\Delta _{\text{g}}}$ 3σg11πu41πg23σu2 (50.21%) 3σg21πu31πg33σu1 (35.45%)
    ${{2}^{2}}{{\Sigma }}_{\text{g}}^{+}$ 3σg21πu31πg33σu1 (85.66%)
    ${{3}^{2}}{{\Sigma }}_{\text{g}}^{+}$ 3σg21πu31πg33σu1 (42.42%) 3σg11πu21πg43σu2 (35.42%) 3σg11πu41πg23σu2 (29.42%)
    ${3}{}^{2}{{{\Pi }}_{\text{u}}}$ 3σg11πu41πg33σu1 (73.79%) 3σg21πu31πg43σu0 (30.12%)
    ${1}{}^{2}{{\Phi }}_{\text{u}}$ 3σg21πu31πg23σu2 (50.00%)
    ${2}{}^{2}{\Delta _{\text{u}}}$ 3σg11πu31πg33σu2 (49.87%) 3σg21πu41πg23σu1 (28.13%) 3σg21πu21πg43σu1 (21.31%)
    ${{3}^{2}}{{\Sigma }}_{\text{u}}^{+}$ 3σg11πu31πg33σu2 (40.05%) 3σg21πu41πg23σu1 (37.78%) 3σg21πu21πg43σu1 (30.08%)
    下载: 导出CSV

    表 3  ${{\text{X}}^{2}}{{{\Pi }}_{\text{g}}}$态和${{\text{A}}^{2}}{{{\Pi }}_{\text{u}}}$态的光谱常数

    Table 3.  Spectroscopic constants for the ${{\text{X}}^{2}}{{{\Pi }}_{\text{g}}}$ and ${{\text{A}}^{2}}{{{\Pi }}_{\text{u}}}$ states.

    Te/cm–1Re/nmωe/cm–1ωeχe/cm–1Be/cm–1102αe/cm–1De/eV
    ${{\text{X}}^{2}}{{{\Pi }}_{\text{g}}}$本文0.000.13501073.67.81.15261.454.2284
    Cal.[27]0.000.13461122.28.81.16011.314.2764
    Exp.[35]0.000.1348(8)1108(20)[9]1.1610—4.1724
    Exp.[6]0.00—————4.2484
    Exp.[34]0.000.1351090.08.0(1)——4.1573
    Exp.[4]0.000.1347(5)1073(50)————
    Cal.[21]0.000.1441010.0———4.0000
    Cal.[24]0.000.13481132.0———4.0762
    Cal.[35]0.000.13561112.0————
    Cal.[36]0.000.13561098.09.01.13501.514.1290
    Cal.[18]0.000.13521130.012.71.14301.564.2100
    Cal.[5]0.000.13541163.09.2———
    Cal.[20]0.000.1365————3.9300
    Cal.[37]0.000.13731065.08.8———
    Cal.[22]0.000.13621107.213.01.13611.374.0560
    ${{\text{A}}^{2}}{{{\Pi }}_{\text{u}}}$本文25775.210.1790547.26.90.65620.911.0327
    Cal.[27]25707.720.1787553.26.80.67211.450.9731
    Exp.[34](25300.00)—(574.5)(7.1)———
    Exp.[15]27310.000.1730592.06.0———
    Exp.[6]—0.1680————0.77±0.15
    Cal.[36]—0.1828484.611.10.62601.370.7550
    Cal.[18]27400.000.1817506.310.40.63301.270.8130
    Cal.[19]23632.040.1920452.14.00.57000.791.2300
    Cal.[5]28580.000.1743604.06.0———
    Cal.[35]27342.180.1758557.0————
    Cal.[25]25003.180.1806535.08.9———
    Cal.[20]—0.1847————0.7500
    下载: 导出CSV

    表 4  第一解离极限5个束缚二重态的光谱常数

    Table 4.  Spectroscopic constants for five bound doublet states in the first dissociation limit.

    Te /cm–1Re /nmωe /cm–1ωeχe/cm–1Be /cm–1102αe/cm–1De /eV
    ${{1}^{2}}{{{\Delta }}_{\text{u}}}$本文25773.250.1949423.26.70.55351.011.0501
    Cal.[27]25744.150.1948426.46.40.55581.031.0636
    Cal.[19]22664.170.1980524.74.80.54000.651.3500
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $本文37694.720.1761530.93.70.67791.850.1445
    Cal.[27]
    (1st well)36812.480.1758526.72.50.69775.050.1019
    (2 nd well)34143.010.63438.91.30.04840.190.0074
    Cal.[19]39682.460.1950603.224.10.55001.951.1400
    Cal.[25]38391.980.1776538.05.0———
    ${{1}^{2}}{{\Sigma }}_{\text{u}}^ + $本文27050.770.2039366.86.00.50560.990.8917
    Cal.[27]27043.010.2027366.22.10.51210.920.9121
    Cal.[19]23228.760.2000514.44.90.52000.631.2800
    ${{1}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$本文27485.000.2156361.35.80.45230.880.8379
    Cal.[27]27540.340.2161358.95.70.45110.950.8087
    Cal.[19]24357.930.2180451.53.50.44000.451.1400
    ${{1}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$本文29701.210.1914434.88.20.57380.940.5633
    Cal.[27]29783.150.1912447.17.20.57621.010.3411
    Cal.[36]—0.2010439.010.00.51901.000.4000
    Cal.[19]30407.090.1990484.412.90.53001.040.3900
    下载: 导出CSV

    表 5  第一解离极限7个束缚四重态的光谱常数

    Table 5.  Spectroscopic constants of seven bound quartet states in the first dissociation limit.

    Te /cm–1Re /nmωe /cm–1ωeχe/cm–1Be /cm–1102αe/cm–1De /eV
    ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$(1st well)16385.200.12001612.79.31.45911.641.0826
    Cal.[27]9661.490.11941612.39.92.169450.241.8791
    (2 nd well)18779.710.1837546.36.20.62260.461.2756
    Cal.[27]18854.630.1832546.16.00.62840.861.6961
    Cal.[36]19357.300.1850582.09.60.60801.001.6700
    Cal.[19]16534.360.1880604.83.40.60000.612.0700
    Cal.[5]22540.000.1846572.05.6———
    Cal.[35]19357.300.1808569.0————
    Cal.[25]16534.360.1880604.83.40.60000.612.1100
    ${{1}^{4}}{{{\Delta }}_{\text{g}}}$本文25061.910.2132390.33.40.46250.821.1346
    Cal.[27]25032.620.2126397.25.70.46640.811.1131
    Cal.[19]20970.410.2120503.72.90.47000.391.5300
    ${{1}^{4}}{{\Sigma }}_{\text{g}}^{+}$本文25289.440.2143383.85.50.45790.811.1064
    Cal.[27]25324.300.2134391.75.50.46280.811.1371
    Cal.[19]21051.060.2130504.13.00.46000.371.5500
    ${{1}^{4}}{{{\Pi }}_{\text{u}}}$本文31129.290.2408233.05.70.36261.010.3675
    Cal.[27]31221.580.2389240.65.70.36951.010.3806
    Exp.[34]97800.00—1044.010.0———
    Cal.[19]31052.330.2480345.68.90.34000.040.3100
    ${{1}^{4}}{{\Sigma }}_{\text{g}}^{{ - }}$本文33621.360.2792112.16.70.26961.530.0684
    Cal.[27]33784.610.2784118.26.70.27291.410.0385
    ${{2}^{4}}{{{\Pi }}_{\text{u}}}$本文33819.650.304594.55.40.22681.270.0398
    Cal.[27]33914.100.4770151.142.60.081341.480.0443
    ${{1}^{4}}{{{\Pi }}_{\text{g}}}$本文34022.340.47691.14.20.09253.280.0088
    Cal.[27]34163.640.458655.68.30.09951.230.0134
    下载: 导出CSV

    表 6  第二解离极限8个束缚态的光谱常数

    Table 6.  Spectroscopic constants of eight bound states in the second dissociation limit.

    Te /cm–1 Re /nm ωe /cm–1 ωeχe/cm–1 Be /cm–1 102αe/cm–1 De /eV
    ${{3}^{2}}{{{\Pi }}_{\text{g}}}$ 48109.82 0.2896 160.7 3.8 0.2508 0.62 0.2048
    ${{2}^{2}}{{{\Delta }}_{\text{g}}}$ 48397.03 0.2812 131.1 2.2 0.2659 0.59 0.1839
    ${{2}^{2}}{{\Sigma }}_{\text{g}}^{+}$ 37199.41 0.1760 508.0 5.4 0.6787 1.12 1.5565
    ${{3}^{2}}{{\Sigma }}_{\text{g}}^{+}$ 48872.32 0.3153 128.7 3.9 0.2115 0.72 0.1573
    ${{3}^{2}}{{{\Pi }}_{\text{u}}}$ 45234.02 0.2303 296.8 4.9 0.3965 1.01 0.5552
    ${{1}^{2}}{{\Phi }}_{\text{u}}$ 49874.49 0.3158 73.4 5.6 0.2109 1.68 0.0258
    ${{2}^{2}}{{{\Delta }}_{\text{u}}}$ 49752.52 0.6162 54.6 1.6 0.0554 0.44 0.0290
    ${{3}^{2}}{{\Sigma }}_{\text{u}}^{+}$ 48753.89 0.3139 135.9 3.9 0.2134 0.67 0.1268
    下载: 导出CSV

    表 7  由${\text{O}}_{2}^{{ - }}$第一解离极限5个Π态产生的16个Ω态的光谱常数

    Table 7.  Spectroscopic constants of the 16 Ω states generated by the 5 Π states in the first dissociation limit of the ${\text{O}}_{2}^{{ - }}$.

    Te /cm–1Re /nmωe /cm–1Be /cm–1De /eV
    ${{\text{X}}^{2}}{{{\Pi }}_{{\text{g, 3/2}}}}$本文0.000.13541083.071.14714.2520
    Cal.[27]0.000.13531123.34—4.2663
    ${{\text{X}}^{2}}{{{\Pi }}_{{\text{g, 1/2}}}}$本文166.720.13531078.971.14814.2405
    Cal.[27]154.290.13531093.64—4.2485
    ${{\text{A}}^{2}}{{{\Pi }}_{{\text{u, 1/2}}}}$本文26008.900.1810547.040.64121.0273
    Cal.[27]25725.940.1785550.50—0.9681
    ${{\text{A}}^{2}}{{{\Pi }}_{{\text{u, 3/2}}}}$本文26131.120.1811547.200.64101.0213
    Cal.[27]25844.450.1785551.40—0.9754
    ${{1}^{4}}{{{\Pi }}_{{\text{g, 5/2}}}}$本文33938.020.486216.800.08890.0121
    Cal.[27]34153.980.457352.43—0.0135
    ${{1}^{4}}{{{\Pi }}_{{\text{g, 3/2}}}}$本文33985.590.486016.450.08900.0122
    Cal.[27]34217.410.458050.49—0.0136
    ${{1}^{4}}{{{\Pi }}_{{\text{g, 1/2}}}}$本文34033.170.481519.320.09070.0122
    Cal.[27]34255.160.458450.87—0.0134
    ${{1}^{4}}{{{\Pi }}_{{\text{g, - 1/2}}}}$本文34080.740.481419.090.09070.0122
    Cal.[27]34267.450.458652.36—0.0135
    ${{1}^{4}}{{{\Pi }}_{{\text{u, - 1/2}}}}$本文31043.470.2408233.140.36270.3399
    Cal.[27]31224.440.2388240.87—0.3844
    ${{1}^{4}}{{{\Pi }}_{{\text{u, 1/2}}}}$本文31092.180.2408233.090.36260.3397
    Cal.[27]31273.820.2388240.29—0.3820
    ${{1}^{4}}{{{\Pi }}_{{\text{u, 3/2}}}}$本文31140.890.2408233.050.36260.3396
    Cal.[27]31322.320.2384237.18—0.3808
    ${{1}^{4}}{{{\Pi }}_{{\text{u, 5/2}}}}$本文31189.600.2408233.000.36260.3395
    Cal.[27]31371.480.2384237.23—0.3799
    ${{2}^{4}}{{{\Pi }}_{{\text{u, - 1/2}}}}$本文33993.000.301992.790.23060.0484
    Cal.[27]33933.850.4765151.63—0.0442
    ${{2}^{4}}{{{\Pi }}_{{\text{u, 1/2}}}}$本文34036.110.309688.010.21940.0485
    Cal.[27]33946.630.4786150.73—0.0432
    ${{2}^{4}}{{{\Pi }}_{{\text{u, 3/2}}}}$本文34079.230.303193.860.22890.0434
    Cal.[27]33967.940.4774153.22—0.0438
    ${{2}^{4}}{{{\Pi }}_{{\text{u, 5/2}}}}$本文34122.350.303093.970.22890.0432
    Cal.[27]34000.350.4769149.84—0.0445
    下载: 导出CSV

    表 8  由${\text{O}}_{2}^{{ - }}$第一解离极限5个Δ态产生的6个Ω态的光谱常数

    Table 8.  Spectroscopic constants of the six Ω states generated by the five Δ states in the first dissociation limit of the ${\text{O}}_{2}^{{ - }}$.

    Te /cm–1Re /nmωe /cm–1Be /cm–1De /eV
    ${{1}^{2}}{{{\Delta }}_{{\text{u, 5/2}}}}$本文26005.190.1960414.180.54711.0476
    Cal.[27]25820.310.1948426.27—1.0660
    ${{1}^{2}}{{{\Delta }}_{{\text{u, 3/2}}}}$本文26017.400.1960414.320.54721.0525
    Cal.[27]25894.060.1943423.62—1.0613
    ${{1}^{4}}{{{\Delta }}_{{\text{g, 7/2}}}}$本文25190.590.2129388.260.46361.1344
    Cal.[27]25013.300.2125397.39—1.1184
    ${{1}^{4}}{{{\Delta }}_{{\text{g, 5/2}}}}$本文25281.540.2127387.980.46471.1345
    Cal.[27]25091.220.2126397.31—1.1146
    ${{1}^{4}}{{{\Delta }}_{{\text{g, 3/2}}}}$本文25372.490.2129390.390.46401.1345
    Cal.[27]25211.930.2125395.57—1.1133
    ${{1}^{4}}{{{\Delta }}_{{\text{g, 1/2}}}}$本文25463.440.2127388.440.46471.1346
    Cal.[27]25290.280.2126393.75—1.1115
    下载: 导出CSV

    表 9  由${\text{O}}_{2}^{{ - }}$第二解离极限4个Λ-S态产生的8个Ω态的光谱常数

    Table 9.  Spectroscopic constants of the eight Ω states generated by the four Λ-S states in the second dissociation limit of the ${\text{O}}_{2}^{{ - }}$.

    Te / cm–1 Re /nm ωe / cm–1 Be / cm–1 De /eV
    ${{3}^{2}}{{{\Pi }}_{{\text{g, 1/2}}}}$ 48084.30 0.2916 155.27 0.2472 0.1952
    ${{3}^{2}}{{{\Pi }}_{{\text{g, 3/2}}}}$ 48109.85 0.2907 158.14 0.2487 0.2017
    ${{3}^{2}}{{{\Pi }}_{{\text{u, 1/2}}}}$ 45212.53 0.2316 291.66 0.3920 0.5514
    ${{3}^{2}}{{{\Pi }}_{{\text{u, 3/2}}}}$ 45226.50 0.2319 291.93 0.3910 0.5587
    ${{1}^{2}}{{\Phi }}_{{\text{u, 5/2}}}$ 49926.23 0.3158 73.24 0.2108 0.0257
    ${{1}^{2}}{{\Phi }}_{{\text{u, 7/2}}}$ 50055.56 0.3156 73.49 0.2111 0.0259
    ${{2}^{2}}{{{\Delta }}_{{\text{g, 3/2}}}}$ 48942.47 0.2841 126.81 0.2605 0.1671
    ${{2}^{2}}{{{\Delta }}_{{\text{g, 5/2}}}}$ 48997.29 0.2814 130.77 0.2655 0.1672
    下载: 导出CSV
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