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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 .-
Keywords:
- ${\text{O}}_{2}^{{ - }}$ /
- MRCI+Q /
- spin-orbit coupling /
- spectroscopic constants
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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
Figure 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.
图 2 ${\text{O}}_{2}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $与 ${{2}^{2}}{{\Sigma }}_{\text{g}}^ + $态PECs
Figure 2. ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $ and ${{2}^{2}}{{\Sigma }}_{\text{g}}^ + $ potential energy curves of ${\text{O}}_{2}^{{ - }}$.
图 3 不同基组及冻结电子情况下${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$和${{2}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ PECs的比较
Figure 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.
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
Figure 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.
图 5 由4重Π态产生的4个Ω态的PECs (Ω = –1/2)
Figure 5. Potential energy curves for 4 Ω states generated by quadruple Π state (Ω = –1/2).
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 ${{\rm X}}{}^{2}{{{\Pi }}_{{\rm g}}}$ ${{\rm X}}{}^{2}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${{\rm X}}{}^{2}{{{\Pi }}_{{{\rm g, 1/2}}}}$ ${2}{}^{2}{{{\Pi }}_{{\rm g}}}$ ${2}{}^{2}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${2}{}^{2}{{{\Pi }}_{{{\rm g, 1/2}}}}$ ${1}{}^{2}{{{\Delta }}_{{\rm g}}}$ ${1}{}^{2}{{{\Delta }}_{{{\rm g, 5/2}}}}$, ${1}{}^{2}{{{\Delta }}_{{{\rm g, 3/2}}}}$ ${{1}^{2}}{{\Sigma }}_{{\rm g}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{{\rm g, 1/2}}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{\rm g}}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{{{\rm g, 1/2}}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{\rm g}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{{\rm g, 1/2}}}^{{ - }}$ ${{\rm A}}{}^{2}{{{\Pi }}_{{\rm u}}}$ ${{\rm A}}{}^{2}{{{\Pi }}_{{{\rm u, 1/2}}}}$, ${{\rm A}}{}^{2}{{{\Pi }}_{{{\rm u, 3/2}}}}$ ${2}{}^{2}{{{\Pi }}_{{\rm u}}}$ ${2}{}^{2}{{{\Pi }}_{{{\rm u, 1/2}}}}$, ${2}{}^{2}{{{\Pi }}_{{{\rm u, 3/2}}}}$ ${1}{}^{2}{\Delta _{{\rm u}}}$ ${1}{}^{2}{\Delta _{{{\rm u, 5/2}}}}$, ${1}{}^{2}{\Delta _{{{\rm u, 3/2}}}}$ ${{1}^{2}}{{\Sigma }}_{{\rm u}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{{\rm u, 1/2}}}^{+}$ ${{1}^{2}}{{\Sigma }}_{{\rm u}}^{{ - }}$ ${{1}^{2}}{{\Sigma }}_{{{\rm u, 1/2}}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{\rm u}}^{{ - }}$ ${{2}^{2}}{{\Sigma }}_{{{\rm u, 1/2}}}^{{ - }}$ ${1}{}^{4}{{{\Pi }}_{{\rm g}}}$ ${1}{}^{4}{{{\Pi }}_{{{\rm g, 5/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm g, 1/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm g, -1/2}}}}$ ${2}{}^{4}{{{\Pi }}_{{\rm g}}}$ ${2}{}^{4}{{{\Pi }}_{{{\rm g, 5/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm g, 1/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm g, -1/2}}}}$ ${1}{}^{4}{{{\Delta }}_{{\rm g}}}$ ${1}{}^{4}{{{\Delta }}_{{{\rm g, 7/2}}}}$, ${1}{}^{4}{{{\Delta }}_{{{\rm g, 5/2}}}}$, ${1}{}^{4}{{{\Delta }}_{{{\rm g, 3/2}}}}$, ${1}{}^{4}{{{\Delta }}_{{{\rm g, 1/2}}}}$ $ {{1}^{4}}{{\Sigma }}_{{\rm g}}^{+} $ $ {{1}^{4}}{{\Sigma }}_{{{\rm g, 1/2}}}^{+} $, $ {{1}^{4}}{{\Sigma }}_{{{\rm g, 3/2}}}^{+} $ $ {{1}^{4}}{{\Sigma }}_{{\rm g}}^{{ - }} $ $ {{1}^{4}}{{\Sigma }}_{{{\rm g, 1/2}}}^{{ - }} $, $ {{1}^{4}}{{\Sigma }}_{{{\rm g, 3/2}}}^{{ - }} $ $ {{2}^{4}}{{\Sigma }}_{{\rm g}}^{{ - }} $ $ {{2}^{4}}{{\Sigma }}_{{{\rm g, 1/2}}}^{{ - }} $, $ {{2}^{4}}{{\Sigma }}_{{{\rm g, 3/2}}}^{{ - }} $ ${1}{}^{4}{{{\Pi }}_{{\rm u}}}$ ${1}{}^{4}{{{\Pi }}_{{{\rm u, 5/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm u, 3/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm u, 1/2}}}}$, ${1}{}^{4}{{{\Pi }}_{{{\rm u, -1/2}}}}$ ${2}{}^{4}{{{\Pi }}_{{\rm u}}}$ ${2}{}^{4}{{{\Pi }}_{{{\rm u, 5/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm u, 3/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm u, 1/2}}}}$, ${2}{}^{4}{{{\Pi }}_{{{\rm u, -1/2}}}}$ ${1}{}^{4}{{{\Delta }}_{{\rm u}}}$ $1^4\Delta_{\rm u, 7/2}, 1^4\Delta_{\rm u, 5/2},1^4\Delta_{\rm u, 3/2}, 1^4\Delta_{\rm u, 1/2} $ $ {{1}^{4}}{{\Sigma }}_{{\rm u}}^{+} $ $ {1}^{4}{\Sigma}_{{\rm u}, {\rm 1/2}}^{+} $, $ {1}^{4}{\Sigma}_{{\rm u}, {\rm 3/2}}^{+} $ ${{{\rm a}}^{4}}{{\Sigma }}_{{\rm u}}^{{ - }}$ $ {{\rm a}}^{4}{\Sigma}_{{\rm u}, {\rm 1/2}}^{-} $, $ {{\rm a}}^{4}{\Sigma}_{{\rm u}, {\rm 3/2}}^{-} $ ${{2}^{4}}{{\Sigma }}_{{\rm u}}^{{ - }}$ $ {2}^{4}{{\Sigma}}_{{\rm u}, {1/2}}^{-} $, $ {2}^{4}{{ \Sigma}}_{{\rm u}, {3/2}}^{-} $ O(2s22p4 1Dg)+O–(2s22p5 2Pu) 15878.24 15867.86 ${3}{}^{2}{{{\Pi }}_{{\rm g}}}$ ${3}{}^{2}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${3}{}^{2}{{{\Pi }}_{{{\rm g, 1/2}}}}$ ${4}{}^{2}{{{\Pi }}_{{\rm g}}}$ ${4}{}^{2}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${4}{}^{2}{{{\Pi }}_{{{\rm g, 1/2}}}}$ ${5}{}^{2}{{{\Pi }}_{{\rm g}}}$ $5{}^{2}{{{\Pi }}_{{{\rm g, 3/2}}}}$, ${5}{}^{2}{{{\Pi }}_{{{\rm g, 1/2}}}}$ ${1}{}^{2}{{\Phi }}_{{\rm g}}$ ${1}{}^{2}{{\Phi }}_{{{\rm g, 7/2}}}$, ${1}{}^{2}{{\Phi }}_{{{\rm g, 5/2}}}$ ${2}{}^{2}{{{\Delta }}_{{\rm g}}}$ ${2}{}^{2}{{{\Delta }}_{{{\rm g, 5/2}}}}$, ${2}{}^{2}{{{\Delta }}_{{{\rm g, 3/2}}}}$ ${3}{}^{2}{{{\Delta }}_{{\rm g}}}$ ${3}{}^{2}{{{\Delta }}_{{{\rm g, 5/2}}}}$, ${3}{}^{2}{{{\Delta }}_{{{\rm g, 3/2}}}}$ ${{2}^{2}}{{\Sigma }}_{{\rm g}}^{+}$ $ {2}^{2}{\Sigma}_{{\rm g}, {\rm 1/2}}^{+} $ ${{3}^{2}}{{\Sigma }}_{{\rm g}}^{+}$ $ {3}^{2}{\Sigma}_{{\rm g}, {\rm 1/2}}^{+} $ ${{3}^{2}}{{\Sigma }}_{{\rm g}}^{{ - }}$ $ {3}^{2}{\Sigma}_{{\rm g}, {\rm 1/2}}^{-} $ ${3}{}^{2}{{{\Pi }}_{{\rm u}}}$ ${3}{}^{2}{{{\Pi }}_{{{\rm u, 3/2}}}}$, ${3}{}^{2}{{{\Pi }}_{{{\rm u, 1/2}}}}$ ${4}{}^{2}{{{\Pi }}_{{\rm u}}}$ ${4}{}^{2}{{{\Pi }}_{{{\rm u, 3/2}}}}$, ${4}{}^{2}{{{\Pi }}_{{{\rm u, 1/2}}}}$ ${5}{}^{2}{{{\Pi }}_{{\rm u}}}$ ${5}{}^{2}{{{\Pi }}_{{{\rm u, 3/2}}}}$, ${5}{}^{2}{{{\Pi }}_{{{\rm u, 1/2}}}}$ ${1}{}^{2}{{\Phi }}_{{\rm u}}$ ${1}{}^{2}{{\Phi }}_{{{\rm u, 7/2}}}$, ${1}{}^{2}{{\Phi }}_{{{\rm u, 5/2}}}$ ${2}{}^{2}{{{\Delta }}_{{\rm u}}}$ ${2}{}^{2}{{{\Delta }}_{{{\rm u, 5/2}}}}$, ${2}{}^{2}{{{\Delta }}_{{{\rm u, 3/2}}}}$ ${3}{}^{2}{{{\Delta }}_{{\rm u}}}$ ${3}{}^{2}{{{\Delta }}_{{{\rm u, 5/2}}}}$, ${3}{}^{2}{{{\Delta }}_{{{\rm u, 3/2}}}}$ ${{2}^{2}}{{\Sigma }}_{{\rm u}}^{+}$ $ {2}^{2}{\Sigma}_{{\rm u}, {\rm 1/2}}^{+} $ ${{3}^{2}}{{\Sigma }}_{{\rm u}}^{+}$ $ {3}^{2}{\Sigma}_{{\rm u}, {\rm 1/2}}^{+} $ ${{3}^{2}}{{\Sigma }}_{{\rm u}}^{{ - }}$ $ {3}^{2}{\Sigma}_{{\rm u}, {\rm 1/2}}^{-} $ 
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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.
$\Lambda$-S态 $\Lambda$-S态在$R_{e}$处的主要组态 ${\mathrm{X}}^{2}\Pi_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{0}$ (98.05%) $1^{2}\Sigma^+_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{0}$ (96.32%) $1^{2}\Sigma^-_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (97.30%) ${\mathrm{A}}^{2}\Pi_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{0}$ (92.88%) $1^{2}\Delta_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (60.17%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{2}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (34.59%) $1^{2}\Sigma ^-_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (73.86%) $1^{4}\Pi_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (99.97%) $1^{4}\Delta_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (70.71%) $1^{4}\Sigma^+_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (70.71%) $1^{4}\Sigma^-_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{2}$ (69.48%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (48.39%) $1^{4}\Pi_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (99.85%) $2^{4}\Pi_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{2}$ (99.87%) ${\mathrm{a}}^{4}\Sigma^-_{\mathrm{u}}$ (1st well) $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (97.21%) ${\mathrm{a}}^{4}\Sigma^-_{\mathrm{u}}$ (2nd well) $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (61.53%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (32.34%) $3^{2}\Pi_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (63.92%) $2^{2}\Delta_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{2}$ (50.21%) $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (35.45%) $2^{2}\Sigma^+_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (85.66%) $3^{2}\Sigma^+_{\mathrm{g}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (42.42%)$3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{2}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{2}$ (35.42%)$3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{2}$ (29.42%) $3^{2}\Pi_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{1}$ (73.79%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{0}$ (30.12%) $1^{2}\Phi_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{2}$ (50.00%) $2^{2}\Delta_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{2}$ (49.87%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (28.13%) $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{2}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (21.31%) $3^{2}\Sigma ^+_{\mathrm{u}}$ $3\sigma_{\mathrm{g}}^{1}1\pi_{\mathrm{u}}^{3}1\pi_{\mathrm{g}}^{3}3\sigma_{\mathrm{u}}^{2}$ (40.05%)$3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{4}1\pi_{\mathrm{g}}^{2}3\sigma_{\mathrm{u}}^{1}$ (37.78%) $3\sigma_{\mathrm{g}}^{2}1\pi_{\mathrm{u}}^{2}1\pi_{\mathrm{g}}^{4}3\sigma_{\mathrm{u}}^{1}$ (30.08%)
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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–1 Re/nm ωe/cm–1 ωeχe/cm–1 Be/cm–1 αe/(102 cm–1) De/eV ${{\text{X}}^{2}}{{{\Pi }}_{\text{g}}}$ 本文 0 0.1350 1073.6 7.8 1.1526 1.45 4.2284 Cal.[27] 0 0.1346 1122.2 8.8 1.1601 1.31 4.2764 Exp.[35] 0 0.1348(8) 1108(20) [9] 1.1610 — 4.1724 Exp.[6] 0 — — — — — 4.2484 Exp.[34] 0 0.135 1090.0 8.0(1) — — 4.1573 Exp.[4] 0 0.1347(5) 1073(50) — — — — Cal.[21] 0 0.144 1010.0 — — — 4.0000 Cal.[24] 0 0.1348 1132.0 — — — 4.0762 Cal.[35] 0 0.1356 1112.0 — — — — Cal.[36] 0 0.1356 1098.0 9.0 1.1350 1.51 4.1290 Cal.[18] 0 0.1352 1130.0 12.7 1.1430 1.56 4.2100 Cal.[5] 0 0.1354 1163.0 9.2 — — — Cal.[20] 0 0.1365 — — — — 3.9300 Cal.[37] 0 0.1373 1065.0 8.8 — — — Cal.[22] 0 0.1362 1107.2 13.0 1.1361 1.37 4.0560 ${{\text{A}}^{2}}{{{\Pi }}_{\text{u}}}$ 本文 25775.21 0.1790 547.2 6.9 0.6562 0.91 1.0327 Cal.[27] 25707.72 0.1787 553.2 6.8 0.6721 1.45 0.9731 Exp.[34] (25300.00) — (574.5) (7.1) — — — Exp.[15] 27310.00 0.1730 592.0 6.0 — — — Exp.[6] — 0.1680 — — — — 0.77±0.15 Cal.[36] — 0.1828 484.6 11.1 0.6260 1.37 0.7550 Cal.[18] 27400.00 0.1817 506.3 10.4 0.6330 1.27 0.8130 Cal.[19] 23632.04 0.1920 452.1 4.0 0.5700 0.79 1.2300 Cal.[5] 28580.00 0.1743 604.0 6.0 — — — Cal.[35] 27342.18 0.1758 557.0 — — — — Cal.[25] 25003.18 0.1806 535.0 8.9 — — — Cal.[20] — 0.1847 — — — — 0.7500
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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–1 Re/nm ωe/cm–1 ωeχe/cm–1 Be/cm–1 102αe/cm–1 De/eV ${{1}^{2}}{{{\Delta }}_{\text{u}}}$ 本文 25773.25 0.1949 423.2 6.7 0.5535 1.01 1.0501 Cal.[27] 25744.15 0.1948 426.4 6.4 0.5558 1.03 1.0636 Cal.[19] 22664.17 0.1980 524.7 4.8 0.5400 0.65 1.3500 ${{1}^{2}}{{\Sigma }}_{\text{g}}^ + $ 本文 37694.72 0.1761 530.9 3.7 0.6779 1.85 0.1445 Cal.[27] (1st well) 36812.48 0.1758 526.7 2.5 0.6977 5.05 0.1019 Cal.[27] (2nd well) 34143.01 0.6343 8.9 1.3 0.0484 0.19 0.0074 Cal.[19] 39682.46 0.1950 603.2 24.1 0.5500 1.95 1.1400 Cal.[25] 38391.98 0.1776 538.0 5.0 — — — ${{1}^{2}}{{\Sigma }}_{\text{u}}^ + $ 本文 27050.77 0.2039 366.8 6.0 0.5056 0.99 0.8917 Cal.[27] 27043.01 0.2027 366.2 2.1 0.5121 0.92 0.9121 Cal.[19] 23228.76 0.2000 514.4 4.9 0.5200 0.63 1.2800 ${{1}^{2}}{{\Sigma }}_{\text{g}}^{{ - }}$ 本文 27485.00 0.2156 361.3 5.8 0.4523 0.88 0.8379 Cal.[27] 27540.34 0.2161 358.9 5.7 0.4511 0.95 0.8087 Cal.[19] 24357.93 0.2180 451.5 3.5 0.4400 0.45 1.1400 ${{1}^{2}}{{\Sigma }}_{\text{u}}^{{ - }}$ 本文 29701.21 0.1914 434.8 8.2 0.5738 0.94 0.5633 Cal.[27] 29783.15 0.1912 447.1 7.2 0.5762 1.01 0.3411 Cal.[36] — 0.2010 439.0 10.0 0.5190 1.00 0.4000 Cal.[19] 30407.09 0.1990 484.4 12.9 0.5300 1.04 0.3900
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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–1 Re/nm ωe/cm–1 ωeχe/cm–1 Be/cm–1 αe/(102 cm–1) De/eV ${{\text{a}}^{4}}{{\Sigma }}_{\text{u}}^{{ - }}$ 本文(1st well) 16385.20 0.1200 1612.7 9.3 1.4591 1.64 1.0826 Cal.[27] 9661.49 0.1194 1612.3 9.9 2.1694 50.24 1.8791 本文(2nd well) 18779.71 0.1837 546.3 6.2 0.6226 0.46 1.2756 Cal.[27] 18854.63 0.1832 546.1 6.0 0.6284 0.86 1.6961 Cal.[36] 19357.30 0.1850 582.0 9.6 0.6080 1.00 1.6700 Cal.[19] 16534.36 0.1880 604.8 3.4 0.6000 0.61 2.0700 Cal.[5] 22540.00 0.1846 572.0 5.6 — — — Cal.[35] 19357.30 0.1808 569.0 — — — — Cal.[25] 16534.36 0.1880 604.8 3.4 0.6000 0.61 2.1100 ${{1}^{4}}{{{\Delta }}_{\text{g}}}$ 本文 25061.91 0.2132 390.3 3.4 0.4625 0.82 1.1346 Cal.[27] 25032.62 0.2126 397.2 5.7 0.4664 0.81 1.1131 Cal.[19] 20970.41 0.2120 503.7 2.9 0.4700 0.39 1.5300 ${{1}^{4}}{{\Sigma }}_{\text{g}}^{+}$ 本文 25289.44 0.2143 383.8 5.5 0.4579 0.81 1.1064 Cal.[27] 25324.30 0.2134 391.7 5.5 0.4628 0.81 1.1371 Cal.[19] 21051.06 0.2130 504.1 3.0 0.4600 0.37 1.5500 ${{1}^{4}}{{{\Pi }}_{\text{u}}}$ 本文 31129.29 0.2408 233.0 5.7 0.3626 1.01 0.3675 Cal.[27] 31221.58 0.2389 240.6 5.7 0.3695 1.01 0.3806 Exp.[34] 97800.00 — 1044.0 10.0 — — — Cal.[19] 31052.33 0.2480 345.6 8.9 0.3400 0.04 0.3100 ${{1}^{4}}{{\Sigma }}_{\text{g}}^{{ - }}$ 本文 33621.36 0.2792 112.1 6.7 0.2696 1.53 0.0684 Cal.[27] 33784.61 0.2784 118.2 6.7 0.2729 1.41 0.0385 ${{2}^{4}}{{{\Pi }}_{\text{u}}}$ 本文 33819.65 0.3045 94.5 5.4 0.2268 1.27 0.0398 Cal.[27] 33914.10 0.4770 151.1 42.6 0.0813 41.48 0.0443 ${{1}^{4}}{{{\Pi }}_{\text{g}}}$ 本文 34022.34 0.4769 1.1 4.2 0.0925 3.28 0.0088 Cal.[27] 34163.64 0.4586 55.6 8.3 0.0995 1.23 0.0134
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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 αe/(102 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
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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–1 Re/nm ωe/cm–1 Be/cm–1 De/eV ${{\text{X}}^{2}}{{{\Pi }}_{{\text{g, 3/2}}}}$ 本文 0 0.1354 1083.07 1.1471 4.2520 Cal.[27] 0 0.1353 1123.34 — 4.2663 ${{\text{X}}^{2}}{{{\Pi }}_{{\text{g, 1/2}}}}$ 本文 166.72 0.1353 1078.97 1.1481 4.2405 Cal.[27] 154.29 0.1353 1093.64 — 4.2485 ${{\text{A}}^{2}}{{{\Pi }}_{{\text{u, 1/2}}}}$ 本文 26008.90 0.1810 547.04 0.6412 1.0273 Cal.[27] 25725.94 0.1785 550.50 — 0.9681 ${{\text{A}}^{2}}{{{\Pi }}_{{\text{u, 3/2}}}}$ 本文 26131.12 0.1811 547.20 0.6410 1.0213 Cal.[27] 25844.45 0.1785 551.40 — 0.9754 ${{1}^{4}}{{{\Pi }}_{{\text{g, 5/2}}}}$ 本文 33938.02 0.4862 16.80 0.0889 0.0121 Cal.[27] 34153.98 0.4573 52.43 — 0.0135 ${{1}^{4}}{{{\Pi }}_{{\text{g, 3/2}}}}$ 本文 33985.59 0.4860 16.45 0.0890 0.0122 Cal.[27] 34217.41 0.4580 50.49 — 0.0136 ${{1}^{4}}{{{\Pi }}_{{\text{g, 1/2}}}}$ 本文 34033.17 0.4815 19.32 0.0907 0.0122 Cal.[27] 34255.16 0.4584 50.87 — 0.0134 ${{1}^{4}}{{{\Pi }}_{{\rm {g,-1/2}}}}$ 本文 34080.74 0.4814 19.09 0.0907 0.0122 Cal.[27] 34267.45 0.4586 52.36 — 0.0135 ${{1}^{4}}{{{\Pi }}_{{\rm {u,-1/2}}}}$ 本文 31043.47 0.2408 233.14 0.3627 0.3399 Cal.[27] 31224.44 0.2388 240.87 — 0.3844 ${{1}^{4}}{{{\Pi }}_{{\text{u, 1/2}}}}$ 本文 31092.18 0.2408 233.09 0.3626 0.3397 Cal.[27] 31273.82 0.2388 240.29 — 0.3820 ${{1}^{4}}{{{\Pi }}_{{\text{u, 3/2}}}}$ 本文 31140.89 0.2408 233.05 0.3626 0.3396 Cal.[27] 31322.32 0.2384 237.18 — 0.3808 ${{1}^{4}}{{{\Pi }}_{{\text{u, 5/2}}}}$ 本文 31189.60 0.2408 233.00 0.3626 0.3395 Cal.[27] 31371.48 0.2384 237.23 — 0.3799 ${{2}^{4}}{{{\Pi }}_{{\text{u, - 1/2}}}}$ 本文 33993.00 0.3019 92.79 0.2306 0.0484 Cal.[27] 33933.85 0.4765 151.63 — 0.0442 ${{2}^{4}}{{{\Pi }}_{{\text{u, 1/2}}}}$ 本文 34036.11 0.3096 88.01 0.2194 0.0485 Cal.[27] 33946.63 0.4786 150.73 — 0.0432 ${{2}^{4}}{{{\Pi }}_{{\text{u, 3/2}}}}$ 本文 34079.23 0.3031 93.86 0.2289 0.0434 Cal.[27] 33967.94 0.4774 153.22 — 0.0438 ${{2}^{4}}{{{\Pi }}_{{\text{u, 5/2}}}}$ 本文 34122.35 0.3030 93.97 0.2289 0.0432 Cal.[27] 34000.35 0.4769 149.84 — 0.0445
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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–1 Re/nm ωe/cm–1 Be/cm–1 De/eV ${{1}^{2}}{{{\Delta }}_{{\text{u, 5/2}}}}$ 本文 26005.19 0.1960 414.18 0.5471 1.0476 Cal.[27] 25820.31 0.1948 426.27 — 1.0660 ${{1}^{2}}{{{\Delta }}_{{\text{u, 3/2}}}}$ 本文 26017.40 0.1960 414.32 0.5472 1.0525 Cal.[27] 25894.06 0.1943 423.62 — 1.0613 ${{1}^{4}}{{{\Delta }}_{{\text{g, 7/2}}}}$ 本文 25190.59 0.2129 388.26 0.4636 1.1344 Cal.[27] 25013.30 0.2125 397.39 — 1.1184 ${{1}^{4}}{{{\Delta }}_{{\text{g, 5/2}}}}$ 本文 25281.54 0.2127 387.98 0.4647 1.1345 Cal.[27] 25091.22 0.2126 397.31 — 1.1146 ${{1}^{4}}{{{\Delta }}_{{\text{g, 3/2}}}}$ 本文 25372.49 0.2129 390.39 0.4640 1.1345 Cal.[27] 25211.93 0.2125 395.57 — 1.1133 ${{1}^{4}}{{{\Delta }}_{{\text{g, 1/2}}}}$ 本文 25463.44 0.2127 388.44 0.4647 1.1346 Cal.[27] 25290.28 0.2126 393.75 — 1.1115
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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
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