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因为AuB分子的电子态信息缺乏相关实验测量, 本文采用高精度的组态相互作用方法开展对AuB分子激发态电子结构的研究, 计算得到12 个Λ-S态的势能曲线. 基于势能曲线, 束缚态的光谱常数通过数值求解薛定谔方程获得. 计算还包括部分低激发态的偶极矩, 展示了分子不同电子态的电荷分布信息. 在计算中也考虑了自旋轨道耦合效应对电子态的影响. 其中能量最低的4个Λ-S态之间的自旋轨道耦合矩阵元, 因为自旋轨道耦合的影响, 这4 个Λ-S态会劈裂为12个Ω态. 由于自旋轨道耦合矩阵元并没有交叉现象, 所以这4个Λ-S态不存在预解离的情况. 本文最后计算得到Ω基态
$ {{\mathrm{A}}}^{1}{{{\Pi}}}_{1} $ 和第一激发态$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $ 的光学跃迁矩阵元等信息, 分析Franck-Condon因子和辐射寿命, 发现AuB分子中该光吸收模式被激光冷却的可能性较小. 本文数据集可在https://www.doi.org/10.57760/sciencedb.j00213.00009 中访问获取.High-level configuration interaction method including the spin-orbit coupling is used to investigate the low-lying excited electronic states of AuB that is not reported experimentally. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by using the state-averaged complete active space self-consistent field (SACASSCF). Finally, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly correlated dynamic multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to solve the size-consistence problem caused by the MRCI method. To ensure the accuracy, the spin-orbit effect and correlation for inner shell electrons and valence shell electrons are considered in our calculation. The potential energy curves of 12 Λ-S electronic states are obtained. According to the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analyze the influence of electronic state configuration on the dipole moment by using the variation of dipole moment with nuclear distance. The spin-orbit matrix elements for parts of low-lying exciting states are computed, and the relation between spin-orbit coupling and predissociation is discussed. The predissociation is analyzed by using the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to the absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying exciting states will not occur. Finally, the properties of optical transition between the ground Ω state$ {\rm A}^{1}{{{\Pi}}}_{1} $ and first excited Ω state$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $ are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful in deepening the understanding of AuB, especially the structures of electronic states, interaction between excited states, and optical transition properties. All the data presented in this paper are openly available athttps://www.doi.org/10.57760/sciencedb.j00213.00009 .-
Keywords:
- excited state /
- configuration interaction /
- spectroscopic constants /
- laser-cooling
[1] Yannopoulos J C 1991 The Extractive Metallurgy of Gold (Boston, MA: Springer
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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
[29] Fitch N J, Tarbutt M R 2021 Adv. Atom. Mol. Opt. Phys. 70 157
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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
[37] Le Roy R 2007 Chemical Physics Research Report CP-663. (University of Waterloo
[38] Halkier A, Helgaker T, Jorgensen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243
Google Scholar
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图 1 基于多参考组态相互作用方法计算的AuB分子12个Λ-S态的势能曲线随原子核间距的变化
Fig. 1. Potential energy curves of 12 Λ-S states for AuB molecule at multi-reference configuration interaction level.
图 2 AuB分子的6个单重态偶极矩随核间距的变化, 电子态分别为$ {{\mathrm{X}}}^{1}{{{\Sigma }}}^{+} $, $ {{\mathrm{A}}}^{1}{{\Pi}} $, $ {{\mathrm{C}}}^{1}{{{\Sigma }}}^{-} $, $ {{\mathrm{F}}}^{1}{{{\Sigma }}}^{-} $, $ {{\mathrm{E}}}^{1}{{\Pi}} $ 和 $ {{\mathrm{D}}}^{1}{{{\Sigma }}}^{+} $
Fig. 2. Dipole moments of AuB for 6 singlet states versus the bond length, the states are $ {{\mathrm{X}}}^{1}{{{\Sigma }}}^{+} $, $ {{\mathrm{A}}}^{1}{{\Pi}} $, $ {{\mathrm{C}}}^{1}{{{\Sigma }}}^{-} $, $ {{\mathrm{F}}}^{1}{{{\Sigma }}}^{-} $, $ {{\mathrm{E}}}^{1}{{\Pi}} $ and $ {{\mathrm{D}}}^{1}{{{\Sigma }}}^{+} $.
图 3 AuB分子的4个三重态偶极矩随核间距的变化, 电子态分别为$ {{\mathrm{a}}}^{3}{{{\Sigma }}}^{+} $, $ {{\mathrm{b}}}^{3}{{\Pi}} $, $ {{\mathrm{d}}}^{3}{{\Pi}} $ 和 $ {{\mathrm{e}}}^{3}{{\Pi}} $
Fig. 3. Dipole moments of AuB for 4 triplet states versus the bond length. The states are $ {{\mathrm{a}}}^{3}{{{\Sigma }}}^{+} $, $ {{\mathrm{b}}}^{3}{{\Pi}} $, $ {{\mathrm{d}}}^{3}{{\Pi}} $ and $ {{\mathrm{e}}}^{3}{{\Pi}} $.
图 4 AuB分子部分电子态之间的自旋轨道耦合矩阵元随核间距的变化, 这些矩阵元主要包含4个低激发态, 分别为$ {{\mathrm{X}}}^{1}{{{\Sigma }}}^{+} $, $ {{\mathrm{A}}}^{1}{{\Pi}} $, $ {{\mathrm{a}}}^{3}{{{\Sigma }}}^{+} $ 和 $ {{\mathrm{b}}}^{3}{{\Pi}} $
Fig. 4. Absolute values of spin-orbit matrix elements of AuB as a function of bond length. The elements mainly include the four low-lying electronic states which are $ {{\mathrm{X}}}^{1}{{{\Sigma }}}^{+} $, $ {{\mathrm{A}}}^{1}{{\Pi}} $, $ {{\mathrm{a}}}^{3}{{{\Sigma }}}^{+} $ and $ {{\mathrm{b}}}^{3}{{\Pi}} $.
图 5 AuB分子态跃迁$ {{\mathrm{A}}}^{1}{{{\Pi}}}_{1}-{{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $的跃迁偶极矩随核间距的变化
Fig. 5. The transition dipole moment of AuB for the transition $ {{\mathrm{A}}}^{1}{{{\Pi}}}_{1}-{{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $ via internuclear distance.
表 1 势能曲线在不同基组情况下, 核间距1.9 Å能量值与当前计算结果的误差, 其中, 基组分别为tz, qz及外推的cbs
Table 1. The error between the energy value with the nuclear distance of 1.9 Å under different basis sets and the current calculation result. The basis sets are tz, qz, and cbs.
基组 $ {{\mathrm{A}}}^{1}{{{\Pi}}}_{} $ $ {{\mathrm{a}}}^{3}{{{{\Sigma }}}^{+}}_{} $ $ {{\mathrm{b}}}^{3}{{{\Pi}}}_{} $ $ {{\mathrm{C}}}^{1}{{{{\Sigma }}}^{-}}_{} $ $ {{\mathrm{d}}}^{3}{{{\Pi}}}_{} $ $ {{\mathrm{D}}}^{1}{{{\Sigma }}}^{+} $ $ {{\mathrm{E}}}^{1}{{{\Pi}}}_{} $ $ {{\mathrm{e}}}^{3}{{{\Pi}}}_{} $ $ {{\mathrm{F}}}^{1}{{{{\Sigma }}}^{-}}_{} $ Tz 0.23% 0.54% 0.20% 0.45% 0.09% 0.09% 0.03% 0.03% 0.06% Qz 0.44% 0.40% 0.52% 0.12% 0.51% 0.44% 0.11% 0.51% 0.85% Cbs 0.60% 0.30% 0.75% 0.12% 0.75% 0.69% 0.17% 0.87% 1.43% 
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表 2 AuB分子的束缚电子态的光谱常数, 分别为态能量$ {T}_{{\mathrm{e}}} $, 平衡核间距$ {R}_{{\mathrm{e}}} $, 振动和转动频率$ {\omega }_{{\mathrm{e}}} $, $ {B}_{{\mathrm{e}}} $
Table 2. Spectroscopic constants of AuB. Specifically speaking, state energy $ {T}_{{\mathrm{e}}} $, equilibrium internuclear distance $ {R}_{{\mathrm{e}}} $, vibrational and rotational frequency $ {\omega }_{{\mathrm{e}}} $, $ {B}_{{\mathrm{e}}} $.
State $ {T}_{{\mathrm{e}}} $/cm–1 $ {R}_{{\mathrm{e}}} $/Å $ {\omega }_{{\mathrm{e}}} $/cm–1 $ {\omega }_{{\mathrm{e}}}{x}_{{\mathrm{e}}} $/cm–1 $ {B}_{{\mathrm{e}}} $/cm–1 $ {{\mathrm{X}}}^{1}{{{\Sigma }}}^{+} $ 0 1.9199 653.4689 4.3072 0.4383 $ {{\mathrm{A}}}^{1}{{{\Pi}}}_{} $ 21645.3 1.9588 563.2682 12.4886 0.4182 $ {{\mathrm{a}}}^{3}{{{{\Sigma }}}^{+}}_{} $ 23332.1 1.9615 619.1107 16.4840 0.4199 $ {{\mathrm{b}}}^{3}{{{\Pi}}}_{} $ 13971.6 1.9200 642.5563 5.5869 0.4384 $ {{\mathrm{C}}}^{1}{{{{\Sigma }}}^{-}}_{} $ 34906.1 2.0642 458.6218 6.5214 0.3835 $ {{\mathrm{d}}}^{3}{{{\Pi}}}_{} $ 34844.9 2.0462 500.3464 5.2960 0.3858 $ {{\mathrm{D}}}^{1}{{{\Sigma }}}^{+} $ 40356.2 1.8714 718.7886 39.3081 0.4619 $ {{\mathrm{E}}}^{1}{{{\Pi}}}_{} $ 41526.9 2.0421 203.6828 3.8583 0.2750 $ {{\mathrm{e}}}^{3}{{{\Pi}}}_{} $ 41359.1 2.2946 285.2192 8.3651 0.3082
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表 3 AuB分子态跃迁$ {{\mathrm{A}}}^{1}{{{\Pi}}}_{1}-{{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $的爱因斯坦系数$ {A}_{{\nu }'{\nu }''} $(单位s–1)和Franck-Condon因子$ {F}_{{\nu }'{\nu }''} $, 注意本表格中考虑的最高振动态能级是$ \nu =4 $
Table 3. Einstein coefficients $ {A}_{{\nu }'{\nu }''} $ (in s–1) and Franck-Condon factors $ {F}_{{\nu }'{\nu }''} $ for the transition $ {{\mathrm{A}}}^{1}{{{\Pi}}}_{1}-{{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $. Noting that the highest vibrational level $ \nu =4 $.
$ {\nu }'=0 $ $ {\nu }'=1 $ $ {\nu }'=2 $ $ {\nu }'=3 $ $ {\nu }'=4 $ $ {\nu }''=0 $ $ {A}_{{\nu }'{\nu }''} $ 231785 44573.3 1814.68 0.006897 30.7593 $ {F}_{{\nu }'{\nu }''} $ 0.812704 0.176892 0.010213 0.000151 0.000025 $ {\nu }''=1 $ $ {A}_{{\nu }'{\nu }''} $ 50531.0 142718 72172.0 12638.8 708.147 $ {F}_{{\nu }'{\nu }''} $ 0.154591 0.503995 0.278366 0.057703 0.005151 $ {\nu }''=2 $ $ {A}_{{\nu }'{\nu }''} $ 9276.93 78255.0 59740.6 94354.8 32173.3 $ {F}_{{\nu }'{\nu }''} $ 0.029056 0.238252 0.213114 0.351535 0.135485 $ {\nu }''=3 $ $ {A}_{{\nu }'{\nu }''} $ 1125.95 21601.7 91794.9 4457.90 79060.3 $ {F}_{{\nu }'{\nu }''} $ 0.003433 0.066290 0.279793 0.019213 0.288028 $ {\nu }''=4 $ $ {A}_{{\nu }'{\nu }''} $ 63.7560 3977.66 48473.7 63146.9 9349.84 $ {F}_{{\nu }'{\nu }''} $ 0.000168 0.012065 0.149099 0.194296 0.024241
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[1] Yannopoulos J C 1991 The Extractive Metallurgy of Gold (Boston, MA: Springer
[2] Saradesh K M, Vinodkumar G S 2020 J. Mater. Res. Tech. 9 2009
Google Scholar
[3] Matsuda F, Nakata K, Morikawa M 1984 Science 17 55
[4] Eguchi S, Hoyt J L, Leitz C W, Fitzgerald E A 2002 Appl. Phys. Lett. 80 1743
Google Scholar
[5] Janke C, Jones R, Coutinho J, Öberg S, Briddon P R 2008 Mater. Sci. Semicond. Process. 11 324
Google Scholar
[6] Bisognin G, Vangelista S, Berti M, Impellizzeri G, Grimaldi M G 2010 J. Appl. Phys. 107 103512
Google Scholar
[7] Jones K S, Haller E E 1987 J. Appl. Phys. 61 2469
Google Scholar
[8] Uppal S, Willoughby A F W, Bonar J M, et al. 2001 J. Appl. Phys. 90 4293
Google Scholar
[9] Wang L 2004 J. Appl. Phys. 96 1939
Google Scholar
[10] Mirabella S, De Salvador D, Napolitani E, Bruno E, Priolo F 2013 J. Appl. Phys. 113 031101
Google Scholar
[11] Tzeli D, Mavridis A 2001 J. Phys. Chem. A 105 1175
Google Scholar
[12] Tzeli D, Mavridis A 2001 J. Phys. Chem. A 105 7672
Google Scholar
[13] Smith AM, Lorenz M, Agreiter J, Bondybey VE 1996 Mol. Phys. 88 247
Google Scholar
[14] Viswanathan R, Schmude R W, Gingerich K A 1996 J. Phys. Chem. 100 10784
Google Scholar
[15] Xing W, Shi D H, Sun J L, Zhu Z F 2017 Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 173 939
Google Scholar
[16] Metz B, Stoll H, Dolg M 2000 J. Chem. Phys. 113 2563
Google Scholar
[17] Pontes M A P, de Oliveira M H, Fernandes G F S, et al. 2018 J. Quant. Spectrosc. Ra. 209 156
Google Scholar
[18] Uppal S, Willoughby A F W, Bonar J M, Cowern N E B, Grasby T 2004 J. Appl. Phys. 96 1376
Google Scholar
[19] Echeverría E, Dong B, Liu A, et al. 2017 Surf. Coat. Tech. 314 51
Google Scholar
[20] Demille D, Shuman E S, Barry J F 2010 Nature 467 820
Google Scholar
[21] Norrgard E, Mccarron D, Steinecker M, Demille D. 2014 Nature 512 286
Google Scholar
[22] Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001
Google Scholar
[23] Truppe S, Williams H J, Hambach M, Caldwell L, Fitch N J, Hinds E A, Sauer B E, Tarbutt M R 2017 Nat. Phys. 13 1173
Google Scholar
[24] Zhelyazkova V, Cournol A, Wall T E, et al. 2014 Phys. Rev. A 89 053416
Google Scholar
[25] Zhang Y G, Zhang H, Song H Y, Yu Y, Wan M J 2017 Phys. Chem. Chem. Phys. 19 24647
Google Scholar
[26] Yuan X, Guo H J, Wang Y M, Xue J L, Xu H F, Yan B 2019 J. Chem. Phys. 150 224305
Google Scholar
[27] Stuhl B K, Sawyer B C, Wang D J, Ye J 2008 Phys. Rev. Lett. 101 243002
Google Scholar
[28] Yang R, Gao Y F, Tang B, Gao T 2015 Phys. Chem. Chem. Phys. 17 1900
Google Scholar
[29] Fitch N J, Tarbutt M R 2021 Adv. Atom. Mol. Opt. Phys. 70 157
[30] Werner H J, Knowles P J, Knizia G, Manby F R, Schtz M 2012 Rev. Comput. Mol. Sci. 2 242
Google Scholar
[31] Werner H J, Knowles P J, Knizia G, Manby F R, Schtz M 2012 http://www.molpro.net.
[32] Werner H J, Knowles P J 1985 J. Chem. Phys. 82 5053
Google Scholar
[33] Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259
Google Scholar
[34] Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803
Google Scholar
[35] Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61
Google Scholar
[36] Peterson K A, Dunning T H J 1993 J. Chem. Phys. 98 1358
Google Scholar
[37] Le Roy R 2007 Chemical Physics Research Report CP-663. (University of Waterloo
[38] Halkier A, Helgaker T, Jorgensen P, Klopper W, Koch H, Olsen J, Wilson A K 1998 Chem. Phys. Lett. 286 243
Google Scholar
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