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GeO分子激发态的电子结构和跃迁性质的组态相互作用方法研究

刘晓军 苗凤娟 李瑞 张存华 李奇楠 闫冰

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Citation:

GeO分子激发态的电子结构和跃迁性质的组态相互作用方法研究

刘晓军, 苗凤娟, 李瑞, 张存华, 李奇楠, 闫冰

Configuration interaction study on electronic structures and transitional properties of excited states of GeO molecule

Liu Xiao-Jun, Miao Feng-Juan, Li Rui, Zhang Cun-Hua, Li Qi-Nan, Yan Bing
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  • 应用多参考组态相互作用方法计算了GeO分子的第一解离极限(Ge(3Pg)+O(3Pg))对应的18个Λ-S电子态的电子结构. 计算中纳入了Ge原子的3d轨道电子的内壳层-价壳层电子关联效应、标量相对论效应和Davidson修正. 基于计算的电子态的电子结构, 通过求解径向Schrödinger方程获得了束缚电子态的光谱常数Re, Te, ωe, ωeχe, Be, 理论计算给出的这些电子态的光谱常数与之前的实验结果符合得很好. 计算了电子态的电偶极矩随核间距的变化, 分析了电子态的组态成分的变化对电偶极矩的影响. 计算的势能曲线表明, 激发态A1Π, 11Σ-, D1Δ, a3Π, a’3Σ+, d3Δ 和 e3Σ-的绝热激发能密集地分布于26000-37000 cm-1范围内, 这些密集分布的电子态之间的相互作用对振动波函数有明显扰动作用. 借助于激发态之间的自旋-轨道耦合矩阵元, 阐明了邻近的激发态对A1Π和a3Π的扰动作用. 基于计算的A1Π-X1Σ+和A’1Σ+-X1Σ+跃迁的电偶极跃迁矩和Franck-Condon 因子, 给出了A1Π 和A’1Σ+态的最低的六个振动能级的辐射寿命.
    GeO molecule, which plays an important role in fabricating integrated optics and semiconductor components, has received much attention. However, the electronic state density of the molecule is very large, and the electric structures and transitional properties of the molecule have not been well investigated. In this work, the 18 Λ -S states correlated to the lowest dissociation limit (Ge(3Pg)+O(3Pg)) are calculated by a complete active space self-consistent field (CASSCF) method, through using the previous Hatree-Fock molecular orbitals as the starting orbitals. Furthermore, we take all configurations in the configuration interaction expansions of the CASSCF wave functions as a reference configuration, and calculate the energies of the 18Λ-S states by a high-level multireference configuration interaction method. The core-valence correlation effect of the 3d orbit of Ge atom, the scalar relativistic effect, and the Davidson correction are taken into consideration in the calculations. On the basis of the calculated potential energy curves of the bound and quasibound electronic states, the spectroscopic constants (Re, Te, ωe, ωeχe, and Be), vibrational energy levels, vibrational wave functions, and Franck-Condon factors (FCFs) are obtained by solving the radical Schrödinger equation. The computed spectroscopic constants of these electronic states are well consistent with previously available experimental results. We calculate the electric dipole moments of electronic states with different bound lengths, and analyze the influences of the variation of electron configuration on the electric dipole moment. The calculated potential energy curves indicate that the adiabatic transition energies of A1Π, 11Σ-, D1Δ, a3Π, a’3Σ+, d3Δ, and e3Σ- sates are located in a range of 26000-37000 cm-1, and the spin-orbit coupling of the states can obviously affect the corresponding vibrational wave functions. With the help of calculated spin-orbit coupling matrix elements, the perturbations of the nearby states to a3Π and A1Π are discussed in detail. Our calculation results indicate that the spin-orbit coupling between A1Π and e3Σ- states has an evident perturbation on the v’> 4 vibrational levels of A1Π, and the v’≥ 0 vibrational levels of a3Π state are perturbed by the crossing states a’3Σ+, d3Δ, e3Σ-, 11Σ-, and D1Δ. On the basis of computed transition dipole moments and FCFs of A1Π-X1Σ+ and A’1Σ+-X1Σ+ transitions, the radiative lifetimes of the six lowest vibrational levels of the two singlet excited states are computed.
    • 基金项目: 国家自然科学基金(批准号:11404180,61204127)和黑龙江省自然科学基金(批准号:F201335,F201438,A2015010)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11404180, 61204127) and the Natural Science Foundation of Heilongjiang Province, China (Grant Nos. F201335, F201438, A2015010).
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    [30]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61

    [31]

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

    [32]

    Hess B A 1986 Phys. Rev. A 33 3742

    [33]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823

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  • [1]

    Vega F, Afonso C N, Solis J 1993 Appl. Surf. Sci. 69 403

    [2]

    Lee E G, Seto J Y, Hirao T, Bernath P F, Le Roy R J 1999 J. Mol. Spectrosc. 194 197

    [3]

    Jevons W, Bashford L A, Briscoe H V A 1937 Proc. Phys. Soc. 49 543

    [4]

    Raymonda J W, Muenter J S, Klemperer W A 1970 J. Chem. Phys. 52 3458

    [5]

    Meyer B, Smith J J, Spitzer K 1970 J. Chem. Phys. 53 3616

    [6]

    Meyer B, Jones Y, Smith J J, Spitzer K 1971 J. Mol. Spectrosc. 37 100

    [7]

    Copelle G A, Brom Jr J M 1975 J. Chem. Phys. 63 5168

    [8]

    Lagerqvist A, Renhorn I 1982 Phys. Scr. 25 241

    [9]

    Leszczynski J, Kwiatkowski J S 1993 J. Phys. Chem. 97 12189

    [10]

    Kalcher J 2002 Phys. Chem. Chem. Phys. 4 3311

    [11]

    Jalbout A F, Li X H, Abou R H 2007 Int. J. Quantum Chem. 107 522

    [12]

    Sefyani F L, Schamps J, Duflot D 1995 J. Quant. Spectrosc. Radiat. Transf. 54 1027

    [13]

    Shi D H, Liu H, Sun J F, Zhu Z L, Liu Y F 2010 J. Mol. Struct. Theochem. 960 40

    [14]

    Li R, Wei C L, Sun Q X, Sun E P, Xu H F, Yan B 2013 J. Phys. Chem. A 117 2373

    [15]

    Gao X Y, You K, Zhang X M, Liu Y L, Liu Y F 2013 Acta Phys. Sin. 62 233302 (in Chinese) [高雪艳, 尤凯, 张晓美, 刘彦磊, 刘玉芳 2013 物理学报 62 233302]

    [16]

    Yuan L, Fan Q C, Sun W G, Fan Z X, Feng H 2014 Acta Phys. Sin. 63 043102 (in Chinese) [袁丽, 樊群超, 孙卫国, 范志祥, 冯灏 2014 物理学报 63 043102]

    [17]

    Li R, Sun E P, Jin M X, Xu H F, Yan B 2014 J. Phys. Chem. A 118 2629

    [18]

    Li G X, Jiang Y C, Ling C C, Ma H Z, Li P 2014 Acta Phys. Sin. 63 127102 (in Chinese) [李桂霞, 姜永超, 凌翠翠, 马红章, 李鹏 2014 物理学报 63 127102]

    [19]

    Liao J W, Yang C L 2014 Chin. Phys. B 23 073401

    [20]

    Werner H J, Knowles P J, Knizia G, Manby F R, Schtz M, Celani P, Korona T, Lindh R, Mitrushenkov A, Rauhut G, Shamasundar K R, Adler T B, Amos R D, Bernhardsson A, Berning A, Cooper D L, Deegan M J O, Dobbyn A J, Eckert F, Goll E, Hampel C, Hesselmann A, Hetzer G, Hrenar T, Jansen G, Köppl C, Liu Y, Lloyd A W, Mata R A, May A J, McNicholas S J, Meyer W, Mura M E, Nicklass A, Neill D P, Palmieri P, Peng D, Pflger K, Pitzer R, Reiher M, Shiozaki T, Stoll H, Stone A J, Tarroni R, Thorsteinsson T, Wang M 2010 MOLPRO: a package of ab initio programs

    [21]

    Wilson A K, Woon D E, Peterson K A, Dunning Jr T H 1999 J. Chem. Phys. 110 7667

    [22]

    De Jong W A, Harrison R J, Dixon D A 2001 J. Chem. Phys. 114 48

    [23]

    Peterson K A, Dunning Jr T H 2002 J. Chem. Phys. 117 10548

    [24]

    De Yonker N J, Peterson K A, Wilson A K 2007 J. Phys. Chem. A 111 11383

    [25]

    Moore C E 1971 Atomic Energy Levels (Washington, DC: National Bureau of Standards Publications) pp135-140

    [26]

    Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259

    [27]

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

    [28]

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

    [29]

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

    [30]

    Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61

    [31]

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

    [32]

    Hess B A 1986 Phys. Rev. A 33 3742

    [33]

    Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823

    [34]

    Le Roy R J 2002 LEVEL 7.5: a Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-655)

    [35]

    Huber K P, Herzberg G 1979 Molecular Spectra and Molecular Structure IV: Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) pp236-237

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出版历程
  • 收稿日期:  2014-10-31
  • 修回日期:  2015-01-22
  • 刊出日期:  2015-06-05

GeO分子激发态的电子结构和跃迁性质的组态相互作用方法研究

  • 1. 齐齐哈尔大学理学院, 齐齐哈尔 161006;
  • 2. 吉林大学, 吉林省应用原子与分子光谱重点实验室, 长春 130012;
  • 3. 齐齐哈尔大学通信与电子工程学院, 齐齐哈尔 161006;
  • 4. 吉林大学原子与分子物理研究所, 长春 130012
    基金项目: 国家自然科学基金(批准号:11404180,61204127)和黑龙江省自然科学基金(批准号:F201335,F201438,A2015010)资助的课题.

摘要: 应用多参考组态相互作用方法计算了GeO分子的第一解离极限(Ge(3Pg)+O(3Pg))对应的18个Λ-S电子态的电子结构. 计算中纳入了Ge原子的3d轨道电子的内壳层-价壳层电子关联效应、标量相对论效应和Davidson修正. 基于计算的电子态的电子结构, 通过求解径向Schrödinger方程获得了束缚电子态的光谱常数Re, Te, ωe, ωeχe, Be, 理论计算给出的这些电子态的光谱常数与之前的实验结果符合得很好. 计算了电子态的电偶极矩随核间距的变化, 分析了电子态的组态成分的变化对电偶极矩的影响. 计算的势能曲线表明, 激发态A1Π, 11Σ-, D1Δ, a3Π, a’3Σ+, d3Δ 和 e3Σ-的绝热激发能密集地分布于26000-37000 cm-1范围内, 这些密集分布的电子态之间的相互作用对振动波函数有明显扰动作用. 借助于激发态之间的自旋-轨道耦合矩阵元, 阐明了邻近的激发态对A1Π和a3Π的扰动作用. 基于计算的A1Π-X1Σ+和A’1Σ+-X1Σ+跃迁的电偶极跃迁矩和Franck-Condon 因子, 给出了A1Π 和A’1Σ+态的最低的六个振动能级的辐射寿命.

English Abstract

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