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TiAl电子态结构的ab initio计算

张树东 王传航 唐伟 孙阳 孙宁泽 孙召玉 徐慧

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TiAl电子态结构的ab initio计算

张树东, 王传航, 唐伟, 孙阳, 孙宁泽, 孙召玉, 徐慧

Ab initio calculation of electronic state structure of TiAl

Zhang Shu-Dong, Wang Chuan-Hang, Tang Wei, Sun Yang, Sun Ning-Ze, Sun Zhao-Yu, Xu Hui
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  • 应用完全活动基自洽场方法, 结合N电子价态微扰近似(NEVPT2), 对TiAl金属二聚体的基态和若干最低电子激发态的势能曲线进行了计算. 完全活动空间由Al的3个价电子(3s23p1)轨道和Ti的4个价电子(3d24s2)轨道构成, 计算基组选用Karlsruhe group的价分裂全电子基组def2-nZVPP(n = T, Q). 在确认TiAl的基态为四重态的基础上, 在核间距R = 0.200—0.500 nm范围内, 扫描获得了TiAl基态和最低二个激发态的完整势能曲线, 并对电子态进行了标识, 发现在0.255 nm附近存在电子态结构的“突变”. 在R > 0.255 nm区域, 基态和两个激发态分别为X4Δ, A4Π和B4Γ; 在R < 0.255 nm区域, 基态仍为X4Δ, 但两个激发态变为A'4Φ和B'4Π, 且存在激发态简并解除的现象. 基于NEVPT2修正后的势能曲线, 获得了TiAl电子态的平衡核间距、束缚能、激发能、跃迁偶极矩等特征参数, 并解释了实验上观测不到TiAl电子跃迁光谱的原因. 电子激发态存在“突变”的结构特征, 可为分析理解TiAl合金在室温下的脆性问题提供参考.
    The potential energy curves (PECs) of the low-lying electronic states of TiAl are calculated with the complete active space self-consistent field (CASSCF) method combined with the N-electron valence perturbation theory (NEVPT2) approximation. The complete active space is mainly composed of the (3s23p1) valence orbital of Al and (3d24s2) valence orbital of Ti. Moreover, the valence splitting all-electron basis set def2-nZVPP (n = T, Q) proposed by Karlsruhe group is used in the calculation. On the basis of confirming that the ground state of TiAl is a quadruple state, the PECs of the ground state and the lowest two excited states of TiAl are obtained in a range of nuclear distance R of 0.200–0.500 nm, and the electronic states are identified. It is found that there is a “break” of the electronic structure near R = 0.255 nm. In the R > 0.255 nm region, the ground state and the two excited states are X4Δ, A4Π and B4Γ respectively; in the R < 0.255 nm region, the ground state is still X4Δ, but the two excited states become A'4Φ and B'4Π, and the degeneracy of the excited state tends to be eliminated. Based on the PECs of TiAl obtained by the dynamic correlation correction with NEVPT2, the characteristic parameters of three low-lying quadruple electronic states (such as equilibrium nuclear distance, binding energy, adiabatic excitation energy) and transition dipole moment, are obtained, and these parameters are used to explain the reason why the electronic transition spectrum of TiAl is not observed experimentally. The characteristic of “break” in the electronic state structure also provides a meaningful reference for analyzing and understanding the brittleness of TiAl alloy at room temperature.
      通信作者: 张树东, zhangsd2@126.com
    • 基金项目: 国家自然科学基金(批准号: 11705101)资助的课题
      Corresponding author: Zhang Shu-Dong, zhangsd2@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11705101)
    [1]

    Lewandowski J J, Seifi M 2016 Annu. Rev. Mater. Res. 46 151Google Scholar

    [2]

    Hug G, Loiseau A, Lasalmonie A 1986 Philos. Mag. A 54 47Google Scholar

    [3]

    Hong T, Watsonyang T, Guo X, Freeman A, Oguchi T, Xu J 1990 Phys. Rev. B 41 12462Google Scholar

    [4]

    Hall E L, Huang S C 1989 J. Mater. Res. 4 595Google Scholar

    [5]

    Hussain A, Hayat S S, Choudhry M A 2011 Physica B 406 1961Google Scholar

    [6]

    Yuan X, Yin S, Lian Y, Yan P Y, Xu H F, Yan B 2019 Chin. Phys. B 28 043101Google Scholar

    [7]

    Zhao H Y, Ma H M, Wang J, Liu Y 2016 Chin. Phys. Lett. 33 108105Google Scholar

    [8]

    Tang F D, Du Q H, Petrovic C, Zhang W, He M Q, Zhang L Y 2019 Chin. Phys. B 28 037104Google Scholar

    [9]

    Wan M J, Jin C G, Yu Y, Huang D H, Shao J X 2017 Chin. Phys. B 26 033101Google Scholar

    [10]

    Chen G, Peng Y, Zheng G, Qi Z, Wand M, Yu H, Dong C, Liu C T 2016 Nat. Mater. 15 876Google Scholar

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    李兴华, 杨绍利 2011 材料导报 25 94

    Li X H, Yang S L 2011 Mater. Reports 25 94

    [12]

    宋成粉, 樊沁娜, 李蔚, 刘永利, 张林 2011 物理学报 60 063104Google Scholar

    Song C F, Fan X N, Li W, Liu Y L, Zhang L 2011 Acta Phys. Sin. 60 063104Google Scholar

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    闫蕴琪, 张振祺 2000 材料导报 14 31Google Scholar

    Yan Y Q, Zhang Z Q 2000 Mater. Reports 14 31Google Scholar

    [14]

    Behm J M, Morse M D 1994 J. Chem. Phys. 101 6500Google Scholar

    [15]

    Behm J M, Brugh D J, Morse M D 1994 J. Chem. Phys. 101 6487Google Scholar

    [16]

    Behm J M, Arrington C A, Langenberg J D, Morse M D 1993 J. Chem. Phys. 99 6394Google Scholar

    [17]

    宋庆功, 秦国顺, 杨宝宝, 蒋清杰, 胡雪兰 2016 物理学报 65 046102Google Scholar

    Song Q G, Qin G S, Yang B B, Jiang Q J, Hu X L 2016 Acta Phys. Sin. 65 046102Google Scholar

    [18]

    Zope R R, Mishin Y 2003 Phys. Rev. B 68 024102Google Scholar

    [19]

    Hu H, Ren Y S, Wu X Z, Liu W G, Luo J J 2019 Int. J. Mod. Phys. B 33 1950097Google Scholar

    [20]

    Jeong B, Kim J, Lee T, Kim S W, Ryu S 2018 Sci. Rep. 8 15200Google Scholar

    [21]

    Ouyang Y, Wang J, Liu F, Liu Y, Du Y, He Y 2009 J. Mol. Struc. Theochem 905 106Google Scholar

    [22]

    Neese F 2012 Comput. Mol. Sci. 2 73Google Scholar

    [23]

    Gerard H, Davidson E R, Eisenstein O 2002 Mol. Phys. 100 533Google Scholar

    [24]

    Larsson S 2011 Int. J. Quantum Chem. 111 3424Google Scholar

    [25]

    Zhang S D, Wand M X, Wand Z F, Xu K, Dong J P 2017 J. Phys. Soc. Jpn. 86 074301Google Scholar

    [26]

    Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297Google Scholar

    [27]

    Barysz M 2016 J. Chem. Theory Comput. 12 1614Google Scholar

    [28]

    NIST Standard Reference Database 78 https://dx.doi.org/10.18434/T4W30F [2019-9-4]

    [29]

    Smith E B 2014 Basic Physical Chemistry: The Route to Understanding (London: Imperial College Press)

  • 图 1  SA-CAS (7, 10)对TiAl最低6条电子态势能曲线的扫描计算, 其中采用的基组分别是(a) def2-TZVP; (b) def2-TZVPP, (c) def2-QZVPP

    Fig. 1.  The lowest 6 potential energy curves of TiAl calculated by SA-CAS (7, 10) with basis set of (a) def2-TZVP; (b) def2-TZVPP; (c) def2-QZVPP.

    图 2  活动基轨道能量随核间距的变化

    Fig. 2.  Variation of CAS orbital energy with nuclear distance.

    图 3  活动基轨道上电子占居数随核间距的变化

    Fig. 3.  Variation of occupied electrons in the CAS orbital with nuclear distance.

    图 4  TiAl最低四重电子态的标识(SA-CAS计算结果)

    Fig. 4.  Identification of the lowest quadruple electronic state of TiAl (SA-CAS calculation results).

    图 5  TiAl电子态势能曲线的SC-NEVPT2动态相关修正计算

    Fig. 5.  Dynamic correlation correction calculation of SC-NEVPT2 for TiAl electronic potential energy curve.

    表 1  CAS (7, 10)/def2-TZVP计算的活动基分子轨道(MO14−MO23)系数(Eh = 2625.5 kJ/mol)

    Table 1.  Coefficients of the CAS orbital (MO14−MO23) calculated by CAS (7, 10)/def2-TZVP.

    MO No.14151617181920212223
    Energy/Eh–0.4035–0.18380.0029–0.0159–0.01590.07430.07430.04390.17140.1714
    Number of occupied electron1.9571.7720.6690.5950.5950.4940.4940.2220.0990.099
    Symbolσσσππδδσππ
    Tisσ12.147.57.7000013.400
    Tipzσ7.52.61.2000038.200
    Tipxπ0004.9000000
    Tipy0001.8000000
    Tidz2σ71.786.1000010.400
    Tidxzπ00031.411.400034.631.2
    Tidyz00011.431.400031.234.6
    Tidx2y2δ0000082.617.2000
    Tidxy0000017.282.6000
    Alsσ72.97.81.20000000
    Alpzσ0.539.23.2000036.600
    Alpxπ00034.412.500016.715.1
    Alpy00012.534.400015.116.7
    下载: 导出CSV

    表 2  两组${\text{π}}$轨道的组成分析

    Table 2.  Composition analysis of two π orbits

    OrbitalR = 0.200 nmR = 0.240 nmR = 0.280 nmR = 0.490 nm
    ${\rm{(1{\text{π}})(2{\text{π}})}}$$\begin{aligned}& {\rm{Ti(}}3{{\rm{p}}_x}, {\rm{ }}3{{\rm{p}}_y}{\rm{) }}7{\rm{\% }} \\& {\rm{Ti(}}3{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}{\rm{) }}60{\rm{\% }} \\ &{\rm{Al(}}3{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) }}28{\rm{\% }}\end{aligned} $$\begin{aligned}& {\rm{Ti(3}}{{\rm{p}}_x}, {\rm{ 3}}{{\rm{p}}_y}{\rm{) }}7{\rm{\% }} \\& {\rm{Ti(3}}{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}{\rm{) }}5{\rm{7\% }} \\& {\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) }}3{\rm{2\% }}\end{aligned} $$\begin{aligned}& {\rm{Ti(3}}{{\rm{p}}_x}, {\rm{ }}3{{\rm{p}}_y}{\rm{) 3\% }} \\ &{\rm{Ti(3}}{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}{\rm{) 73\% }} \\& {\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 21\% }}\end{aligned} $${\rm{Ti}}(3{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}){\rm{ }}1{\rm{00}}\% $
    ${\rm{(3{\text{π}})(4{\text{π}})}}$$\begin{aligned} &{\rm{Ti(3}}{{\rm{d}}_{xz}}{\rm{, 3}}{{\rm{d}}_{yz}}{\rm{) 52\% }} \\ &{\rm{Al(3}}{{\rm{p}}_x}{\rm{, 3}}{{\rm{p}}_y}{\rm{) 36\% }}\end{aligned} $$\begin{aligned} &{\rm{Ti(3}}{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}{\rm{) 52\% }} \\& {\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 40\% }}\end{aligned} $$\begin{aligned}& {\rm{Ti(3}}{{\rm{p}}_x}, {\rm{ }}3{{\rm{p}}_y}{\rm{) 12\% }} \\ &{\rm{Ti(3}}{{\rm{d}}_{xz}}, 3{{\rm{d}}_{yz}}{\rm{) 34\% }} \\ &{\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 52\% }}\end{aligned} $${\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 99\% }}$
    下载: 导出CSV

    表 3  R = 0.490 nm处活动基分子轨道MO14-MO23组成

    Table 3.  Composition of CAS orbitals MO14-MO23 at R = 0.490 nm.

    Orbital No121314151617
    Energy/Hartree–1.79778–1.7976–0.37486–0.215130.020010.03822
    Occupied electron2.000002.00001.919761.899000.624630.55980
    Ti s002.894.500
    Ti pz099.80.5000
    Ti px55.70.10000
    Ti py44.300000
    Ti dxz000055.843.6
    Ti dyz000044.155.2
    Al s0095.82.800
    Orbital No181920212223
    Energy/Hartree–0.00791–0.006820.08850.089790.056510.1227
    Occupied electron0.517860.517500.410580.406450.101590.04283
    Ti pz0000.091.45.3
    Ti dx2y2001.498.600
    Ti dxy0098.41.400
    Al pz0000792.7
    Al px55.343.30000
    Al py43.754.80000
    下载: 导出CSV

    表 4  基态及最低激发态的组态及跃迁偶极矩

    Table 4.  Configuration and transition dipole moment of the ground state and the lowest excited state

    R/nmstateMain configurationExcitation energy/cm–1Transition dipole moment T2/Debye2Possible quartet stateIdetified state
    0.285Ground state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{1}}}{{\text{π}}^{\rm{0}}}$04ΔX4Δ
    1st excited state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{0}}}{{\text{π}}^{\rm{1}}}$32120.0344ΠA4Π
    2nd excited state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{1}}}{{\rm{\text{δ} }}^{\rm{1}}}{{\text{π}}^{\rm{1}}}$346204Σ, 4Δ(2), 4ΓB4Γ
    0.240Ground state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{1}}}$04ΔX4Δ
    1st excited state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$41400.008244Π, 4ΦA'4Φ
    2nd excited state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$47270.008694Π, 4ΦB'4Π
    3rd excited state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$50740.005514Π, 4ΦB'4Π
    下载: 导出CSV

    表 5  TiAl最低3个四重态的结构参数

    Table 5.  Structural parameters of the lowest three quadruple states of TiAl.

    StateRe/nmDe/cm–1
    CASNEVPT2CASNEVPT2
    X4Δ0.2880.26630168151
    A4Π0.320$\left\{\begin{aligned}& {0.248} \\ & {0.296} \end{aligned} \right.$796$\left\{\begin{aligned}& {3845} \\ & {3406} \end{aligned} \right.$
    B4Γ0.324$\left\{\begin{aligned}& {0.248} \\ & {0.306} \end{aligned} \right.$711$\left\{\begin{aligned}& {2884} \\ & {3406} \end{aligned} \right.$
    下载: 导出CSV
  • [1]

    Lewandowski J J, Seifi M 2016 Annu. Rev. Mater. Res. 46 151Google Scholar

    [2]

    Hug G, Loiseau A, Lasalmonie A 1986 Philos. Mag. A 54 47Google Scholar

    [3]

    Hong T, Watsonyang T, Guo X, Freeman A, Oguchi T, Xu J 1990 Phys. Rev. B 41 12462Google Scholar

    [4]

    Hall E L, Huang S C 1989 J. Mater. Res. 4 595Google Scholar

    [5]

    Hussain A, Hayat S S, Choudhry M A 2011 Physica B 406 1961Google Scholar

    [6]

    Yuan X, Yin S, Lian Y, Yan P Y, Xu H F, Yan B 2019 Chin. Phys. B 28 043101Google Scholar

    [7]

    Zhao H Y, Ma H M, Wang J, Liu Y 2016 Chin. Phys. Lett. 33 108105Google Scholar

    [8]

    Tang F D, Du Q H, Petrovic C, Zhang W, He M Q, Zhang L Y 2019 Chin. Phys. B 28 037104Google Scholar

    [9]

    Wan M J, Jin C G, Yu Y, Huang D H, Shao J X 2017 Chin. Phys. B 26 033101Google Scholar

    [10]

    Chen G, Peng Y, Zheng G, Qi Z, Wand M, Yu H, Dong C, Liu C T 2016 Nat. Mater. 15 876Google Scholar

    [11]

    李兴华, 杨绍利 2011 材料导报 25 94

    Li X H, Yang S L 2011 Mater. Reports 25 94

    [12]

    宋成粉, 樊沁娜, 李蔚, 刘永利, 张林 2011 物理学报 60 063104Google Scholar

    Song C F, Fan X N, Li W, Liu Y L, Zhang L 2011 Acta Phys. Sin. 60 063104Google Scholar

    [13]

    闫蕴琪, 张振祺 2000 材料导报 14 31Google Scholar

    Yan Y Q, Zhang Z Q 2000 Mater. Reports 14 31Google Scholar

    [14]

    Behm J M, Morse M D 1994 J. Chem. Phys. 101 6500Google Scholar

    [15]

    Behm J M, Brugh D J, Morse M D 1994 J. Chem. Phys. 101 6487Google Scholar

    [16]

    Behm J M, Arrington C A, Langenberg J D, Morse M D 1993 J. Chem. Phys. 99 6394Google Scholar

    [17]

    宋庆功, 秦国顺, 杨宝宝, 蒋清杰, 胡雪兰 2016 物理学报 65 046102Google Scholar

    Song Q G, Qin G S, Yang B B, Jiang Q J, Hu X L 2016 Acta Phys. Sin. 65 046102Google Scholar

    [18]

    Zope R R, Mishin Y 2003 Phys. Rev. B 68 024102Google Scholar

    [19]

    Hu H, Ren Y S, Wu X Z, Liu W G, Luo J J 2019 Int. J. Mod. Phys. B 33 1950097Google Scholar

    [20]

    Jeong B, Kim J, Lee T, Kim S W, Ryu S 2018 Sci. Rep. 8 15200Google Scholar

    [21]

    Ouyang Y, Wang J, Liu F, Liu Y, Du Y, He Y 2009 J. Mol. Struc. Theochem 905 106Google Scholar

    [22]

    Neese F 2012 Comput. Mol. Sci. 2 73Google Scholar

    [23]

    Gerard H, Davidson E R, Eisenstein O 2002 Mol. Phys. 100 533Google Scholar

    [24]

    Larsson S 2011 Int. J. Quantum Chem. 111 3424Google Scholar

    [25]

    Zhang S D, Wand M X, Wand Z F, Xu K, Dong J P 2017 J. Phys. Soc. Jpn. 86 074301Google Scholar

    [26]

    Weigend F, Ahlrichs R 2005 Phys. Chem. Chem. Phys. 7 3297Google Scholar

    [27]

    Barysz M 2016 J. Chem. Theory Comput. 12 1614Google Scholar

    [28]

    NIST Standard Reference Database 78 https://dx.doi.org/10.18434/T4W30F [2019-9-4]

    [29]

    Smith E B 2014 Basic Physical Chemistry: The Route to Understanding (London: Imperial College Press)

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出版历程
  • 收稿日期:  2019-09-05
  • 修回日期:  2019-10-23
  • 上网日期:  2019-11-27
  • 刊出日期:  2019-12-01

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