Acta Physica Sinica, Volume. 68, Issue 24, 243101-1(2019)

Ab initio calculation of electronic state structure of TiAl

Shu-Dong Zhang*, Chuan-Hang Wang, Wei Tang, Yang Sun, Ning-Ze Sun, Zhao-Yu Sun, and Hui Xu
Figures & Tables(10)
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.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
Variation of CAS orbital energy with nuclear distance.活动基轨道能量随核间距的变化
Variation of occupied electrons in the CAS orbital with nuclear distance.活动基轨道上电子占居数随核间距的变化
Identification of the lowest quadruple electronic state of TiAl (SA-CAS calculation results).TiAl最低四重电子态的标识(SA-CAS计算结果)
Dynamic correlation correction calculation of SC-NEVPT2 for TiAl electronic potential energy curve.TiAl电子态势能曲线的SC-NEVPT2动态相关修正计算
  • Table 1.

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

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

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    Table 1.

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

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

    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
  • Table 2. Composition analysis of two π orbits两组 轨道的组成分析

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    Table 2. Composition analysis of two π orbits两组 轨道的组成分析

    OrbitalR = 0.200 nm R = 0.240 nm R = 0.280 nm R = 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\% }}$
  • Table 3.

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

    R = 0.490 nm处活动基分子轨道MO14-MO23组成

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    Table 3.

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

    R = 0.490 nm处活动基分子轨道MO14-MO23组成

    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
  • Table 4.

    Configuration and transition dipole moment of the ground state and the lowest excited state

    基态及最低激发态的组态及跃迁偶极矩

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    Table 4.

    Configuration and transition dipole moment of the ground state and the lowest excited state

    基态及最低激发态的组态及跃迁偶极矩

    R/nm stateMain 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}}}$04Δ X4Δ
    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}}}$32120.0344Π A4Π
    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}}}$346204Σ, 4Δ(2), 4Γ B4Γ
    0.240Ground state${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{1}}}$04Δ X4Δ
    1st excited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$41400.008244Π, 4Φ A'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, 4Φ B'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, 4Φ B'4Π
  • Table 5.

    Structural parameters of the lowest three quadruple states of TiAl.

    TiAl最低3个四重态的结构参数

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    Table 5.

    Structural parameters of the lowest three quadruple states of TiAl.

    TiAl最低3个四重态的结构参数

    StateRe/nm De/cm–1
    CASNEVPT2CASNEVPT2
    X4Δ 0.2880.26630168151
    A4Π 0.320$\left\{\begin{aligned}& {0.248} \\ & {0.296} \end{aligned} \right.$796$\left\{\begin{aligned}& {3845} \\ & {3406} \end{aligned} \right.$
    B4Γ 0.324$\left\{\begin{aligned}& {0.248} \\ & {0.306} \end{aligned} \right.$711$\left\{\begin{aligned}& {2884} \\ & {3406} \end{aligned} \right.$
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Shu-Dong Zhang, Chuan-Hang Wang, Wei Tang, Yang Sun, Ning-Ze Sun, Zhao-Yu Sun, Hui Xu. Ab initio calculation of electronic state structure of TiAl [J]. Acta Physica Sinica, 2019, 68(24): 243101-1

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Paper Information

Received: Sep. 5, 2019

Accepted: --

Published Online: Sep. 17, 2020

The Author Email:

DOI:10.7498/aps.68.20191341

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