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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(3s 23p 1)轨道和Ti的4个价电子(3d 24s 2)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X 4Δ, A 4Π和B 4Γ; 在 R< 0.255 nm区域, 基态仍为X 4Δ, 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 (3s 23p 1) valence orbital of Al and (3d 24s 2) 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 Rof 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 X 4Δ, A 4Π and B 4Γ respectively; in the R< 0.255 nm region, the ground state is still X 4Δ, 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.
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Keywords:
- TiAl/
- excited state/
- potential energy curve/
- complet active space self-consistent field/
- Nelectronic valence perturbation theory approximation
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MO No. 14 15 16 17 18 19 20 21 22 23 Energy/Eh –0.4035 –0.1838 0.0029 –0.0159 –0.0159 0.0743 0.0743 0.0439 0.1714 0.1714 Number of occupied electron 1.957 1.772 0.669 0.595 0.595 0.494 0.494 0.222 0.099 0.099 Symbol σ σ σ π π δ δ σ π π Ti s σ 12.1 47.5 7.7 0 0 0 0 13.4 0 0 Ti pz σ 7.5 2.6 1.2 0 0 0 0 38.2 0 0 Ti px π 0 0 0 4.9 0 0 0 0 0 0 Ti py 0 0 0 1.8 0 0 0 0 0 0 Ti dz2 σ 7 1.7 86.1 0 0 0 0 10.4 0 0 Ti dxz π 0 0 0 31.4 11.4 0 0 0 34.6 31.2 Ti dyz 0 0 0 11.4 31.4 0 0 0 31.2 34.6 Ti dx2y2 δ 0 0 0 0 0 82.6 17.2 0 0 0 Ti dxy 0 0 0 0 0 17.2 82.6 0 0 0 Al s σ 72.9 7.8 1.2 0 0 0 0 0 0 0 Al pz σ 0.5 39.2 3.2 0 0 0 0 36.6 0 0 Al px π 0 0 0 34.4 12.5 0 0 0 16.7 15.1 Al py 0 0 0 12.5 34.4 0 0 0 15.1 16.7 
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Orbital R= 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} $ ${\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 99\% }}$ 下载:
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Orbital No 12 13 14 15 16 17 Energy/Hartree –1.79778 –1.7976 –0.37486 –0.21513 0.02001 0.03822 Occupied electron 2.00000 2.0000 1.91976 1.89900 0.62463 0.55980 Ti s 0 0 2.8 94.5 0 0 Ti pz 0 99.8 0.5 0 0 0 Ti px 55.7 0.1 0 0 0 0 Ti py 44.3 0 0 0 0 0 Ti dxz 0 0 0 0 55.8 43.6 Ti dyz 0 0 0 0 44.1 55.2 Al s 0 0 95.8 2.8 0 0 Orbital No 18 19 20 21 22 23 Energy/Hartree –0.00791 –0.00682 0.0885 0.08979 0.05651 0.1227 Occupied electron 0.51786 0.51750 0.41058 0.40645 0.10159 0.04283 Ti pz 0 0 0 0.0 91.4 5.3 Ti dx2y2 0 0 1.4 98.6 0 0 Ti dxy 0 0 98.4 1.4 0 0 Al pz 0 0 0 0 7 92.7 Al px 55.3 43.3 0 0 0 0 Al py 43.7 54.8 0 0 0 0 下载:
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R/nm state Main configuration Excitation energy/cm–1 Transition dipole momentT2/Debye2 Possible quartet state Idetified state 0.285 Ground state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{1}}}{{\text{π}}^{\rm{0}}}$ 0 4Δ X4Δ 1stexcited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{0}}}{{\text{π}}^{\rm{1}}}$ 3212 0.034 4Π A4Π 2ndexcited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{1}}}{{\rm{\text{δ} }}^{\rm{1}}}{{\text{π}}^{\rm{1}}}$ 3462 0 4Σ,4Δ(2),4Γ B4Γ 0.240 Ground state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{2}}}{{\text{π}}^{\rm{2}}}{{\rm{\text{δ} }}^{\rm{1}}}$ 0 4Δ X4Δ 1stexcited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$ 4140 0.00824 4Π,4Φ A'4Φ 2ndexcited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$ 4727 0.00869 4Π,4Φ B'4Π 3rdexcited state ${{\rm{\text{σ} }}^{\rm{2}}}{{\rm{\text{σ} }}^{\rm{1}}}{{\text{π}}^{\rm{3}}}{{\rm{\text{δ} }}^{\rm{1}}}$ 5074 0.00551 4Π,4Φ B'4Π 下载:
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State Re/nm De/cm–1 CAS NEVPT2 CAS NEVPT2 X4Δ 0.288 0.266 3016 8151 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 $\left\{\begin{aligned}& {2884} \\ & {3406} \end{aligned} \right.$ 下载:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
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