<i>Ab initio</i> calculation of electronic state structure of TiAl

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Abstract

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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Corresponding author:Zhang Shu-Dong,zhangsd2@126.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11705101)

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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	p_z	σ	7.5	2.6	1.2	0	0	0	0	38.2	0	0
Ti	p_x	π	0	0	0	4.9	0	0	0	0	0	0
Ti	p_y	π	0	0	0	1.8	0	0	0	0	0	0
Ti	d_z₂	σ	7	1.7	86.1	0	0	0	0	10.4	0	0
Ti	d_xz	π	0	0	0	31.4	11.4	0	0	0	34.6	31.2
Ti	d_yz	π	0	0	0	11.4	31.4	0	0	0	31.2	34.6
Ti	d_x₂_y₂	δ	0	0	0	0	0	82.6	17.2	0	0	0
Ti	d_xy	δ	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	p_z	σ	0.5	39.2	3.2	0	0	0	0	36.6	0	0
Al	p_x	π	0	0	0	34.4	12.5	0	0	0	16.7	15.1
Al	p_y	π	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} $	${\rm{Al(3}}{{\rm{p}}_x}, 3{{\rm{p}}_y}{\rm{) 99\% }}$

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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 p_z	0	99.8	0.5	0	0	0
Ti p_x	55.7	0.1	0	0	0	0
Ti p_y	44.3	0	0	0	0	0
Ti d_xz	0	0	0	0	55.8	43.6
Ti d_yz	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 p_z	0	0	0	0.0	91.4	5.3
Ti d_x₂_y₂	0	0	1.4	98.6	0	0
Ti d_xy	0	0	98.4	1.4	0	0
Al p_z	0	0	0	0	7	92.7
Al p_x	55.3	43.3	0	0	0	0
Al p_y	43.7	54.8	0	0	0	0

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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
	1^stexcited 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
	2^ndexcited 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
	1^stexcited 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
	2^ndexcited 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
	3^rdexcited 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

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State	R_e/nm		D_e/cm^–1
State	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	$\left\{\begin{aligned}& {2884} \\ & {3406} \end{aligned} \right.$

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Vol. 68, Issue 24 - 2019-12-20

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