Theoretical study on electronic structure and transition properties of excited states for SeH<sup>+</sup> anion

Hua Ya-Wen; Liu Yi-Liang; Wan Ming-Jie

doi:10.7498/aps.69.20200278

Abstract

Potential energy curves of dipole moments for 12 electronic states correlating with the Se⁺(⁴Su) + H(²Sg), Se⁺(²Du) + H(²Sg) and Se⁺(²Pu) + H(²Sg) dissociation channels of SeH⁺ anion are calculated by the ic-MRCI + Q method. The AV5Z-DK basis set for Se atom and H atom are chosen. Scalar relativistic effect, core-valence correction, and spin-orbit coupling effect are also taken into account. In MRCI calculations, Se(1s2s) orbitals are frozen, H(1s) and Se(4s4p) orbitals are selected as active space, and the remaining orbitals are used for the core-valence correlation.Spectroscopic parameters of 12 Λ–S states and 9 low-lying Ω states are obtained. All Λ–S states we selected are bound states. The X³Σ^–, a¹Δ, b¹Σ⁺, A³Π and c¹Π states each possess a large well, but the others each have a shallow well. The a¹Δ, b¹Σ⁺, A³Π, c¹Π and 1⁵Σ^– states cross in 30000–40000 cm^–1 regions. The X³Σ^–, a¹Δ and b¹Σ⁺ come from the 4π² electronic configuration around the equilibrium region, and three states have similar values of R_e. The splitting dissociation channels are obtained at a spin-orbital coupling level. The calculated energy differences among five dissociation channels are in excellent agreement with the experimental data, and the maximal error is smaller than 0.5%. Due to the avoided crossing between the low-lying Ω states, the a2, b0⁺, A₁2, A₂1, A₃0^–, A₄0⁺ and c1 states all have two wells. The splitting parameters A^SO of the X³Σ^– state and the A³Π state are predicted at the same time, i. e. A^SO(X₂1 – X₁0⁺) = 252.4 cm^–1, A^SO(A₂1 – A₁2) = 858.9 cm^–1, A^SO(A₃0^– – A₂1) = 1213.5 cm^–1 and A^SO(A₄0⁺ – A₃0^–) = 199.5 cm^–1. The transition dipole moments of the A³Π $ \leftrightarrow $ X³Σ^– and A₂1 $ \leftrightarrow $ X₁0⁺ transitions are obtained. The oscillator strengths, Franck-Condon factors, and radiative lifetimes of these two transitions are also predicted. The radiative lifetime of A³Π state and A₂1 state are 746.6 and 787.8 ns, respectively. It implies the ability of electron transition for these two transitions.

Keywords:

multi-reference configuration interaction /
spin-orbit coupling effect /
spectroscopic constants /
spontaneous radiative lifetimes

Authors and contacts

1.
College of Electrical and Information Engineering, Southwest Minzu University, Chengdu 610225, China
2.
Computational Physics Key Laboratory of Sichuan Province, Yibin University, Yibin 644007, China

Corresponding author: Hua Ya-Wen, yawen0215@163.com

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References

[1]	Ram R S, Bernath P F 2000 J. Mol. Spectrosc. 203 9 Google Scholar
[2]	Lindgren B 1968 J. Mol. Spectrosc. 28 536 Google Scholar
[3]	Davies P B, Handy B J, Lloyd E K M, Russell D K 1978 J. Chem. Phys. 68 3377 Google Scholar
[4]	Brown J M, Carrington A, Sears T J 1979 Mol. Phys. 37 1837 Google Scholar
[5]	Cliff D I, Davies P B, Handy J J, Thrush B A 1980 Chem. Phys. Lett. 75 9 Google Scholar
[6]	Bollmark, Lindgren B, Sassenberg U 1980 Phys. Scr. 21 811 Google Scholar
[7]	Brown J M, Fackerell A D 1982 Phys. Scr. 25 351 Google Scholar
[8]	Ashworth S H, Brown J M 1991 Chem. Phys. Lett. 182 73 Google Scholar
[9]	Balasubramanian K, Liao M Z, Han M 1987 Chem. Phys. Lett. 139 551 Google Scholar
[10]	Moore C E 1971 Atomic Energy Levels (Vol. 1) (Washington, DC: National Bureau of Standards Publications) pp2, 153
[11]	Binning J R C, Curtiss L A 1990 J. Chem. Phys. 92 3688 Google Scholar
[12]	Guberman S L 1995 J. Chem. Phys. 102 1699 Google Scholar
[13]	Khadri F, Ndome H, Lahmar S, Lakhdar Z B, Hochlaf M 2006 J. Mol. Spectrosc. 237 232 Google Scholar
[14]	Santos L G dos, Oliveira A G S de, Ornellas F R 2015 J. Chem. Phys. 142 024316 Google Scholar
[15]	Song Y Z, Zhang L L, Gao S B, Meng Q T 2016 Sci. Rep. 6 37734 Google Scholar
[16]	Zhang L L, Gao S B, Meng Q T, Pan J, Song Y Z 2018 J. Chem. Phys. 149 154303 Google Scholar
[17]	施德恒, 刘慧, 孙金锋, 朱遵略, 刘玉芳 2010 物理学报 59 227 Google Scholar Shi D H, Liu H, Sun J F, Zhu Z L, Liu Y F 2010 Acta Phys. Sin. 59 227 Google Scholar
[18]	赵书涛, 梁桂颖, 李瑞等 2017 物理学报 66 063103 Google Scholar Zhao S T, Liang G Y, Li R, et al. 2017 Acta Phys. Sin. 66 063103 Google Scholar
[19]	Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010)
[20]	Knowles P J Werner H J 1985 J. Chem. Phys. 82 5053 Google Scholar
[21]	Knowles P J Werner H J 1985 Chem. Phys. Lett. 115 259 Google Scholar
[22]	Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803 Google Scholar
[23]	Knowles P J Werner H J 1988 Chem. Phys. Lett. 145 514 Google Scholar
[24]	Dunning T H Jr 1989 J. Chem. Phys. 90 1007 Google Scholar
[25]	Wilson A K, Woon D E, Peterson K A, Dunning T H Jr 1999 J. Chem. Phys. 110 7667 Google Scholar
[26]	Douglas M, Kroll N M 1974 Ann. Phys. 82 89 Google Scholar
[27]	Hess B A 1986 Phys. Rev. A 33 3742 Google Scholar
[28]	Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823 Google Scholar
[29]	Le Roy R J 2007 Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[30]	Stollenwerk P R, Kokish M G, Antonio G. S. Oliveira-Filho de A G S, Ornellas F R, Odom B C 2018 Atoms 6 53 Google Scholar
[31]	Kjaergaard H G, Yu H, Schattka B J, Henry B R, Tarr A W 1990 J. Chem. Phys. 93 6239 Google Scholar

Cited By

图 1 SeH⁺离子的12个Λ—S态的势能曲线

Figure 1. Potential energy curves of the Λ－S states of SeH⁺.

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图 2 SeH⁺离子的9个Ω态的势能曲线

Figure 2. Potential energy curves of nine Ω states of SeH⁺.

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图 3 SeH⁺离子的偶极矩和跃迁偶极矩跃迁偶极矩　(a) 自旋无关水平下; (b) SOC水平下

Figure 3. Dipole moments and transition dipole moments of SeH⁺: (a) At spin-free level; (b) at SOC level.

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表 1 SeH⁺离子Λ—S态的离解关系

Table 1. Dissociation relationships of Λ－S states of SeH⁺.

原子态	Λ–S态	相对能量/cm^–1
原子态	Λ–S态	本文工作^a
Se⁺(⁴S_u) + H(²S_g)	^{3, 5}Σ^–	0
Se⁺(²D_u) + H(²S_g)	^{1, 3}Σ^–, ^{1, 3}Π, ^{1, 3}Δ	13590.3
Se⁺(²P_u) + H(²S_g)	^{1, 3}Σ⁺, ^{1, 3}Π	22896.5
^a同一离解极限对应的所有电子态的平均能量.

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表 2 SeH⁺离子Λ—S态的光谱常数

Table 2. Spectroscopic constants of the Λ–S states of SeH⁺.

电子态	R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/eV	T_e/cm^–1
X³Σ^–	1.4659	2387.48	45.81	7.8816	3.369	0
	1.474^[11]
a¹Δ	1.4642	2393.52	40.79	7.8999	3.920	9179.3
b¹Σ⁺	1.4622	2406.68	40.39	7.9224	4.006	17761.9
1⁵Σ^–	3.5894	152.17	25.85	1.3340	0.030	26930.2
A³Π	1.6395	1505.52	57.16	6.2961	1.207	30953.8
c¹Π	1.8168	989.95	59.14	5.1488	0.515	36530.2
B³Σ^–	2.8262	490.08	47.96	2.1460	0.157	39522.1
1¹Σ^–	3.6892	162.98	19.18	1.2109	0.042	40461.9
1³Δ	3.5593	139.94	20.44	1.2964	0.030	40552.3
2³Π	2.6009	603.15	50.66	2.5253	0.223	48259.6
2¹Π	2.7701	400.92	43.54	2.2291	0.116	49124.6
1³Σ⁺	3.6000	151.41	25.73	1.3258	0.029	49835.4

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表 3 第Ⅵ主簇氢化物正离子低电子态的光谱常数

Table 3. Spectroscopic constants of the low-lying states for the Ⅵ hydride cations.

离子	文献	电子态	R_e /Å	ω_e /cm^–1	ω_eχ_e /cm^–1	B_e /cm^–1	D_e /eV	T_e /cm^–1
SH⁺	[13]	X³Σ^–	1.361	2555.2	49.00	9.279	3.488	0
	[13]	a¹Δ	1.362	2567.2	47.48	9.285	4.102	10186.7
	[13]	b¹Σ⁺	1.362	2576.7	47.34	9.298	4.208	18881.3
TeH⁺	[14]	X³Σ^–	1.6425	2147.8	36.23	6.2351	2.846	0
	[14]	a¹Δ	1.6404	2171.0	36.57	6.2547	3.287	7590
	[14]	b¹Σ⁺	1.6383	2184.2	36.24	6.2711	3.351	15467

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表 4 SeH⁺离子Ω 态的离解关系

Table 4. Dissociation relationships of Ω states of SeH⁺.

原子态	Ω态	相对能量/cm^–1
原子态	Ω态	本文工作	文献^[9]^a	实验值^[10]
Se⁺(⁴S_3/2) + H(²S_1/2)	2, 1, 1, 0⁺, 0^–	0	0	0
Se⁺(²D_3/2) + H(²S_1/2)	2, 1, 1, 0⁺, 0^–	13189.0	17745	13168.2
Se⁺(²D_5/2) + H(²S_1/2)	3, 2, 2, 1, 1, 0⁺, 0^–	13806.5	18347	13784.4
Se⁺(²P_1/2) + H(²S_1/2)	1, 0⁺, 0^–	23115.9		23038.3
Se⁺(²P_3/2) + H(²S_1/2)	2, 1, 1, 0⁺, 0^–	23928.7		23894.8
^a根据文献[9]的计算数据推导得到.

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表 5 SeH⁺离子Ω态的光谱常数

Table 5. Spectroscopic constants of the Ω states of SeH⁺.

电子态		R_e /Å	ω_e /cm^–1	ω_eχ_e /cm^–1	B_e /cm^–1	D_e /eV	T_e /cm^–1
X₁0⁺		1.4661	2385.56	45.66	7.8802	3.380	0
X₂1		1.4662	2386.15	46.02	7.8790	3.348	252.4
a2	第一势阱	1.4645	2392.76	41.29	7.8967	2.525	9408.2
a2	第二势阱	3.5800	168.60	33.67	1.3399	0.030	27016.9
b0⁺		1.4631	2406.94	44.20	7.9127	2.758	18213.8
A₁2	第一势阱	1.6418	1396.10	53.29	6.3333	0.340	30201.1
A₁2	第二势阱	2.4132	2295.44	131.22	2.9938	1.262	30248.9
A₂1	第一势阱	1.6457	1381.37	53.81	6.3229	0.329	31060.0
A₂1	第二势阱	3.5900	152.22	25.81	1.3353	0.030	27018.9
A₃0^–	第一势阱	1.6429	1391.28	55.78	6.3715	0.307	32273.5
A₃0^–	第二势阱	3.6000	151.93	25.77	1.3339	0.030	27019.3
A₄0⁺	第一势阱	1.6368	1385.24	18.09	6.3123	0.962	32473.0
A₄0⁺	第二势阱	2.7918	676.20	90.61	2.1897	0.167	39685.4
c1	第一势阱	1.8161	—	—	—	0.044	36979.9
c1	第二势阱	2.1793	1781.89	149.33	3.5614	0.687	34921.9

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表 6 $ {{\rm{A}}^3}\Pi \leftrightarrow {{\rm{X}}^3}{\Sigma ^ - }$和$ {{\rm{A}}_2}1 \leftrightarrow {{\rm{X}}_1}{0^ + }$跃迁的弗兰克-康登因子(单位s^-1)、总辐射速率和辐射寿命(单位: ns)

Table 6. Franck-Condon Factors, Emission rates (unit of s^–1) and radiative lifetimes τ (unit of ns) of the $ {{\rm{A}}^3}\Pi \leftrightarrow {{\rm{X}}^3}{\Sigma ^ - }$ and $ {{\rm{A}}_2}1 \leftrightarrow {{\rm{X}}_1}{0^ + }$ transitions.

跃迁	ν'	ν'' = 0	ν'' = 1	ν'' = 2	ν'' = 3	ν'' = 4	ν'' = 5	ΣA	τ = 1/(ΣA)
$ {\rm A^3}\Pi \leftrightarrow {\rm X^3}{\Sigma ^ - }$	0	0.4079	0.3685	0.1666	0.0470	0.0088	0.0011	1339434	746.6
$ {\rm A^3}\Pi \leftrightarrow {\rm X^3}{\Sigma ^ - }$	1	0.3271	0.0013	0.2122	0.2713	0.1398	0.0405	1310290	763.2
$ {\rm A_2}1 \leftrightarrow {\rm X_1}{0^ + }$	0	0.3841	0.3688	0.1787	0.0549	0.0116	0.0017	1269392	787.8
$ {\rm A_2}1 \leftrightarrow {\rm X_1}{0^ + }$	1	0.3186	0.0001	0.1761	0.2695	0.1629	0.0558	1212188	825.0

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[1]	Ram R S, Bernath P F 2000 J. Mol. Spectrosc. 203 9 Google Scholar
[2]	Lindgren B 1968 J. Mol. Spectrosc. 28 536 Google Scholar
[3]	Davies P B, Handy B J, Lloyd E K M, Russell D K 1978 J. Chem. Phys. 68 3377 Google Scholar
[4]	Brown J M, Carrington A, Sears T J 1979 Mol. Phys. 37 1837 Google Scholar
[5]	Cliff D I, Davies P B, Handy J J, Thrush B A 1980 Chem. Phys. Lett. 75 9 Google Scholar
[6]	Bollmark, Lindgren B, Sassenberg U 1980 Phys. Scr. 21 811 Google Scholar
[7]	Brown J M, Fackerell A D 1982 Phys. Scr. 25 351 Google Scholar
[8]	Ashworth S H, Brown J M 1991 Chem. Phys. Lett. 182 73 Google Scholar
[9]	Balasubramanian K, Liao M Z, Han M 1987 Chem. Phys. Lett. 139 551 Google Scholar
[10]	Moore C E 1971 Atomic Energy Levels (Vol. 1) (Washington, DC: National Bureau of Standards Publications) pp2, 153
[11]	Binning J R C, Curtiss L A 1990 J. Chem. Phys. 92 3688 Google Scholar
[12]	Guberman S L 1995 J. Chem. Phys. 102 1699 Google Scholar
[13]	Khadri F, Ndome H, Lahmar S, Lakhdar Z B, Hochlaf M 2006 J. Mol. Spectrosc. 237 232 Google Scholar
[14]	Santos L G dos, Oliveira A G S de, Ornellas F R 2015 J. Chem. Phys. 142 024316 Google Scholar
[15]	Song Y Z, Zhang L L, Gao S B, Meng Q T 2016 Sci. Rep. 6 37734 Google Scholar
[16]	Zhang L L, Gao S B, Meng Q T, Pan J, Song Y Z 2018 J. Chem. Phys. 149 154303 Google Scholar
[17]	施德恒, 刘慧, 孙金锋, 朱遵略, 刘玉芳 2010 物理学报 59 227 Google Scholar Shi D H, Liu H, Sun J F, Zhu Z L, Liu Y F 2010 Acta Phys. Sin. 59 227 Google Scholar
[18]	赵书涛, 梁桂颖, 李瑞等 2017 物理学报 66 063103 Google Scholar Zhao S T, Liang G Y, Li R, et al. 2017 Acta Phys. Sin. 66 063103 Google Scholar
[19]	Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010)
[20]	Knowles P J Werner H J 1985 J. Chem. Phys. 82 5053 Google Scholar
[21]	Knowles P J Werner H J 1985 Chem. Phys. Lett. 115 259 Google Scholar
[22]	Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803 Google Scholar
[23]	Knowles P J Werner H J 1988 Chem. Phys. Lett. 145 514 Google Scholar
[24]	Dunning T H Jr 1989 J. Chem. Phys. 90 1007 Google Scholar
[25]	Wilson A K, Woon D E, Peterson K A, Dunning T H Jr 1999 J. Chem. Phys. 110 7667 Google Scholar
[26]	Douglas M, Kroll N M 1974 Ann. Phys. 82 89 Google Scholar
[27]	Hess B A 1986 Phys. Rev. A 33 3742 Google Scholar
[28]	Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823 Google Scholar
[29]	Le Roy R J 2007 Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[30]	Stollenwerk P R, Kokish M G, Antonio G. S. Oliveira-Filho de A G S, Ornellas F R, Odom B C 2018 Atoms 6 53 Google Scholar
[31]	Kjaergaard H G, Yu H, Schattka B J, Henry B R, Tarr A W 1990 J. Chem. Phys. 93 6239 Google Scholar

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Theoretical study on electronic structure and transition properties of excited states for SeH⁺ anion

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Theoretical study on electronic structure and transition properties of excited states for SeH+ anion

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Theoretical study on electronic structure and transition properties of excited states for SeH⁺ anion