Electronic structures and transition properties of AsH<sup>+</sup> cation

Hou Qiu-Yu; Guan Hao-Yi; Huang Yu-Lu; Chen Shi-Lin; Yang Ming; Wan Ming-Jie

doi:10.7498/aps.71.20221104

Abstract

Potential energy curves (PECs), dipole moments (DMs) and transition dipole moments (TDMs) of the X²Π, a⁴Σ^–, A²Σ^–, b⁴Π, B²Δ, C²Σ⁺, D²Π, 2²Σ⁺ states correlating with the three lowest dissociation channels of AsH⁺ cation are calculated by using the multireference configuration interaction (MRCI) method. The Davidson correction, core-valence (CV) correlation, and spin-orbit coupling (SOC) effect are all considered. The aug-cc-pV5Z all-electron basis set of H atom and the aug-cc-pwCV5Z-PP pseudopotential basis set of As atom are both selected in the calculation.In the complete active space self-consistent field (CASSCF) calculation, H (1s) and As (4s4p) shell are selected as active orbitals, As (3p3d) shells are selected as closed orbitals, which keeps doubly occupation, the remaining electrons are in the frozen orbitals. In the MRCI calculation, As (3p3d) shells are used for CV correlation, and the calculation accuracy can be improved. The SOC effects are considered with Breit-Pauli operators.All calculated states are bound states. The X²Π is the ground state, which is a deep potential well, the dissociation energy is 3.100 eV. The b⁴Π, C²Σ⁺ and D²Π are weakly bound states. The spectroscopic parameters are obtained by solving radial Schrodinger equation. To the best of our knowledge, there has been no study of the spectroscopy of AsH⁺ cation so far. Comparing with Ⅴ-hydride cations MH⁺ (M = N, P, As), the orders of the energy levels of the low-lying states for three ions are identical. The dissociation energy and harmonic frequency both decrease with the increase of the atomic weight of M.At spin-free level, the PEC of b⁴Π state and the PEC of B²Δ state cross at about 1.70 Å. When SOC effects are taken into account, according to the rule of avoid-crossing, the $ {{{\rm{B}}^2}}{\Delta _{3/2}} $state and $ {{{\rm{B}}^2}}{\Delta _{5/2}} $state change to the double potential wells, and the avoided crossing between the $ {{{\rm{B}}^2}}{\Delta _{3/2}} $ ($ {{{\rm{B}}^2}}{\Delta _{3/2}} $) state and ${{\rm{b}}^4}{\Pi _{3/2}}$ (${{\rm{b}}^4}{\Pi _{5/2}}$) state is observed. The transition dipole moment (TDM) of the $ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $, $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ and $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ transition are also calculated. The TDM at the equilibrium distance of the $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ spin-forbidden reaches 0.036 Debye, therefore, the SOC effect plays an important role. Based on the accurate PECs and PDMs, the Franck-Condon factors, spontaneous radiative coefficients, and spontaneous radiative lifetimes of the $ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $, $ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $, and $ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $ transition are also calculated.

Keywords:

Authors and contacts

Faculty of Science, Yibin University, Yibin 644007, China

Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com

Funds: Project supported by the Pre-Research Project of Yibin University, China (Grant No. 2019YY06), the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University, China (Grant No. YBXYJSWL-ZD-2020-001), and the Cultivation Project of Yibin University, China (Grant No. 2021PY71).

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References

[1]	Dixon R N, Duxbury G, Lamberton H M 1968 Proc. R. Soc. London, Ser. A. 305 271 Google Scholar
[2]	Arens M, Richter W 1990 J. Chem. Phys. 93 7094 Google Scholar
[3]	Beutel M, Setzer K D, Shestakov O, Fink E H 1996 J. Mol. Spectrosc. 178 165 Google Scholar
[4]	Pettersson L G, Langhoff S R 1986 J. Chem. Phys. 85 3130 Google Scholar
[5]	Matsushita T, Marian C M, Klotz R, Peyerimho S D 1987 Can. J. Phys. 65 155 Google Scholar
[6]	Balasubramanian K, Nannegari V 1989 J. Mol. Spectrosc. 138 482 Google Scholar
[7]	Shi D H, Liu H, Sun J F, Zhang J P, Liu Y F, Zhu Z L 2009 J. Mol. Struct. 911 8 Google Scholar
[8]	Bian W S, Li D H, Cao J W, Ma H T 2022 Phys. Chem. Chem. Phys. 24 10114 Google Scholar
[9]	赵东锋, 秦成兵, 张群, 陈旸 2009 科学通报 54 3190 Google Scholar Zhao D F, Qin C B, Zhang Q, Chen Y 2009 Chin. Sci. Bull. 54 3190 Google Scholar
[10]	Wan M J, Zhang Y G, Song C Q, Gao Tao 2008 J. Phys. B:At. Mol. Opt. Phys. 41 215102 Google Scholar
[11]	Yang C L, You Y, Wang M S, Ma X G, Liu W W 2015 Phys. Rev. A 92 032502 Google Scholar
[12]	Bruna P J, Hirsch G, Peyerimhoff S D, Buenker R J 1981 Mol. Phys. 42 875 Google Scholar
[13]	Li G X, Gao T, Zhang Y G 2008 Chin. Phys. B 17 2040 Google Scholar
[14]	Yan B, Zhang X, Li X 2015 Spectrochim. Acta, Part A 142 1 Google Scholar
[15]	邢伟, 孙金锋, 施德恒, 朱遵略 2018 67 193101 Google Scholar Xing W, Sun J F, Shi D H, Zhu Z L 2018 Acta Phys. Sin. 67 193101 Google Scholar
[16]	滑亚文, 刘以良, 万明杰 2020 69 153101 Google Scholar Hua Y W, Liu Y L, Wan M J 2020 Acta Phys. Sin. 69 153101 Google Scholar
[17]	高峰, 张红, 张常哲, 赵文丽, 孟庆田 2021 70 153301 Google Scholar Gao F, Zhang H, Zhang C Z, Zhao W L, Meng Q T 2021 Acta Phys. Sin. 70 153301 Google Scholar
[18]	Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010.1)
[19]	Dunning Jr. T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[20]	Peterson K A, Yousaf K E 2010 J. Chem. Phys. 133 174116 Google Scholar
[21]	Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053 Google Scholar
[22]	Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259 Google Scholar
[23]	Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803 Google Scholar
[24]	Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514 Google Scholar
[25]	Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61 Google Scholar
[26]	Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823 Google Scholar
[27]	Le Roy R J 2007 LEVEL 8.0: a Computer Program for Solving the Radial Schröinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[28]	Moore C E 1971 Atomic Energy Levels vol. Ⅱ (Washington, DC: US Govt Printing Office) p144
[29]	Huber K, Herzberg G 1979 Molecular Spectra and Molecular Structure Vol. 4. Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) p460
[30]	Tarroni R, Palmieri P, Mitrushenkov A, Tosi P, Bassi D 1997 J. Chem. Phys. 106 10265 Google Scholar
[31]	Colin R 1989 J. Mol. Spectrosc. 136 387 Google Scholar
[32]	Li R, Zhai Z, Zhang X M, Jin M X, Xu H F, Yan B 2015 J. Quant. Spectrosc. Radiat. Transfer 157 42 Google Scholar
[33]	Xiao L D, Liu Y, Li R, Xiao Z Y, Yan B 2021 J. Quant. Spectrosc. Radiat. Transfer 266 107593 Google Scholar

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图 1 AsH⁺离子X²Π, a⁴Σ^–, A²Σ^–, b⁴Π, B²Δ, C²Σ⁺, D²Π和2²Σ⁺态的势能曲线

Figure 1. Potential energy curves of the X²Π, a⁴Σ^–, A²Σ^–, b⁴Π, B²Δ, C²Σ⁺, D²Π and 2²Σ⁺ states of AsH⁺ cation.

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图 2 电子态之间的自旋-轨道矩阵元.

Figure 2. Spin-orbit matrix elements of the AsH⁺ anion.

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图 3 Ω态的势能曲线

Figure 3. Potential energy curves of the Ω states of AsH⁺ cation.

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图 4 Ω态的偶极矩

Figure 4. Dipole moments of the Ω states of AsH⁺ cation.

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图 5 AsH⁺离子的跃迁偶极矩

Figure 5. Transition dipole moments of AsH⁺ cation.

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表 1 AsH⁺离子Λ-S态的离解关系

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

原子态	Λ-S态	ΔE/cm^–1
原子态	Λ-S态	本文工作	实验值^[28]
As⁺(³P_g)+H(²S_g)	X²Π, a⁴Σ^–, A²Σ^–, b⁴Π	0	0
As⁺(¹D_g)+H(²S_g)	B²Δ, C²Σ⁺, D²Π	8222.18	8752
As⁺(¹S_g)+H(²S_g)	2²Σ⁺	20400.69	21252

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表 2 Λ-S的光谱常数

Table 2. Spectroscopic parameters of the Λ-S states.

Λ-S states	R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/eV	T_e/cm^–1
X²∏	1.5131	2222.58	42.08	7.3632	3.100	0
a⁴Σ^–	1.6211	1433.42	52.39	6.4528	1.208	15260.18
A²Σ^–	2.0523	598.03	35.70	4.0257	0.313	22481.02
b⁴∏	3.9651	111.89	27.81	1.1024	0.015	24885.54
B²Δ	1.7260	1139.52	49.11	5.6847	0.821	26654.73
C²Σ⁺	3.2885	140.54	22.86	1.6101	0.028	32911.82
D²∏	3.3767	172.32	29.15	1.5005	0.035	32993.70
2²Σ⁺	2.4140	532.54	47.36	2.9263	0.188	43887.70

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表 3 第五主族氢化物离子的光谱常数对比

Table 3. Comparison of the spectroscopy parameters of the Ⅴ-group hydride cations.

分子离子	Λ-S态	R_e/Å	ω_e/cm^–1	D_e/eV	T_e/cm^–1
NH⁺	X²∏	1.080^a	2810.6^a	4.40^a	0
	a⁴Σ^–	～1.105^b	～2520^b	3.66^c	509^d
	A²Σ^–	1.206^a	1578.2^a	1.76^a	22161.27^a
	B²Δ	1.161^a	2011.2^a	3.25^a	23331^a
PH⁺	X²∏	1.4226^e	2412.79^e	3.525^e	0
	a⁴Σ^–	1.4816^e	1832.51^e	1.790^e	13998^e
	A²Σ^–	1.7914^e	823.68^e	0.490^e	24476^e
	B²Δ	1.5454^e	1512.20^e	1.277^e	26322^e
AsH⁺	X²∏	1.5131^f	2222.58^f	3.100^f	0
	a⁴Σ^–	1.6211^f	1433.42^f	1.208^f	15260.18^f
	A²Σ^–	2.0523^f	598.03^f	0.313^f	22481.02^f
	B²Δ	1.7260^f	1139.52^f	0.188^f	43887.70^f
注: ^a文献[10] , ^b文献[29] , ^c文献[30] , ^d文献[31] , ^e文献[14], ^e本文计算值.

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表 4 AsH⁺离子Ω态的离解关系

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

原子态	Ω态	ΔE/cm^–1
原子态	Ω态	本文工作	实验值^[28]
As⁺(³P₀)+H(²S_1/2)	1/2	0	0
As⁺(³P₁)+H(²S_1/2)	3/2, 1/2, 1/2	1090.35	1061
As⁺(³P₂)+H(²S_1/2)	5/2, 3/2, 3/2, 1/2, 1/2	2721.66	2540
As⁺(¹D₂)+H(²S_1/2)	5/2, 3/2, 3/2, 1/2, 1/2	11252.94	10093
As⁺(¹S₀)+H(²S_1/2)	1/2	24909.88	22593

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表 5 Ω的光谱常数

Table 5. Spectroscopic parameters of the Ω states.

Ω states		R_e /Å	ω_e /cm^–1	ω_eχ_e /cm^–1	B_e /cm^–1	D_e /eV	T_e /cm^–1
$ {{{\rm{X}}^2}}{\Pi _{1/2}} $		1.5146	2339.14	41.99	7.3592	3.314	0
$ {{{\rm{X}}^2}}{\Pi _{3/2}} $		1.5121	2344.11	42.99	7.3647	3.216	1696.92
$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - $		1.6222	1535.88	58.51	6.4447	1.248	17777.19
$ {{{\rm{a}}^4}}\Sigma _{3/2}^ - $		1.6210	1688.21	69.69	6.4554	1.249	17910.08
$ {{{\rm{A}}^2}}\Sigma _{1/2}^ - $		2.0581	685.64	35.99	3.9976	0.400	25773.03
$ {{{\rm{B}}^2}}{\Delta _{3/2}} $	第一势阱	1.7285	1175.34	58.14	5.6857	0.321	30513.22
$ {{{\rm{B}}^2}}{\Delta _{3/2}} $	第二势阱	3.2405	333.26	49.99	1.7215	0.076	28497.77
$ {{{\rm{B}}^2}}{\Delta _{5/2}} $	第一势阱	1.7259	1186.52	51.97	5.6923	0.356	30548.89
$ {{{\rm{B}}^2}}{\Delta _{5/2}} $	第二势阱	3.3318	283.60	49.29	1.5654	0.055	29071.95

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表 6 AsH⁺离子的弗兰克-康登因子(单位: s^-1)、总自发辐射速率和自发辐射寿命(单位: μs)

Table 6. Franck-Condon Factors, spontaneous emission rates (unit of s^-1) and spontaneous radiative lifetimes τ (unit of μs) of the AsH⁺ cation.

跃迁	ν′	ν″ = 0	ν″ = 1	ν″ = 2	ν″ = 3	ν″ = 4	ν″ = 5	ΣA	τ = 1/ΣA
A²Σ^– ↔ X²Π	0	0.0056	0.0280	0.0722	0.1275	0.1715	0.1843
A²Σ^– ↔ X²Π	0	2295.52	5374.75	6276.27	4791.31	2627.48	1065.87	22838.76	43.75
$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $	0	0.6817	0.2447	0.0613	0.0107	0.0014	0.0001
	0	1545.42	319.72	60.84	8.08	0.74	0.04	1934.85	517
$ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $	0	0.0041	0.0216	0.0588	0.1098	0.1565	0.1789
	0	3036.67	7910.09	10373.6	8987.8	5672.57	2703.67	40012.76	24.99

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map

[1]	Dixon R N, Duxbury G, Lamberton H M 1968 Proc. R. Soc. London, Ser. A. 305 271 Google Scholar
[2]	Arens M, Richter W 1990 J. Chem. Phys. 93 7094 Google Scholar
[3]	Beutel M, Setzer K D, Shestakov O, Fink E H 1996 J. Mol. Spectrosc. 178 165 Google Scholar
[4]	Pettersson L G, Langhoff S R 1986 J. Chem. Phys. 85 3130 Google Scholar
[5]	Matsushita T, Marian C M, Klotz R, Peyerimho S D 1987 Can. J. Phys. 65 155 Google Scholar
[6]	Balasubramanian K, Nannegari V 1989 J. Mol. Spectrosc. 138 482 Google Scholar
[7]	Shi D H, Liu H, Sun J F, Zhang J P, Liu Y F, Zhu Z L 2009 J. Mol. Struct. 911 8 Google Scholar
[8]	Bian W S, Li D H, Cao J W, Ma H T 2022 Phys. Chem. Chem. Phys. 24 10114 Google Scholar
[9]	赵东锋, 秦成兵, 张群, 陈旸 2009 科学通报 54 3190 Google Scholar Zhao D F, Qin C B, Zhang Q, Chen Y 2009 Chin. Sci. Bull. 54 3190 Google Scholar
[10]	Wan M J, Zhang Y G, Song C Q, Gao Tao 2008 J. Phys. B:At. Mol. Opt. Phys. 41 215102 Google Scholar
[11]	Yang C L, You Y, Wang M S, Ma X G, Liu W W 2015 Phys. Rev. A 92 032502 Google Scholar
[12]	Bruna P J, Hirsch G, Peyerimhoff S D, Buenker R J 1981 Mol. Phys. 42 875 Google Scholar
[13]	Li G X, Gao T, Zhang Y G 2008 Chin. Phys. B 17 2040 Google Scholar
[14]	Yan B, Zhang X, Li X 2015 Spectrochim. Acta, Part A 142 1 Google Scholar
[15]	邢伟, 孙金锋, 施德恒, 朱遵略 2018 67 193101 Google Scholar Xing W, Sun J F, Shi D H, Zhu Z L 2018 Acta Phys. Sin. 67 193101 Google Scholar
[16]	滑亚文, 刘以良, 万明杰 2020 69 153101 Google Scholar Hua Y W, Liu Y L, Wan M J 2020 Acta Phys. Sin. 69 153101 Google Scholar
[17]	高峰, 张红, 张常哲, 赵文丽, 孟庆田 2021 70 153301 Google Scholar Gao F, Zhang H, Zhang C Z, Zhao W L, Meng Q T 2021 Acta Phys. Sin. 70 153301 Google Scholar
[18]	Werner H J, Knowles P J, Knizia G, et al. 2010 MOLPRO, a Package of ab initio Programs (version 2010.1)
[19]	Dunning Jr. T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[20]	Peterson K A, Yousaf K E 2010 J. Chem. Phys. 133 174116 Google Scholar
[21]	Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053 Google Scholar
[22]	Knowles P J, Werner H J 1985 Chem. Phys. Lett. 115 259 Google Scholar
[23]	Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803 Google Scholar
[24]	Knowles P J, Werner H J 1988 Chem. Phys. Lett. 145 514 Google Scholar
[25]	Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61 Google Scholar
[26]	Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823 Google Scholar
[27]	Le Roy R J 2007 LEVEL 8.0: a Computer Program for Solving the Radial Schröinger Equation for Bound and Quasibound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[28]	Moore C E 1971 Atomic Energy Levels vol. Ⅱ (Washington, DC: US Govt Printing Office) p144
[29]	Huber K, Herzberg G 1979 Molecular Spectra and Molecular Structure Vol. 4. Constants of Diatomic Molecules (New York: Van Nostrand Reinhold) p460
[30]	Tarroni R, Palmieri P, Mitrushenkov A, Tosi P, Bassi D 1997 J. Chem. Phys. 106 10265 Google Scholar
[31]	Colin R 1989 J. Mol. Spectrosc. 136 387 Google Scholar
[32]	Li R, Zhai Z, Zhang X M, Jin M X, Xu H F, Yan B 2015 J. Quant. Spectrosc. Radiat. Transfer 157 42 Google Scholar
[33]	Xiao L D, Liu Y, Li R, Xiao Z Y, Yan B 2021 J. Quant. Spectrosc. Radiat. Transfer 266 107593 Google Scholar

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Electronic structures and transition properties of AsH⁺ cation

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Electronic structures and transition properties of AsH+ cation

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Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com

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Electronic structures and transition properties of AsH⁺ cation