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

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Abstract

Potential energy curves (PECs), dipole moments (DMs) and transition dipole moments (TDMs) of the X ²Π, a ⁴Σ ^–, A ²Σ ^–, b ⁴Π, B ²Δ, C ²Σ ⁺, D ²Π, 2 ²Σ ⁺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 X ²Π is the ground state, which is a deep potential well, the dissociation energy is 3.100 eV. The b ⁴Π, C ²Σ ⁺and D ²Π 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 b ⁴Π state and the PEC of B ²Δ 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.

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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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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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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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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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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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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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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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Vol. 71, Issue 21 - 2022-11-05

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