Spectroscopic and transition properties of SeH<sup>–</sup> anion including spin-orbit coupling

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Abstract

Potential energy curves (PECs), permanent dipole moments (PDMs) and transition dipole moments (TMDs) of five Λ-S states of SeH ⁻anion are calculated by the MRCI + Qmethod with ACVQZ-DK basis set. The core-valence corrections, Davidson corrections, scalar relativistic corrections, and spin-orbit coupling (SOC) effects are also considered. In the CASSCF step, Se(1s2s2p3s3p) shells are put into the frozen orbitals, which are not optimized. Six molecular orbitals are chosen as active space, including H(1s) and Se(4s4p5s) shells, and eight electrons are distributed in a (4, 1, 1, 0) active space, which is referred to as CAS (8, 6), and the Se(3d) shell is selected as a closed-shell, which keeps doubly occupation. In the MRCI step, the remaining Se(3d) shell is used for core-valence calculations of SeH ⁻anion. The SOC effects are taken into account in the one- and two- electron Breit-Pauli operators. The b ³Σ ⁺state is a repulsive state. Other excited states are bound, and all states possess two potential wells. The $ {{\rm{b}}^{{3}}}\Sigma _{{0^ - }}^ + $ and $ {{\rm{b}}^3}\Sigma _{{1}}^ + $ both turn into bound states when the SOC effect is considered. All spectroscopic parameters of Λ-S states and Ω states are reported for the first time. The TDMs of the $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ , $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ , $ {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ , $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{1}}}$ , and $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$ transitions are also calculated. The TDMs of the $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ and $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ transitions are large in the Franck-Condon region, which are about –2.05 Debye (D) and 1.45 D at R _e. Notably, the TDMs of the $ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $ transition cannot be ignored. The value of TDM at R _eequals –0.15 D. Based on the accurately PECs and PDMs, the values of Franck-Condon factor f _υ′υ″, vibrational branching ratio R _υ′υ″and radiative coefficient of the $ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ , $ {{\rm{a}}^{{3}}}{{{\Pi }}_{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^{{1}}}{{\Sigma }}_{{0^ + }}^ + $ , and $ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $ transitions are also calculated. Highly diagonally distributed Franck-Condon factor f ₀₀and the values of vibrational branching ratio R ₀₀of the $ {{\rm{a}}^{{3}}}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ , $ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ , and $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transitions are obtained, respectively. Spontaneous radiation lifetimes of the $ {{\rm{a}}^3}{\Pi _{{1}}}$ , $ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$ , and $ {{\rm{A}}^1}{\Pi _{{1}}}$ excited states are all short for rapid laser cooling. The influences of intervening states of the $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transition can be ignored. The proposed cooling wavelengths using the $ {{\rm{a}}^3}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + (\upsilon '')$ , $ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ , and $ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$ transitions are all in the visible region.

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Authors and contacts

Corresponding author:Huang Duo-Hui,hdhzhy912@163.com

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

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Λ-S态	来源		R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/eV	T_e/cm^–1
X¹Σ⁺	ACVQZ-DK		1.4694	2300.77	46.10	7.8507	3.487	0
	AVQZ-DK		1.4614	2380.32	45.57	7.9326	3.711
	实验^[17]		1.4696^a			7.7289^c
	实验^[17]		1.4806^b			7.7289^c
a³Π	本文工作	第一势阱	1.4778	2206.52	123.45	7.8428	0.519	20642.90
a³Π	本文工作	第二势阱	2.1787	839.87	49.66	3.44016	0.450	24549.11
A¹Π	本文工作	第一势阱	1.4726	2373.65	127.14	7.8391	0.734	21240.75
A¹Π	本文工作	第二势阱	2.2780	437.62	44.07	3.0932	0.147	26997.57
b³Σ⁺	本文工作		repulsive
2¹Σ⁺	本文工作	第一势阱	1.6188	1336.45	—	6.1955	0.228	51684.73
2¹Σ⁺	本文工作	第二势阱	4.0808	198.90	9.96	1.0190	0.135	46349.30
注:^a为SeH分子基态的平衡核间距的实验值来源于文献[18];^b为SeH分子基态的平衡核间距的实验值来源于文献[33], 结果不准确; ^c为采用最小二乘法得到转动惯量B.

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阴离子	来源	R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/eV
OH^–	文献[14]	0.9645	3722.10	87.93	19.1111	4.9857
SH^–	文献[15]	1.3435	2622.04	46.66	9.5590	3.8793
SeH^–	本文工作	1.4694	2300.77	46.10	7.8507	3.487
TeH^–	文献[16]	1.6631	1973.73	36.8272	6.0996	3.0568

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离解通道	分子态(Ω)	相对能量/cm^–1
离解通道	分子态(Ω)	ACVQZ-DK	AVQZ-DK	实验^[34-36]
Se^–(²P_3/2) + H(²S_1/2)	2, 1, 1, 0⁺, 0^–	0	0	0
Se^–(²P_1/2) + H(²S_1/2)	1, 0⁺, 0^–	2303.77	2192.98	—
Se(¹D₂) + H^–(¹S₀)	0⁺	20032.24	19047.45	19790.88

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Ω态		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}}^1}\Sigma _{{0^ + }}^ + $		1.4694	2301.31	47.01	7.8499	3.395	0
${{\rm{a}}^3}{\Pi _2}$	第一势阱	1.4777	2207.22	122.39	7.8416	0.523	19787.17
${{\rm{a}}^3}{\Pi _2}$	第二势阱	2.1739	861.02	52.10	3.4081	0.454	23751.54
${{\rm{a}}^3}{\Pi _{{1}}}$	第一势阱	1.4759	2232.16	111.70	7.8434	0.560	20036.27
${{\rm{a}}^3}{\Pi _{{1}}}$	第二势阱	2.1822	818.11	55.64	3.3929	0.386	24301.10
${{\rm{a}}^3}{\Pi _{{{{0}}^ - }}}$	第一势阱	1.4778	2205.83	124.97	7.8485	0.513	21472.52
${{\rm{a}}^3}{\Pi _{{{{0}}^ - }}}$	第二势阱	2.1986	778.28	73.70	3.4048	0.267	25261.96
${{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$	第一势阱	1.4777	2208.03	122.90	7.8422	0.522	21477.12
${{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$	第二势阱	2.1619	904.15	49.02	3.4355	0.527	25454.22
${{\rm{A}}^1}{\Pi _{{1}}}$	第一势阱	1.4744	2368.50	144.22	7.8262	0.686	21821.04
${{\rm{A}}^1}{\Pi _{{1}}}$	第二势阱	排斥态
${{\rm{b}}^3}\Sigma _{{0^ - }}^ + $	第一势阱	3.1807	318.89	35.64	1.6988	0.096	28945.41
${{\rm{b}}^3}\Sigma _{{1}}^ + $	第二势阱	3.2046	239.13	30.94	1.6662	0.066	29184.63
${2^1}\Sigma _{{0^ + }}^ + $	第一势阱	1.6190	1332.50	—	6.1895	0.225	51714.58
${2^1}\Sigma _{{0^ + }}^ + $	第二势阱	4.0800	190.57	8.84	1.0190	0.135	46351.94

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Index		${{\rm{a}}^3}{\Pi _{{1}}} \leftrightarrow $ ${{\rm{X}}^1}\Sigma _{{0^ + }}^ + $	${{\rm{a}}^{{3}}}{\Pi _{{0^ + }}} \leftrightarrow $ ${{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $	${{\rm{A}}^1}{\Pi _1} \leftrightarrow$ $ {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $
${f_{\upsilon '\upsilon ''}}$	f₀₀	0.9949	0.9922	0.9974
	f₀₁	0.0047	0.0072	0.0025
	f₀₂	0.0004	0.0006	0.0001
	f₁₀	0.0051	0.0079	0.0026
	f₁₁	0.9541	0.9324	0.9792
	f₁₂	0.0337	0.0486	0.0159
${A_{\upsilon '\upsilon ''}}\rm /s$	A₀₀	5.02×10⁶	8.02×10⁴	1.36×10⁷
	A₀₁	1.88×10²	4.28×10³	1.87×10⁴
	A₀₂	2.81×10¹	7.48×10¹	2.00×10³
	A₁₀	1.10×10⁵	6.50×10²	5.79×10⁴
	A₁₁	4.13×10⁶	9.13×10⁴	1.32×10⁷
	A₁₂	1.32×10⁴	1.57×10⁴	1.45×10⁵
${R_{\upsilon '\upsilon ''}}$	R₀₀	0.99996	0.9484	0.9985
	R₀₁	3.7×10^–5	0.0506	0.0014
	R₀₂	5.6×10^–6	0.0009	0.0001
	R₁₀	0.02592	0.0060	0.0043
	R₁₁	0.9707	0.8394	0.9836
	R₁₂	0.0031	0.1446	0.0108

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Vol. 70, Issue 3 - 2021-02-05

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