Spectroscopic and transition properties of LiCl<sup>–</sup> anion

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Abstract

The electronic structure of the X ²Σ ⁺, A ²Π, B ²Σ ⁺, 3 ²Σ ⁺, and 2 ²Π state of LiCl ^–anion are performed at an MRCI+Q level. Davison correction, core-valence correction and spin-orbit coupling effect are also considered. The ground state X ²Σ ⁺of LiCl ^–anion correlates with the lowest dissociation channel Li( ²S _g) + Cl ^–( ¹S _g); the A ²∏ state and B ²Σ ⁺state correlate with the second dissociation channel Li( ²P _u) + Cl ^–( ¹S _g); the 3 ²Σ ⁺state and 2 ²Π state correlate with the third dissociation channel Li ^–( ¹S _g) + Cl ^–( ²P _u). Spectroscopic parameters are calculated by solving the radial Schröedinger equation. The equilibrium internuclear distance R _eof the ground state X ²Σ ⁺is 2.1352 Å, which is a little bigger than the experimental datum, with an error being 0.5%. It is a deep potential well, and the dissociation energy D _eis 1.886 eV. These values are in good agreement with experimental data. The A ²∏ state is at 13431.93 cm ^–1above the X ²Σ ⁺state. The R _eis 2.1198 Å, which is only 0.0154 Å smaller than that of the X ²Σ ⁺state. The values of energy level G _νand rotational constant B _νof five Λ-S states are also calculated. The values are in good agreement with available theoretical ones. The electronic structures of the excited states are also reported. The SOC effect weakly influences the spectroscopic parameters for the $ {\text{X}}{}^2\Sigma _{1/2}^ + $ , $ {\text{A}}{}^2{\Pi _{1/2}} $ , $ {\text{A}}{}^2{\Pi _{3/2}} $ , and $ {\text{B}}{}^2\Sigma _{1/2}^ + $ state. From the analysis of the SO matrix, it can be seen that the SOC effect plays a little role in realizing the A ²Π $\leftrightarrow $ X ²Σ ⁺transition, so, it can be ignored. The scheme of laser cooling of LiCl ^–anion has constructed at a spin – free level. The A ²∏( ν ′) $\leftrightarrow $ X ²Σ ⁺( $v'' $ ) transition has a highly diagonally distributed Franck-Condon factor f ₀₀= 0.9898, the calculated branching ratio of the diagonal term R ₀₀is 0.9893, and spontaneous radiative lifetime of A ²∏ is 35.45 ns. A main pump laser and two repumping lasers for driving the A ²∏( ν ′) $\leftrightarrow $ X ²Σ ⁺( $v'' $ ) transitions are required. The laser wavelengths are 744.10, 774.30 and 772.42 nm, respectively. Owing to the summation of R ₀₀, R ₀₁, and R ₀₂being closer to 1, the A ²∏( ν ′) $\leftrightarrow $ X ²Σ ⁺( $v'' $ ) transition is a quasicycling transition. These results imply that the LiCl ^–anion is a candidate for laser cooling.

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Authors and contacts

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

Funds:Project supported by the National Undergraduate Training Program for Innovation， Entrepreneurship of Yibin University (Grant No. 202110641022) and 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 (Grant No. YBXYJSWL-ZD-2020-001)

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		ΔE/cm^–1
原子态	分子态	本文工作	实验值^[36–38]
Li(²S_g)+Cl^–(¹S_g)	X²Σ⁺	0	0
Li(²P_u)+ Cl^–(¹S_g)	A²Π, B²Σ⁺	14903.79	14253.13
Li^–(¹S_g)+Cl(²P_u)	3²Σ⁺, 2²Π	23703.61	24594.67

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电子态	R_e/Å	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	D_e/eV	D₀/eV	T_e/cm^–1
X²Σ⁺	2.1352	535.33	5.8173	0.7205	1.8886	1.856	0
实验值^[20]	2.18(4)						0
实验值^[21]	2.123(15)					1.75(2)	0
理论值^[22]	2.12^a						0
理论值^[23]	2.1354	537.7^b	6.34^b	0.7203^b		1.81	0
A²∏	2.1198	554.65	5.7157	0.7310	1.9902	1.9559	13431.93
B²Σ⁺	2.0282	652.79	6.1252	0.7985	1.6653	1.6250	17491.75
3²Σ⁺	5.8594	30.19	0.8483	0.0963	0.0362	0.0353	38607.64
2²∏	7.1411	39.08	0.5616	0.0638	0.0136	0.0112	38855.32
^a采用HF方法计算得到基态的核间距.

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ν	X²Σ⁺				A²∏		B²Σ⁺		3²Σ⁺		2²∏
	G_ν		B_ν		G_ν	B_ν	G_ν	B_ν	G_ν	B_ν	G_ν	B_ν
	本文工作	文献[23]	本文工作	文献[23]	本文工作	本文工作	本文工作	本文工作	本文工作	本文工作	本文工作	本文工作
0	266.72	264.07	0.7146	0.7143	276.48	0.7252	325.33	0.7927	14.96	0.0940	6.12	0.0631
1	790.93	791.77	0.7029	0.7023	820.21	0.7136	966.07	0.7811	43.02	0.0893	18.15	0.0618
2	1303.27	1307.01	0.6911	0.6903	1352.13	0.7021	1594.23	0.7697	68.84	0.0857	28.92	0.0572
3	1803.71	1809.92	0.6794	0.6784	1872.34	0.6907	2210.02	0.7584	93.22	0.0826	29.30	0.0095
4	2292.31	2300.65	0.6677	0.6666	2380.97	0.6793	2813.56	0.7471	116.24	0.0796	31.32	0.0112
5	2769.15	2779.34	0.6560	0.6548	2878.13	0.6680	3404.89	0.7359	138.17	0.0765	33.19	0.0125
6	3234.29	3246.11	0.6444	0.6430	3363.87	0.6567	3984.09	0.7247	158.98	0.0725	35.07	0.0140
7	3687.83	3701.10	0.6328	0.6313	3838.29	0.6455	4551.20	0.7135	178.26	0.0678	36.53	0.0310
8	4129.88	4144.45	0.6212	0.6197	4301.42	0.6343	5106.17	0.7023	195.60	0.0626	37.33	0.0257
9	4560.61	4576.29	0.6097	0.6081	4753.37	0.6231	5648.95	0.6911	210.77	0.0571	39.11	0.0188

DownLoad: CSV

		ΔE/cm^–1
原子态	分子态 Ω	本文工作	实验值^[36–38]
Li(²S_1/2)+Cl^–(¹S₀)	1/2	0	0
Li(²P_1/2)+ Cl^–(¹S₀)	1/2	14252.77	14903.62
Li(²P_3/2)+ Cl^–(¹S₀)	1/2, 3/2	14253.50	14903.96
Li^–(¹S₀)+Cl(²P_3/2)	1/2, 3/2	23415.41	24153.49
Li^–(¹S₀)+Cl(²P_1/2)	1/2	24288.48	25035.84

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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
$ {\text{X}}{}^2\Sigma _{1/2}^ + $	2.1352	535.32	5.8172	0.7205	1.8886	0
$ {\text{A}}{}^2{\Pi _{1/2}} $	2.1196	554.87	5.7153	0.7311	2.0094	13419.77
$ {\text{A}}{}^2{\Pi _{3/2}} $	2.1200	554.41	5.7160	0.7308	2.0059	13444.07
$ {\text{B}}{}^2\Sigma _{1/2}^ + $	2.0282	652.79	6.1253	0.7985	1.6679	17491.75

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SO矩阵元
$ {\text{S}}{{\text{O}}_1} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_2} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_3} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_4} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_5} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_6} = \left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_7} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_8} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_9} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{10}} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_{11}} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{12}} = \left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_{13}} = {\text{i}}\left\langle {{{\text{A}}^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{14}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{15}} = {\text{i}}\left\langle {{2^2}{\Pi _y}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_{16}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $

DownLoad: CSV

跃迁	f₀₀	f₀₁	f₀₂	f₀₃
	A₀₀	A₀₁	A₀₂	A₀₃	τ= 1/ΣA
	f₁₀	f₁₁	f₁₂	f₁₃
	A₁₀	A₁₁	A₁₂	A₁₃
A²∏ $\leftrightarrow $ X²Σ⁺	0.9898	0.0101	0.0001	8.70(–7)
	27904200	298313	3848.85	44.60	35.45
	0.0102	0.9686	0.0209	0.0004
	269660	27336600	607335	12332	35.43
B²Σ⁺$\leftrightarrow $ X²Σ⁺	0.5908	0.2909	0.0894	0.0225
	18316800	7658290	2038730	452210	34.99
	0.3266	0.1286	0.2888	0.1671
	12279600	4261780	7988480	3979390	33.00

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SO矩阵元
$ {\text{S}}{{\text{O}}_1} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_2} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_3} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_4} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_5} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_6} = \left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_7} = - {\text{i}}\left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_8} = \left\langle {{{\text{X}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_9} = - {\text{i}}\left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{10}} = \left\langle {{{\text{B}}^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_{11}} = - {\text{i}}\left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{12}} = \left\langle {{3^2}{\Sigma ^ + }} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _x}} \right\rangle $
$ {\text{S}}{{\text{O}}_{13}} = {\text{i}}\left\langle {{{\text{A}}^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{14}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _y}} \right\rangle $	$ {\text{S}}{{\text{O}}_{15}} = {\text{i}}\left\langle {{2^2}{\Pi _y}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{{\text{A}}^2}{\Pi _x}} \right\rangle $	$ {\text{S}}{{\text{O}}_{16}} = {\text{i}}\left\langle {{2^2}{\Pi _x}} \right\|\hat H_{{\text{SO}}}^{{\text{BP}}}\left\| {{2^2}{\Pi _y}} \right\rangle $

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