Spectral characteristics of low excited state of strontium monobromide molecule

Wu Dong-Lan; Guo Zi-Yi; Zhou Jun-Jie; Ruan Wen; Zeng Xue-Feng; Xie An-Dong

doi:10.7498/aps.71.20221052

Abstract

The electronic structures and single point energy of 14 lowest electronic states of ⁸⁸Sr⁷⁹Br molecule are optimized by using the internal contraction multi-reference configuration interaction method and relativistic effective core pseudo-potential basis. Because ⁸⁸Sr⁷⁹Br molecule belongs to heavy element system, the single point energy must be corrected to obtain more accurate spectral parameters. Therefore, Davidson is introduced to correct the energy inconsistency, nuclear valence correlation is used to correct the electron correlation effect of inner shell and valence shell, and the relativistic scalar effect is corrected by calculating the third-order Douglas-Kroll-Hess Hamilton single electron integral. According to the single point energy calculated by the modified optimization, the potential energy curves, electric dipole moments, and transition dipole moments of 14 lowest electronic states are obtained. Using the latest LEVEL8.0 program to fit the modified potential energy curve, the spectral constants, molecular constants and vibration energy levels of 5 lowest bound states of ⁸⁸Sr⁷⁹Br molecule are given. In order to explain the changing trend of spectral constants of homologous compounds, the spectral parameters of each compound are compared and analyzed in this paper. At the same time, the vibration energy levels and molecular constants of ⁸⁸Sr⁸¹Br molecule are also fitted and calculated for analyzing the influence of isotopes. The comparative analysis shows that the results of ⁸⁸Sr⁷⁹Br molecule are in better agreement with the experimental values. Finally, the Franck-Condon factors are gained by fitting the optimized single point energy and transition dipole moment of ⁸⁸Sr⁷⁹Br molecule. The transition band with the largest factor and obvious diagonalization is selected by analyzing the Franck-Condon factor of each transition band, and whether it meets the conditions for selecting laser cooling molecular system is judged. The radiation lifetimes of the transitions from the lowest two excited states to the ground state are calculated by combining the transition dipole moment, Franck-Condon factor, single point energy and vibration energy level of each electronic state. The results of this paper are in good agreement with the experimental values, which shows that the method in this paper is reliable. These spectral characteristic parameters provide theoretical support for further experimental measurement and construction of molecular laser cooling scheme of ⁸⁸Sr⁷⁹Br molecule.

Keywords:

Authors and contacts

College of Mathematic and Physical, Jinggangshan University, Ji’an 343009, China

Corresponding author: Wu Dong-Lan, wudonglan1216@sina.com

Funds: Project supported by the National Natural Science Foundation of China (Grand Nos. 11564019, 11147158), and Jiangxi Provincial Education Department Project, China (Grand No. GJJ211015).

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References

[1]	Yang C L, Zhang X Y, Gao F, Ren T Q 2007 J. Mol. Struct. THEOCHEM 807 147 Google Scholar
[2]	Wang C, Li N, Xia Y, Zhang X, Ge M, Liu Y, Li Q 2011 Comput. Theor. Chem. 963 319 Google Scholar
[3]	Short C I, Hauschildt P H 2006 Astrophys. J. 641 494 Google Scholar
[4]	Carlson K D, Claydon C R 1967 Adv. High Temp. Chem. 1 43 Google Scholar
[5]	Hansen C J, Bergemann M, Cescutti G, Francois P, Arcones A, Karakas A I, Lind K, Chiappini C 2013 Astron. Astrophys. 551 1 Google Scholar
[6]	Bergemann M, Hansen C J, Bautista M, Ruchti G 2012 Astron. Astrophys. 546 1 Google Scholar
[7]	Caffau E, Andrievsky S, Korotin S, Origlia L, Oliva E, Sanna N, Ludwig H G, Bonifacio P 2016 Astron. Astrophys. 585 44 Google Scholar
[8]	Törring T, Doebl K, Weiler G 1985 Chem. Phys. Lett. 117 539 Google Scholar
[9]	Ernst W E, Schröder J O 1986 Z. Phys. D:At. Mol. Clusters 1 103 Google Scholar
[10]	Keijzer F, Teule J M, Bulthuis J, de Graaff G J, Hilgeman M H, Janssen M H M, van Kleef E H, van Leuken J J, Stolte S 1996 Chem. Phys. 207 261 Google Scholar
[11]	Coxon J A, Dickinson C S 1998 J. Mol. Spectrosc. 190 150 Google Scholar
[12]	Gurvich L V, Ryabova V G, Khitrov A N 1973 Faraday Symp. Chem. Soc. 8 83 Google Scholar
[13]	Hildenbrand D L 1977 J. Chem. Phys. 66 3526 Google Scholar
[14]	Ernst W E, Schröder J O 1986 J. Mol. Spectrosc. 117 444 Google Scholar
[15]	Dickinson C S, Coxon J A 2003 J. Mol. Spectrosc. 221 269 Google Scholar
[16]	Schröder J O, Ernst W E 1985 J. Mol. Spectrosc. 112 413 Google Scholar
[17]	Castano F, Sanchez Rayo M N, Pereira R, Adams J W, Husain D, Schiﬁno J 1994 J. Photochem. Photobiol. , A 83 79 Google Scholar
[18]	Gunduz S, Akman S 2014 Microchem. J. 116 1 Google Scholar
[19]	Werner H J, Knowles P J, Knizia G, et al. 2012 MOLPRO, version 2012.1, a package of ab initio Programs
[20]	Peterson K A, Figgen D, Goll E, Stoll H, Dolg M 2003 J. Chem. Phys. 119 11099 Google Scholar
[21]	Werner H-J, Knowles P 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]	Le Roy R J 2007 LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasi-bound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[26]	Wu D L, Tan B, Wen Y F, Zeng X F, Xie A D, Yan B 2016 Spectrochim. Acta, Part A 161 101 Google Scholar
[27]	Fu M K, Ma H T, Cao J W, Bian W S 2017 J. Chem. Phys. 146 134309 Google Scholar
[28]	Adema Z, Makhlouf S, Taher F 2016 Comput. Theor. Chem. 1093 48 Google Scholar
[29]	Liu L, Yang C L, Wang M S, Ma X G, Sun Z P 2019 Spectrochim. Acta, Part A 164 162 Google Scholar
[30]	Huber K P, Herzberg G 1979 Constants of Diatonic Molecules, Molecular spectra molecular structure (Vol. IV) (NewYork: Van Nostrand Reinhold)
[31]	Wu D L, Lin C Q, Wen Y F, Xie A D, Yan B 2017 Chin. Phys. B 594 083101 Google Scholar
[32]	魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 65 163101 Google Scholar Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta. Phys. Sin. 65 163101 Google Scholar
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[35]	Zou W L, Liu W J 2005 J. Comput. Chem. 26 106 Google Scholar
[36]	Bahrini C, Augé-Rochereau F, Rostas J, Taïeb G 2006 Chem. Phys. 330 130 Google Scholar

Cited By

图 1 ⁸⁸Sr⁷⁹Br分子5个激发态的势能曲线

Figure 1. The potential energy curves of 5 lowest electronic states of ⁸⁸Sr⁷⁹Br.

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图 2 ⁸⁸Sr⁷⁹Br分子5个束缚态的电偶极矩

Figure 2. The permanent dipole moments of 5 lowest electronic states of ⁸⁸Sr⁷⁹Br.

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图 3 ⁸⁸Sr⁷⁹Br分子5个束缚态的跃迁偶极矩

Figure 3. The transition dipole moments of 5 bound states of ⁸⁸Sr⁷⁹Br.

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表 1 5个束缚态的光谱常数

Table 1. The spectroscopic constants of the 5 lowest electronic states.

Λ-S 态	T_e/cm^–1	R_e/nm	ω_e/cm^–1	ω_eχ_e/cm^–1	B_e/cm^–1	α_e/(10^–4cm^–1)	D_e/eV	R_e附近主要电子组态/%
X²Σ⁺	0.0	0.2740	216.17	0.499	0.0538	1.731	3.310	11σ²12σ^α13σ⁰6π⁴7π²(80.2) 11σ²12σ⁰13σ^α6π⁴7π²(6.9)
理论^[28]	0.0	0.2746	212.78	0.509	0.0535	—	—
理论^[29]	0.0	0.2799	205.6	0.53	0.051	1.742	—
实验^[30]	0.0	0.2735	216	0.51	0.0541	—	—
A²Π	14679.348	0.2701	222.38	0.5346	0.0549	1.213	1.334	11σ²12σ⁰13σ⁰6π⁴7π³(86.1)
理论^[28]	14657	0.272	220	0.57	0.0544	—	—
理论^[29]	14269.9	0.275	215.1	0.54	0.052	1.241	—
实验^[30]	14850	0.2717	222	0.53	0.0545	—	—
B²Σ⁺	15376.803	0.2702	223.03	0.5272	0.0552	1.799	1.597	11σ²12σ⁰13σ^α6π⁴7π²(79.2) 11σ²12σ^α13σ⁰6π⁴7π²(6.1)
理论^[28]	15208	0.2710	220.5	0.52	0.0547	—	—
理论^[29]	15222.8	0.2749	214.5	0.56	0.053	1.831	—
实验^[30]	15352	0.2701	222	0.53	0.0552	—	—
C²Π	24947.818	0.3373	201.07	0.5012	0.0515	2.369	1.500	11σ²12σ²13σ⁰6π³7π³(80.0) 11σ²12σ⁰13σ⁰6π⁴7π³(2.2) 11σ²12σ⁰13σ⁰6π³7π⁴(2.8) 11σ^α12σ^α13σ⁰6π⁴7π³(2.7)
理论^[28]	25491	0.2810	197	0.49	0.0509	—	—
理论^[29]	25323.2	0.285	191.2	0.46	0.049	2.477	—
实验^[30]	24665	—	205	0.49	—	—	—
3²Σ⁺	29079.756	0.3548	238.98	0.4556	0.0542	1.653	1.109	11σ²12σ^α13σ⁰6π⁴7π²(1.3) 11σ^α12σ²13σ⁰6π⁴7π²(69.4) 11σ²12σ⁰13σ^α6π⁴7π²(5.3) 11σ²12σ^α13σ⁰6π³7π³(2.9) 11σ²12σ⁰13σ^α6π⁴7π¹(.9)
理论^[28]	28117	0.266	242	0.54	0.0567	—	—
理论^[29]	27228.9	0.27	235.8	0.54	0.055	1.660	—
实验^[30]	28958	—	247	0.55	—	—	—

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表 2 ⁸⁸Sr⁷⁹Br分子5个束缚态的G_ν, B_ν和D_ν值

Table 2. The values of G_ν, B_ν and D_ν of 5 lowest electronic states for ⁸⁸Sr⁷⁹Br molecule.

	ν	0	1	2	3	4	5	6	7	8	9
X²Σ⁺	G_ν/cm^–1	0	217.21	422.31	648.92	863.52	1077.13	1289.84	1501.60	1712.39	1922.24
	B_ν/cm^–1	0.054170	0.054003	0.053836	0.053663	0.053494	0.053330	0.053165	0.052997	0.052827	0.052659
	D_ν/(10^–8cm^–1)	1.299301	1.303053	1.284638	1.297713	1.299115	1.295311	1.296435	1.298790	1.296092	1.292529
A²Π	G_ν/cm^–1	14691.87	14934.23	15175.25	15415.96	15656.46	15896.12	16134.07	16369.73	16603.1	16834.89
	B_ν/cm^–1	0.055780	0.055620	0.055462	0.055295	0.055124	0.054976	0.054861	0.054772	0.054687	0.054578
	D_ν/(10^–8cm^–1)	1.347703	1.355108	1.331605	1.313371	1.331860	1.390480	1.454430	1.476056	1.452901	1.372534
B²Σ⁺	G_ν/cm^–1	15376.52	15507.84	15738.33	15967.89	16196.74	16425.06	16652.61	16878.97	17103.8	17327.04
	B_ν/cm^–1	0.055152	0.054998	0.054842	0.054679	0.054501	0.054326	0.054170	0.054020	0.053860	0.053722
	D_ν/(10^–8cm^–1)	1.383536	1.380925	1.382206	1.370045	1.352258	1.361286	1.370500	1.430538	1.454700	1.453644
C²Π	G_ν/cm^–1	25067.11	25478.29	25768.5	25995.01	26202.12	26394.03	26575.33	26748.69	26915.65	27077.76
	B_ν/cm^–1	0.051613	0.051929	0.052694	0.053118	0.0536173	0.053991	0.054389	0.054762	0.055104	0.055412
	D_ν/(10^–8cm^–1)	7.342555	2.052993	4.137982	4.629906	5.880088	6.862856	7.6697626	8.6153136	9.298999	9.430722
3²Σ⁺	G_ν/cm^–1	31178.79	31534.74	31825.03	32085.24	32324.03	32546.51	32756.77	32958.15	33153	33342.76
	B_ν/cm^–1	0.052457	0.052986	0.053498	0.053999	0.054484	0.054959	0.055414	0.055843	0.056246	0.056634
	D_ν/(10^–8cm^–1)	8.487942	1.681584	2.237826	2.904620	3.611947	4.250499	4.782100	5.233730	5.676720	6.069434

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表 3 ⁸⁸Sr⁷⁹Br分子A²Π–X²Σ⁺和B²Σ⁺–X²Σ⁺跃迁的Franck-Condon因子

Table 3. The Franck-Condon factors of the transitions A²Π–X²Σ⁺和B²Σ⁺–X²Σ⁺ of ⁸⁸Sr⁷⁹Br.

	ν'' = 0	1	2	3	4	5	6	7	8	9
A²Π–X²Σ⁺
ν' = 0	0.645022	0.336688	0.098008	0.017772	0.002264	0.000225	0.000019	0.000001	0.000000	0.000000
1	0.436688	0.083076	0.303189	0.190372	0.661533	0.165378	0.003316	0.000568	0.000087	0.000011
2	0.098008	0.434973	0.000835	0.180970	0.223953	0.113214	0.036827	0.009054	0.001812	0.000305
3	0.017772	0.293991	0.318827	0.055875	0.070256	0.256239	0.170741	0.062531	0.018499	0.004301
4	0.002263	0.053921	0.247678	0.100225	0.125148	0.010981	0.177146	0.190350	0.089728	0.031718
5	0.000225	0.009392	0.099735	0.271659	0.024898	0.160484	0.001473	0.098532	0.170079	0.114744
6	0.000019	0.001159	0.022742	0.145408	0.236122	0.000076	0.155129	0.024834	0.046417	0.151117
7	0.000000	0.000110	0.003473	0.042832	0.181875	0.178132	0.014614	0.150355	0.062132	0.011646
8	0.000000	0.000008	0.000391	0.008050	0.068736	0.202633	0.095379	0.050504	0.073401	0.096387
9	0.000000	0.000000	0.000034	0.001075	0.015763	0.098088	0.204697	0.042685	0.089124	0.031198
B²Σ⁺–X²Σ⁺
ν' = 0	0.825605	0.238234	0.033347	0.002666	0.000142	0.000006	0.000000	0.000000	0.000000	0.000000
1	0.388234	0.634880	0.110814	0.094271	0.088490	0.062873	0.040384	0.000047	0.000006	0.000000
2	0.033347	0.414395	0.520552	0.090304	0.084878	0.077853	0.067309	0.051175	0.000165	0.000020
3	0.002666	0.083449	0.366773	0.423286	0.082800	0.072301	0.061320	0.014268	0.002657	0.000419
4	0.000142	0.009678	0.107691	0.317402	0.350042	0.097638	0.0602219	0.055584	0.023573	0.005001
5	0.000006	0.000654	0.052162	0.087692	0.280018	0.317641	0.083112	0.07925	0.068340	0.044978
6	0.000000	0.000000	0.000117	0.006341	0.098918	0.277382	0.309402	0.081296	0.063711	0.051334
7	0.000000	0.000000	0.000093	0.003861	0.057313	0.055610	0.245025	0.292709	0.036511	0.075513
8	0.000000	0.000000	0.000004	0.000245	0.007248	0.080579	0.069675	0.186559	0.227752	0.010265
9	0.000000	0.000000	0.000000	0.000012	0.000552	0.012263	0.036322	0.069989	0.121499	0.152774

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表 4 ⁸⁸Sr⁷⁹Br分子A²Π–X²Σ⁺和B²Σ⁺–X²Σ⁺跃迁的辐射寿命

Table 4. The radiative lifetimes of the transitions A²Π–X²Σ⁺ and B²Σ⁺–X²Σ⁺ of ⁸⁸Sr⁷⁹Br.

Transition	Radiative lifetimes/ns
Transition	ν′ = 0	ν′ = 1	ν′ = 2
A²Π–X²Σ⁺	32.23	32.35	32.56
B²Σ⁺–X²Σ⁺	40.93	40.95	41.22

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map

[1]	Yang C L, Zhang X Y, Gao F, Ren T Q 2007 J. Mol. Struct. THEOCHEM 807 147 Google Scholar
[2]	Wang C, Li N, Xia Y, Zhang X, Ge M, Liu Y, Li Q 2011 Comput. Theor. Chem. 963 319 Google Scholar
[3]	Short C I, Hauschildt P H 2006 Astrophys. J. 641 494 Google Scholar
[4]	Carlson K D, Claydon C R 1967 Adv. High Temp. Chem. 1 43 Google Scholar
[5]	Hansen C J, Bergemann M, Cescutti G, Francois P, Arcones A, Karakas A I, Lind K, Chiappini C 2013 Astron. Astrophys. 551 1 Google Scholar
[6]	Bergemann M, Hansen C J, Bautista M, Ruchti G 2012 Astron. Astrophys. 546 1 Google Scholar
[7]	Caffau E, Andrievsky S, Korotin S, Origlia L, Oliva E, Sanna N, Ludwig H G, Bonifacio P 2016 Astron. Astrophys. 585 44 Google Scholar
[8]	Törring T, Doebl K, Weiler G 1985 Chem. Phys. Lett. 117 539 Google Scholar
[9]	Ernst W E, Schröder J O 1986 Z. Phys. D:At. Mol. Clusters 1 103 Google Scholar
[10]	Keijzer F, Teule J M, Bulthuis J, de Graaff G J, Hilgeman M H, Janssen M H M, van Kleef E H, van Leuken J J, Stolte S 1996 Chem. Phys. 207 261 Google Scholar
[11]	Coxon J A, Dickinson C S 1998 J. Mol. Spectrosc. 190 150 Google Scholar
[12]	Gurvich L V, Ryabova V G, Khitrov A N 1973 Faraday Symp. Chem. Soc. 8 83 Google Scholar
[13]	Hildenbrand D L 1977 J. Chem. Phys. 66 3526 Google Scholar
[14]	Ernst W E, Schröder J O 1986 J. Mol. Spectrosc. 117 444 Google Scholar
[15]	Dickinson C S, Coxon J A 2003 J. Mol. Spectrosc. 221 269 Google Scholar
[16]	Schröder J O, Ernst W E 1985 J. Mol. Spectrosc. 112 413 Google Scholar
[17]	Castano F, Sanchez Rayo M N, Pereira R, Adams J W, Husain D, Schiﬁno J 1994 J. Photochem. Photobiol. , A 83 79 Google Scholar
[18]	Gunduz S, Akman S 2014 Microchem. J. 116 1 Google Scholar
[19]	Werner H J, Knowles P J, Knizia G, et al. 2012 MOLPRO, version 2012.1, a package of ab initio Programs
[20]	Peterson K A, Figgen D, Goll E, Stoll H, Dolg M 2003 J. Chem. Phys. 119 11099 Google Scholar
[21]	Werner H-J, Knowles P 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]	Le Roy R J 2007 LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasi-bound Levels (Waterloo: University of Waterloo) Chemical Physics Research Report CP-663
[26]	Wu D L, Tan B, Wen Y F, Zeng X F, Xie A D, Yan B 2016 Spectrochim. Acta, Part A 161 101 Google Scholar
[27]	Fu M K, Ma H T, Cao J W, Bian W S 2017 J. Chem. Phys. 146 134309 Google Scholar
[28]	Adema Z, Makhlouf S, Taher F 2016 Comput. Theor. Chem. 1093 48 Google Scholar
[29]	Liu L, Yang C L, Wang M S, Ma X G, Sun Z P 2019 Spectrochim. Acta, Part A 164 162 Google Scholar
[30]	Huber K P, Herzberg G 1979 Constants of Diatonic Molecules, Molecular spectra molecular structure (Vol. IV) (NewYork: Van Nostrand Reinhold)
[31]	Wu D L, Lin C Q, Wen Y F, Xie A D, Yan B 2017 Chin. Phys. B 594 083101 Google Scholar
[32]	魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 65 163101 Google Scholar Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta. Phys. Sin. 65 163101 Google Scholar
[33]	Zhang X M, Liang G Y, Li R, Shi D D, Liu Y C, Liu X S, Xu H F, Yan B 2014 Chem. Phys. 443 142 Google Scholar
[34]	Okabe H 1978 Photochemistry of Small Molecules (New York: Wiley-Interscience)
[35]	Zou W L, Liu W J 2005 J. Comput. Chem. 26 106 Google Scholar
[36]	Bahrini C, Augé-Rochereau F, Rostas J, Taïeb G 2006 Chem. Phys. 330 130 Google Scholar

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Vol. 71, Issue 22 - 2022-11-20

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