High-precision electron structure calculation of CaSH molecules and theoretical analysis of its application to laser-cooled target molecules

Feng Zhuo; Suo Bing-Bing; Han Hui-Xian; Li An-Yang

doi:10.7498/aps.73.20230742

Abstract

The CaSH molecule is an important target in the field of laser cooling non-linear polyatomic molecules. Successful cooling of such molecules marks a breakthrough of the technical limitations of laser cooling diatomic and linear triatomic molecules. To identify the possible optical cycle in cooling CaSH, precise geometries of the CaSH ground state and the three lowest excited states, along with their excitation energy, are determined by utilizing the EA-EOM-CCSD (electron attachment equation-of-motion coupled cluster singles and doubles) method, in combination with energy extrapolation using cc-pVXZ/cc-pCVXZ (X = T, Q ) serial basis sets. Geometric parameters of the ground state $ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $ are found to be R_CaS= 2.564 Å, R_SH= 1.357 Å, and∠CaSH= 91.0°. Additionally, the equilibrium geometries of three excited states are also obtained. The $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $ state has a similar equilibrium structure to the ground state, while the $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $ and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ states exhibit significant conformer distortions. Specifically, the CaS bond of the $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $ state and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ state tend to contract, and the CaSH angel bends by 5° relative to the ground state. The vertical excitation energy from the ground state to $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $, $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $ and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ are of 1.898, 1.945 and 1.966 eV, respectively, which are in good agreement with the previous experimental results. Moreover, the potential energy surfaces of the four lowest electronic states of CaSH are calculated by EA-EOM-CCSD with 3ζ level of basis sets. The nuclear equations of motion are solved to obtain the vibrational frequencies of the CaS bond stretching and CaSH bending. The vibrational frequencies of the (0,1,0) mode and the CaS stretching frequency of four states are 316 cm^–1, 315 cm^–1, 331 cm^–1 and 325 cm^–1, which are in close agreement with the available experimental results. The frequencies of the CaSH bending mode are presented for the first time, with the values of 357 cm^–1, 396 cm^–1, 384 cm^–1, 411 cm^–1 for the $ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $, $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $, $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $ and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ states, respectively. Theoretical calculations give the Frank-Condon factors of 0.9268, 0.9958 and 0.9248 for the $ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $ to $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $, $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $ and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $ transitions. All three excited states are the bright states with considerable oscillator strength relative to the ground state. Based on the Frank-Condon factor and lifetime of excited states, the $ {{\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0)\to \tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $ transition is regarded as the main cooling cycle for the CaSH molecule. The corresponding pump light wavelength is 678 nm. By exciting the vibrational excited states (0,1,0) and (0,0,1) of the $ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $ state to $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $ using lasers at 666 nm and 668 nm, respectively, the optical cooling branch ratio of CaSH is expected to exceed 0.9998.

Keywords:

Authors and contacts

1.
Shaanxi Key Laboratory of Theoretical Physic Frontiers, Institute of Modern Physics, Northwest University, Xi’an 710127, China
2.
School of Physics, Northwest University, Xi’an 710127, China
3.
School of Chemistry and Materials Science, Northwest University, Xi’an 710127, China

Corresponding author: Suo Bing-Bing, bsuo@nwu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 21873077) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2021JM-311).

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Supplements

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References

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[2]	Wu Y, Bao W S, Cao S R, et al. 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[3]	Andreev V, Ang D G, Demille D, Doyle J M, Gabrielse G, Haefner J, Hutzler N R, Lasner Z, Meisenhelder C, O'Leary B R, Panda C D, West A D, West E P, Wu X 2018 Nature 562 355 Google Scholar
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[5]	Barry J F, Mccarron D J, Norrgard E B, Steinecker M H, Demille D 2014 Nature 512 286 Google Scholar
[6]	Norrgard E B, McCarron D J, Steinecker M H, Tarbutt M R, DeMille D 2016 Phys. Rev. Lett. 116 063004 Google Scholar
[7]	Truppe S, Williams H J, Fitch N J, Hambach M, Wall T E, Hinds E A, Sauer B E, Tarbutt M R 2017 New J. Phys. 19 022001 Google Scholar
[8]	Kozyryev I, Baum L, Matsuda K, Augenbraun B L, Anderegg L, Sedlack A P, Doyle J M 2017 Phys. Rev. Lett. 118 173201 Google Scholar
[9]	Augenbraun B L, Lasner Z D, Frenett A, Sawaoka H, Miller C, Steimle T C, Doyle J M 2020 New J. Phys. 22 022003 Google Scholar
[10]	Baranov M A 2008 Phys. Rep. 464 71 Google Scholar
[11]	Ni K K, Ospelkaus S, De Miranda M H, Hg M, Pe'Er A, Neyenhuis B, Zirbel J J, Kotochigova S, Julienne P S, Jin D S, Ye J 2008 Science 322 231 Google Scholar
[12]	Shuman E S, Barry J F, DeMille D 2010 Nature 467 820 Google Scholar
[13]	Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001 Google Scholar
[14]	Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E, Tarbutt M, Sauer B 2014 Phys. Rev. A 89 053416 Google Scholar
[15]	Gao Y, Wan M 2017 Phys. Chem. Chem. Phys. 19 5519 Google Scholar
[16]	陈涛, 颜波 2019 68 043701 Google Scholar Chen T, Yan B 2019 Acta Phys. Sin. 68 043701 Google Scholar
[17]	Wells N, Lane I C 2011 Phys. Chem. Chem. Phys. 13 19018 Google Scholar
[18]	Li D, Fu M, Ma H, Bian W, Du Z, Chen C A 2020 Front. Chem. 8 20
[19]	Li D, Cao J, Ma H, Bian W 2022 Phys. Chem. Chem. Phys. 24 10114
[20]	Ivanov M V, Bangerter F H, Krylov A I 2019 Phys. Chem. Chem. Phys. 21 19447 Google Scholar
[21]	Augenbraun B L, Doyle J M, Zelevinsky T, Kozyryev I 2020 Phys. Rev. X 10 031022 Google Scholar
[22]	Liu L, Yang C L, Sun Z P, Wang M S, Ma X G 2021 Phys. Chem. Chem. Phys. 23 2392 Google Scholar
[23]	Fernando W T M L, Ram R S, O'Brien L C, Bernath P F 1991 J. Phys. Chem. 95 2665 Google Scholar
[24]	Jarman C N, Bernath P F 1993 J. Chem. Phys. 98 6697 Google Scholar
[25]	Ortiz J V 1990 Chem. Phys. Lett. 169 116 Google Scholar
[26]	Scurlock C T, Henderson T, Bosely S, Jung K Y, Steimle T C 1994 J. Chem. Phys. 100 5481 Google Scholar
[27]	Taleb-Bendiad A, Scappini F, Amano T, Watson J K 1996 J. Chem. Phys. 104 7431 Google Scholar
[28]	Sheridan P M, Dick M J, Wang J G, Bernath P F 2007 Mol. Phys. 105 569 Google Scholar
[29]	Nooijen M, Bartlett R J 1995 J. Chem. Phys. 102 3629 Google Scholar
[30]	Pritchard B P, Altarawy D, Didier B T, Gibson T D, Windus T L 2019 J. Chem. Inf. Model. 59 4814 Google Scholar
[31]	Koput J, Peterson K A 2002 J. Chem. Phys. 116 9255 Google Scholar
[32]	Woon D E, Dunning T H 1995 J. Chem. Phys. 100 4572 Google Scholar
[33]	Dunning T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[34]	Müller T, Dallos M, Lischka H, Dubrovay Z, Szalay P G 2001 Theor. Chem. Acc. 105 227 Google Scholar
[35]	Lanczos C 1950 J. Res. Nat. Bur. Stand. 45 255 Google Scholar
[36]	Goldfield E M, Gray S K, Harding L B 1993 J. Chem. Phys. 99 5812 Google Scholar
[37]	Light J C, Carrington Jr T 2000 Adv. Chem. Phys. 114 263 Google Scholar
[38]	Lill J V, Parker G A, Light J C 1986 J. Chem. Phys. 85 900 Google Scholar
[39]	Liu W J, Hong Y G, Dai D D, Li L M, Dolg M 1997 Theor. Chem. Acc. 96 75 Google Scholar
[40]	Zhang Y, Suo B B, Wang Z K, Zhang N, Li Z D, Lei Y B, Zou W L, Gao J, Peng D L, Pu Z C, Sun Q M, Wang F, Ma Y T, Wang X P, Liu W J 2020 J. Chem. Phys. 152 064113 Google Scholar
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[43]	Wang Z F, Hu S, Wang F, Guo J W 2015 J. Chem. Phys. 142 144109 Google Scholar
[44]	Cao Z L, Li Z D, Wang F, Liu W J 2017 Phys. Chem. Chem. Phys. 19 3713 Google Scholar
[45]	李永红, 李俊峰, 王连宾, 张敬来 2008 河南大学学报(自然科学版) 38 4 Li Y H, Li J F, Wang L B, Zhang J L 2008 J. Henan Univ. (Nat. Sci.) 38 4
[46]	Baum L, Vilas N B, Hallas C, Augenbraun B L, Raval S, Mitra D, Doyle J M 2020 Phys. Rev. Lett. 124 133201 Google Scholar
[47]	Kozyryev I, Baum L, Aldridge L, Yu P, Eyler E E, Doyle J M 2018 Phys. Rev. Lett. 120 063205 Google Scholar
[48]	Franck-Condon factors in the harmonic approximation , Wójcik P, Gozem S, Mozhayskiy V, Krylov A I. http:// iopenshell.usc.edu/downloads [2023-5-3

Cited By

图 1 CaSH分子前线轨道图　(a) $ 15{{\mathrm{a}}}^{\prime} ; $ (b) $ 16{{\mathrm{a}}}^{\prime} ; $ (c) $ 5{{\mathrm{a}}}^{{{\prime} }{{\prime} }}; $ (d) $ 17{\mathrm{a}}^{{\prime} } $

Figure 1. Frontier orbital diagram of the CaSH molecule: (a) $ 15{{\mathrm{a}}}^{\prime} ; $ (b) $ 16{{\mathrm{a}}}^{\prime} ; $ (c) $ 5{{\mathrm{a}}}^{{{\prime} }{{\prime} }}; $ (d) $ 17{\mathrm{a}}^{{\prime} } $ .

DownLoad: Full-Size Img PowerPoint

图 2 CaSH激光冷却光学循环示意图, 实线代表激发光, 虚线为自发辐射通道

Figure 2. Schematic diagram of optical cycle of laser cooling of CaSH, solid lines represent the excitation light, dash lines are spontaneous emission channels.

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表 1 CaSH分子基态和3个低能级激发态的平衡结构

Table 1. Equilibrium structures of the ground state and three low-lying excited states of the CaSH molecule.

State	r₀ (Ca-S)/Å	r₀ (S—H)/Å	θ (Ca—S—H)/(°)	Method	Ref.
$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $	2.557	1.338	91.0	EA-EOM-CCSD	This work
	2.614	1.346	100.0	MP2	Calc.^[23]
	2.607	1.339	97.1	MP2	Calc.^[25]
	2.647	1.347	93.1	CCSD(T)	Calc.^[24]
	2.560	1.346	96.6		Expt.^[22]
	2.564	1.357	91.0		Expt.^[26]
$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $	2.528	1.343	86.0	EA-EOM-CCSD	This work
	2.513	1.346	94.6		Expt.^[22]
	2.517	1.357	89.1		Expt.^[26]
$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $	2.554	1.338	91.0	EA-EOM-CCSD	This work
$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $	2.550	1.357	89.1		Expt.^[26]
$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $	2.525	1.345	86.0	EA-EOM-CCSD	This work
$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $	2.562	1.357	91.0		Expt.^[26]

DownLoad: CSV

表 2 CaSH 基态到3个低能级激发态激发能的对比

Table 2. Comparison of excitation energies from the ground state to three low-lying excited states of the CaSH.

		$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} \to {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} \to {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} \to {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $
EA-EOM-CCSD	VEE ^a)	1.945	2.000	2.093	3ζ
		1.915	1.966	2.016	4ζ
		1.898	1.945	1.966	Basis set limit
	AEE ^b)	1.894	1.944	1.961	Basis set limit
SA-CASSCF	VEE	1.884	1.937	2.216	3ζ
SA-CASSCF	f ^c)	0.2628	0.2589	0.1621
Expt.		1.907	1.966	1.993	Ref. [26]
Expt.		1.905	1.960	1.987	Ref. [21]
Calc.		1.860	1.930	2.110	Ref. [23]
Calc.	VEE ^a)	2.000	2.060	2.330	Ref. [43]
注: ^a) 垂直激发能; ^b)绝热激发能; ^c) 偶极跃迁振子强度.

DownLoad: CSV

表 3 CaSH分子Ca—S键伸缩和CaSH弯曲振动模式的频率(cm^–1)^a)

Table 3. Frequencies of the Ca—S stretching and CaSH bending vibrational modes of the CaSH molecule (cm^–1) ^a).

	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $	$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $	$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $	$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $
(0, 1, 0)	316 (326) ^b)	315 (318) ^b)	331 (320) ^b)	326 (312) ^b)
(0, 0, 1)	357	396	384	411
(0, 2, 0)	634	632	661	653
(0, 1, 1)	681	724	722	742
(0, 0, 2)	704	785	760	808
(0, 3, 0)	953	949	990	981
(0, 2, 1)	1007	1051	1058	1074
(0, 1, 2)	1034	1122	1102	1145
(0, 0, 3)	1039	1167	1130	1188
(0, 4, 0)	1271	1266	1318	1308
注: ^a)(0, 1, 0)CaS 伸缩振动模式, (0, 0, 1)CaSH键角弯曲振动模式; ^b) 括号内值为实验值^[23].

DownLoad: CSV

表 4 CaSH分子激发态$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $, $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $和$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $到基态$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $的跃迁FC因子

Table 4. The Frank-Condon factor of the excited states $ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $, $ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $ and $ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ transition to ground state $ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $ of the CaSH molecule.

	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} {\to} {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} {\to} {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $	$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} {\to} {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $
(0, 0, 0) → (0, 0, 0)	0.9268	0.9958	0.9248
(0, 1, 0) → (0, 0, 0)	0.0627	0.0011	0.0626
(0, 0, 1) → (0, 0, 0)	0.0094	0.0002	0.0114
(0, 1, 1) → (0, 0, 0)	0.0006	2.4×10^–7	0.0008
(0, 2, 0) → (0, 0, 0)	0.0001	0.0006	2.2×10^–5
(0, 0, 2) → (0, 0, 0)	6.0×10^–5	0.0003	5×10^–6

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map

[1]	Balakrishnan N 2016 J. Chem. Phys. 145 150901 Google Scholar
[2]	Wu Y, Bao W S, Cao S R, et al. 2021 Phys. Rev. Lett. 127 180501 Google Scholar
[3]	Andreev V, Ang D G, Demille D, Doyle J M, Gabrielse G, Haefner J, Hutzler N R, Lasner Z, Meisenhelder C, O'Leary B R, Panda C D, West A D, West E P, Wu X 2018 Nature 562 355 Google Scholar
[4]	Baron J, Campbell W C, DeMille D, Doyle J M, Gabrielse G, Gurevich Y V, Hess P W, Hutzler N R, Kirilov E, Kozyryev I, O’Leary B R, Panda C D, Parsons M F, Petrik E S, Spaun B, Vutha A C, West A D 2014 Science 343 269 Google Scholar
[5]	Barry J F, Mccarron D J, Norrgard E B, Steinecker M H, Demille D 2014 Nature 512 286 Google Scholar
[6]	Norrgard E B, McCarron D J, Steinecker M H, Tarbutt M R, DeMille D 2016 Phys. Rev. Lett. 116 063004 Google Scholar
[7]	Truppe S, Williams H J, Fitch N J, Hambach M, Wall T E, Hinds E A, Sauer B E, Tarbutt M R 2017 New J. Phys. 19 022001 Google Scholar
[8]	Kozyryev I, Baum L, Matsuda K, Augenbraun B L, Anderegg L, Sedlack A P, Doyle J M 2017 Phys. Rev. Lett. 118 173201 Google Scholar
[9]	Augenbraun B L, Lasner Z D, Frenett A, Sawaoka H, Miller C, Steimle T C, Doyle J M 2020 New J. Phys. 22 022003 Google Scholar
[10]	Baranov M A 2008 Phys. Rep. 464 71 Google Scholar
[11]	Ni K K, Ospelkaus S, De Miranda M H, Hg M, Pe'Er A, Neyenhuis B, Zirbel J J, Kotochigova S, Julienne P S, Jin D S, Ye J 2008 Science 322 231 Google Scholar
[12]	Shuman E S, Barry J F, DeMille D 2010 Nature 467 820 Google Scholar
[13]	Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001 Google Scholar
[14]	Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E, Tarbutt M, Sauer B 2014 Phys. Rev. A 89 053416 Google Scholar
[15]	Gao Y, Wan M 2017 Phys. Chem. Chem. Phys. 19 5519 Google Scholar
[16]	陈涛, 颜波 2019 68 043701 Google Scholar Chen T, Yan B 2019 Acta Phys. Sin. 68 043701 Google Scholar
[17]	Wells N, Lane I C 2011 Phys. Chem. Chem. Phys. 13 19018 Google Scholar
[18]	Li D, Fu M, Ma H, Bian W, Du Z, Chen C A 2020 Front. Chem. 8 20
[19]	Li D, Cao J, Ma H, Bian W 2022 Phys. Chem. Chem. Phys. 24 10114
[20]	Ivanov M V, Bangerter F H, Krylov A I 2019 Phys. Chem. Chem. Phys. 21 19447 Google Scholar
[21]	Augenbraun B L, Doyle J M, Zelevinsky T, Kozyryev I 2020 Phys. Rev. X 10 031022 Google Scholar
[22]	Liu L, Yang C L, Sun Z P, Wang M S, Ma X G 2021 Phys. Chem. Chem. Phys. 23 2392 Google Scholar
[23]	Fernando W T M L, Ram R S, O'Brien L C, Bernath P F 1991 J. Phys. Chem. 95 2665 Google Scholar
[24]	Jarman C N, Bernath P F 1993 J. Chem. Phys. 98 6697 Google Scholar
[25]	Ortiz J V 1990 Chem. Phys. Lett. 169 116 Google Scholar
[26]	Scurlock C T, Henderson T, Bosely S, Jung K Y, Steimle T C 1994 J. Chem. Phys. 100 5481 Google Scholar
[27]	Taleb-Bendiad A, Scappini F, Amano T, Watson J K 1996 J. Chem. Phys. 104 7431 Google Scholar
[28]	Sheridan P M, Dick M J, Wang J G, Bernath P F 2007 Mol. Phys. 105 569 Google Scholar
[29]	Nooijen M, Bartlett R J 1995 J. Chem. Phys. 102 3629 Google Scholar
[30]	Pritchard B P, Altarawy D, Didier B T, Gibson T D, Windus T L 2019 J. Chem. Inf. Model. 59 4814 Google Scholar
[31]	Koput J, Peterson K A 2002 J. Chem. Phys. 116 9255 Google Scholar
[32]	Woon D E, Dunning T H 1995 J. Chem. Phys. 100 4572 Google Scholar
[33]	Dunning T H 1989 J. Chem. Phys. 90 1007 Google Scholar
[34]	Müller T, Dallos M, Lischka H, Dubrovay Z, Szalay P G 2001 Theor. Chem. Acc. 105 227 Google Scholar
[35]	Lanczos C 1950 J. Res. Nat. Bur. Stand. 45 255 Google Scholar
[36]	Goldfield E M, Gray S K, Harding L B 1993 J. Chem. Phys. 99 5812 Google Scholar
[37]	Light J C, Carrington Jr T 2000 Adv. Chem. Phys. 114 263 Google Scholar
[38]	Lill J V, Parker G A, Light J C 1986 J. Chem. Phys. 85 900 Google Scholar
[39]	Liu W J, Hong Y G, Dai D D, Li L M, Dolg M 1997 Theor. Chem. Acc. 96 75 Google Scholar
[40]	Zhang Y, Suo B B, Wang Z K, Zhang N, Li Z D, Lei Y B, Zou W L, Gao J, Peng D L, Pu Z C, Sun Q M, Wang F, Ma Y T, Wang X P, Liu W J 2020 J. Chem. Phys. 152 064113 Google Scholar
[41]	Yang D D, Wang F, Guo J W 2012 Chem. Phys. Lett. 531 236 Google Scholar
[42]	Tu Z Y, Wang F, Li X Y 2012 J. Chem. Phys. 136 174102 Google Scholar
[43]	Wang Z F, Hu S, Wang F, Guo J W 2015 J. Chem. Phys. 142 144109 Google Scholar
[44]	Cao Z L, Li Z D, Wang F, Liu W J 2017 Phys. Chem. Chem. Phys. 19 3713 Google Scholar
[45]	李永红, 李俊峰, 王连宾, 张敬来 2008 河南大学学报(自然科学版) 38 4 Li Y H, Li J F, Wang L B, Zhang J L 2008 J. Henan Univ. (Nat. Sci.) 38 4
[46]	Baum L, Vilas N B, Hallas C, Augenbraun B L, Raval S, Mitra D, Doyle J M 2020 Phys. Rev. Lett. 124 133201 Google Scholar
[47]	Kozyryev I, Baum L, Aldridge L, Yu P, Eyler E E, Doyle J M 2018 Phys. Rev. Lett. 120 063205 Google Scholar
[48]	Franck-Condon factors in the harmonic approximation , Wójcik P, Gozem S, Mozhayskiy V, Krylov A I. http:// iopenshell.usc.edu/downloads [2023-5-3

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