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作为非对称多原子分子制冷的一个重要目标分子, CaSH的冷却有望打破双原子分子及线性三原子分子在激光冷却中的技术局限. 本文使用高精度的EA-EOM-CCSD (electron attachment equation-of-motion coupled cluster singles and doubles)方法, 通过cc-pV XZ/cc-pCV XZ ( X= T, Q)系列基组外推至基组极限, 得到了CaSH基态和3个最低激发态精确的几何结构及基态到激发态的跃迁能. 其中, 基态
$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}' $ 几何结构参数分别为 R CaS= 2.564 Å; R SH= 1.357 Å; ∠CaSH= 91.0°; 从$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $ 到$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $ ,$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{\prime\prime} } $ 和$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $ 的垂直激发能分别为1.898, 1.945和1.966 eV, 与已有实验符合得很好. 进一步, 在3ζ级别基组上, 计算了该分子4个最低电子态的势能面, 并通过求解核运动方程给出CaS键伸缩、CaSH弯曲两个振动模的频率. 最后, 理论计算给出的$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0, 0}}, 0) $ 态到激发态$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0, 0}}, 0) $ ,$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{\prime\prime} }({\mathrm{0, 0}}, 0) $ 和$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0, 0}}, 0) $ 跃迁的Frank-Condon (FC)因子分别为0.9268, 0.9958和0.9248. 结合Frank-Condon因子和激发态寿命分析, 本文给出了可能用于CaSH冷却的光学循环, 为CaSH的激光冷却提供了理论参考.-
关键词:
- 激光冷却/
- 激发态/
- Franck-Condon因子/
- 光学循环
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-pV XZ/cc-pCV XZ ( 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 –1and 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 –1for 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:
- laser cooling/
- excited state/
- Franck-Condon factor/
- optical cycle
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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 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 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 2.562 1.357 91.0 Expt.[26] 
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$ {\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 VEEa) 1.945 2.000 2.093 3ζ 1.915 1.966 2.016 4ζ 1.898 1.945 1.966 Basis set limit AEEb) 1.894 1.944 1.961 Basis set limit SA-CASSCF VEE 1.884 1.937 2.216 3ζ fc) 0.2628 0.2589 0.1621 Expt. 1.907 1.966 1.993 Ref. [26] 1.905 1.960 1.987 Ref. [21] Calc. 1.860 1.930 2.110 Ref. [23] VEEa) 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. 下载:
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$ {\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]. 下载:
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$ {\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 下载:
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