High-precision electron structure calculation of CaSH molecules and theoretical analysis of its application to laser-cooled target molecules
Authors: Feng Zhuo , Suo Bing-Bing , Han Hui-Xian , Li An-Yang ,   Shaanxi Key Laboratory of Theoretical Physic Frontiers, Institute of Modern Physics, Northwest University, Xi’an 710127, China,   School of Physics, Northwest University, Xi’an 710127, China,   School of Chemistry and Materials Science, Northwest University, Xi’an 710127, China
Published: October 2023

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<i>X</i>Z/cc-pCV<i>X</i>Z (<i>X</i> = T, Q ) serial basis sets. Geometric parameters of the ground state <inline-formula><tex-math id="M10">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M10.png"/></alternatives></inline-formula> are found to be <i>R</i><sub>CaS</sub>= 2.564 Å, <i>R</i><sub>SH</sub>= 1.357 Å, and<i>∠</i>CaSH= 91.0°. Additionally, the equilibrium geometries of three excited states are also obtained. The <inline-formula><tex-math id="M11">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M11.png"/></alternatives></inline-formula> state has a similar equilibrium structure to the ground state, while the <inline-formula><tex-math id="M12">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M12.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M13.png"/></alternatives></inline-formula> states exhibit significant conformer distortions. Specifically, the CaS bond of the <inline-formula><tex-math id="M14">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M14.png"/></alternatives></inline-formula> state and <inline-formula><tex-math id="M15">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M15.png"/></alternatives></inline-formula> state tend to contract, and the CaSH angel bends by 5° relative to the ground state. The vertical excitation energy from the ground state to <inline-formula><tex-math id="M16">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M16.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M17">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M17.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M18">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M18.png"/></alternatives></inline-formula> are of 1.898, 1.945 and 1.966 eV, respectively, which are in good agreement with the previous experimental results. Moreover, the potential energy surfaces of the four lowest electronic states of CaSH are calculated by EA-EOM-CCSD with 3ζ level of basis sets. The nuclear equations of motion are solved to obtain the vibrational frequencies of the CaS bond stretching and CaSH bending. The vibrational frequencies of the (0,1,0) mode and the CaS stretching frequency of four states are 316 cm<sup>–1</sup>, 315 cm<sup>–1</sup>, 331 cm<sup>–1</sup> and 325 cm<sup>–1</sup>, which are in close agreement with the available experimental results. The frequencies of the CaSH bending mode are presented for the first time, with the values of 357 cm<sup>–1</sup>, 396 cm<sup>–1</sup>, 384 cm<sup>–1</sup>, 411 cm<sup>–1</sup> for the <inline-formula><tex-math id="M19">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M19.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M20">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M20.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M21">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{\prime\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M21.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M22">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M22.png"/></alternatives></inline-formula> states, respectively. Theoretical calculations give the Frank-Condon factors of 0.9268, 0.9958 and 0.9248 for the <inline-formula><tex-math id="M23">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M23.png"/></alternatives></inline-formula> to <inline-formula><tex-math id="M24">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M24.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M25">\begin{document}$ {\tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M25.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M26">\begin{document}$ {\tilde{{\mathrm{C}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M26.png"/></alternatives></inline-formula> transitions. All three excited states are the bright states with considerable oscillator strength relative to the ground state. Based on the Frank-Condon factor and lifetime of excited states, the <inline-formula><tex-math id="M27">\begin{document}$ {{\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0)\to \tilde{{\mathrm{B}}}}^{2}{{\mathrm{A}}}^{{{\prime} }{{\prime} }}({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M27.png"/></alternatives></inline-formula> transition is regarded as the main cooling cycle for the CaSH molecule. The corresponding pump light wavelength is 678 nm. By exciting the vibrational excited states (0,1,0) and (0,0,1) of the <inline-formula><tex-math id="M28">\begin{document}$ {\tilde{{\mathrm{X}}}}^{2}{{\mathrm{A}}}^{\prime} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M28.png"/></alternatives></inline-formula> state to <inline-formula><tex-math id="M29">\begin{document}$ {\tilde{{\mathrm{A}}}}^{2}{{\mathrm{A}}}^{\prime} ({\mathrm{0,0}},0) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20230742_M29.png"/></alternatives></inline-formula> using lasers at 666 nm and 668 nm, respectively, the optical cooling branch ratio of CaSH is expected to exceed 0.9998.