Theoretical study of laser-cooled SH<sup>–</sup> anion
Authors: Wan Ming-Jie , Li Song , Jin Cheng-Guo , Luo Hua-Feng ,   Computational Physics Key Laboratory of Sichuan Province, Yibin University, Yibin 644007, China,   School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China,   College of Chemistry and Chemical Engineering, Yibin University, Yibin 644007, China
Published: December 2020

The potential energy curves, dipole moments, and transition dipole moments for the <inline-formula><tex-math id="M13">\begin{document}${{\rm{X}}^1}{\Sigma ^ + }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M13.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M14">\begin{document}${{\rm{a}}^3}\Pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M14.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M15">\begin{document}${{\rm{A}}^1}\Pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M15.png"/></alternatives></inline-formula> electronic state of sulfur hydride anion (SH<sup>–</sup>) are calculated by using the multi-reference configuration interaction method plus Davidson corrections (MRCI+<i>Q</i>) with all-electron basis set. The scalar relativistic corrections and core-valence correlations are also considered. In the CASSCF calculations, H(1s) and S(3s3p4s) shells are chosen as active space, and the rest orbitals S(1s2s2p) as closed-shell. In the MRCI+<i>Q</i> calculations, the S(1s2s2p) shells are used for the core-valence correlation. Spectroscopic parameters, Einstein spontaneous emission coefficient, Franck-Condon factors, and spontaneous radiative lifetimes are obtained by using Le Roy’s LEVEL8.0 program. The calculated spectroscopic parameters are in good agreement with available experimental data and theoretical values. Spin-orbit coupling (SOC) effects are evaluated with Breit-Pauli operators at the MRCI+<i>Q</i> level. Transition dipole moments (TDMs) for the <inline-formula><tex-math id="M16">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M16.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M17">\begin{document}${{\rm{a}}^3}{\Pi _{{0^ + }}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M17.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M18">\begin{document}${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M18.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M19">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _{{0^ + }}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M19.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M20">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{a}}^3}{\Pi _1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M20.png"/></alternatives></inline-formula> transitions are also calculated. The strength for the <inline-formula><tex-math id="Z-20190315031218-1">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_Z-20190315031218-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_Z-20190315031218-1.png"/></alternatives></inline-formula> is the strongest in these five transitions, the value of TDM at <i>R</i><sub>e</sub> is –1.3636 D. We find that the value of TDM for the <inline-formula><tex-math id="M21">\begin{document}${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M21.png"/></alternatives></inline-formula> transition at <i>R</i><sub>e</sub> is 0.5269 D. Therefore, this transition must be taken into account to build the scheme of laser-cooled SH<sup>–</sup> anion. Highly diagonally distributed Franck-Condon factor <i>f</i><sub>00</sub> for the <inline-formula><tex-math id="M22">\begin{document}${{\rm{a}}^3}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M22.png"/></alternatives></inline-formula> <inline-formula><tex-math id="M22-1">\begin{document}$ (\nu '' = 0)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M22-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M22-1.png"/></alternatives></inline-formula> transition is 0.9990 and the value for the <inline-formula><tex-math id="M23">\begin{document}${{\rm{A}}^1}{\Pi _1}(\nu ' = 0) \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\nu '' = 0)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M23.png"/></alternatives></inline-formula> transition is 0.9999. Spontaneous radiative lifetimes of <inline-formula><tex-math id="M24">\begin{document}$\tau \left( {{{\rm{a}}^3}{\Pi _1}} \right)= 1.472 \;{\text{μ}}{\rm{s}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M24.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M25">\begin{document}$\tau \left( {{{\rm{A}}^1}{\Pi _1}} \right)=0.188 \;{\text{μ}}{\rm{s}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M25.png"/></alternatives></inline-formula> are obtained, which can ensure that laser cools SH<sup>–</sup> anion rapidly. To drive the <inline-formula><tex-math id="M26">\begin{document}${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M26.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M27">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M27.png"/></alternatives></inline-formula> transitions, just one laser wavelength is required. The wavelengths are 492.27 nm and 478.57 nm for two transitions, respectively. Notably, the influences of the intervening states <inline-formula><tex-math id="M28">\begin{document}${{\rm{a}}^3}{\Pi _1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M28.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M29">\begin{document}${{\rm{a}}^3}{\Pi _{{0^{\rm{ + }}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M29.png"/></alternatives></inline-formula> on the <inline-formula><tex-math id="M30">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {X^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M30.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M30.png"/></alternatives></inline-formula> transition are small enough to implement a laser cooling project. A spin-forbidden transition and a three-electronic-level transition optical scheme of laser-cooled SH<sup>–</sup> anion are constructed, respectively. In addition, the Doppler temperatures and recoil temperatures for the <inline-formula><tex-math id="M31">\begin{document}${{\rm{a}}^3}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M31.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M31.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M32">\begin{document}${{\rm{A}}^1}{\Pi _1} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M32.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182039_M32.png"/></alternatives></inline-formula> transitions of laser-cooled SH<sup>–</sup> anion are also obtained, respectively.