Spectroscopic and transition properties of SeH<sup>–</sup> anion including spin-orbit coupling
Authors: Wan Ming-Jie , Liu Fu-Ti , Huang Duo-Hui ,   Faculty of Science, Yibin University, Yibin 644007, China
Published: January 2021

<sec>Potential energy curves (PECs), permanent dipole moments (PDMs) and transition dipole moments (TMDs) of five Λ-S states of SeH<sup>−</sup> anion are calculated by the MRCI + <i>Q</i> method with ACVQZ-DK basis set. The core-valence corrections, Davidson corrections, scalar relativistic corrections, and spin-orbit coupling (SOC) effects are also considered. In the CASSCF step, Se(1s2s2p3s3p) shells are put into the frozen orbitals, which are not optimized. Six molecular orbitals are chosen as active space, including H(1s) and Se(4s4p5s) shells, and eight electrons are distributed in a (4, 1, 1, 0) active space, which is referred to as CAS (8, 6), and the Se(3d) shell is selected as a closed-shell, which keeps doubly occupation. In the MRCI step, the remaining Se(3d) shell is used for core-valence calculations of SeH<sup>−</sup> anion. The SOC effects are taken into account in the one- and two- electron Breit-Pauli operators.</sec><sec>The b<sup>3</sup>Σ<sup>+</sup> state is a repulsive state. Other excited states are bound, and all states possess two potential wells. The <inline-formula><tex-math id="M13">\begin{document}$ {{\rm{b}}^{{3}}}\Sigma _{{0^ - }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M13.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M14">\begin{document}$ {{\rm{b}}^3}\Sigma _{{1}}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M14.png"/></alternatives></inline-formula> both turn into bound states when the SOC effect is considered. All spectroscopic parameters of Λ-S states and Ω states are reported for the first time. The TDMs of the <inline-formula><tex-math id="M15">\begin{document}$ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M15.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M16">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M16.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M17">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M17.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M18">\begin{document}$ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{1}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M18.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M19">\begin{document}$ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{a}}^{{3}}}{\Pi _{{{{0}}^{{ + }}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M19.png"/></alternatives></inline-formula> transitions are also calculated. The TDMs of the <inline-formula><tex-math id="M20">\begin{document}$ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M20.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M21">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M21.png"/></alternatives></inline-formula> transitions are large in the Franck-Condon region, which are about –2.05 Debye (D) and 1.45 D at <i>R</i><sub>e</sub>. Notably, the TDMs of the <inline-formula><tex-math id="M22">\begin{document}$ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M22.png"/></alternatives></inline-formula> transition cannot be ignored. The value of TDM at <i>R</i><sub>e</sub> equals –0.15 D.</sec><sec>Based on the accurately PECs and PDMs, the values of Franck-Condon factor <i>f</i><sub><i>υ</i>′<i>υ</i>″</sub>, vibrational branching ratio <i>R</i><sub><i>υ</i>′<i>υ</i>″</sub> and radiative coefficient of the <inline-formula><tex-math id="M23">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M23.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M24">\begin{document}$ {{\rm{a}}^{{3}}}{{{\Pi }}_{{{{0}}^{{ + }}}}} \leftrightarrow {{\rm{X}}^{{1}}}{{\Sigma }}_{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M24.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M25">\begin{document}$ {{\rm{A}}^{{1}}}{\Pi _{{1}}} \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M25.png"/></alternatives></inline-formula> transitions are also calculated. Highly diagonally distributed Franck-Condon factor <i>f</i><sub>00</sub> and the values of vibrational branching ratio <i>R</i><sub>00</sub> of the <inline-formula><tex-math id="M26">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M26.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M27">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M27.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M28">\begin{document}$ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M28.png"/></alternatives></inline-formula> transitions are obtained, respectively. Spontaneous radiation lifetimes of the <inline-formula><tex-math id="M29">\begin{document}$ {{\rm{a}}^3}{\Pi _{{1}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M29.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M30">\begin{document}$ {{\rm{a}}^3}{\Pi _{{{{0}}^{{ + }}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M30.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M30.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M31">\begin{document}$ {{\rm{A}}^1}{\Pi _{{1}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M31.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M31.png"/></alternatives></inline-formula> excited states are all short for rapid laser cooling. The influences of intervening states of the <inline-formula><tex-math id="M32">\begin{document}$ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M32.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M32.png"/></alternatives></inline-formula> transition can be ignored. The proposed cooling wavelengths using the <inline-formula><tex-math id="M33">\begin{document}$ {{\rm{a}}^3}{\Pi _{{1}}}(\upsilon ') \leftrightarrow {{\rm{X}}^{{1}}}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M33.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M33.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M34">\begin{document}$ {{\rm{a}}^{{3}}}{\Pi _{{0^ + }}}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M34.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M34.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M35">\begin{document}$ {{\rm{A}}^1}{\Pi _1}(\upsilon ') \leftrightarrow {{\rm{X}}^1}\Sigma _{{0^ + }}^ + (\upsilon '')$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M35.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201413_M35.png"/></alternatives></inline-formula> transitions are all in the visible region.</sec>