Electronic structures and transition properties of AsH⁺ cation

Abstract

<sec>Potential energy curves (PECs), dipole moments (DMs) and transition dipole moments (TDMs) of the X²Π, a⁴Σ^–, A²Σ^–, b⁴Π, B²Δ, C²Σ⁺, D²Π, 2²Σ⁺ states correlating with the three lowest dissociation channels of AsH⁺ cation are calculated by using the multireference configuration interaction (MRCI) method. The Davidson correction, core-valence (CV) correlation, and spin-orbit coupling (SOC) effect are all considered. The aug-cc-pV5Z all-electron basis set of H atom and the aug-cc-pwCV5Z-PP pseudopotential basis set of As atom are both selected in the calculation.</sec><sec>In the complete active space self-consistent field (CASSCF) calculation, H (1s) and As (4s4p) shell are selected as active orbitals, As (3p3d) shells are selected as closed orbitals, which keeps doubly occupation, the remaining electrons are in the frozen orbitals. In the MRCI calculation, As (3p3d) shells are used for CV correlation, and the calculation accuracy can be improved. The SOC effects are considered with Breit-Pauli operators.</sec><sec>All calculated states are bound states. The X²Π is the ground state, which is a deep potential well, the dissociation energy is 3.100 eV. The b⁴Π, C²Σ⁺ and D²Π are weakly bound states. The spectroscopic parameters are obtained by solving radial Schrodinger equation. To the best of our knowledge, there has been no study of the spectroscopy of AsH⁺ cation so far. Comparing with Ⅴ-hydride cations <i>M</i>H⁺ (<i>M</i> = N, P, As), the orders of the energy levels of the low-lying states for three ions are identical. The dissociation energy and harmonic frequency both decrease with the increase of the atomic weight of <i>M</i>.</sec><sec>At spin-free level, the PEC of b⁴Π state and the PEC of B²Δ state cross at about 1.70 Å. When SOC effects are taken into account, according to the rule of avoid-crossing, the <inline-formula><tex-math id="M5">\begin{document}$ {{{\rm{B}}^2}}{\Delta _{3/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M5.png"/></alternatives></inline-formula>state and <inline-formula><tex-math id="M6">\begin{document}$ {{{\rm{B}}^2}}{\Delta _{5/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M6.png"/></alternatives></inline-formula>state change to the double potential wells, and the avoided crossing between the <inline-formula><tex-math id="M7">\begin{document}$ {{{\rm{B}}^2}}{\Delta _{3/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M7.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M8">\begin{document}$ {{{\rm{B}}^2}}{\Delta _{3/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M8.png"/></alternatives></inline-formula>) state and <inline-formula><tex-math id="M9">\begin{document}${{\rm{b}}^4}{\Pi _{3/2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M9.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M10">\begin{document}${{\rm{b}}^4}{\Pi _{5/2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M10.png"/></alternatives></inline-formula>) state is observed. The transition dipole moment (TDM) of the <inline-formula><tex-math id="M11">\begin{document}$ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M11.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M12">\begin{document}$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M12.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M13.png"/></alternatives></inline-formula> transition are also calculated. The TDM at the equilibrium distance of the <inline-formula><tex-math id="M14">\begin{document}$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M14.png"/></alternatives></inline-formula> spin-forbidden reaches 0.036 Debye, therefore, the SOC effect plays an important role. Based on the accurate PECs and PDMs, the Franck-Condon factors, spontaneous radiative coefficients, and spontaneous radiative lifetimes of the <inline-formula><tex-math id="M15">\begin{document}$ {{{\rm{A}}^2}}{\Sigma ^ - } \to {{{\rm{X}}^2}}\Pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M15.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M16">\begin{document}$ {{{\rm{a}}^4}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M16.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M17">\begin{document}$ {{{\rm{A}}^2}}\Sigma _{1/2}^ - \to {{{\rm{X}}^2}}{\Pi _{1/2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20221104_M17.png"/></alternatives></inline-formula> transition are also calculated.</sec>