Exploring the excited states of the GeH⁺ radical cation including spin-orbit interaction: A revisited study

In this paper, we have carried out high-level ab initio calculations on the electronic states of GeH⁺ with the configuration interaction method. The spin-orbit coupling (SOC), core-valence correlation (CV), scalar relativistic effects and Davidson correction (+Q) are included. The potential energy curves (PECs) of 13 Λ-S correlated with the four lowest dissociation limits and 32 Ω electronic states generated from those Λ-S states are obtained. Our results indicate that the first ³Σ^- and second ³Π states are adiabatically correlated with the dissociation limit Ge(³P_g) + H⁺(¹S), which is different from the previously reported Ge⁺(⁴P_g) + H(²S_g). From the computed PECs, the spectroscopic constants of the Λ-S and Ω states are determined, which are in good agreement with previous experiments. The dipole moments (DMs) for Λ-S electronic states are also investigated. With the help of spin-orbit coupling matrix involving the 1³Σ^- and 2³Π states, the intricate couplings related with the crossing states are revealed, and the weak predissociation for ν' ≥0 vibrational levels of 1³Σ^- and the perturbations for vibrational levels of 2¹Σ⁺ (ν' ≥1) and 1¹Δ (ν' ≥0) states are analyzed. Finally, the transition properties of five transitions are predicted, including the Franck-Condon Factors (FCFs), transition dipole moments (TDMs), and the spontaneous radiative lifetimes of lower vibrational states. This study will improve our comprehension on the detailed electronic structure and spectroscopy of GeH⁺ radical cation.