Theoretical Investigations On The Spectroscopic Properties For Some Low-lying Electronic States Of SO~+ Cation

The potential energy function of molecules has always been an important research direction in the study of atomic and molecular physics,while the molecular configuration and potential energy function of diatomic molecules are relatively simple,which is a basic and important part in the study of atomic and molecular physics,as well as the basic part of many important experimental research and theoretical calculation.In this paper,SO⁺ion is selected for theoretical calculation and research.Starting from the potential energy curves,the spectroscopic constants,transition properties,and radiation lifetimes of each electronic state are calculated.In this paper,the potential energy curves of 24Λ-S states of SO⁺ion are calculated,that is,11 doublet states,11 quartet states,and 2 sextet states.In addition,considering the spin-orbit coupling effect,four electronic states are selected.The potential energy curves of the 10Ωstates generated by X²Π,A²Π,a⁴Πand b⁴Σ^–are calculated,and the internuclear separation used in the calculation ranges from 1.11 to 4.46?.In order to obtain high-precision theoretical calculation results,the Hartree-Fock method and the complete active space self-consistent field（CASSCF）method are used to optimize the reference wave function,then the ic MRCI+Q method with Davidson correction is used to calculate the potential energy curves.In order to further improve the accuracy of theoretical calculation,this paper uses the tight-d type function to calculate SO⁺ion,and extrapolates the correlation consistent basis group of aug-cc-pv（5+d）Z and aug-cc-pv（6+d）Z,and the core-valence correlation and scalar relativistic corrections are included.The potential energy curves of the first two dissociation limits of SO⁺ions are calculated at the level of ic MRCI+Q/56-d+CV+DK.The transition dipole moments between them are calculated as well.Combining the potential energy curves and the transition dipole moment,we calculated the radiative lifetime of each electronic state.The radiative lifetimes were on the order of 10^–6s for the A²Π,C²Π,b⁴Σ^–and 1²Σ⁺states,approximately 10^–6–10^–7s for the 1²Δand B²Σ^–states,and on the order of 0^–7s for the2²Σ⁺state.The radiative lifetimes of these states were short,suggesting that the spontaneous emissions generated from them occurred readily.Many transitions are strong,including A²Π–C²Π,C²Π–X²Π,C²Π–A²Π,B²Σ^––X²Π,B²Σ^––A²Π,1²Δ–X²Π,1²Δ–A²Π,and b⁴Σ^––a⁴Π.In addition,the transitions from the first well of the 1²Σ⁺state to the X²Πstate,and from the first well of the 2²Σ⁺to the X²Π,A²Π,and C²Πstates,are also strong.These strong transitions were easy to measure through spectroscopy.The properties of the transitions between certainΩstates generating from the X²Π,A²Π,a⁴Π,and b⁴Σ^–states were investigated,including several electric dipole-forbidden transitions.The A²Π_1/2–X²Π_1/2,A²Π_3/2–X²Π_1/2,b⁴Σ^–_3/2–a⁴Π_5/2,b⁴Σ^–_1/2–a⁴Π_1/2,and b⁴Σ^–_1/2–a⁴Π_3/2transitions are strong.The radiative lifetimes of the A²Π_1/2,A²Π_3/2,a⁴Π_–1/2,a⁴Π_1/2,a⁴Π_3/2,a⁴Π_5/2,b⁴Σ^–_1/2,and b⁴Σ^–_3/2states were calculated and the distributions of their radiative lifetime varying as rotational angular momentum quantum number J were studied.The radiative lifetimes of the a⁴Π_1/2and a⁴Π_3/2states are on the order of several ms;those of the a⁴Π_5/2state are approximately several-ten ms;while those of the a⁴Π_–1/2state are on the order of several s.The results calculated herein can provide some useful guidelines for further experimental and astronomical observations and theoretical studies.