The study of BaLi⁺ and its reactivity plays a crucial role in advancing our understanding of chemical bonding or reaction mechanisms. The aim of this work is to represent a complete and extended theoretical study of BaLi⁺ molecular ion including ground and highly excited electronic states of ^1,3Σ, ^1,3Π and ^1,3Δ symmetries, dissociated to the first seven dissociation limits. The corresponding potential energy curves (PECs), permanent and transition dipole moments have been investigated. These calculations were performed using the multireference configuration interaction (MRCI) method in combination with optimized basis sets and non-empirical pseudopotentials (ECP) for both Ba and Li atoms. Afterwards, the spin–orbit (SO) operator is incorporated in valence MRCI calculation using optimized relativistic spin–orbit pseudopotentials and 16 Ω states are generated and splitted into Λ-S states. The SO effect gives rise to a more complicated structure of electronic states presented in PEC and permanent and transition dipole moments. Nonadiabatic coupling matrix elements between the five lowest ¹Σ⁺ states are also presented for the nonrelativistic results. Based on the vibrational radiative lifetime and Franck–Condon calculation, the possibilities of laser cooling of this system have been also discussed.

Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of ^1,3Σ⁺, ^1,3Π, and ^1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr⁺ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 1¹Σ⁺ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f ₀₀ = 0.987, f ₁₁ = 0.959 and f ₂₂ = 0.919 were obtained for the 1¹Π (v′ = 0, 1, 2)→ 1¹Σ⁺ (v = 0, 1, 2) transition making the BeFr⁺ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.

Several electronic states with Σ, Π, and Δ symmetries for both Mg⁺-Kr and Mg-Kr systems are studied using an ab initio approach. These calculations employ pseudopotential techniques, core polarization potentials, full configuration interaction calculations, and large basis function sets centered on the krypton and magnesium atoms. Additionally, the core-core interaction, represented by Mg²⁺-Kr, is accounted for using the CCSD(T) method. Moreover, the spin-orbit effect is included for the first excited B²Σ⁺ and A²Π electronic states, as well as for the X²Σ⁺ → A²Π_1/2,3/2 and X²Σ⁺ → B²Σ⁺_1/2 transition dipole moments. Our spectroscopic parameters for the ground state and lower excited states are compared with the available experimental and theoretical data.

Using an ab initio methodology that incorporates pseudopotential technique in conjunction with pair potential approaches, core polarization potentials (CPP), large basis sets of Gaussian type, and full configuration interaction calculations, we investigate interaction of neutral and charged Sr^q+(q = 0,1,2) with helium atom. In this context, the core-core interaction of Sr²⁺-He is included using an accurately performed potential for the ground state at CCSD(T) level of calculation. Also, the potential energy curves and permanent and transition dipole moments of the ground state and numerous excited states have been performed respectively for Sr⁺He and SrHe systems. Subsequently, the spin-orbit effect is considered by utilizing a semiempirical method for states dissociating into Sr⁺(5p) + He, Sr⁺(6p) + He, Sr⁺(4d) + He, Sr⁺(5d) + He, Sr(5s5p) + He, and Sr(5s4d) + He. The spectroscopic constants of the Sr^q+(q = 0, 1, 2) He states, with and without spin-orbit interaction, are derived and assessed in comparison to the existing theoretical and experimental studies. Such comparison has revealed good agreement, especially, for the Sr⁺He ionic system. Additionally, the spin-orbit effect is considered for the X²Σ⁺ → 2²Π_1/2,3/2 and X²Σ⁺ → 3²Σ_1/2 ⁺ transition dipole moments for Sr⁺He.