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The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earthmetal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr−(Ca + , Sr + , Ba + ). We adopt a computational scheme without spin−orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr + , Ca 2+ , Sr 2+ , and Ba 2+ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the 1,3 Σ u,g + and 1,3 Σ + electronic states for Fr 2 and Fr−AEM + , respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s 2 , 4s4p, 4s3d), Sr(5s 2 , 5s5p, 5s4d), Ba(6s 2 , 6s6p, 6s5d) + Fr + }, and {Ca + (4s, 3d), Sr + (5s, 4d), Ba + (6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom−ion collisions in the diverse charge or excited states. The Σ + −Σ + transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.

The current paper reports a global investigation of all excited states below the ionic limit Fr+Na– of FrNa molecule following diabatic and adiabatic representations. The adiabatic and diabatic potential energy curves (PECs) for Σ+, Π, and Δ symmetries have been calculated for a dense grid of internuclear distances. The transition and permanent dipole moments (TDM and PDM) have been reported for both representations. Regarding the pseudopotential approach and full valence configuration interaction (FCI), the ab initio computation has been performed. Furthermore, the diabatization method was achieved by the use of the variational effective Hamiltonian theory (VEH). This latter served to assess the nonadiabatic coupling between the treated adiabatic states and to eliminate it employing a suitable unitary transformation matrix. The detailed computation of the PECs and PDM and TDM curves of the ground and excited states play a key role to coordinate experimental efforts in order to create cold and ultracold molecules in their ground stable rovibrational levels.

Potential energy curves, spectroscopic parameters, electric dipole moments (PEDM and TEDM) and vibrational levels’ spacing for 141Σ+, 133Σ+, 81,3Π, and 31,3Δ electronic states, including the ionic limit K−Cs+, are highly computed and presented in adiabatic representation. These properties are determined by the use of an ab initio method involving non-empirical pseudo-potentials, the core polarization potentials, the l-dependent cut-off functions, and the full valence configuration interaction. An important shape where an ionic state behaving as (−1/R), has been clearly pointed out in the 1Σ+ symmetry. This irregularity has been made due to the ionic charge transfer state (K−Cs+), which induces a series of avoided crossings at intermediate and long internuclear ranges. It is interesting to note that the ionic character linked to the ionic charge transfer K−Cs+ state has been clearly illustrated in the PEDM. The current calculations on the KCs molecule are complementary to the published theoretical works, including recently observed electronic states that had not been calculated previously. For the low-lying electric states, spectroscopic constants, PEDM, as well as TEDM are in good agreement with the available experimental data. The relevant data of the KCs molecule are meaningful and useful in several prospective experiments such as photo-association experiments or the manipulation of ultra-cold molecules.

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