Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the $X^1{\mathrm{\Sigma }}^{+}$ and $a^3{\mathrm{\Sigma }}^{+}$ electronic states, 36 alkali-metal–alkaline-earth-metal molecules in the $X^2{\mathrm{\Sigma }}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the $X^1{\mathrm{\Sigma }}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.

We highlight the spectroscopic and electronic structure of BeCs⁺ ion, theoretically investigating ground and low lying excited states as well as the cold ion–atom elastic collisions proprieties and laser cooling possibility.

We study the energetics of chemical reactions between ultracold ground-state alkaline-earth-metal diatomic molecules. We show that the atom-exchange reactions forming homonuclear dimers are energetically allowed for all heteronuclear alkaline-earth-metal combinations. We perform high-level electronic structure calculations on the potential energy surfaces of all possible homo- and heteronuclear alkaline-earth-metal trimers and show that trimer formation is also energetically possible in collisions of all considered dimers. Interactions between alkaline-earth-metal diatomic molecules lead to the formation of deeply bound reaction complexes stabilized by large nonadditive interactions. We check that there are no barriers to the studied chemical reactions. This means that all alkaline-earth-metal diatomic molecules are chemically unstable at ultralow temperature, and optical lattice or shielding schemes may be necessary to segregate the molecules and suppress losses.

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.