We present a theoretical analysis of optical pathways for formation of cold ground-state
(NaCa)+ molecular ions via an intermediate state. The formation schemes are based on ab initio potential energy curves and transition dipole moments calculated using effective-core-potential methods of quantum chemistry. In the proposed approach, starting from a mixture of cold trapped
Ca+ ions immersed into an ultracold gas of Na atoms,
(NaCa)+ molecular ions are photoassociated in the excited $E^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ electronic state and allowed to spontaneously decay either to the ground electronic state or an intermediate state from which the population is transferred to the ground state via an additional optical excitation. By analyzing all possible pathways, we find that the efficiency of a two-photon scheme, via either the $B^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ or $C^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ potential, is sufficient to produce significant quantities of ground-state
(NaCa)+ molecular ions. A single-step process results in lower formation rates that would require either a high-density sample or a very intense photoassociation laser to be viable.
Alkaline-earth dimers are now been used, as new grounds for, testing fundamental physics laws, precision measurements and quantum computation. As a starting point for such experiments, one needs a very good knowledge of the electronic structure, energetics and long-range behavior of these molecular ions. We perform accurate ab initio calculations for the ground and low-lying excited states of Be2+, Mg2+, Ca2+ and Sr2+ molecular ions. We have also calculated the spectroscopic constants, electronic transition dipole moments, polarizabilities and long-range dispersion coefficients for the various alkaline-earth ionic dimers. We have extended our calculations to study heteronuclear species of alkaline-earth molecular ions, like BeCa+, and also mixed alkali alkaline-earth species like NaCa+. We calculated photoassociation (PA) pathways for formation of cold molecular ions and also studied corrections to the Born-Oppenheimer Hamiltonian: non-adiabatic couplings and hyperfine structure due to nuclear spins and electric quadrupoles. We believe, this work would lay foundation, not only for new experiments in ultracold physics and chemistry, but would also provide valuable starting point for theoretical calculations involving low temperature scattering and resonant charge transfer.