Calculation of \textit{ab initio} potential curves for ground and low lying excited states of heteronuclear alkaline earth dimers BeCa$^+$, BeMg$^+$ and MgCa$^+$*

We report \textit{ab initio} calculations on the ground and low lying excited states of $^2\Sigma$ and $^2\Pi$ symmetry for BeCa$^+$, BeMg$^+$ and MgCa$^+$. Valence multireference configuration interaction (MRCI) calculations were performed using complete active space self consistent field (CASSCF) orbitals. We use augmented correlation consistent valence quintuple zeta (aug-cc-pV5Z) basis set for our valence calculations. Core-valence and scalar relativistic effects are included at the CCSDT/cc-pwCVTZK level of theory. Spectroscopic constants and bound vibrational levels are calculated, as well as Frank-Condon factors and electronic dipole transition moments between the dipole--allowed states. The static dipole and quadrupole polarizabilities, along with long range expansion coefficients are also reported.