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We report \textit{ab initio} calculations of the X $^2 \Sigma_{u}^+$, A$^2\Pi_u$ and B $^2 \Sigma_{g}^+$ states of the Ca$_{2}^+$ dimer. All electronCAS+MRCI calculations are performed for the X $^2 \Sigma_{u}^+$ and B $^2\Sigma_{g}^+$ states, while valence CAS+MRCI calculations using an effectivecore potential are used to describe the A $^2\Pi_u$ state. A double well isfound in the B $^2 \Sigma_{g}^+$ state. Spectroscopic constants, vibrationallevels, transition moments and radiative lifetimes are calculated for the mostabundant isotope of calcium ($^{40}$Ca). The static dipole and quadrupolepolarizabilities, and the leading order van der Waals coefficients are alsocalculated for all three states.

Ab initio potential curves for the X $^2\Sigma_u^+$, A $^2\Pi_u$ and B $^2\Sigma_g^+$ states of Ca$_{2}^+$