Calculation of potential curves for the $X^2 \Sigma_{u}^+$ and $A^2 \Sigma_{g}^+$ states of Be$_{2}^+$ : Existence of a double minimum

We report \textit{ab initio} calculations performed on the ground $X^2 \Sigma_{u}^+ $ and $A^2 \Sigma_{g}^+$ states of the Be$_{2}^+$ dimer. We have analyzed the ground $X^2 \Sigma_{u}^+ $ state and predict the location of all bound vibrational levels. We have also found two local minima, separated by a large barrier, in the otherwise expected repulsive $A^2 \Sigma_{g}^+$ state. Bound vibrational levels have been calculated for both wells. Spectroscopic constants, Frank-Condon factors, transition dipole moments and lifetimes of these levels have also been calculated. For the \textit{ab initio} calculations we have used a full valence CI , taking into account core-core and core-valence correction separately. We have also predicted some of the long-range van der Waals coefficients by extrapolating our \textit{ab initio} data at large separations.