  We report ab initio calculations of the X $^2 \Sigma_{u}^+ $ and B $^2
\Sigma_{g}^+$ states of the Be$_{2}^+$ dimer. Full valence configuration
interaction calculations were performed using the aug-cc-pVnZ basis sets and
the results were extrapolated to the CBS limit. Core-core, core-valence effects
are included at the CCSDT/MTsmall level of theory. Two local minima, separated
by a large barrier, are found in the expected repulsive B $^2 \Sigma_{g}^+$
state. Spectroscopic constants have been calculated and good agreement is found
with the recent measurements of Merritt et al. Bound vibrational levels,
transition moments and lifetimes have also been calculated.
