  The electronic structures of the manifold of potential energy surfaces
generated in the lower energy range by the interaction of the
MgH$^+$(X$^1\Sigma^+$) cationic molecule with Rb($^2$S), neutral atom are
obtained over a broad range of Jacobi coordinates from strongly correlated
\emph{ab initio} calculations which use a Multireference (MR) wavefunction
within a Complete Active Space (CAS) approach. The relative features of the
lowest five surfaces are analyzed in terms of possible collisional outcomes
when employed to model the ultracold dynamics of ionic molecular partners.
