  Hybrid ion-atom systems provide an excellent platform for studies of
state-resolved quantum chemistry at low temperatures, where quantum effects may
be prevalent. Here we study theoretically the process of vibrational relaxation
of an initially weakly bound molecular ion due to collisions with the
background gas atoms. We show that this inelastic process is governed by the
universal long-range part of the interaction potential, which allows for using
simplified model potentials applicable to multiple atomic species. The product
distribution after the collision can be estimated by making use of the
distorted wave Born approximation. We find that the inelastic collisions lead
predominantly to small changes in the binding energy of the molecular ion.
