  Sympathetic cooling of molecular ions through the Coulomb interaction with
laser-cooled atomic ions is an efficient tool to prepare translationally cold
molecules. Even at relatively high collisional energies of about 1$\,$eV
($T\sim 10000 \,$K), the nearest approach in the ion-ion collisions never gets
closer than $\sim$$1\,$nm such that naively perturbations of the internal
molecular state are not expected. The Coulomb field may, however, induce
rotational transitions changing the purity of initially quantum state prepared
molecules. Here, we investigate such rotational state changing collisions for
both polar and apolar diatomic molecular ions and derive closed-form estimates
for rotational excitation based on the initial scattering energy and the
molecular parameters.
