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Sympathetic cooling of molecular ions through the Coulomb interaction withlaser-cooled atomic ions is an efficient tool to prepare translationally coldmolecules. Even at relatively high collisional energies of about 1$\,$eV($T\sim 10000 \,$K), the nearest approach in the ion-ion collisions never getscloser than $\sim$$1\,$nm such that naively perturbations of the internalmolecular state are not expected. The Coulomb field may, however, inducerotational transitions changing the purity of initially quantum state preparedmolecules. Here, we investigate such rotational state changing collisions forboth polar and apolar diatomic molecular ions and derive closed-form estimatesfor rotational excitation based on the initial scattering energy and themolecular parameters.

Fundamental bounds on rotational state change in sympathetic cooling of molecular ions