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We present models for a heteronuclear diatomic molecular ion in a linear Paultrap in a rigid-rotor approximation, one purely classical, the other where thecenter-of-mass motion is treated classically while rotational motion isquantized. We study the rotational dynamics and their influence on the motionof the center-of-mass, in the presence of the coupling between the permanentdipole moment of the ion and the trapping electric field. We show that thepresence of the permanent dipole moment affects the trajectory of the ion, andthat it departs from the Mathieu equation solution found for atomic ions. Forthe case of quantum rotations, we also evidence the effect of theabove-mentioned coupling on the rotational states of the ion.

Rotational dynamics of a diatomic molecular ion in a Paul trap