In this work we discuss the rotational structure of Rydberg molecules. We calculate the complete wave function in a laboratory fixed frame and derive the transition matrix elements for the pho- toassociation of free ground state atoms. We discuss the implications for the excitation of different rotational states as well as the shape of the angular nuclear wave function. We find a rather com- plex shape and unintuitive coupling strengths, depending on the angular momenta coupling that are relevant for the states. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be directly transferred to different molecular states, atomic species or molecular coupling cases.
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