Models that are used to predict and explain phenomena related to molecular vibration and rotation are ubiquitous in physical chemistry, and are of importance in many related fields. Yet, little work has been done to characterize student use and application of these models. We describe the results of a multi-year, multi-institutional qualitative study to investigate how students work with and apply models of molecular vibration and rotation. Our findings indicate that a sizable fraction of students (1) struggle to interpret the meaning of wavefunctions, (2) do not appropriately build potential and kinetic energy terms into models, and (3) conflate portions of various model systems. The data suggests that the ordering of content in the quantum chemistry course impacts students' ideas about the rotational and vibrational behavior of molecules. The results are analyzed through the lenses of a two theoretical frameworks: one for scientific modeling, and one for heuristics in the context of chemistry. Implications for research and teaching practice are provided.