In this paper we analyze the controllability of quantum systems arising in molecular dynamics. We model these systems as systems with finite numbers of levels, and examine their controllability. To do this we pass to their unitary generators and use results on the controllability of invariant systems on Lie groups. Examples of molecular systems, modeled as finite-dimensional control systems, are provided. A simple algorithm to detect the controllability of a molecular system is provided. Finally, we apply this algorithm to a five-level system.