We first introduce some preliminary concepts that allow us to define molecular structure beyond the BOA. The coordinate vectors of the nuclei R contain subscripts that label the different positions of indistinguishable particles. Furthermore, they correspond to a certain orientation of the molecule in space. Molecular structure is a concept that is invariant under rotations. For example, in a diatomic molecule, the molecular structure is completely determined by the interatomic distance, while the direction of the bond axis in space is irrelevant. We exclude space inversion since different enantiomers are commonly considered to have unique structures. This leads to the definition of labeled configurations. A labeled configuration [R] rot for a given coordinate vector R is the whole set of coordinate vectors that are related to R by a simple rotation in space. Similarly, an unlabeled configuration