  Many molecular "quantum" theories, like "quantum chemistry", conceal that
they are actually quantum-classical approaches---they treat one set of
molecular degrees of freedom classically while the remaining degrees of freedom
follow the laws of quantum mechanics. We show that the prominent "frozen-nuclei
approximation", which is often used in molecular control communities, is a
further example for such theory reduction: It treats the nuclei of the molecule
as classical particles. Here, we demonstrate that the ignorance about the
quantum nature of nuclei has far-reaching consequences for the theoretical
description of molecules. We analyse the symmetry of oriented and aligned rigid
molecules with feasible permutations of identical nuclei and show: The
presumption of fixed nuclei corresponds to a localized state that is impossible
to create if the existence of stable nuclear spin isomers is a justifiable
assumption for the controlled molecule. The results of studies on molecules
containing identical nuclei have to be re-evaluated and properly
anti-symmetrised, because for such molecules the premise of frozen nuclei is
inherently wrong: Molecular wave functions have to obey the spin-statistics
theorem twice.
