On the possibility of frozen nuclei.

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 localised 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 take into account the spin-statistics theorem twice. [ABSTRACT FROM AUTHOR]