On the impossibility of frozen nuclei

TL;DR

The paper argues that the frozen-nuclei approximation in molecular quantum theories is fundamentally flawed because it neglects nuclear quantum effects, impacting the symmetry and wave function properties of molecules with identical nuclei.

Contribution

It demonstrates that the frozen-nuclei approximation is incompatible with nuclear spin symmetry and quantum statistics, requiring a re-evaluation of molecular quantum models.

Findings

Frozen-nuclei approximation conflicts with nuclear spin symmetry.

Molecular wave functions must obey spin-statistics twice.

Studies on molecules with identical nuclei need re-analysis.

Abstract

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.