The discussion revolves around the concept of rotational symmetry in a system consisting of two nuclei, particularly in the context of diatomic molecules. Participants explore the implications of rotational symmetry on the energy levels of electrons and the conditions under which such symmetry is defined.
Participants express differing views on the nature of rotational symmetry in the context of distinct versus identical nuclei, and whether the definition provided is adequate to support claims about electron energy levels. The discussion remains unresolved regarding the implications of rotational symmetry.
Participants highlight the need for clarity on the definitions and conditions under which rotational symmetry is applied, particularly in relation to the distinctness of the nuclei and the specific rotational angles considered.
I still don't see it. If the nuclei are distinct (say, oxygen and hydrogen), and they are initially at (0,1) and (0,-1), respectively, then only rotation through 360[itex]^\circ[/itex] will leave the system unchanged. If the nuclei are not distinct, however, then I see how rotation through 180[itex]^\circ[/itex] will leave the system unchanged. But I'm not assuming that the nuclei are identical.Doc Al said:Keep reading; especially the section titled "n-fold rotational symmetry".
Sorry; maybe I should be more specific. I'm reading a paper, and the argument is made that, because of the "rotational symmetry" of a diatomic molecule, the energy levels of the electrons depend only on the magnitude of the distance between the two nuclei. Does the fact that the system is invariant under 360-degree rotation mean it has rotational symmetry? If so, why should that be sufficient for us to conclude that the electron energy levels are only dependent on the distance between the nuclei and not their orientation?Doc Al said:OK, then I don't get your point. Where does it claim that such a system has anything other than trivial rotational symmetry (except about its central axis, of course)?
The rotational symmetry referred to is with respect to the central axis (the line between the two nuclei).AxiomOfChoice said:I'm reading a paper, and the argument is made that, because of the "rotational symmetry" of a diatomic molecule, the energy levels of the electrons depend only on the magnitude of the distance between the two nuclei.