For any molecule with open or closed shells considering the electronic state to be the ground state:
- Is the exact electron density totally symmetric?
- is the Kohn-Sham electron density totally symmetric?
(spatially upon symmetry operations of the molecular point group). I refer to "exact" as the density built using the wave function of the molecular Hamiltonian in the Born-Oppenheimer approximation. And I refer as the KS electron density as the one built by a single Slater determinant solution of the KS equations with the exact exchange-correlation functional or approximations. In principle due to the Hogenberg-Kohn theorems these two electron densities should be the same, nevertheless it seems that they cannot be in certain cases. This is why I distinguish the two densities.