Hartree-Fock (HF) and local-density approximation (LDA) calculations of holes in symmetric molecular ions lead to conflicting results on the sign of the energy associated with reducing the symmetry. According to the HF theory, this energy can only be negative because it corresponds to a less restricted wave function. According to the LDA, it can only be positive because it is mostly electrostatic force that concentrate the hole charge in the vicinity of a single atom. In the present paper, we discuss these diverging views and present some LDA results for molecular ions with broken symmetry.43733483354