Is density functional theory free of spatial symmetry breaking? The case of the linear carbon radical cations: C3+, C5+, C7+, and C9+

Spatial symmetry breaking is examined numerically for the linear Cn+ (n=3, 5, 7, 9) radical cations with hybrid B3LYP and local BP86 functionals. B3LYP clearly breaks spatial symmetry for 2Σu+ D∞h structures for C3+ and C5+. BP86 does not break spatial symmetry but generates lower-symmetry lower-energy 2ΣC∞v solutions which are not connected with the 2Σu+ D∞h structures starting from C5+. The 2Πg and 2Πu electronic states do not suffer from spatial symmetry breaking. The bent C3+, kinked C5+, and quasi-linear C2v and C2h structures of C7+ and C9+ are the lowest energy chains.