The electronic structure of linear Beryllium chains has been theoretically studied by using ab initio methods. It turns out that, for internuclear distances close to the equilibrium structure, two partially filled edge orbitals ('end states') localize at the chain ends. This gives rise to two low-lying states, a singlet ground state, (1)Sigma(g), and a quasi-degenerate triplet, (3)Sigma(u). The energy splitting goes rapidly to zero as the number of atoms in the chain is increased. Preliminary investigations indicate that this could be a general behavior shared by the metals belonging to the Groups 2 and 12. (c) 2008 Elsevier B. V. All rights reserved.