Non-Closed-Shell Linear Chain: TheH4nSystem

The low-lying energy levels of a non-closed-shell linear chain consisting of $4n$ hydrogen atoms, each occupying a vertex of a regular polygon of $4n$ sides and contributing a single $1s$ electron, are studied with electron correlation taken into consideration in an approximate way within the framework of Löwdin's extension of the Hartree-Fock method. The nature of the wave functions and energy expressions for such a system with both orbital and spin degeneracies is discussed. It is shown that in the $n=3\mathrm{}$ case the energy levels have the correct asymptotic behavior as the interatomic separation $R$ assumes large values, and that a change of lattice spacing in the limit of small $R$ could lead to a magnetic transition.