Pathological aspects of RHF band calculations for metallic chains

By analyzing the convergence properties of the lattice sums in the exchange part of the restricted Hartree–Fock orbital energy, we isolate the source of the nonanalytic behavior of a partially occupied band at the Fermi energy. This analysis shows how an extended system behaves qualitatively differently from a finite system but also provides a possibility of following the development of nonanalyticity as the size of the system grows.