Hartree-Fock density of states for extended systems

The density of states (DOS) of extended systems, calculated at the rigorous Hartree-Fock (HF) level, can have a number of unphysical features. It is shown analytically that in partially filled band systems (crystals, thin films, polymers) the HF DOS vanishes at the Fermi energy, regardless of Fermi-surface shape. HF DOS will also vanish, in the (rare) event that an equienergetic surface $S$ for an energy different from the Fermi energy coincides with the Fermi surface $S_F$. Additional features such as shoulders, peaks, or near gaps can occur at energies with surfaces $S$ close to $S_F$. No HF-related zero DOS arises in filled-band extended systems. Published HF DOS are discussed. A detailed summary of expressions for crystal HF matrix elements in momentum representation is given. Their modification for thin films and polymers is indicated.