  In this short paper, the validity of Koopmans' theorem in the Hartree-Fock
theory at non-zero temperature (Hartree-Fock statistical theory) is
investigated. It is shown that Koopmans' theorem does not apply in the
grand-canonical ensemble, due to a missing contribution to the energy
proportional to the interaction between two electrons belonging to the same
orbital. Hartree-Fock statistical theory has also been applied in the canonical
ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of
photo-absorption calculations. In that case, the Hartree-Fock
self-consistent-field equations are derived in the super-configuration
approximation. It is shown that Koopmans' theorem does not hold in the
canonical ensemble, but that a restricted version of the theorem can be
obtained, by assuming that a particular quantity multiplying the interaction
matrix element in the expression of the energy does not change during the
removal of an electron.
