Natural energy orbitals and the one‐particle Green's function

It is shown how the properties of the one‐particle Green's function lead naturally to the definition of the so‐called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock‐like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock‐like energy expression. Moreover these orbitals form the basis for a self‐consistent scheme to calculate the one‐particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.