Energy of many-electron systems in an approximation related to an extension of Koopmans’ theorem

One-electron energies (ionization potentials and electron affinities) and corresponding orbitals (one-particle overlap integrals) obtained in terms of an extension of Koopmans’ theorem were used to calculate the total energy of an electron system. The operators of the equations of the extended Koopmans’ theorem were expressed in terms of the zero and first moments of the frequency distribution of the one-particle Green’s function. As a result, along with the nonlinear Dyson equation, a closed system of equations was obtained, which can be solved self-consistently.