K. Peirs

Green’s function techniques are powerful tools for studying interacting many-fermion systems in a structural and diagrammatical way. The central equation in this method is the Dyson equation which determines, through an approximation for the self-energy, the Green’s function of the system. In a previous paper [J. Chem. Phys. 115, 15 (2001)] a self-consistent solution scheme of the Dyson equation up to second order in the interaction, the Dyson(2) scheme, has been presented for closed-shell atoms. In this context, self-consistency means that the electron propagators appearing in a conserving approximation for the self-energy are the same as the solutions of the Dyson equation, i.e., they are fully dressed. In the present paper this scheme is extended to open-shell atoms. The extension is not trivial, due to the loss of spherical symmetry as a result of the partially occupied shells, but can be simplified by applying an appropriate angular averaging procedure. The scheme is validated by studying the second-row atomic systems B, C, N, O, and F. Results for the total binding energy, ionization energy and single-particle levels are discussed in detail and compared with other computational tools and with experiment. In open-valence-shell atoms a new quantity—the electron affinity—appears which was not relevant in closed-shell atoms. The electron affinities are very sensitive to the treatment of electron correlations, and their theoretical estimate is a stringent test for the adequacy of the applied scheme. The theoretical predictions are in good agreement with experiment. Also, the Dyson(2) scheme confirms the nonexistence of a stable negative ion of N. The overall effect of the self-consistent Dyson(2) scheme with regard to the Dyson(1) (i.e., Hartree–Fock) concept, is a systematic shift of all quantities, bringing them closer to the experimental values. The second-order effects turn out to be indispensable for a reasonable reproduction of the electron affinity. © 2002 American Institute of Physics.

In this paper, the single-particle Green’s function approach is applied to the atomic many-body problem. We present the self-consistent solution of the Dyson equation up to second order in the self-energy for nonrelativistic spin-compensated atoms. This Dyson second-order scheme requires the solution of the Hartree–Fock integro-differential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a basis set). To cope with the huge amount of poles generated in the iterative approach to tackle Dyson’s equation in second order, the BAGEL (BAsis GEnerated by Lanczos) algorithm is employed. The self-consistent scheme is tested on the atomic systems He, Be, Ne, Mg, and Ar with spin-saturated ground state 1S0. Predictions of the total binding energy, ionization energy, and single-particle levels are compared with those of other computational schemes [density functional theory, Hartree–Fock (HF), post-HF, and configuration interaction] and with experiment. The correlations included in the Dyson second-order algorithm produce a shift of the Hartree–Fock single-particle energies that allow for a close agreement with experiment. © 2001 American Institute of Physics.