Self-consistent solution of Dyson's equation up to second order for atomicsystems

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 th e Dyson equation up to second order in the self-energy for nonrelativistic spin-compensated atoms. This Dyson second-order scheme requires the solutio n of the Hartree-Fock integro-differential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a ba sis 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 GEner ated by Lanczos) algorithm is employed. The self-consistent scheme is teste d on the atomic systems He, Be, Ne, Mg, and Ar with spin-saturated ground s tate S-1(0). Predictions of the total binding energy, ionization energy, an d single-particle levels are compared with those of other computational sch emes [density functional theory, Hartree-Fock (HF), post-HF, and configurat ion interaction] and with experiment. The correlations included in the Dyso n second-order algorithm produce a shift of the Hartree-Fock single-particl e energies that allow for a close agreement with experiment. (C) 2001 Ameri can Institute of Physics.