## Self-consistent solution of Dyson's equation up to second order for closed- and open-shell atomic systems

### Abstract

Green's function techniques offer new methods based upon perturbation theory to study many-body systems. The computational cost in these schemes is substantially higher than in density functional theory (DFT), but they offer a clear picture of the nature of correlations included in the calculations. In this way, a connection between the Green's function scheme and DFT can learn more about the underlying mechanisms of the latter. Therefore, we need the correlated density of some carefully selected systems. In this work, a numerical scheme is presented to solve the Dyson equation up to second order self-consistently for a few closed-shell (He, Be, Ne, Mg, and Ar) and open-shell (B, C, N, O, and F) atoms in coordinate space. A detailed discussion is held on the reproduction of total binding energies, ionization energies, electron affinities, and spectral strength distributions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003