  We have recently proposed a Nonequilibrium Green's Function (NEGF) approach
to include Auger decay processes in the ultrafast charge dynamics of
photoionized molecules. Within the so called Generalized Kadanoff-Baym Ansatz
the fundamental unknowns of the NEGF equations are the reduced one-particle
density matrix of bound electrons and the occupations of the continuum states.
Both unknowns are one-time functions like the density in Time-Dependent
Functional Theory (TDDFT). In this work we assess the accuracy of the approach
against Configuration Interaction (CI) calculations in one-dimensional model
systems. Our results show that NEGF correctly captures qualitative and
quantitative features of the relaxation dynamics provided that the energy of
the Auger electron is much larger than the Coulomb repulsion between two holes
in the valence shells. For the accuracy of the results dynamical
electron-electron correlations or, equivalently, memory effects play a pivotal
role. The combination of our NEGF approach with the Sham-Schl\"uter equation
may provide useful insights for the development of TDDFT exchange-correlation
potentials with a history dependence.
