Hedin derived a closed set of equations that define the single-particle Green's function G 1 (r 1 t 1 , r 2 t 2 ) for an interacting set of electrons . The main idea is to truncate an infinite hierarchy of equations of motions for G 1 depending on higher-order Green's functions G 2 , G 3 , ... by the introduction of the self-energy Σ(r 1 t 1 , r 2 t 2 ) which is an effective non-local, non-Hermitian potential, accounting for all many-body exchange and correlation terms that are beyond the scope of Hartree contributions.