  The frequency dependence of the self energy of a general many--body problem
is identified as a main obstacle in correlation calculations based on local
approaches. A frequency independent formulation is proposed instead and proven
to yield exactly the same numerical results as the original common scheme. Our
approach is embedded in a general local-orbital based ab initio frame to obtain
the Green's function for large heterogenous systems. First a Green's function
formalism is introduced. Then the self energy is constructed from an
incremental scheme. Subsequently we apply the proposed frequency independent
formulation. The theory is applied to para-ditholbenzene as a realistic system
and the numerical accuracy of the correlation contributions obtained from our
frequency independent access are carefully tested against the exact frequency
dependent results. Perfect agreement is reached and a speed--up of a factor 50
is established for the incremental scheme.
