Towards a frequency independent incremental ab initio scheme for the self energy

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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.