Towards a Frequency Independent Incremental Ab Initio Scheme for the Self Energy

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-dithiolbenzene 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.