Treatments of interelectronic repulsion that avoid four-center integrals have been incorporated in ab initio, electron-propagator calculations with diagonal self-energy matrices. Whereas the formal scaling of arithmetic operations in the propagator calculations is unaffected, the reduction of storage requirements is substantial. Moreover, the scaling of integral transformations to the molecular orbital base is lowered by one order. Four-index, electron-repulsion integrals are regenerated from three-index intermediates. Test calculations with widely applied self-energy approximations demonstrate the accuracy of this approach. Only small errors are introduced when this technique is used with quasiparticle virtual orbitals, provided that conventional techniques of integral evaluation are used in the construction of density-difference matrices.

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