A correlation potential for molecular systems from the single particle Green’s function

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Abstract
It is well known that the correlated ground state energy can be derived from a knowledge of the single particle Green’s function of a system, even though the two density cannot be obtained from it. In this paper it is shown that the single particle Green’s function in fact contains more detailed information than the total energy alone, to the extent that the local Slater‘xnLöwdin correlation potential can be obtained from it. This potential can be used as a more detailed criterion to judge the quality of approximate Green’s functions than the total energy by itself. The formalism leads moreover to a natural partitioning of the correlation energy into terms depending on the correlation correction to the one density alone and a remaining ‘‘true’’ correlation contribution. In this paper we calculate the single particle Green’s function using the second order approximation to the self-energy for a series of small model systems (He, Be, H2, LiH, and H2O). The correlation potential and the partitioning of the correlation energy are used to analyze this approximation and to assess its accuracy in these systems.