Correlation energy density from ab initio first- and second-order density matrices: A benchmark for approximate functionals

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Abstract
A procedure has been proposed to construct numerically the exchange‐correlation εxc(r) and correlation ε c (r) energy densities of density functional theory using the correlated first‐ and second‐order density matrices from ab initio calculations. ε c (r) as well as its kinetic and potential components have been obtained for the two‐electron He atom and H2 molecule. The way various correlation effects manifest themselves in the form of ε c (r) has been studied. The ε c (r) have been compared with some density functional local and gradient‐corrected models ε c mod(r). The investigation of the shape of the model energy densities ε c mod(r) has been extended to the Be2 and F2 molecules and the corresponding correlation energies E c have been calculated and discussed for a number of atomic and molecular systems. The results show the importance of a proper modeling of ε c (r) in the molecular bond midpoint region.