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

A procedure has been proposed to construct numerically the exchange-correlation εxc(r) and correlation εc(r) energy densities of density functional theory using the correlated first- and second-order density matrices from ab initio calculations. εc(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 εc(r) has been studied. The εc(r) have been compared with some density functional local and gradient-corrected models εcmod(r). The investigation of the shape of the model energy densities εcmod(r) has been extended to the Be2 and F2 molecules and the corresponding correlation energies Ec have been calculated and discussed for a number of atomic and molecular systems. The results show the importance of a proper modeling of εc(r) in the molecular bond midpoint region.