A comparative study of Kohn–Sham, Brueckner and Hartree–Fock orbitals

Local correlation potentials from Brueckner coupled-cluster theory

Local correlation potentials have been obtained from the nonlocal Brueckner coupled-cluster correlation potentials for the rare-gas atoms He, Ne, and Ar and the CO molecule. It is shown that the local correlation potential can mainly be expressed as a sum of two components: a "pure" correlation part and a relaxation contribution. While the total correlation potentials show an oscillating behavior near the nuclei, indicating the atomic shell structure, their components decrease rather monotonously, with a step structure in case of Ne and Ar. By looking at the determinantal overlap and one-electron properties it has been found that the orbitals obtained from these local potentials form a determinant which very well corresponds with the Brueckner determinant. Thus the previously found closeness between the Hartree-Fock determinant and the exchange-only Kohn-Sham determinant [Della Sala and Gorling, J. Chem. Phys. 115, 5718 (2001)] is confirmed also for the correlated case.

Ab initio Correlation Effects in Density Functional Theories: An Electron-Distribution-Based Study for Neon

We have briefly reviewed the idea of studies aiming at such a bridging of the methodological gap between ab initio methods (or wave function theory (WFT)) and density functional theory (DFT) that would afford carrying over results concerning details of the structure of correlation effects from one method to the other. Special attention is paid to the problem of coverage of the WFT correlation effects by the exchange-correlation functionals of DFT. A short survey of the concept of supplementing energy-based investigations in this field by electron-density-based studies is given and illustrated by results for the Ne atom. DFT densities are generated for representatives of all four generations of presently used exchange-correlation functionals, including the recently developed orbital-dependent one. These densities are compared with WFT densities calculated at the MP2, MP3, and Brueckner determinant levels. It is found that the exchange-only parts of the local, gradient-corrected, and hybrid functionals account for the bulk of WFT correlation effects. The impact of the associated correlation functionals is very small and their physical nature is not quite clear. The situation is different for the orbital-dependent functional for which the exchange-only functional provides an almost exact description of the Hartree-Fock density. Here, the correlation effects are entirely represented by the correlation functional. Attention is also paid to the suitability of Kohn-Sham orbitals for the description of WFT correlation effects and to their presumptive similarity with Brueckner orbitals.