Brueckner Orbitals and Density-Functional Theory

By means of Many-Body Perturbation Theory (MBPT) it is shown that minimizing the energy expectation value of a closed-shell system in a certain order of the preturbation expansion by varying the partitioning of the Hamiltonian, leads to a zeroth-order function, which – as the order of perturbation increases and provided the expansion converges properly – approaches a determinant of Brueckner orbitals. It is also shown that the energy eigenvalues of the Brueckner orbitals represent the corresponding ionization energies of the system, including orbital-relaxation and correlation effects to all orders of perturbation theory. This is a generalization of the Koopmans theorem in Hartree-Fock theory. The MBPT treatment is used for a discussion of the Density-Functional Theory (DFT), and a new model is proposed – referred to as the Brueckner–Kohn-Sham (BKS) scheme – where also the electron correlation is included in the functional. This leads to a non-local exchange-correlation potential, quite similar to that of Brueckner orbitals (BO), implying that the orbitals of the new scheme are essentially BO. Arguments are given that also the orbitals of other schemes with a purely local potential, such as the standard Kohn Sham (KS) scheme, would be close to BO. This has been conjectured by Heßelmann and Jansen (J. Chem. Phys. 112, 6949 (2000)), and the present work gives more direct evidence of that. This might explain the recent observations that the KS orbitals and energy eigenvalues do have more physical significance than was originally anticipated.