On the connections between Brueckner–coupled-cluster,density-dependent Hartree–Fock,and density functional theory

The existence of an effective one-particle Hamiltonian in the Brueckner coupled cluster model naturally leads to the definition of an effective interaction G, which is a function of the T₂ amplitudes. Two types of approximations to G are proposed: One is purely phenomenological, while the other is based on approximations to the Brueckner T₂ equation. In both cases, the resulting effective interaction may be viewed as electron-density-dependent. Generalizing Hartree–Fock theory to accommodate density-dependent interactions (DDHF ), a method is obtained that is capable of accounting for correlation effects in an independent particle framework. The heuristic Skyrme force, successfully used in nuclear physics to model nucleon–nucleon interactions, is presented here as an example of an effective electron–electron correlation interaction. Due to the δ-function character of the Skyrme force, it is possible to express the energy in this model by an integral over an energy density, thus formally providing a connection between DDHF and density functional theory for this particular case. An approximation to the Brueckner T₂ equation is also proposed in the coordinate representation. In this model, the density-matrix dependence of T₂ is reduced to a nonlocal electron density dependence by means of an expansion which introduces terms that depend on the gradient of the density. The first term in this expansion amounts to a “local density approximation” to Brueckner coupled cluster theory. © 1995 John Wiley & Sons, Inc.