Current Density Functional Theory

Abstract

The basic concern of density functional theory is the groundstate energy of an inhomogeneous interacting many-particle system as a function of the external potential acting on its density (and possibly as a function of the particle number, allowing for the consideration of ionization energies, affinities, and excitation gaps). This groundstate energy function is replaced by its Legendre transform as a function of the particle density, and the Legendre back transformation leads via insertion of an interaction-free reference system to an effective one-particle equation whose solution finds the ground-state energy and density to any given external potential. As was seen in Part I, this theory provides rather a reformulation than a solution of the many-body problem for the groundstate, because it does not explicitly provide the Legendre transform H[n] to E[v, N] (cf. (6.35, 6.31, and 6.36). The original many-body problem is now contained in H[n] which only can be guessed, although not without success.