Weakly Inhomogeneous Electron Gas

The existence of the first HK theorem is quite surprising since electron-electron repulsion is a two-electron phenomenon and the electron density depends only on one set of electronic coordinates. Unfortunately, the universal functional is unknown and a plethora of different forms have been suggested that have been inspired by model systems such as the uniform or weakly inhomogeneous electron gas, the helium atom, or simply in an ad hoc way. A recent review describes the major classes of presently used density functionals [10]. 

Here we provide some details on inhomogeneous systems from the viewpoint of a weakly perturbed electron gas, i.e. we consider the external potential in the Hamiltonian (2.20) as a small perturbation. In this case one can expand the four current 6j r) induced by a static perturbation in a power series with respect to... 

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