Weighted-density-functional theories for the freezing of jellium

Quantum freezing of electrons in a uniform neutralizing background (jellium) at T=0 is studied by suitable extensions of classical density-functional schemes of the weighted-density type. We give a derivation of the schemes that clarifies (i) the basic approximations behind them, and (ii) the modifications---with respect to the case of uncharged particles---arising from the long range of Coulomb interactions. In particular, we present an application to quantum freezing of the so-called weighted-density approximation (WDA) and generalized effective liquid approximation. We also consider the modified WDA, a simplified version of the WDA introduced by Denton and Ashcroft, and recently tested on the quantum freezing of Bose hard spheres. All approaches use as input thermodynamic and structural information of the uniform quantum liquid and yield a reasonable description of the freezing transition. The results of the various approximations are critically examined and compared with both the predictions of quantum Monte Carlo and of the Ramakrishnan and Yussouff second-order theory.