Metallic state of the free-electron gas within the self-interaction-corrected local-spin-density approximation

The uniform-density electron gas is studied within the framework of the Wannier-function (WF) formulation of the self-interaction-corrected local-spin-density approximation (SIC-LSD). While the results of the present work follow rigorously from a variational formulation, they may also be qualitatively understood in terms of the local-bonding-site concept introduced by Mott in his theory of the metal-insulator transition. SIC-LSD admits metallic-state solutions at ordinary electron densities just as in traditional LSD theory. The result of introducing SIC to the metallic state is an overall downward shift of the LSD eigenvalues. This shift is largest for states near k=0 and vanishes for states near the Fermi energy ${\varepsilon }_F$. As such, the orbital energies at ${\varepsilon }_F$ are found to be in exact agreement with both the exchange-only version of LSD and Hartree-Fock (HF). Beyond metallic-state solutions, this formulation of SIC-LSD also admits insulator solutions at very low electron densities and may thus have important application to the problem of Wigner crystallization.