Exchange and correlation as a functional of the local density of states

A functional $E_{xc}[\rho(\r,\epsilon)]$ is presented, in which the exchange and correlation energy of an electron gas depends on the local density of occupied states. A simple local parametrization scheme is proposed, entirely from first principles, based on the decomposition of the exchange-correlation hole in scattering states of different relative energies. In its practical Kohn-Sham-like form, the single-electron orbitals become the independent variables, and an explicit formula for the functional derivative is obtained.Comment: 5 pages. Expanded version. Will appear in Phys. Rev.