Kohn-Sham equations for multicomponent systems: The exchange and correlation energy functional

Kohn-Sham equations for multicomponent systems are derived in a rigorous way that permits the precise definition and discussion of the exchange and correlation energy, of the System as a functional of the densities of the components. In the case of a two-component electron-ion system, with n(e),n(I) the electron and ion densities, the exchange and correlation energy of the system E-XC[n(e),n(I)] is composed of E-XC[n(e)] the electron-electron exchange and correlation energy, E-XC(II)[n(I)] the ion-ion exchange and correlation energy, and E-c(eI)[n(e),n(I)] the electron-ion correlation energy. E-XC[n(e)] is exactly the functional encountered in the Kohn-Sham theory of electronic systems. The behavior of E-XC(II)[n(I)] is investigated in the limit of a large ion mass and its relation with E-XC[n(e)] for n(e) = n(I), is discussed. The structure of E-c(eI)[n(e),n(I)] is analyzed in the adiabatic approximation. In the special case of perfectly localized ion densities, E-XC(II)[n(I)] results in a self-interaction correction while E-c(eI)[n(e),n(I)] vanishes.