Variational total energies from phi- and Psi-derivable theories

Starting from many-body perturbation theory we have constructed a new varia tional expression for the total energy of many-electron systems. This expre ssion is a functional of two independent variables, the one-electron Green function and the screened Coulomb interaction. The new functional as well a s a much older variational expression by Luttinger and Ward (LW) are tested on the interacting electron gas. Both functionals yield extraordinary accu rate total energies although the new functional requires a much cruder inpu t and is therefore easier to apply to more realistic systems.