Variational energy functionals of the Green function tested on molecules

It was recently proposed to use variational functionals based on manybody perturbation theory for the calculation of the total energies of many-electron systems. The accuracy of such functionals depends on the degree of sophistication of the underlying perturbation expansions. The energy functionals are variational in the sense that they can be evaluated at rather crude approximations to their independent variables which are the one-electron Green function, or the one-electron Green function and the dynamically screened electron interaction. The functionals were previously applied to the electron gas and shown to be extraordinarily accurate already at the level of the so-called GW approximation (GWA). In the current work we have tested the functional due to Luttinger and Ward, which is a functional of the Green function. Using density functional theory (DFT) and Hartree-Fock Green functions as input variables, we have calculated total energies of diatomic molecules at the level of the GWA as well as with second-order exchange effects included. We will also discuss various other variational energy functionals, including DFT orbital functionals based on many-body perturbation theory. (C) 2004 Wiley Periodicals, Inc.