  We present an approach which is based on the one-particle irreducible (1PI)
generating functional formalism and includes electronic correlations on all
length-scales beyond the local correlations of dynamical mean field theory
(DMFT). This formalism allows us to unify aspects of the dynamical vertex
approximation (D\GammaA) and the dual fermion (DF) scheme, yielding a
consistent formulation of non-local correlations at the one- and two-particle
level beyond DMFT within the functional integral formalism. In particular, the
considered approach includes one-particle reducible contributions from the
three- and more-particle vertices in the dual fermion approach, as well as some
diagrams not included in the ladder version of D\GammaA. To demonstrate the
applicability and physical content of the 1PI approach, we compare the
diagrammatics of 1PI, DF and D\GammaA, as well as the numerical results of
these approaches for the half-filled Hubbard model in two dimensions.
