Understanding the Fermi surface and low-energy excitations of iron or cobalt pnictides is crucial for assessing electronic instabilities such as magnetic or superconducting states. Here, we propose and implement a new approach to compute the low-energy properties of correlated electron materials, taking into account both screened exchange beyond the local density approximation and local dynamical correlations. The scheme allows us to resolve the puzzle of BaCo2As2, for which standard electronic structure techniques predict a ferromagnetic instability not observed in nature.PACS numbers: 71.27.+a, 71.45.Gm, 74.70.Xa, The discovery of unconventional superconductivity in iron pnictides and chalcogenides in 2008 has aroused strong interest into the Fermi surfaces and low-energy excitations of transition metal pnictides and related compounds. Angle-resolved photoemission spectroscopy (ARPES) has been used to systematically map out quasiparticle dispersions, and to identify electron and hole pockets potentially relevant for low-energy instabilities [1][2][3][4][5][6][7]. Density functional theory (DFT) calculations have complemented the picture, yielding information about orbital characters [8], or the dependence of the topology of the Fermi surface on structural parameters or element substitution [9,10]. DFT within the local density approximation (LDA) or generalized gradient schemes has also served as a starting point for refined many-body calculations addressing band renormalizations and quasiparticle dispersions directly from a theoretical perspective (see e.g. Ref. [11][12][13][14][15][16][17][18]), and its combination with dynamical mean field theory (LDA+DMFT) [19][20][21][22][23][24][25] is nowadays the state-of-the-art ab initio many-body approach to low-energy properties of transition metal pnictides. Despite tremendous successes, however, limitations have also been pointed out e.g. in the description of the Fermi surfaces. Prominent examples include Ba(Fe,Co) 2 As 2 [26,27] or LiFeAs [14,26]. Interestingly, many-body perturbation theory approximating the selfenergy by its first order term in the screened Coulomb interaction W (so-called "GW approximation") results in a substantially improved description: calculations using the quasi-particle self-consistent (QS)GW method [28] have pinpointed non-local self-energy corrections to the LDA Fermi surfaces not captured in LDA+DMFT as pivotal [26]. Yet, as a perturbative method, GW cannot be expected to describe materials away from the weak coupling limit [29], and the description of incoherent regimes [13,17] including coherence-incoherence crossovers [30], local moment behavior [15] or the subtle effects of doping or temperature changes [17] are still reserved for DMFT.In this Letter, we propose and implement a new approach to the spectral properties of correlated electron materials taking into account screened exchange beyond the local density approximation and correlations as described by dynamical mean field theory with frequency-dependent local Hubbard inter...