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We present an approach that combines the local density approximation (LDA)and the dynamical mean-field theory (DMFT) in the framework of thefull-potential linear augmented plane waves (FLAPW) method. Wannier-likefunctions for the correlated shell are constructed by projecting local orbitalsonto a set of Bloch eigenstates located within a certain energy window. Thescreened Coulomb interaction and Hund's coupling are calculated from afirst-principle constrained RPA scheme. We apply this LDA+DMFT implementation,in conjunction with continuous-time quantum Monte-Carlo, to study theelectronic correlations in LaFeAsO. Our findings support the physical pictureof a metal with intermediate correlations. The average value of the massrenormalization of the Fe 3d bands is about 1.6, in reasonable agreement withthe picture inferred from photoemission experiments. The discrepancies betweendifferent LDA+DMFT calculations (all technically correct) which have beenreported in the literature are shown to have two causes: i) the specific valueof the interaction parameters used in these calculations and ii) the degree oflocalization of the Wannier orbitals chosen to represent the Fe 3d states, towhich many-body terms are applied. The latter is a fundamental issue in theapplication of many-body calculations, such as DMFT, in a realistic setting. Weprovide strong evidence that the DMFT approximation is more accurate and morestraightforward to implement when well-localized orbitals are constructed froma large energy window encompassing Fe-3d, As-4p and O-2p, and point out severaldifficulties associated with the use of extended Wannier functions associatedwith the low-energy iron bands. Some of these issues have important physicalconsequences, regarding in particular the sensitivity to the Hund's coupling.

Dynamical Mean-Field Theory within an Augmented Plane-Wave Framework: Assessing Electronic Correlations in the Iron Pnictide LaFeAsO