  We investigate the DFT+U approach as a viable solution to describe the
low-lying states of ligated and unligated iron heme complexes. Besides their
central role in organometallic chemistry, these compounds represent a
paradigmatic case where LDA, GGA, and common hybrid functionals fail to
reproduce the experimental magnetic splittings. In particular, the imidazole
pentacoordinated heme is incorrectly described as a triplet by all usual DFT
flavors. In this study we show that a U parameter close to 4 eV leads to spin
transitions and molecular geometries in quantitative agreement with
experiments, and that DFT+U represents an appealing tool in the description of
iron porphyrin complexes, at a much reduced cost compared to correlated
quantum-chemistry methods. The possibility of obtaining the U parameter from
first-principles is explored through a self-consistent linear-response
formulation. We find that this approach, which proved to be successful in other
iron systems, produces in this case some overestimation with respect to the
optimal values of U.
