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We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion <inline-formula> <math display="inline"> <semantics> <msup> <mi>U</mi> <mo>′</mo> </msup> </semantics> </math> </inline-formula> and Hund exchange <i>J</i>. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, <inline-formula> <math display="inline"> <semantics> <msup> <mi>U</mi> <mo>′</mo> </msup> </semantics> </math> </inline-formula> changes the relative position of the peaks in the density of states, particularly on the iron <inline-formula> <math display="inline"> <semantics> <msub> <mi>d</mi> <msup> <mi>z</mi> <mn>2</mn> </msup> </msub> </semantics> </math> </inline-formula> orbital, which is expected to affect the binding of ligands greatly.