This record contains distributions explored by a Markov chain Monte Carlo. It also contains the Density Functional Theory (DFT) modeling of a selected number of iron-based compounds. The DFT modeling was performed using Vienna Ab initio Simulation Package (VASP). The following describes the included files: 1. POSCAR : Initial crystal structure 2. CONTCAR : Final crystal structure 3. KPOINTS : Mesh grid used in the sampling of the momentum space 4. INCAR : VASP input variables such as the plane-wave expansion cutoff energy, Hubbard parameters, etc. 5. LDA.txt : Points sampled from the U and J Hubbard parameter space using the local density approximation. The first, second, and third columns represent U, J, and psi, respectively. 6. PBE.txt : Points sampled from the U and J Hubbard parameter space using the generalized gradient approximations PBEsol. The first, second, and third columns represent U, J, and psi, respectively. 7. PBEsol.txt : Points sampled from the U and J Hubbard parameter space using the generalized gradient approximations PBEsol. The first, second, and third columns represent U, J, and psi, respectively.