This paper reports extensive calculations on the structural, thermodynamic, and mid-infrared spectroscopic properties of neutral and cationic model iron-polycyclic aromatic hydrocarbon (PAH) complexes of astrophysical interest for three PAHs of increasing size, namely, naphthalene (C10H8), pyrene (C16H10), and coronene (C24H12). Geometry optimizations and frequency calculations were performed using hybrid Hartree-Fock/density functional theory (DFT) methods. The use of DFT methods is mandatory in terms of computational cost and efficiency to describe the electronic and vibrational structures of such large organometallic unsaturated species that present several low-energy isomers of different structures and electronic and spin states. The calculated structures for the low-energy isomers of the model Fe-PAH and Fe-PAH(+) complexes are presented and discussed. Iron-PAH binding energies are extracted, and the consequences of the coordination of iron on the infrared spectra of neutral and cationic PAHs are shown with systematic effects on band intensities and positions being demonstrated. The first results are discussed in terms of astrophysical implications. This work is the first step of an ongoing effort in our group to understand the photophysics and spectroscopy of iron-PAH complexes in the conditions of the interstellar medium using a synergy between observations, laboratory experiments, and theory.