The single-molecule magnet behavior found in mononuclear tetra-coordinate Fe-II complexes with trigonal monopyramidal coordination due to large magnetic anisotropy has been analyzed using theoretical methods based on CASSCF-RASSI calculations. We focus our study on the dependence of such magnetic properties on the geometrical parameters of the complexes (asymmetry of the ligands and the out-of-plane shift of the Fe-II cation with respect to the three equatorial nitrogen atoms) and the influence of the basicity of the N ligands. Low basicity, larger shifts, and larger distortions of the FeN4 central framework decrease the D value and increase the E value. Also, we predict similar magnetic properties for similar pentacoordinate complexes adding an axial ligand that will increase the chemical stability of such systems.