Magnetic properties of the family of Mn-6 complexes with oximato bridging ligands, some of them showing the highest anisotropy energy barriers known to date, have been studied using theoretical methods based on density functional theory. The different magnetic behaviors, total spin values from 4 to 12, are well reproduced by the calculated exchange coupling constants. The analysis of the magnetostructural correlations indicates that the Mn-N-O-Mn torsion angles play a crucial role, with the out-of-plane shift of the central oxo bridging ligand involved to a lesser degree. The Mn-N-O-Mn torsion angles are mainly controlled by the existence of an intramolecular hydrogen bond between the NO group of the bridging ligand and the substituents of the equatorial oximato bridging ligand and the presence of bulky substituents in the axial carboxylato ligands.