The preceding results indicate that there are some important differences in the manner in which the hydroxamate groups of DFO and 4HMS envelope the Zr 4+ ion. In order to quantify these differences, we examined the orientation of the hydroxamate groups relative to the Zr 4+ ion, specifically in the free energy minima of DFO and 4HMS. For both systems, we considered two angles for each hydroxamate group: one formed by Zr 4+ -Oxygen-Nitrogen and another formed by Zr 4+ -Oxygen-Carbon, as depicted in the top panel of Fig. . In DFO, (bottom left panel of Fig. ), there are three groups correspondingly color-coded, with each group yielding two angles, while in 4HMS, (bottom right panel of Fig. ), there are four groups.