The coordination geometry of the iron center in the active site of hemoglobin is an octahedral geometry. In this geometry, the iron II atom is coordinated to six ligands. Four of these ligands are nitrogen atoms from the imidazole rings of histidine residues in the protein, forming a planar porphyrin ring. The fifth ligand is a nitrogen atom from a histidine residue called the proximal histidine that lies below the porphyrin plane. The sixth coordination site, which is above the porphyrin plane, is where oxygen binds.When oxygen is not bound to the iron center, the iron II atom is slightly out of the porphyrin plane, and the coordination geometry is distorted. Upon binding of oxygen, the iron II atom moves into the porphyrin plane, and the coordination geometry becomes more regular. This change in geometry is transmitted through the protein structure, leading to a conformational change in the hemoglobin molecule. This conformational change increases the affinity of the other subunits in the hemoglobin tetramer for oxygen, a phenomenon known as cooperativity.In summary, the octahedral coordination geometry of the iron center in the active site of hemoglobin plays a crucial role in the binding of oxygen. The geometry change upon oxygen binding leads to conformational changes in the protein, which in turn affect the oxygen-binding properties of the entire hemoglobin molecule.