The coordination geometry of the active site in the metalloprotein hemoglobin is an octahedral geometry. Hemoglobin is a tetrameric protein, consisting of four subunits, each containing a heme group with an iron Fe atom at its center. The heme group is responsible for binding and releasing oxygen molecules.In the octahedral geometry, the iron atom is coordinated to six ligands. Four of these ligands are nitrogen atoms from the porphyrin ring of the heme group, which form a square plane around the iron atom. The fifth ligand is a nitrogen atom from a histidine residue in the protein, which is positioned below the plane. The sixth coordination site, positioned above the plane, is available for binding to an oxygen molecule.The octahedral geometry allows for the selective binding and release of oxygen in the blood due to the following reasons:1. Steric hindrance: The oxygen-binding site is partially shielded by the surrounding protein structure, which prevents larger molecules like carbon dioxide CO2 and nitrogen N2 from binding to the iron atom.2. Cooperative binding: The binding of oxygen to one heme group in hemoglobin increases the affinity of the other heme groups for oxygen. This is due to a conformational change in the protein structure, which makes it easier for additional oxygen molecules to bind. This cooperative binding allows hemoglobin to efficiently pick up oxygen in the oxygen-rich environment of the lungs and release it in the oxygen-poor environment of the tissues.3. Allosteric regulation: Hemoglobin's affinity for oxygen is also regulated by allosteric effectors, such as protons H+ , carbon dioxide CO2 , and 2,3-bisphosphoglycerate 2,3-BPG . These molecules bind to hemoglobin at sites distinct from the oxygen-binding site and stabilize the low-affinity, deoxygenated form of the protein. This promotes the release of oxygen in the tissues, where the concentration of these allosteric effectors is higher.In summary, the octahedral coordination geometry of the active site in hemoglobin, along with the protein's structural features and allosteric regulation, allows for the selective binding and release of oxygen in the blood, ensuring efficient oxygen transport throughout the body.