The coordination geometry of the heme group in the active site of hemoglobin is a distorted octahedral geometry. The heme group consists of a central iron Fe atom coordinated to a porphyrin ring, which is a large organic molecule with four nitrogen atoms. The iron atom forms six coordination bonds in total: four equatorial bonds with the nitrogen atoms of the porphyrin ring, one axial bond with a nitrogen atom from a histidine residue of the protein called the proximal histidine , and one remaining axial bond available for oxygen binding called the distal site .The distorted octahedral geometry of the heme group facilitates oxygen binding and release through a mechanism called "induced fit." When oxygen is not bound to the heme group, the iron atom is slightly out of the plane of the porphyrin ring. Upon oxygen binding, the iron atom moves into the plane of the porphyrin ring, causing a conformational change in the histidine residue and the overall protein structure. This change in the protein structure stabilizes the binding of oxygen and increases the affinity of the other heme groups within the hemoglobin tetramer for oxygen, a phenomenon known as cooperativity.When hemoglobin is in a low-oxygen environment, such as in the tissues, the protein conformation changes again, causing the iron atom to move out of the plane of the porphyrin ring. This change in geometry weakens the bond between the iron atom and the oxygen molecule, facilitating the release of oxygen to the surrounding tissues.In summary, the distorted octahedral coordination geometry of the heme group in hemoglobin plays a crucial role in the binding and release of oxygen, allowing hemoglobin to efficiently transport oxygen from the lungs to the tissues and return carbon dioxide to the lungs for exhalation.