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Why are coordination numbers below 3 and above 8 relatively rare?

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Structural diagram of the vitamin B12 coenzyme molecule, highlighting its organometallic core with five nitrogen-cobalt bonds and one cobalt-carbon bond at the center, surrounded by complex organic groups. — coordination compound Coordination compounds contain a central metal atom surrounded by nonmetal atoms or groups of atoms, called ligands. For example, vitamin B₁₂ is made up of a central metallic cobalt ion bound to multiple nitrogen-containing ligands.

The coordination number of a coordination compound is determined by a balance of factors, including the relative sizes of the central metal atom and the ligands, spatial (steric) constraints, and electronic factors such as the electronic configuration of the metal ion.1

While coordination numbers ranging from 1 to 16 are theoretically possible, those below 3 and above 8 are relatively rare due to these physical and electronic limitations. Specifically:1

Steric Constraints: The number of ligands that can be packed around a central metal atom is limited by the physical space available. If the central ion is too small, it cannot accommodate a high number of ligands without significant repulsion. Conversely, very low coordination numbers are less common because they often fail to satisfy the electronic stability requirements of the metal center.12
Electronic Factors: For many covalent complexes, the 18-electron rule serves as a guide for stability, favoring configurations that allow the metal to approach a stable valence shell. The number of available orbitals for bonding, which is influenced by the ligand field, also dictates the preferred coordination geometry and number.12