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How does a ligand use an unshared electron pair to form a coordinate bond with a metal?

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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.

In the context of coordination chemistry, a ligand forms a coordinate bond with a metal ion by acting as a Lewis base, while the metal ion functions as a Lewis acid.12

The formation of this bond relies on the donation of an electron pair from the ligand to the metal. Specifically, the process involves the overlap of a filled orbital on the ligand—which contains an unshared pair of electrons—with an unoccupied (vacant) orbital on the central metal ion.132

This interaction is a type of covalent bond where both electrons in the shared pair are contributed by the ligand rather than being shared equally between the two atoms. Because the metal ion acts as an electron-pair acceptor, it can often accommodate multiple ligands simultaneously, depending on the available vacant orbitals and the spatial constraints of packing those ligands around the central atom. This coordinate bond is sometimes represented by an arrow pointing from the donor ligand to the acceptor metal ion.1423