coordination number
/ abbreviated CN /
How crowded is the metal? Around any central metal there is room for only so many groups to crowd in and bond. The coordination number is simply the count of those directly bonded points — how many donor atoms are actually touching the metal. It is Werner's 'secondary valence' under its modern name.
Precisely, the coordination number is the number of donor atoms bonded directly to the central metal in a complex. Crucially, it counts donor atoms, not ligands: in [Co(NH3)6]3+ six ammonias give a coordination number of 6, but in [Co(en)3]3+ the three bidentate ethylenediamine ligands also give a coordination number of 6, because each en supplies two donor nitrogens. The most common numbers are 6 (the king of the field), 4, then 2 and 5; higher numbers like 7, 8, and 9 appear with large metals and small ligands, especially among the lanthanides. What sets it is a balance: a small, highly charged metal wants many ligands; bulky ligands and a small metal allow only a few.
Coordination number is the first thing you establish about a complex because it dictates the geometry: 2 usually means linear, 4 means tetrahedral or square planar, 6 means octahedral. From there follow the possible isomers and much of the chemistry. It is also why the same metal in different oxidation states or with different ligands can adopt different shapes — coordination number is not fixed by the metal alone.
[PtCl4]2- and [Co(en)3]3+ both look like they have a handful of ligands, but their coordination numbers differ. Platinum here has coordination number 4 (four chloride donors). Cobalt has coordination number 6 — three ethylenediamines, but each supplies two nitrogen donors, so 3 x 2 = 6.
Count donor atoms, not ligands: three bidentate ligands still give a coordination number of six.
The classic trap is counting ligands instead of donor atoms. One bidentate ligand contributes two to the coordination number, and one EDTA can contribute six all by itself. Always ask how many atoms actually bond, not how many molecules are present.