Coordination number

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In chemistry, the coordination number (c.n.) is the sum of the total number of neighbors of a central atom in a chemical compound and the number of lone pairs on it. In methane the coordination number for the carbon atom is 4. In inorganic chemistry the number of sigma bonds between ligand and the central atom count but not the number of pi bonds.

In materials science, the bulk coordination number is the number of atoms touching any other atom in a crystal lattice. It differs significantly from the chemistry definition because while diamond (which is entirely made of carbon) has a coordination number of 4, graphite (which is also entirely made out of carbon) has a coordination number of 3. It differs from the surface coordination number which is always less than the bulk coordination number. The surface coordination number is dependent on which Miller index the surface uses. In a body-centered cubic (BCC) crystal, the bulk coordination number is 8, whereas for the (100) surface, the surface coordination number is 4.

There are many definitions of the term coordination number, but there is no one simple unambiguous definition that works in all cases. For simple monodentate and chelating ligands, the coordination number can be defined as the number of atoms or ligands directly bonded to the metal atom. For example, [Fe(NH3)6]3+ and [Fe(en)3]3+ are both 6-coordinate complexes. But complications quickly arise when one considers the bonding of alkene or alkenyl fragments such as ethylene and cyclopentadienyl. For example, in ferrocene all ten cyclopentadienyl carbons are equally bonded to the iron center, but few would call this a 10-coordinate complex. Given the reactivity and bonding of ferrocene, calling it a 2-coordinate complex doesn't seem quite right either. The general consensus is to consider ferrocene a six coordinate species because there are six electron pairs on the ligands that participate in bonding (using the ionic formalism).

While this method seems to alleviate the problem, it adds further complications. Here are some examples:

Alkoxide, imido and oxo ligands can donate one, two or three pairs of electrons to a metal center, but in all cases each only occupies one coordination site.

Cp2TiCl2 would not be considered an 8-coordinate complex by most chemists!

Alkene complexes can be drawn as neutral two electron donors but are sometimes considered dianionic bidentate ligands. Either way, alkenes are usually considered to occupy only one coordination site. Whew! This isn't easy. The way that I suggest is to count each pair of electrons donated to the metal, ignoring any pi-donation that is localized on a single atom. This allows you to count the pi and delta-type orbitals on cyclopentadiene, but ignore the pi-electrons from an imido ligand.