Coordination number

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In chemistry, coordination number (c.n.), as defined originally in 1893 by Alfred Werner, is the total number of neighbors of a central atom in a chemical compound ^{[1] [2]}. 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. The highest bulk coordination number is 12, found in both hexagonal close-packed (HCP) and cubic close-packed (CCP) structures. This value of 12 corresponds to the theoretical limit of the kissing number problem.

Examples of high coordination number compounds are uranium and thorium bidentate nitrate-coordinated cluster compounds U(NO₃)₆^2- and Th(NO₃)₆^2-. When the surrounding ligands get smaller even higher coordination numbers are possible. One in silico study found a particularly stable PbHe₁₅²⁺ ion comprised of a central lead ion coordinated with no less than 15 helium atoms.^[3].