Coordination Number Definition

What Is a Coordination Number in Chemistry?

illustration of atoms
The coordination number of diamond is 4. Each carbon atom in the crystal lattice is bound to four other carbon atoms. Alfred Pasieka/Getty Images

The coordination number of an atom in a molecule is the number of atoms bonded to the atom. In chemistry and crystallography, the coordination number describes the number of neighbor atoms with respect to a central atom. The term was originally defined in 1893 by Alfred Werner. The value of the coordination number is determined differently for crystals and molecules. The coordination number can vary from as low as 2 to as high as 16.

The value depends on the relative sizes of the central atom and ligands and by the charge from the electronic configuration of an ion.

The coordination number of an atom in a molecule or polyatomic ion is found by counting the number of atoms bound to it (note, not by counting the number of chemical bonds).

It's more difficult to determine chemical bonding in solid-state crystals, so the coordination number in crystals is found by counting the number of neighboring atoms. Most commonly, the coordination number looks at an atom in the interior of a lattice, with neighbors extending in all directions. However, in certain contexts crystal surfaces are important (e.g., heterogeneous catalysis and material science), where the coordination number for an interior atom is the bulk coordination number and the value for a surface atom is the surface coordination number.

In coordination complexes, only the first (sigma) bond between the central atom and ligands counts.

Pi bonds to the ligands are not included in the calculation.

Coordination Number Examples

  • Carbon has a coordination number of 4 in a methane (CH4) molecule since it has four hydrogen atoms bonded to it.
  • In ethylene (H2C=CH2), the coordination number of each carbon is 3, where each C is bonded to 2H + 1C for a total of 3 atoms.
  • The coordination number of diamond is 4, as each carbon atom rests at the center of a regular tetrahedron formed by four carbon atoms.

How To Calculate Coordination Number

Here are the steps for identifying the coordination number of a coordination compound.

  1. Identify the central atom in the chemical formula. Usually, this is a transition metal.
  2. Locate the atom, molecule, or ion nearest the central metal atom. To do this, find the molecule or ion directly beside the metal symbol in the chemical formula of the coordination compound. If the central atom is in the middle of the formula, there will be neighboring atoms/molecules/ions on both sides.
  3. Add the number of atoms of the nearest atom/molecule/ions. The central atom may only be bonded to one other element, but you still need to note the number of atoms of that element in the formula. If the central atom is in the middle of the formula, you'll need to add up the atoms in the entire molecule.
  4. Find the total number of nearest atoms. If the metal has two bonded atoms, add together both numbers,

Coordination Number Geometry

There are multiple possible geometric configurations for most coordination numbers.

  • Coordination Number 2 - linear
  • Coordination Number 3 - trigonal planar (e.g., CO32-), trigonal pyramid, T-shaped
  • Coordination Number 4 - tetrahedral, square planar
  • Coordination Number 5 - square pyramid (e.g., oxovanadium salts, vanadyl VO2+), trigonal bipyramid, 
  • Coordination Number 6 - hexagonal planar, trigonal prism, octahedral
  • Coordination Number 7 - capped octahedron, capped trigonal prism, pentagonal bipyramid
  • Coordination Number 8 - dodecahedron, cube, square antiprism, hexagonal bipyramid
  • Coordination Number 9 - three-face centered trigonal prism
  • Coordination Number 10 - bicapped square antiprism
  • Coordination Number 11 - all-faced capped trigonal prism
  • Coordination Number 12 - cuboctahedron (e.g., Ceric ammonium nitrate -(NH4)2Ce(NO3)6)
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Helmenstine, Anne Marie, Ph.D. "Coordination Number Definition." ThoughtCo, Feb. 15, 2017, thoughtco.com/definition-of-coordination-number-604956. Helmenstine, Anne Marie, Ph.D. (2017, February 15). Coordination Number Definition. Retrieved from https://www.thoughtco.com/definition-of-coordination-number-604956 Helmenstine, Anne Marie, Ph.D. "Coordination Number Definition." ThoughtCo. https://www.thoughtco.com/definition-of-coordination-number-604956 (accessed November 23, 2017).