Coordination Number

Coordination number, or ligancy, refers to the number of atoms, molecules, or ions (ligands) bonded to the central atom or ion through coordinate/dative covalent bond. 

In Werner’s theory for coordination compounds, the coordination number is also referred to as secondary valency. The secondary valency is unionizable, unlike the primary valency.

For example, in the coordination complex [Mo(CN)8]4-, the coordination number is 8, and in [AlF6]3-, it is 6.


Coordination numbers can be determined using X-ray crystallography and other related techniques such as electron or neutron diffraction.

There are different kinds of forces that hold the species in complexes together, leading to the observed coordination numbers.

In complexes with fluoride ions as ligands, the interactions are electrostatic with the central atom/ion. This is because of the high electronegativity of the fluorine atoms. The coordination number of fluoride complexes of B3+, Fe3+, and Zr4+ are 4, 6, and 7 respectively. The larger size of the central ion allows more fluoride ions to surround it, causing a successive increase in the coordination number. 

This is also the case for hydrated cations, in which the electrostatic force is the coordinating bond between the central cation and the partial negative charge on the oxygen atom of the water molecule.

On the other hand, in many complexes, such as those of cyanide ions, halide ions (except F), carbon dioxide and ammonia molecules, the bonds are characteristically covalent. The coordination number in this case depends on the nature of the bond orbitals of the central atom. 

After the crystal field theory (point charges), the modified ligand field theory assumes that the orbitals available for bonding and hence the coordination number depend on the arrangement and field strength of ligands.

The ligand field strength can be determined from the spectrochemical series.

Coordination numbers and geometries

According to Alfred Werner, the secondary valencies always have a fixed orientation in space around the metal.

A coordination number of 2 results in a linear geometry. Example: [Ag(NH3)2]+

However, a coordination number of 4 may result in the more common tetrahedral geometry, or the square planar one, which is the characteristic of metal ions with 8 d-electrons. [FeCl4] and [Ni(CN)4]2- are examples of tetrahedral and square planar geometries, respectively.

A complex with a coordination number of 6 such as [Co(CN)6]3- will assume an octahedral geometry. Alternatively, complexes with trigonal prismatic geometry also occur, such as [W(CH3)6].

Geometries and Coordination Numbers

Coordination numbers for transition metal complexes range from 2 to 9. 

For f-block element complexes, the coordination number normally ranges from 8 to 12. This is because the lanthanides and actinides are larger in size and have more orbitals available for bonding.

Polyhapto Ligands

The special nature of bonding of unsaturated hydrocarbons with metals with their π-electrons has led to the development of the hapto or eta “𝜂” nomenclature to designate the unique bonding modes of organometallic compounds. 

Various unsaturated organic ligands such as allyl (C3H5), cyclopentadienyl (C5H5), or benzene (C6H6) can bind to a metal ion in more than one way. The different bonding modes being distinguished by the number of carbon atoms participating in the linkage.

The Greek symbol “𝜂” is used to indicate the connectivity between the metal and ligands. The number of atoms in ligands directly coordinated with the metal is indicated by that very number in the superscript of the “𝜂” symbol.

For example, 𝜂6 indicates 6 carbon atoms attached to the metal. Benzene is an example of a hexahapto ligand. Alternatively, if only two carbon atoms of the benzene ring are attached to the metal, it will act as 𝜂2-benzene.

Allotropes of Carbon

The two common allotropes of carbon have different coordination numbers. In diamond, there is a tetrahedral arrangement and each carbon atom is directly bonded to four other carbon atoms, so the coordination number is 4.

As of graphite, each carbon atom is bonded to three other carbon atoms in the form of a single layer, and so the coordination number is 3.

Coordination Number for Lattices

In a NaCl lattice, each sodium ion has 6 chloride ions surrounding it immediately, positioned at the center of each face of a cube (or at the corners of a tetrahedron). Likewise, each chloride ion has 6 sodium ions surrounding it in the same manner, making the coordination number 6:6.

Sodium chloride lattice

Comparatively, in CsCl, each cesium ion has 8 chloride ions immediately surrounding it at the corners of a cube, and each chloride ion has 8 cesium ions surrounding it the same way. So the coordination number is 8.

Caesium chloride lattice

Surface coordination number

Inside a crystal lattice, the coordination numbers are well-defined and counted as the nearest atoms in all directions. This is known as the bulk coordination number.

For surfaces, rather than inside, the nearest number of atoms is lesser. So this surface coordination number is lower than the bulk coordination number. The surface coordination number also depends on the Miller indices of the surface.

Concepts Berg

What is coordination number and example?

Coordination number is the number of atoms, ions, or molecules that a central atom/ion holds nearest to itself in a coordination compound or in a crystal. An example is that of [ZrF7]3-, with a coordination number of 7, since 7 F ligands are bonded to the central Zr4+ ion.

How do you find the coordination number?

The coordination number can be easily identified in coordination compounds or complexes, by counting the number of atoms or molecules or ions directly bonded to the central atom or ion.

In case of crystal lattices, the coordination number is determined by counting the number of nearest neighboring atoms. In the lattice structure of a body-centered cubic (BCC) crystal, each reference ion has 8 ions as its nearest neighbors, and so the coordination number is 8 for BCC crystal.

For solid state crystals, the coordination number is further categorized into the bulk coordination number and surface coordination number. These are specific for different types of lattices e.g., the bulk coordination number for the BCC crystal is 8, whereas that of the FCC crystal is 12. In addition, the surface coordination number for the BCC lattice is 4.

What is coordination number of NaCl?

For a NaCl crystal, each Na+ ion is surrounded by 6 Cl ions, and vice versa. So the coordination number of NaCl is 6:6.

What is coordination number of FCC?

In the FCC crystal, each reference atom is surrounded by 12 nearest neighbor atoms. Hence the coordination number is 12.

What is face centered unit cell?

A face centered unit cell is one in which the atoms are present, one at the center of each face and one at each corner of a cube.

Since there are 6 faces in a cube, and each face is shared between 2 cubes, the number of atoms is given by: 6 / 2 = 3 atoms at the face centers of one unit cell.

On the other hand, there are 8 corners in a cube, and each corner is shared with 8 different cubes, so the number of atoms is given by: 8 / 8 = 1 atom at the corners of each unit cell.

So the total number of atoms in one FCC unit cell is 3 + 1 = 4.

Moreover, the coordination number for FCC unit cell is 12. It can be determined by counting the immediate neighbor atoms of one reference atom at the corner of a cube. That atom at the corner is shared by 4 faces in the x-axis, 4 in the y-axis, and 4 in the z-axis. That atom’s immediate neighboring atoms lie at the center of each of those faces. A total of 4 + 4 + 4 = 12 faces correspond to`12 neighboring atoms, which happens to be the coordination number for a FCC unit cell.

How to find the coordination number of copper?

Copper metal has a face-centered cubic lattice, which has a coordination number of 12.

Cu (II) ion prefers to have the coordination numbers 4 to 6, in its complexes.

What is the coordination number of benzene?

Benzene, being a polyhapto ligand, can have a hapticity of 𝜂2, 𝜂4, or 𝜂6.


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