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Coordination Number

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The coordination number refers to the number of ligands which are directly bonded to the central metal atom or ion in a complex compound. Numerically it is equal to the total number of chemical bonds formed between the central metal ions and the donor atom of the ligand.

The common coordination numbers exhibited by central metal ions are 2, 4 and 6, although coordination numbers 3, 5, 7, 8, 9 and 12 are also shown by some metal ions but these coordination numbers are not common.

Definition

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"Coordination number may be defined as the maximum number of groups (neutral molecules or negative ions) which can be arranged or coordinated around a central metal ion."

Coordination number of metals vary from 2 to 10, but the most common coordination numbers are 4 and 6 but may be 2 or 8 or an odd number in rare cases. The coordination number is previously considered to be a fixed number for a particular metal but many complexes are known in which the metal ions have more than one coordination number.

Determining

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The coordination number of the central metal atom/ion in a given complex compound is equal to the total number of donor atoms which are actually attached to the central metallic atom. In other words the coordination number of the central metallic atom is equal to the number of sites at which the ligands is attached to the central metallic atom.

Coordination numbers of complexes in solution are more difficult to determine and are usually inferred from spectroscopic and conductance data. The coordination numbers of solid complexes can be obtained by X-ray diffraction methods. The coordination number gives an idea about the way in which the ligands are arranged round the central metallic atom.

Coordination Numbers 

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Coordination Numbers 3:


The complexes having coordination number 3 exhibit the following geometries
  • Equilateral triangular
  • Trigonal pyramidal
Among complexes of metallic elements this is a rare coordination number. This was first observed in the amides.

Coordination Numbers 4:


This coordination number has been observed in hundreds of thousands of compounds. This is found in complexes formed by carbon, silicon and germanium. There are two principal geometries
  • Tetrahedral
  • Square planer
Tetrahedral geometry is by far the most prevalent. Tetrahedral complexes or molecules are the only kind of four coordinate ones formed by non-transitional elements.

Coordination Numbers 5:


This coordination number is less common in comparison to coordination numbers 4 and 6. Complexes with coordination number 5 show the following geometries
  • Trigonal bipyramidal
  • Square pyramidal
In trigonal bipyramidal the ligands atoms lie at the vertices of a trigonal bipyramidal and in the case of a square planar arrangement the ligand atoms lie at the vertices of a square pyramid. It is quite easy to inter convert these two structures and a large fraction of known coordinate complexes have structures intermediate between the two.

Coordination Numbers 6:


Complexes with coordination number 6 usually have an octahedral arrangement of ligands around the central metal ion. This is the most common coordination number. The six ligands invariably lie at the vertices of an octahedron or a distorted octahedron. The three principal distortions in octahedron are tetragonal, rhombic and trigonal.

Simple Cubic (SC)

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For simple cubic lattice the coordination number is 6. A simple cubic cell consists of eight corner atoms as shown below.

Coordination Number of Simple Cubic

Let us consider any of the corner atom. For this atom, there are four nearest neighbors in its own plane. There is another nearest neighbor atom in a plane which lies just above this atom and yet another nearest neighbor atom in another plane which lies just below this atom. Therefore the total number of nearest neighbor atom is six and hence the coordination number is 6.

Face Centered Cubic (FCC)

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A face centered cubic (FCC) unit cell consists of eight corner atoms and six face centered atoms. A face centered cubic unit cell is shown below.

Coordination Number of Face Centered Cubic

The coordination number can be calculated by considering a corner atom. In its own plane, that corner atom has four face centered atoms. These face centered atoms are its nearest neighbors. In a plane which lies just above this corner atom it has four face centered atoms as nearest neighbors. In a plane which lies just below this corner atom, it has four more face centered atoms as its nearest neighbors. Therefore for an atom in an FCC unit cell the number of nearest neighbors is 12 (coordination number-12).

Body Centered Cubic (BCC)

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A body centered cubic (BCC) structure has eight corners and one body centered atom. The diagrammatic representation of a body centered cubic structure is shown below. 

Coordination Number of Body Centered Cubic

The coordination number of a body centered cubic unit cell can be calculated by considering body centered atom. The nearest neighbor atom for a body centered atom is a corner atom. A body centered atom is surrounded by eight corner atoms. Therefore, the coordination number of a BCC unit cell is 8.