Coordination Number: Definition and Role in Molecular Geometry

The Coordination number of an atom in a given molecule or a crystal is referred to as the total number of atoms, ion, or molecules bonded to the atom in question. The coordination number of such an atom is also referred to as 'ligacy.' Ligands are atoms, ions, or molecules bound to the central atom (or molecule/ion). In comparison to estimating the actual coordination number of a central atom in a crystal, ligancy of molecules is computed differently. Here we will be learning more about coordination number and discuss some important questions.

Key Terms: Ligands, bonds, electrons, atom, close packing, ion, molecules, electron configuration, coordination number, metal

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What is Coordination Number?

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The number of ligands linked to the central ion is the coordination number in coordination chemistry (more specifically, the number of donor atoms). The usual range of coordination numbers is two to nine. The size, charge, and electron configuration of the metal ion and ligands all influence the number of bonds. 

Interactions between the ligands' s and p molecular orbitals and the metal ions' d orbitals typically dominate the chemistry of complexes. 18 electrons can fit into the metal's s, p, and d orbitals. The maximal coordination number for a given metal is thus determined by the metal ion's electron configuration (particularly, the number of unoccupied orbitals) and the ligands' to metal ion's size ratio. High coordination numbers (e.g., [Mo(CN)₈]₄) result from large metals and tiny ligands. Low coordination numbers result from small metals with big ligands (e.g., Pt[P(CMe₃)]₂). Lanthanides, actinides, and early transition metals have high coordination numbers due to their huge size.

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Coordination Number of a Central Atom

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The coordination number related to a given atom in polyatomic ions and molecules can be computed by counting the total number of atoms to which it is bound, whether it is a single bond or a double/triple bond. The coordination number of the central cation (Cr³⁺) may be counted by the total number of atoms linked to the chromium atom, which is determined to be 6 in the case of the polyatomic ion [Cr(NH₃)₂Cl₂Br₂]^–.

Because the centre cobalt atom is connected to six different nitrogen atoms in the example above, the coordination number of that atom is six. In their solid state structures, crystals' bonds are not as obvious. In such instances, the centre atom's coordination number equals the total number of nearby atoms. The total number of atoms in a crystal's immediate vicinity is determined by the atom's position in the crystal. As a result, the bulk coordination number and the surface coordination number are two separate metrics of ligancy in crystals. Only the sigma bonds between the ligands and the central atom are counted in the computation of the coordination number of the central atom in coordination complexes. In this calculation, Pi bonds are ignored. 

Despite the importance of pi bonding coupled with sigma bonding in such metal carbonyls, the coordination number of the central tungsten atom (denoted by the symbol W) in the compound tungsten hexacarbonyl, represented by the chemical formula W(CO)₆, is 6.

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Geometry of Molecules Based on Coordination Number

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The molecular geometry of the coordination complex can be deduced using the coordination number of the central metal atom/ion. The geometrical pattern is a polyhedron, with the polyhedron's vertices corresponding to the ligands' coordinating atoms' centres. The molecular geometry of coordination compounds is provided as follows based on the coordination number (CN):

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Complications in Coordination Number

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The metal-ligand connections in some compounds may not all be at the same distances. For example, depending on which chlorides are assigned as ligands, the coordination number of Pb²⁺ in PbCl₂ could be seven or nine. Pb-Cl lengths of 280–309 pm are found in seven chloride ligands. With Pb-Cl lengths of 370 pm, two chloride ligands are further apart.

In some circumstances, an alternative definition of coordination number is utilised, which takes into account atoms that are further apart than their nearest neighbours. The International Union of Crystallography, IUCR, has adopted a relatively broad definition that indicates that the coordination number of an atom in a crystalline solid is determined by the chemical bonding model and the method of calculation.

Uneven structures can be found in some metals. Zinc, for example, has a hexagonal close packed deformed structure. Each atom has 12 nearest neighbours and a triangular orthobicupola (also known as an anticuboctahedron or twinned cuboctahedron) coordination polyhedron in a regular hexagonal close packing of spheres. At 266 pm in zinc, there are only six nearest neighbours in the same close packed plane as six other, next-nearest neighbours, equidistant, three in each of the close packed planes above and below at 291 pm. It is seen to be more appropriate to refer to the coordination number as 12 rather than 6.

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Things to Remember

• The aggregate number of atoms, ions, or molecules attached to a given atom in a certain molecule or crystal is referred to as the coordination number of that atom. 
• The coordination number of such an atom is also referred to as 'ligacy.'
• The usual range of coordination numbers is two to nine. 
• Interactions between the ligands' s and p molecular orbitals and the metal ions' d orbitals typically dominate the chemistry of complexes. 
• Only the sigma bonds between the ligands and the central atom are counted in the computation of the coordination number of the central atom in coordination complexes.

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