Coordination Number in Coordination Chemistry

The coordination number is an important concept in chemistry that describes the structure of coordination compounds. It refers to the number of ligand atoms or ions directly bonded to a central metal ion in a coordination complex. The coordination number usually ranges from 2 to 9, depending on factors such as the charge, electronic configuration, and size of the metal ion, as well as the size and nature of the ligands.

These interactions typically involve the s and p orbitals of the ligands and the d orbitals of the metal ion. Larger metal ions with smaller ligands generally allow higher coordination numbers, as seen in complexes like [Mo(CN)₈]⁴⁻.

Coordination Number

The coordination number of a metal ion in a coordination compound is the number of ligand donor atoms to which the metal is directly bonded. This number is crucial in determining the shape or geometry of the coordination complex. In these compounds, the central metal ion acts as a Lewis acid, accepting electrons from ligands that act as Lewis bases.

Alfred Werner was the first to explain the concept and structure of coordination compounds. Coordination compounds are known to retain their identity in solid and liquid states. In crystal structures, the coordination number can also refer to the number of nearest neighbouring atoms, ions, or molecules surrounding a particular particle.

For example, in a face-centred cubic (fcc) close-packed structure, the coordination number is 12. In this arrangement, each sphere is in contact with six spheres in the same plane, three spheres in the plane above, and three spheres in the plane below.

Coordination Number Calculation Formula

The coordination number (CN) of a metal ion can be calculated using the number of ligands attached to the metal and the denticity of each ligand:

Coordination Number (CN) = Number of Ligands × Denticity of Each Ligand

where number of ligands = total ligands bonded to the metal ion, and denticity = number of donor atoms in a ligand that bind with the metal ion.

Example: [Co(NH₃)₆]³⁺ — here, ammonia is a monodentate ligand (denticity = 1). So, CN = 6 × 1 = 6.

Example: [Ni(en)₃]²⁺ — here, ethylenediamine (en) is a bidentate ligand (denticity = 2). So, CN = 3 × 2 = 6.

Thus, the coordination number is obtained by multiplying the number of ligands by their denticity and summing the total donor atoms attached to the central metal ion.

Picture showing tetrahedral and octahedral geometry and coordination number

Coordination Number Geometry

In geometry, when talking about coordination number, there are always various possible configurations for each coordination number.

Geometry is linear for coordination number 2.
For coordination number 3, the geometry is trigonal planar, as seen in [HgI₃]⁻, and in some cases, a T-shaped geometry may also occur.
A CN of 4 may be described as tetrahedral or square planar.
When CN is 5, the geometries can be square pyramidal, as seen in [VO(acetylacetonate)₂], or trigonal bipyramidal, as in [Fe(CO)₅].
For CN of 6, the geometry is octahedral, as seen in [Co(NH₃)₆]³⁺.

Ligands

Ligands are ions or neutral molecules that bind to a central metal atom or ion in a coordination complex by donating one or more pairs of electrons. Since they donate electron pairs to the metal ion, ligands act as Lewis bases, while the metal ion acts as a Lewis acid.

π-bonding Interactions: some ligands can also participate in π-bonding interactions with the metal. In such cases, ligands may behave as π-acid ligands by accepting electron density from the metal's d orbitals, or as π-donor ligands by donating electron density to the metal.

Types of Ligands

Coordination complexes can be classified based on the type of ligands present:

Homoleptic complexes: contain only one type of ligand attached to the metal ion.

Heteroleptic complexes: contain two or more different types of ligands bonded to the central metal ion.

Coordination complexes can also be classified based on the denticity of ligands:

Monodentate ligand: has only 1 donor site, such as ammonia, carbonyl, and phosphine.

Bidentate ligand: has 2 donor sites in the ligand, for example, the oxalate ion.

Polydentate ligand: has more than two donor atoms. For example, EDTA (ethylenediaminetetraacetate) is a hexadentate ligand.

Importance of Coordination Numbers

Determines Geometry

The coordination number has a direct effect on the ligand arrangement around the metal ion, which in turn determines the geometry of the complex.

Stability and Reactivity

Coordination number is also a factor in the stability of complexes. For example, an octahedral complex with six ligands may be more stable than a square planar complex with four ligands, depending on the ligands and the metal.

Influences Physical and Chemical Properties

The coordination number and geometry may influence the magnetic, optical, and reactivity characteristics of coordination compounds. Here is how:

Magnetic Properties (Example: [NiCl₄]²⁻, tetrahedral): [NiCl₄]²⁻ has a coordination number of 4 with a tetrahedral geometry and is paramagnetic in nature because of the presence of unpaired electrons. In contrast, [Ni(CN)₄]²⁻ has the same coordination number of 4 but a square planar geometry, and is diamagnetic because all electrons in the d-orbitals are paired due to the strong ligand field provided by the cyanide ions.

Optical Properties (Example: [Cr(H₂O)₆]³⁺): the octahedral complex [Cr(H₂O)₆]³⁺ absorbs light differently from the tetrahedral complex [CrCl₄]⁻, resulting in different colours for the two solutions. This is because the two complexes have different ligand field strengths and d-orbital splitting energies.

Reactivity Properties (Example: [PtCl₄]²⁻): the coordination number and geometry also influence the reactivity and stability of coordination compounds. For example, the square planar complex [PtCl₄]²⁻ undergoes substitution reactions more readily than many octahedral complexes. This is because the arrangement of ligands around the metal ion affects how easily incoming ligands can approach and replace existing ligands. Changes in coordination number and geometry can therefore alter the reaction rate and mechanism of coordination compounds.

Summing Up

Coordination compounds are chemical compounds in which a central metal atom or ion is bonded to surrounding molecules or ions called ligands through coordinate (dative) bonds. In these compounds, the metal ion acts as a Lewis acid by accepting electron pairs, while the ligands act as Lewis bases by donating electron pairs. The central metal ion, together with the attached ligands, forms a coordination entity or complex ion, which is written inside square brackets. The net charge of the complex is also indicated within the brackets. Ions present outside the brackets are called counterions, which balance the overall charge of the compound.

FAQs

What is the difference between the coordination number and the oxidation number?
Coordination number refers to the number of ligand donor atoms bonded to the metal, whereas oxidation number represents the charge on the metal ion after accounting for ligand charges.

Can a ligand contribute more than one atom to the coordination number?
Yes. Polydentate ligands such as ethylenediamine (en) or EDTA bind through multiple donor atoms and therefore contribute more than one to the coordination number.

What is the most common coordination number in transition metal complexes?
The most common coordination number is 6, which usually forms an octahedral geometry.

Can the coordination number change in chemical reactions?
Yes. During ligand substitution or redox reactions, the coordination number of the metal ion may increase or decrease depending on the ligands involved.