Coordination Number in Chemistry

crystal lattice with a certain coordination number

Core Concepts

In this article, we learn all about coordination number in chemistry, including its meaning in molecules, metal ion complexes, and crystals. We also discuss the implications of coordination numbers in molecular geometry.

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What is Coordination Number?

Chemists use the term “coordination number” (CN) to describe the number of atoms or groups bound to a central atom. Importantly, coordination number applies to all chemical structures involving bonds, including molecules, metal ion complexes, and solid-state crystals. 

Coordination Number in Molecules

In molecules, coordination number does not equal the total number of bonds, but rather just the sigma bonds. For instance, the carbon in methane binds to four hydrogens, involving four sigma bonds, thus having a CN of 4. The carbon in acetone, however, only has a CN of 3, because it has three sigma bonds, binding it to three other atoms: two hydrogens and one oxygen. The pi bond between the carbon and the oxygen does not factor into the CN.

Valence electron configuration has the largest influence coordination number, especially in non-metals. Per the octet rule, carbons, for instance, have four fewer electrons from their noble gas configuration. Thus, carbon becomes most stable when forming four bonds to fill its octet. However, as we’ve observed, pi bonds don’t count toward CN, despite also contributing toward satisfying the octet rule.

Coordination Number in Metal Ion Complexes

In metal ion complexes, coordination number indicates the number of groups bound to a central metal ion. Chemists call these groups “ligands”, and they form coordinate covalent bonds with the metal by donating an electron pair. Thus, when talking about metal complexes, coordination number also goes by the name “ligancy”. If you’d like to learn more about the chemistry of ligands and ion complexes, check out this article

For instance, the copper in [Cu(NH3)4(H2O)2] has six total ligands, indicating a CN or ligancy of 6.

coordination number of the complex is 6

No single trend or rule predicts a metal’s coordination number. However, the sizes of both the metal ion and the ligands tend to have the strongest influence. Specifically, CN most often equals the number of ligands physically capable of “fitting” around the metal. Thus, metals with larger ionic radii can accept electrons from numerous small ligands, resulting in a high CN. Conversely, smaller metals and larger, bulkier ligands are more conducive to low coordination numbers.

Coordination Number in Crystals

In solid-state crystals, the coordination number describes the number of atoms in the vicinity of a given central atom. For instance, in diamonds, a given carbon atom in the interior of the structure bonds with four other carbons, resulting in a CN of 4. 

crystal lattice of diamond, showing a coordination number of 4
Lattice structure of diamond crystal

Similar to molecules, the valence electron configuration and the octet rule have the largest influence on the CN in crystals. However, atoms on the surface of a solid-state crystal bind to fewer atoms than those in the interior. As a result, the “surface coordination number” of a crystal is lower than the “bulk coordination number”, which applies to interior atoms. The surface CN has a lot of importance in solid-state catalysis, as it indicates the number of reactant molecules which can bind to the surface of a solid.

Coordination Number and Molecular Geometry

Importantly, coordination number provides information into the spatial arrangement of groups in a chemical substance. Due to steric inhibition, groups bound to central atoms naturally arrange with the maximum distance between them. In crystals, the CN determines the lattice structure of the solid-state structure.

Two groups bond to opposite poles of a central atom (CN=2), resulting in a linear geometry that maximizes the distance between the groups. To maximize the distance between three groups (CN=3), the molecule expresses a trigonal planar geometry. For four groups (CN=4), a tetrahedral geometry maximizes the distance between all four, and so on. The table below shows the geometry that maximizes the distance between groups at the given CN:

coordination number with molecular geometry

However, all coordination numbers in molecules have alternate geometries, aside from CN=1. For instance, despite having a CN=2, the oxygen in water has a bent geometry, not a linear one. 

This phenomenon is explained by the presence of lone pairs of electrons on the central atom. Basically, these lone pairs act as another group, sterically inhibiting the other groups bonded to the central atom. The oxygen in water has two lone pairs of electrons and two sigma-bonded hydrogens, which totals four “electron terminals”. These four terminals behave like the groups in a molecule with CN=4, resulting in a tetrahedral “electron geometry”. The molecular geometry, not taking into account electron lone pairs, remains bent. 

molecular geometry of water
The bent structure of water, with lone electron pairs.
Table of molecular geometries, electron geometries and coordination numbers.

If you’d like to learn more about molecular geometry and electron geometry, check out this article.