20.4: Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.

Table 1. Coordination Numbers and Molecular Geometry.

Unlike main group atoms in which both the bonding and nonbonding electrons determine the molecular shape, the nonbonding d-electrons do not change the arrangement of the ligands. Octahedral complexes have a coordination number of six, and the six donor atoms are arranged at the corners of an octahedron around the central metal ion. Examples are shown in Figure 1. The chloride and nitrate anions in [Co(H₂O)₆]Cl₂ and [Cr(en)₃](NO₃)₃, and the potassium cations in K₂[PtCl₆], are outside the brackets and are not bonded to the metal ion.

Figure 1. Many transition metal complexes adopt octahedral geometries, with six donor atoms forming bond angles of 90° about the central atom with adjacent ligands. Note that only ligands within the coordination sphere affect the geometry around the metal center.

For transition metals with a coordination number of four, two different geometries are possible: tetrahedral or square planar. In tetrahedral complexes such as [Zn(CN)₄]²⁻ (Figure 3), each of the ligand pairs forms an angle of 109.5°. In square planar complexes, such as [Pt(NH₃)₂Cl₂], each ligand has two other ligands at 90° angles (called the cis positions) and one additional ligand at a 180° angle, in the trans position.

Figure 2. Transition metals with a coordination number of four can adopt a tetrahedral geometry (a) as in K₂[Zn(CN)₄] or a square planar geometry (b) as shown in [Pt(NH₃)₂Cl₂].

This text is adapted from Openstax, Chemistry 2e, Section19.2: Coordination Chemistry of Transition Metals.

Many transition metals exhibit multiple oxidation numbers contributing to their unique properties, such as colors. But how is the metal’s oxidation number determined?

Coordination compounds are electrically neutral species consisting of a coordination complex and counterions with a primary and secondary valence.

The primary valence is the oxidation number of the metal ion. To find the oxidation number start by identifying the charges contributed by the ligands and counter ions. 

Next, sum up the charges and determine the oxidation number of the metal ion. If all ligands are neutral, the complex ion charge becomes the oxidation number of the metal ion.

The secondary valence refers to the number of ligands directly bonded to the central metal ion, also called the coordination number. Here, the coordination number of rhodium is six.

Some metal ions possess one coordination number only. Cobalt(III) and platinum(II) have a coordination number of 6 and 4. However, for many metal ions, the coordination number varies ranging from 2 to 6.

The relative size of ligands and metal ions influences the coordination number. For instance, smaller ligands like fluorine coordinate six times to iron(III), compared to the larger chlorine, which coordinates only four times. 

Negative charges imparted by ligands to the metal ion also influence the coordination number. The coordination number of nickel(II) with neutral water molecules is 6, which is reduced to 4 with anionic chloride ions.

The geometric shape of the complex ion partially depends on the coordination number of a metal ion. A complex with a coordination number of two has a linear geometry, where two ligands are 180° apart on either side of the metal ion.

A complex with a coordination number of 4 exhibits two types of geometry based on the valence electron in the d-subshell. Metal ions with eight d-electrons, such as palladium(II), are square planar. While metal ions with ten d-electrons, such as zinc(II), exhibit a tetrahedral geometry. 

A complex with a coordination number of 6 is octahedral. The six ligands occupy six vertices, four ligands form the corners of a square, and the remaining two the planes above and below at an equivalent distance. Thus, an octahedron appears as two pyramids with a common square base and eight faces.