Coordination Numbers and Geometry
Lecture 2. CHEM1902 Coordination Chemistry

The total number of points of attachment to the central element is termed the coordination number and this can vary from 2 to as many as 16, but is usually 6. In simple terms, the coordination number of a complex is influenced by the relative sizes of the metal ion and the ligands and by electronic factors, such as charge which is dependent on the electronic configuration of the metal ion. These competing effects are described by the term ionic potential which is defined as the charge to radius ratio (q/r).

Based on this, it can be seen that the bigger the charge on the central ion, the more attraction there will be for negatively charged ligands, however at the same time, the bigger the charge the smaller the ion becomes which then limits the number of groups able to coordinate.

Coordination Number 2

This arrangement is not very common for first row transition metal ion complexes and some of the best known examples are for Silver(I). In this case we have a low charge and an ion at the right hand side of the d-block indicating smaller size.

A method that was often employed for the detection of chloride ions involved the formation of the linear diamminesilver(I) complex.
The first step is:
Ag+ + Cl- → AgCl (white ppt)
and to ensure that the precipitate is really the chloride salt, two further tests must be done:
AgCl + 2 NH3 → [Ag(NH3)2]+
[Ag(NH3)2]+ + HNO3 → AgCl (re-ppts)

The reaction of a bidentate ligand such as 1,2-diaminoethane with Ag(I) does not lead to chelated ring systems, but instead to linear two coordinate complexes. One reason for this is that bidentate ligands can NOT exist in trans arrangements, that is they are UNABLE to span 180 degrees.

Coordination Number 3

Once again, this is not very common for first row transition metal ions. Examples with three different geometries have been identified:
coordination number 3

Trigonal planar

Well known for main group species like CO32- etc., this geometry has the four atoms in a plane with the bond angles between the ligands at 120 degrees.

Trigonal pyramid

More common with main group ions.


The first example of a rare T-shaped molecule was found in 1977 however since then several further examples have been reported.

Coordination Number 4

Two different geometries are possible. The tetrahedron is the more common while the square planar is found in particular with metal ions having a d8 electronic configuration.
coordination number 4

Tetrahedral, (Td)

The chemistry of molecules centred around a tetrahedral C atom is covered in organic courses. To be politically correct, please change all occurrences of C to Co. There is a large number of tetrahedral cobalt(II) complexes known.

Square Planar, (D4h)

These are much less common than tetrahedral and are included here since there are some extremely important examples with this shape.

Coordination Number 5

coordination number 5

Square pyramid, (C4v)

Oxovanadium salts (Vanadyl, VO2+) often show square pyramidal geometry, for example, VO(acac)2. Note that the Vanadium(IV) can be considered coordinatively unsaturated and addition of pyridine leads to the formation of an octahedral complex.

Trigonal Bipyramid, (D3h)

The structure of [Cr(en)3][Ni(CN)5] 1.5 H2O was reported in 1968 to be a remarkable example of a complex exhibiting both types of geometry in the same crystal.
The reaction of cyanide ion with Ni2+ proceeds via several steps:
Ni2+ + 2 CN- → Ni(CN)2 yellow
Ni(CN)2 + 2 CN- → [Ni(CN)4]2- orange-red
log(β4) = 30.1
[Ni(CN)4]2- + CN- → [Ni(CN)5]3- deep red

Coordination Number 6

coordination number 6

Hexagonal planar

Unknown for first row transition metal ions, although the arrangement of six groups in a plane is found in some higher coordination number geometries.

Trigonal prism

Most trigonal prismatic compounds have three bidentate ligands such as dithiolates or oxalates and few are known for first row transition metal ions.

Octahedral, (Oh)

The most common geometry found for first row transition metal ions, including all aqua ions.
In some cases distortions are observed and these can sometimes be explained in terms of the Jahn-Teller Theorem.

Coordination Number 7

Three geometries are possible:
Not very common for 1st row complexes and the energy difference between the structures seems small and distortions occur so that prediction of the closest "idealised" shape is generally difficult.
coordination number 7

Capped octahedron, (C3v)

Capped trigonal prism, (C2v)

Pentagonal Bipyramid, (D5h)

Coordination Number 8

coordination number 8

Dodecahedron, (D2d)

Cube, (Oh)

Square antiprism, (D4d)

Hexagonal bipyramid, (D6h)

Coordination Number 9

Three-face centred trigonal prism, (D3h)

Coordination Number 10

Bicapped square antiprism, (D4d)

Coordination Number 11

All-faced capped trigonal prism, (D3h)

Coordination Number 12

coordination number 12

cuboctahedron, (Oh)

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