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Coordination number: what is it, calculation, examples

This number is important because it defines the geometries of the complexes, the densities of their material phases, and even the stereochemical (spatial) character of their reactivities. To simplify its definition, any atom that surrounds a specific center is considered to be a neighbor.

On a surface of coins we can see what is meant by a coordination number

Consider, for example, the floor made of coins in the image above. All the coins are the same size, and if you look at each one it is surrounded by six others; that is, they have six neighbors, and therefore the coordination number (CN) for the coins is 6. This same idea is now extended to three-dimensional space.

If their radii are uneven, they will not all have the same coordination number. For example: the larger the coin, the more neighbors it will have, since it will be able to interact with a greater number of coins around it. The opposite happens with small coins.

Coordination number concept

Ion radii vs. Coordination number

The coordination number is the number of closest neighbors that, in principle, interact directly with a center, which is mostly a metal ion. So we put the coins aside to consider spheres instead.

This metal ion M n + , where n is equal to its oxidation number or valence, interacts with other neighbors (ionic or molecular) called ligands. The larger n (+2, +3, etc.), the smaller M n + will be, and consequently the ligands will be forced closer to each other to interact with M n + .

The following image illustrates the above said:

Variation of the coordination number with the charge of the central ion. Source: Gabriel Bolívar.

2+ in the illustrated complex has a coordination number of 5: it is surrounded by 5 ligands L. While, M 3+ has a coordination number of 4. This is due to the fact that M 3+ , having a greater magnitude of charge, their radius contracts and therefore the L binders must move closer to each other, which increases their electronic repulsions.

That is why bulky central ions, such as those belonging to the metals of block f , or the second or third period of block d , tend to have higher coordination numbers (CN> 6).

Densities

Now suppose that the M 3+ complex is put under a lot of pressure. There will come a point where the pressure will be such that another ligand is likely to coordinate or interact with M 3+ . That is, your coordination number will increase from 4 to 5.

In general, the pressures increase the coordination numbers, since the neighbors are forced to girdle themselves on the central ion or atom. Consequently, the material phases of these substances become denser, more compact.

Geometries

The illustrations above do not say anything about the geometries around M 2+ or M 3+ . However, we know that a square has four vertices or corners, just like a tetrahedron.

From this reasoning it is concluded that the geometry around M 3+ , whose CN is 4, must be tetrahedral or square. But which of the two? Meanwhile, the geometries for M 2+ , whose CN is 5, can be square pyramid or trigonal bipyramidal.

Each CN has several possible geometries associated with it, which position the binders at a favorable distance, in such a way that there is the least repulsion between them.

How is the coordination number calculated or determined?

The coordination number can sometimes be calculated directly from the formula of the compound in question. Suppose the anion complex [Ni (CN) 5 ] 3- . What is the coordination number for the nickel ion, Ni 2+ ? It is enough to observe the stoichiometric coefficient 5, which indicates that there are 5 CN anions  coordinated or interacting with the center of Ni 2+ .

However, it is not always that easy. For example, the compound CuCN appears to have a coordination number of 1 for both Cu 2+ and CN  . However, it actually consists of Cu-CN-Cu-CN polymer chains, so the correct coordination number is 2.

That is why the coordination number is preferable to determine rather than calculate it. How? Determining the ionic or molecular structures of the compounds. This is possible thanks to instrumental techniques such as X-ray, neutron or electron diffraction.

Examples of coordination numbers

Next, and finally, some examples of compounds will be mentioned for each of the most common coordination numbers. Likewise, they will tell each other what their respective geometries are.

CN 2

Here the linear geometry of [Ag (NH3) 2] + is observed. Source: Benjah-bmm27 / Public domain

A CN equal to 2 means that the central atom or ion has only two neighbors. Therefore, we speak of compulsorily composed of linear geometries. Between them we have:

-Hg (CH 3 ) 2

– [Ag (NH 3 ) 2 ] +

-Ph 3 PAuCl

CN 3

Each carbon atom in this sheet of graphite is connected to three others, so it has three neighbors. Source: Benjah-bmm27 / Public domain

A CN equal to 3 means that the central atom or ion is surrounded by three neighbors. We then have geometries such as: trigonal plane (triangular), trigonal pyramid and T-shape. Examples of compounds with this coordination number are:

– [Cu (CN) 3 ] 2-

– [Pt (PCy 3 ) 3 ], where PCy refers to the ligand tricyclohexilophosphine

-Graphite

CN 4

Square geometry of cisplatin, cis-PtCl2 (NH3) 2. Source: Benjah-bmm27 / Public domain

A CN equal to 4 means that the central atom or ion is surrounded by four neighbors. Its possible geometries are tetrahedral or square. Examples of compounds with this coordination number are the following:

-CH 4

-CoCl 2 pyr 2

-cis-PtCl 2 (NH 3 ) 2

– [AlCl 4 ] 

– [MoO 4 ] 2-

-SnCl 4

– [CrO 4 ] 2-

– [MnO 4 ] 2-

All of these examples, with the exception of cis-PtCl 2 (NH 3 ) 2 , are of tetrahedral geometries.

CN 5

Square pyramid geometry for VO (acac) 2. Source: Benjah-bmm27 / Public domain.

A CN equal to 5 means that the central atom or ion coordinates or interacts with five neighbors. Its geometries, already mentioned, are the square pyramid or the trigonal bipyramidal. As examples we have the following:

– [CoBrN (CH 2 CH 2 NMe 2 ) 3 ]

– [Fe (CO) 5 ]

-VO (acac) 2 , where acac is the acetylacetonate ligand

CN 6

In the crystal structure of NaCl, each Na + and Cl- ion have six neighbors, so this is the coordination number for both ions (see octahedra). Source: Solid State / Public domain

This is by far the most common coordination number among all compounds. Recall the example of the coins from the beginning. But instead of its preferred geometry being that of a flat hexagon, it corresponds to that of the octahedron (normal or distorted), in addition to the trigonal prism. Some of many examples of compounds with this coordination number are:

– [AlF 6 ] 3-

– [Co (NH 3 ) 6 ] 3+

– [Zr (CH 3 ) 6 ] 2-

-NaCl (yes, table salt)

-MoS 2 , note that CN for this compound is not 2

Others

Triapicated trigonal prism geometry of the anion [ReH9] 2-. Source: Benjah-bmm27 / Public domain.

There are other coordination numbers, from 7 to 15. For CN to be high, the central ion or atom must be very large, have little charge, and at the same time the ligands must be very small. Some examples of compounds with such CNs are below and finally:

-K 3 [NbOF 6 ], CN 7 and applied octahedron geometry

– [Mo (CN) 8 ] 3-

– [Zr (ox) 4 ] 2- , where ox is the oxalate ligand

– [ReH 9 ] 2-

– [Ce (NO 3 ) 6 ] 2- , CN equal to 12

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