Coordination Number

Coordination number is used to determine the number of neighbors an atom has. It is used in different contexts in the field of chemistry and crystallography. In context of chemistry, coordination number was first defined by Alferd Werner as the total number of neighbors of a central atom in a molecule or ion. In terms of crystallography, coordination number is defined as the number of identical atoms or ions in the interior of a crystal.

How to Find a Coordination Number?
If you have been told to find the coordination number of molecular compounds, or you are just interested in finding out one, refer to the steps mentioned below. There are some things that you should have with you. You will need correct chemical formula of coordination compound, periodic table of elements, a calculator, a pen and a sheet of paper.

1. Check the chemical formula of the compound. It has been generally observed that the central metal atom is a transition element. You can identify this central metal atom by looking at the periodic table of elements.
2. The next thing you need to do is to identify the atom, molecule or the ion which is nearest to the central metal atom. Check the chemical formula to find the atom, molecule or the ion which is besides the symbol of central metal atom. In case the central metal atom is exactly in the middle of the formula, note down all the nearest atoms, molecules or ions.
3. Now, you need to note down what the central metal atom is connected to. If the central metal atom is connected to just one element, calculate number of atoms of that element but if the central metal atom is connected to a molecule or an ion, you need to add the number of atoms in the whole molecule.
4. Finally, calculate the number of nearest neighboring atoms and in case of directly bonded atoms, add both numbers together.

The coordination numbers of transition metals vary from 1 to 12, but usually most of the coordination numbers are 2, 4 and 6. The coordination number of NaCl is 6 whereas the coordination number of gold is 3. The coordination number of fcc, that is face centered cubic shape is 12. The compounds which have coordination number 4 generally have tetrahedral or square planar shapes, the most common example being that of carbon.

Coordination Number and Radius Ratio
Radius ratio is defined as the radius of the positive ion (+) divided by the negative ion (-). Let us take a look at radius ratios of some of the known coordination numbers.

Coordination Number	Radius Ratio
3	0.155 - 0.225
4	0.225 - 0.414
6	0.414 - 0.732
8	0.732 - 1.000

In the year 2010, researchers in US were able to find a compound which broke the previous record for the highest coordination number. The compound is thorium aminodiboranate Th(H₃BNMe₂BH₃)₄ and the coordination number of this compound is 15. Researchers have found out the reason as thorium is extremely large and hydrogen atoms are small. According to Keith Izod an expert in coordination chemistry at Newcastle University in the UK, 'Although the determination of coordination number can be somewhat subjective, the reported 15-coordinate thorium compound certainly pushes the limit of maximum coordination number observed so far.'

The study of coordination numbers is one of the basics of bonding in molecular compounds. A too high coordination number doesn't always mean that the molecule is going to be stable. A coordination number of 4 to 6 implies a stable molecule. This article was just an introduction to coordination numbers, if you want to study the topic in detail, then you need to delve in deeper!