# Difference between the Radial Distribution Function and number density

Hi,

I want to calculate the number density of an atom of my ligand as function of distance from protein heavy atoms. In the manual, it says the following:

The RDFs are normalized by 1) average number of positions in `-ref` (the number of groups with `-surf` ), 2) volume of the bin, and 3) average particle density of `-sel` positions for that selection. To change the normalization, use `-norm` :

`rdf` : Use all factors for normalization. This produces a normal RDF.
`number_density` : Use the first two factors. This produces a number density as a function of distance.

I wanted to know what the difference between the number density and the normal RDF in Gromacs. Apologies if this may sound like a simple question. Any guidance will be much appreciated.

Thanks,

Akash

Hi Akash,

Thanks for posting!

In your case it should be the same, because you only look at one atom, if I understand you correctly. If you had two ligands, then the number density would be twice as much as the “normal” rdf and so on…

Hi,

Thank you for your response. I have hundreds of copies of my ligand in my system, so my understanding on what you said , the number density in this case will be “normal rdf” multiplied by 100 (100 time as much)? Is this if I only choose 1 atom?

Alternatively, what would be the case if I took the center of mass of all my ligands (using -seltype mol_com)? If I wanted to calculate the number density would I then normalise (e.g. -norm number_density)?

Hi Akash,

you will get a factor for every `-sel positions for that selection`. That is, if you look at the center of mass of hundred molecules, you will get one-hundred `-sel positions`, similarly looking at one atom each of hundred molecules will give you the same factor.