# [gmx-users] RDF

Dan Gil dan.gil9973 at gmail.com
Fri Aug 18 13:31:32 CEST 2017

```Hi Rahul,

I can't find the exact papers right now, but I remember seeing some
inconsistency in how people name these functions especially the radial
distribution function and pair correlation functions.

If we go far back into literature, we can see JG Kirkwood using pair
correlation functions as functions of both the distance and the relative
orientation between the pairs [The Journal of Chemical Physics 19, 774
(1951); doi: 10.1063/1.1748352]. I don't know if he is the "inventor" of
the RDF, but he was one of the earliest to use it extensively in theories.
When you average the pair correlation functions over the relative
orientations, you get the radial distribution function which is a function
of distance only. I think I've seen newer papers use RDF/PCF/PDF somewhat
interchangeably although I can't find these right now... Most people mean
the RDF but you can always look at the data to know what they mean.

I never used surface distribution functions, hopefully someone else can
bring you up to date on that one (How is the surface defined?).

But there is also the spatial distribution functions, which now a function
in 3D spherical coordinates. It gives the average density of particles at
given (r, theta, phi). In this paper they normalize it by the bulk density,
I am not sure if everyone does the same. (doi: 10.1063/1.465158)

I think "radial pair distribution function" is synonymous with the RDF like
you said.

Partial radial distribution function is for multicomponent systems. In a
single component system, there is only one RDF and that is the total RDF.
In a two component system, there are 3 (AA, AB, BB) partial radial
distribution functions.

Hope that helps!

Dan

On Fri, Aug 18, 2017 at 2:19 AM, RAHUL SURESH <drrahulsuresh at gmail.com>
wrote:

> Pair Distribution Function and Partial Radial Distribution Function.
>
> What makes the difference in all the four?
>
> Have gone through lot pages and literature. Somehow one or the other piece
> of explanation confuses me.
>
> Can I have a short explanation of all?
>
> RDF and R-pair DF one and the same?
>
> How do I calculate SDF and Partial-RDF if it is different from others?
>
> --
> *Regards,*
> *Rahul Suresh*
> *Research Scholar*
> *Bharathiar University*
> *Coimbatore*
> --
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```