Talk:Radial distribution function

Untitled comments from 2007

In the near future I will be adding the formal derivation of g(r) in the article... 14-02-2007 - Joris Kuipers
Nice, I am thinking that maybe some information about/from experiments might be useful. Like Alan Sopers articles. omermar 30/05/07

Eq. 13

The line below equation 13 reads: "In fact, equation 13 gives us the number of molecules between r and r + d r about a central molecule." However, it looks to me that equation 13 gives us the total number N of the molecules of the system, .... Lwzhou (talk) 12:22, 6 October 2008 (UTC)lwzhou

As I understand, the current version of eq. 13 gives the TOTAL number of molecules in the SYSTEM (since it is from zero to infinity).
I suggest the following correction:
1) Make the range of the integral from r1 to r2.
2) Add/modify the text: Eq. 13 gives the number of molecules in the solvation shell of a central molecule, when r1 & r2 are picked at consecutives minimums of the RDF function. For example - for the number of molecules in the first solvation shell, r1=0 & r2 is picked at the second minimum of g(r).
For water, when r1=0 & r2=3.5 Angstroms, then N ~ 4.5 molecules.

omermar --http://www.fh.huji.ac.il/~omerm 07:56, 7 October 2008 (UTC)

Just a short comment: as far as I understand it in eq. 13 g(r) does not give the number of molecules between r and r+dr. You would still have to multiply it with the particle density and 4Pi r^2. Suggestions 1) and 2) of above are still correct. —Preceding unsigned comment added by 141.24.104.201 (talk) 14:10, 11 November 2008 (UTC)

Is it true that (Rho g(r) 4 Pi r^2 dr) gives the the number of molecules between r and r+dr. Is g(r) here in Eq. 13 means the probability finding a molecule at the distance r from a center molecule, and is often called pair distribution function, while (Rho g(r) 4 Pi r^2 dr) called radial distribution function? It seems that different sources give different definitions of PDF and RDF. It needs to be clarified.

More General Definition of g(r)

In practice, the radial distribution function is not just used as a descriptor for equilibrium systems. For example, the pair distribution function of glasses are measured all the time from scattering experiments, but it is improper to speak of the equilibrium statistical mechanics of such systems. As such, I have provided a definition in terms of well-defined physical quantities for general (i.e. equilibrium and non-equilibrium) systems which is equivalent to the statistical mechanical definition for systems at equilibrium. I will also work on adding a section on how one measures these functions, and adding sources to existing material.Mgibby5 (talk) 23:31, 20 December 2014 (UTC)

Merge proposal

The pair distribution function and radial distribution function are essentially the same concept. I propose the two articles be merged.Polyamorph (talk) 16:13, 23 January 2017 (UTC)

• Agree. I would say that radial distribution function is essentially a special case of pair distribution function for an isotropic medium, or it's an angle-average of radial distribution function. Anyway there's more than enough overlap to warrant merging. I think the radial distribution function is also the same (or essentially the same) as "equal-time correlation function" described in Correlation function (statistical mechanics), but I don't think that article needs to be merged, just linked better to and from this article. --Steve (talk) 13:30, 24 January 2017 (UTC)

Thanks for your comment @Steve: I think we have to be careful with the terminology. I work with liquids and glasses and use XRD and neutron diffraction to measure their "radial distribution functions". But I just call them pair distribution functions. Others in my field describe them as radial distribution functions or pair correlation functions. These terms are all used interchangeably and I think there is a problem that either no one knows or there isn't a correct standardised terminology. So I feel it would just be better on wikipedia to just use pair distribution function and have a section on the special case for non-crystalline materials, but not necessarily call this the radial distribution function. Does that make Sense? Anyway, I'll wait a while to see if there are any other responses to this and then perform the merge. Polyamorph (talk) 16:00, 24 January 2017 (UTC)

If it is true—as currently stated in the wiki articles if I'm reading them right—that pair correlation function is a function of the 3D displacement vector (both distance and direction), and radial correlation function is a function only of distance, then it would be totally unsurprising that the terms would be used interchangeably by the folks who are studying isotropic media like liquids and glasses. So your observation (that you and your glass-studying friends use "radial" and "pair" interchangeably) is IMO extremely weak evidence against the current wiki definitions. So the question is, if you spend time hanging around crystallography labs, do they use the "pair" and "radial" terms interchangeably? Whatever, it's probably best to just look up the definitions used by popular textbooks. --Steve (talk) 21:37, 24 January 2017 (UTC)

OK, thanks for your insight! That makes sense. Polyamorph (talk) 21:48, 24 January 2017 (UTC)

• Disagree. A good number of statistical mechanics books specifically define the pair correlation function as p(r) = g(r) - 1 (see Chandler or McQuarrie, for instance). I don't specifically disagree that these two concepts should be merged in the same article, but the leading sentence of the article now says that p(r) = g(r). You can see how this is bloody confusing, in a subject which needs no confusion added.— Preceding unsigned comment added by 184.175.44.102 (talk) 14:18, 21 July 2017‎ (UTC)

Closed given the absence of consensus for the merge, and discussion now stale. Klbrain (talk) 10:46, 16 August 2018 (UTC)

Correction

The comment

$g^{(n)}$ is called a correlation function, since if the atoms are independent from each other $\rho ^{(n)}$ would simply equal $\rho ^{n}$ and therefore $g^{(n)}$ corrects for the correlation between atoms.

is incorrect. If the atoms are independent from each other then $\rho ^{(n)}$ would still have the factorial terms that are required for the indistinguishably. — Preceding unsigned comment added by 128.4.165.23 (talk) 18:39, 2 November 2017 (UTC)