# [gmx-users] Re: Strange form of RDF curve

Thomas Schlesier schlesi at uni-mainz.de
Tue Nov 20 15:01:15 CET 2012

```The rdf should not depend on the choice 'which is group A and which is
group B'! Not if the system is well equilibrated and not if you consider
only a single snapshot (in that case the rdf looks like garbage if the
system is not really huge, but the RDF(A-B) and RDF(B-A) must be the same).

I mean the the RDF is the radial distribution function. A distribution
direction, or from which point one goes to another.
In an A and B system one has N_A * N_B distances, no matter if A or B is
the reference!

Going to the manual the given equation for the RDF is

g(r) = 1/rho_B 1/N_A sum_A sum_B delta(r_AB - r) / (4pi r^2)

Since after the sums it is clear that there is no difference between A
and B one could argue that

1/rho_B 1/N_A is not equal to 1/rho_A 1/N_B

looking into the picture which defines rho one recognises that rho=N/V

-> g_AB(r) = g_BA(r)

Am 20.11.2012 12:00, schrieb gmx-users-request at gromacs.org:
> the opening statement "from the statistical mechanical standpoint" means a
> thorough sampling has been attained, so I do agree that the reference group
> choice would matter for an every day situation. Thoroughness is not
> attainable
> for most complex systems we might be interested in.
>
> On Tue, Nov 20, 2012 at 1:21 AM, Justin Lemkul<jalemkul at vt.edu>  wrote:
>
>> >
>> >
>> >On 11/19/12 10:04 PM, Andr? Farias de Moura wrote:
>> >
>>> >>from the statistical thermodynamics standpoint, rdf must be the same for
>>> >>both choices of reference group, i.e.,solute-solvent and solvent-solute
>>> >>must yield exactly the same rdf, the only difference being expected for
>>> >>the
>>> >>cumulative numbers, which depend on the particles number density. The
>>> >>reason why rdf's must be the same is the fact that rdf are connected to
>>> >>the
>>> >>pmf between the particles, and the pmf do not depend upon the choice of
>>> >>reference group, just on the reaction coordinate connecting the groups.
>>> >>
>>> >>
>> >Doesn't this explanation assume that the system is homogeneous, or at
>> >least, that the solute (reference group) of interest exhaustively samples
>> >configurations within the solvent?  It's not intuitive to me why one would
>> >expect an Arg-water RDF to be the same as a Water-Arg RDF when the Arg
>> >residue is only part of a 582-residue protein, which means a considerable
>> >portion of the simulation unit cell contains neither the Arg of interest
>> >nor water, a fact that significantly impacts the binning as shown in the
>> >manual.  The actual g_rdf command is essential in this regard, as well,
>> >depending on how the RDF is being calculated.  One can produce wildly
>> >different results by changing only a a single element of the command.
>> >
>> >
>> >-Justin
>> >

```