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

[André Farias de Moura]

Indeed, they must be binary identical to each other, no matter what.
I am sending two rdf plots for a lipid oxygen atom and water oxygen,
plots are identical (lipids inside a spherical micelle).
cheers
Andre

On Tue, Nov 20, 2012 at 12:01 PM, Thomas Schlesier <schlesi at uni-mainz.de>wrote:

> 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
> about distances, and in distances one has no information about 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
>>> >
>>>
>>
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-- 
_____________

Prof. Dr. André Farias de Moura
Department of Chemistry
Federal University of São Carlos
São Carlos - Brazil
phone: +55-16-3351-8090