[gmx-users] xy option in g_rdf

[Andrew DeYoung]

Hi, 

If you have time, I have a question about the -xy option in g_rdf.  I'm a
little afraid that this may be silly question and the answer might be
obvious in hindsight, but I have been having difficulty finding the answer.
Thanks.

As we all know, g_rdf computes radial distribution functions of, for
example, atoms.  With the default options, g_rdf I think computes what I
might naively call "three-dimensional" or "isotropic" radial distribution
functions.  Borrowing a conceptual example from Benjamin Widom's
"Statistical Mechanics: A Concise Introduction for Chemists," I think that
we can think about the situation as follows.  Suppose there is an atom at
some point O.  The mean local density at a distance r from O is given by 

(mean local density at a distance r from O) = rho*g(r)

where rho = N/V is the average number density at a distance r from O, and
g(r) is the RDF at r.  So, basically, I think of a "three-dimensional" RDF
at r as being computed by looking at atoms located at the surface of a
(three-dimensional) shell of radius r centered at O, and then averaging over
both space and time (as described in section 8.4 in the Gromacs Manual).

But what happens if I use the -xy option in g_rdf?  The manual page
(http://manual.gromacs.org/current/online/g_rdf.html) says that with -xy,
the RDF will be "calculated around axes parallel to the z-axis"; in other
words, only the x and y components are included in the computation.  What
does this mean conceptually?  Does it mean that instead of having a
(three-dimensional) shell of radius r centered at O, we now have a
(two-dimensional) RING of radius r centered at O?  (This ring of radius r, I
guess, is parallel to the xy-plane.)  Is the z-component averaged over at
all?  

Even if my guesses in the previous paragraph are correct, though, in general
when is the -xy option useful?  If I have a solid surface parallel to the xy
plane and want to characterize the distribution of water molecules above
that solid surface, then the -xy option would NOT be useful in this case; is
this correct?  On the other hand, if I have a carbon nanotube with its axis
along the z-axis and want to determine the distribution of water molecules
at distances radial from the nanotube axis, then the -xy option WOULD be
useful in this case; is this correct?

Or if you have time, can you please help me think of a conceptual example
that will help me visualize what the -xy option does?

Thanks so much for your time!

Andrew DeYoung
Carnegie Mellon University