# Is it possible to calculate 2D and 3D pair distributions

Dear lammps user,

We know that the lammps has “compute rdf” command to calculate radial distribution function for a system of particles. It assumes symmetry/homogeneity in other two directions (theta and phi).

Is it possible to look calculate pair distribution as the function of r, theta and phi using the “chunk” command or by any other means!

-Sanat

If you mean some form of 2d or 3d pair correlation function,

I think you’d have to modify the code in compute rdf to do that,

e.g. derive a compute rdf/2d or compute rdf/3d.

Steve

I’d be inclined to agree with Steve.

What you’re suggesting using chunk would be a form of double averaging that I have seen people do (and been surprised at its publication), but in terms of doing science its messy for no reason really - you have the particle positions! You can compute it! In some sense this is only a little bit useful for calculating small wave numbers in structure functions, i.e. Fourier Transform of the rdf or two-point velocity correlation.

I'd be inclined to agree with Steve.

What you're suggesting using chunk would be a form of double averaging
that I have seen people do (and been surprised at its publication), but in
terms of doing science its messy for no reason really - you have the
particle positions! You can compute it! In some sense this is only a
little bit useful for calculating small wave numbers in structure
functions, i.e. Fourier Transform of the rdf or two-point velocity
correlation.

in my personal opinion, ​multi-dimensional correlations by distance and
angle typically only make sense, if there is an orientational preference in
the ​system itself, e.g. if you are looking at distributions around atoms
in a surface. this almost always requires writing a custom(ized) code for
the system at hand.

for a more detailed look at more generalized radial distributions in bulk
systems, it may be of more use to resolve the g(r) by projection on
spherical harmonics. i think there is a detailed discussion of that in
"theory of molecular fluids" by gray and gubbins. it may also be worth
looking up some of the work of the group of alfons geiger in dortmund.
there is likely more, but these are two sources i remember well from my
time as a grad student, when i was looking into recovering some of the
information, that is lost by the spherical averaging in g(r)s.

axel.

Great point, visualizing in some 3D systems, e.g. sheared, can be hard enough!

Thanks everyone,

The system I am trying to diagnose a 3-D box filled with point charge particles. The system is homogeneous yet there is a temperature anisotropy. I presume this temperature anisotropy will lead to a pair distribution which might not be spherically symmetric.

@Axel, thanks for the reference. It looks useful not only for pair distributions but for other statistical and thermodynamics stuffs as well.

-Sanat

Thanks everyone,

The system I am trying to diagnose a 3-D box filled with point charge
particles. The system is homogeneous yet there is a temperature anisotropy.
I presume this temperature anisotropy will lead to a pair distribution
which might not be spherically symmetric.

@Axel, thanks for the reference. It looks useful not only for pair
distributions but for other statistical and thermodynamics stuffs as well.

here is one more...​

​given your description, you probably may also benefit from a look at
"theory of simple liquids" by hansen and mcdonald, if you don't own a copy
already. ​i recall that the gray/gubbins book was pretty tough, while the
hansen/mcdonald was more accessible and thus i learned much more from it. i
hold in high regard since and have recommended it frequently.

axel.

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