Equation used in compute_rdf command for g(r)

Dear All,

I am trying to find out the physical meaning of the g® calculated by the compute rdf command. After reading the compute_rdf.cpp file, my understanding of the final equation is like: g®=N(shell,j)/(N(total,i)*N(total,j)*V(shell)). But this does not really make sense to me. Can anyone please explain this g® calculation equation? Thanks in advance.

Best,
Jim

Dear All,

I am trying to find out the physical meaning of the g(r) calculated by the
compute rdf command. After reading the compute_rdf.cpp file, my
understanding of the final equation is like:
g(r)=N(shell,j)/(N(total,i)*N(total,j)*V(shell)). But this does not really
make sense to me. Can anyone please explain this g(r) calculation equation?

can *you* please explain, *why* it doesn't make sense to you?

that is a much easier way to move forward.

thanks,
    axel.

Jingchao,

G(r) is often called the radial distribution function. It represents
the local density correlations, and can easily be thought of as the
density in shell r divided by the expected density if all mass were
uniformally distributed, i.e. uncorrelated. Its physical relevance
depends on the system you are working with.

Hi Axel,

Thanks for your response. I think the g® expression should have the format like: g®=n®/(rho4pir^2dr), which is based on the following information: http://www.physics.emory.edu/~weeks/idl/gofr2.html. But from the cpp file I couldn’t get above equation. So I wonder if I made a mistake simplifying the equation or it uses another method to calculate g®.I did notice that cpp file uses a more accurate method to calculate the shell volume. My major concerns are about the terms n® and rho. Thanks for your time.

Best,
Jingchao

Hi Axel,

Thanks for your response. I think the g(r) expression should have the format
like: g(r)=n(r)/(rho*4*pi*r^2*dr), which is based on the following
information: http://www.physics.emory.edu/~weeks/idl/gofr2.html. But from
the cpp file I couldn't get above equation. So I wonder if I made a mistake

but those are the same. if you integrate 4 pi r**2 dr over the width
of the histogram bin, you get the the volume of the spherical slice
and if you divide the number of items in the histogram bin through the
number of total pairs, you have the local density divided by the
particle density.

axel.