How do I calculate the pair distribution function, g(r), if I know a list of particle centres?

I have a list of particle centre of mass in x, y, and z directions. I want to calculate the pair distribution function, g(r) that basically tells about the probability of finding a particle next to the reference particle. I followed the procedure given in this link How to calculate the pair correlation function g(r) (emory.edu), but didn't get the result as expected. This is what I tried.

count = 0;

for i = 1:np % np is the number of particles

for j = (i+1):np

dist = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2 + (z(i)-z(j))^2) % x, y, and z are the particle centre of mass

for r = 1:del_r:50 % for now i used del_r=1

volume(r) = 4*pi*r^2*del_r;

if (dist < r) && (dist < (r + del_r))

count = count + 1; % the problem is to count the number of particles that satisfy this if condition.

tot_count(r) = count/np;

end

end

end

cnt_ovr_vol = tot_count./volume;

num_den = np/(nx*ny*nz); %nx = ny = nz = 100;

g_r = (cnt_ovr_vol./num_den);

end

Does my code make sense as per the procedure in the link?

[Amirsaman Eghtesad]

According to the link, you have to change (dist < r) to (dist >r).

[Hisay Lama]

You need to take care of edge correction, mentioned here:

https://physics.emory.edu/faculty/weeks/idl/gofr2.html

They used a function checkquadrant for that.

Answer 1

[Aditya Shah]

Hi!

The following MATLAB File Exchange example, explains how to calculate the Pair distribution Function g(r):

https://in.mathworks.com/matlabcentral/fileexchange/70378-pair-distribution-function?tab=reviews