Problem applying Lennard jones equation for large scale

Hi,

I am working on a project which is based on lennard jones potential. I'm trying to make a simulation for two points (or particles) but it doesn't work correctly. In my view, I think it's because this model is used to work with particles instead of large-scale problems. What could I do?

I consider that one particle is without moving.

You can see below the code. Thanks a million

clc
close all 
clear all

epsilon = 5;
sigma = 2;

% initial position of A and B particles

a = [2 3];
b = [2 8];

% List of forces 

f_list = zeros(30,1);

for k = 1:30
    
    % unit vector
    ba = a-b;
    dab = norm(b-a);
    unit_vector = ba /dab;
    
    % force as negative gradient of lennard jones potential
    
    f = 4*epsilon*((12*(sigma^12)/dab^13)-(6*(sigma^6)/dab^7));
    f_list(k,:)= f;
    
    force = unit_vector * f;
    
    % new position
    
    a = a + 0.1 * force;
    
    scatter(a(1),a(2));
    hold on
    scatter(b(1),b(2));
    pause(0.1)
    
end
  

[Cristian Garcia Milan]

Can you say me what is your exatc problem? I see that you are adding the force multiply by 0.1 to the position and I think it should be to the velocity and the velocity shjould be added to the position.