Lennard-Jones / WCA Potential Simulation - c++

Question

i am trying to implement a molecular dynamics simulation with the Lennard Jones potential.
I have the time evolution of the positions and velocities of the particles in multiple config files (n = 0,...,99) in steps of dt, such that t=n dt. So the actual simulation part is taken care of in that sense, for now i only have to calculate the potential energy and the force on each particle.
I already implemented a function to read in the config.dat files and put them in vectors, that part works as far as i know without an error. Then i wrote functions that calculate the force and the potential energy with a given distance r_ij between two particles (also used Newtown's third law so that i don't have to calculate the forces multiple times for the same interaction).
I also (hopefully correctly) implemented the periodic boundary conditions so that the particles can interact with their own images in the image boxes.
To test if my code works, i wanted to plot the total potential energy for all t=n dt.
However that does not work as intended because for some reason the potential energy that is written into the output files is always zero (the function for the potential energy returns zero if r_ij > r_cut, r_cut is where the potential is set to zero).
#include <iostream>
#include <math.h>
#include <fstream>
#include <stdlib.h>
#include <vector>
#include <string>
#include <utility>
#include <stdexcept>
#include <sstream>
using namespace std;
// Python >> C/C++
// Reads the initial states from the files
// The whole simulation in Python would have been as long as the function in c++ that just reads in the input
void read_input(int num_file, vector<double>& n, vector<double>& x, vector<double>& y, vector<double>& vx, vector<double>& vy, double& lx, double& ly) {
// Variable file name + opening it
ifstream file("configurations/config_" + to_string(num_file) + ".dat");
// Temp variables for reading in the file
double num, temp_x, temp_y, temp_vx, temp_vy;
// Looping over it
if (file.is_open()) {
string line;
while (getline(file, line)) {
// For the header; The header contains only the dimensions, e.g, 14 14, there are only 5 characters
if (line.length() == 5) {
stringstream dim_str(line);
dim_str >> lx >> ly;
continue;
}
// For the rest files
stringstream temp_str(line);
temp_str >> num >> temp_x >> temp_y >> temp_vx >> temp_vy;
n.push_back(num);
x.push_back(temp_x);
y.push_back(temp_y);
vx.push_back(temp_vx);
vy.push_back(temp_vy);
}
file.close();
}
}
// Calculates the potential for rij
double calc_pot(double r) {
double sigma = 1.0;
double epsilon = 1.0;
if (r <= pow(2, (1.0 / 6)) * sigma) {
double res = 4.0 * epsilon * (pow(sigma / r, 12) - pow(sigma / r, 6)) + epsilon;
return res;
}
else {
return 0;
}
}
// Calculates the force for rij
double calc_force(double r) {
double sigma = 1.0;
// Replaced the sigma^n with 1 bcs sigma = 1
double epsilon = 1.0;
if (r <= pow(2, (1.0 / 6)) * sigma) {
double res = (48.0 * epsilon / pow(r, 13)) - (24 * epsilon / pow(r, 7));
return res;
}
else {
return 0;
}
}
// Calculates the distance of the
double dist(double rx, double ry) {
return sqrt(rx * rx + ry * ry);
}
int main() {
// Misc. parameters
int N = 144;
double mass = 1.0;
double sigma = 1.0;
double epsilon = 1.0;
// Tau = sqrt(mass*sigma^2/epsilon) = (here) 1
double tau = 1.0;
double dt = 0.02;
// Vectors for the read in values for i and i+1
vector<double> n, x, y, vx, vy;
double lx, ly;
// Vector for the potential and two for the force, x and y
vector<double> epot(N), f_x(N), f_y(N);
for (int i = 0; i < N; i++) {
epot[i], f_x[i], f_y[i] = 0;
}
// Outerloop for time steps (in this case the files n = {0,..,99})
for (int k = 0; k <= 99; k++) {
string fname = "output/epot_" + to_string(k) + ".txt";
ofstream output(fname);
read_input(k, n, x, y, vx, vy, lx, ly);
// Inner two loops to accses every possible interaction without doing them twice
for (int i = 0; i < N - 1; i++) {
// Vecctor for particle i
double rix = x[i];
double riy = y[i];
for (int j = i + 1; j < N; j++) {
// Vector for particle i+1
double rjx = x[j];
double rjy = y[j];
// Periodic boundary cond.
if (rix > lx) {
rix -= lx;
}
if (riy > ly) {
riy -= ly;
}
if (rjx > lx) {
rjx -= lx;
}
if (rjy > ly) {
rjy -= ly;
}
if (rix < 0) {
rix += lx;
}
if (riy < 0) {
riy += ly;
}
if (rjx < 0) {
rjx += lx;
}
if (rjy < 0) {
rjy += ly;
}
// Component wise distance for the force
double dist_x = rix - rjx;
double dist_y = riy - rjy;
// Minimum image convention
if (abs(dist_x) > lx / 2) {
dist_x = (lx - abs(dist_x)) * (-dist_x) / abs(dist_x);
}
if (abs(dist_y) > ly / 2) {
dist_y = (ly - abs(dist_y)) * (-dist_y) / abs(dist_y);
}
// Normalized Force/R
f_x[i] += calc_force(dist_x) * (1 / dist(dist_x, dist_y));
f_y[i] += calc_force(dist_y) * (1 / dist(dist_x, dist_y));
f_y[j] += -calc_force(dist_x) * (1 / dist(dist_x, dist_y));
f_y[j] += -calc_force(dist_y) * (1 / dist(dist_x, dist_y));
// Potential energy
epot[i] += calc_pot(dist(dist_x, dist_y));
}
// Potential energy per particle
output << fixed << std::setprecision(4) << epot[i] / (N) << endl;
}
}
}
A config file looks something like this
14 14
0 0 0 1.0292605474705 0.394157727758591
1 0 1.16666666666667 1.05721528014223 1.9850461002085
2 0 2.33333333333333 1.18385526103892 0.143930912297367
3 0 3.5 -0.938850340823852 1.71993225409788
4 0 4.66666666666667 1.99468650405917 0.952210892864475
5 0 5.83333333333333 -0.985361963654284 3.05201529674118
6 0 7 2.84071317501321 0.0689241023507716
7 0 8.16666666666667 3.56152464385237 2.88858201933488
8 0 9.33333333333333 0.147896423269195 1.40592679110988
The header contains the dimensions of the simulation box, here (14,14).
Then all the lines have the corresponding values of {#Particle, x, y, velocity x, Velocity y).
The file above shows this for the first 9 particles.
I am relatively new to c/c++ so have mercy with me 😄.
Also i am aware that the code has still potential to be optimised but i will deal with that when i can calculate the force on each particle correctly.
Edit:
Here is the formula for the potential energy:
The force can be calculated via F= -d/dr U(r).