Calculating potential energy in a molecular dynamics simulation - c

Question

Background
Imagine that we have N particles inside a box of length L, which interact with each other (through a Lennard Jones potential).
I want to compute the total potential energy of the system. I implemented the function POT which calculates all the contributions from all the particles and gives the correct results (this is tested and can be assumed true).
I also wrote a function POT_ONE which only calculates the potential energy of one particle with respect to all the others. This means that if I want to calculate the total potential energy I will have to call this function N times (making sure that the particle does not interact with itself) and then divide by 2 since I double count the interactions.
Goal
My goal is to make the second function yield the same results as the first one.
Problem
There is something really strange going on: If I put 4 particles, the two functions give the same results. If I put a fifth one then there is deviation. Then for 6,7,8 particles,again, it gives correct results and then for N=9 I am getting a different result. In the case N=1000 the result that I am getting from POT_ONE is somemthing like 113383820348202024.
My results for N=5 are:
-0.003911 with POT and
12.864234 with POT_ONE
In case someone tries to run the code and wants to check the N=4 case, he/she should change the number of particles (np) which is defined as global variable and then comment the line pos[12]=1;pos[13]=1;pos[14]=1;.
Code
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/*GENERAL PARAMETERS*/
int dim=3; //number of dimensions
int np=5; //number of particles
double L=36.413; //box length (A)
double invL=1/36.413; //inverse of box length
/*ARGON CHARACTERISTICS*/
double sig=3.4; // Angstroms (A)
double e=0.001; // eV
double distSQ(double array[]){
/*calculates the squared distance given the array x=[dx,dy,dz]*/
int i;
double r2=0;
for(i=0;i<dim;i++) r2+=array[i]*array[i];
return r2;
}//distSQ
void MIC(double dr[],double L, int dim){
/* MINIMUM IMAGE CONVENTION: dr[] is the array dr = [dx,dy,dz] describing relative
positions of two particles, L is the box length, dim the number
of dimensions */
int i;
for(i=0;i<dim;i++) dr[i]-=round(dr[i]*invL)*L;
}//MIC
void POT(double x1[],double* potential){
/*given the positions of each particle in the form x=[x0,y0,z0;x1,y1,z1;...;xn-1,yn-1,zn-1],
the number of dimensions dim and particles np, it calculates the potential energy of the configuration*/
//variables for potential calculation
int i,j,k;
double *x2;
double r2inv; // 1/r^2
double foo,bar;
double dr[dim];
*potential=0; // set potential energy to zero
//main part of POT
for(i=0;i<np-1;i++){
x2=x1+dim;
for(j=i+1;j<np;j++){
//calculate relative distances between particles i & j
//apply periodic BCs and then calculate squared distance
//and the potential energy between them.
for(k=0;k<dim;k++) dr[k] = x2[k]-x1[k];
MIC(dr,L,dim); //periodic boundary conditions
r2inv=1/distSQ(dr);
//calculate potential energy
foo = sig*sig*r2inv;
bar = foo*foo*foo;
*potential+=bar*(bar-1);
}//for j
x1+=dim;
}//for i
*potential*=4*e; //scale and give energy units
}//POT
void POT_ONE(int particle,double pos[],double* potential){
*potential=0;
int i,k;
double dr[dim];
double r2inv,foo,bar;
double par_pos[dim];
int index=particle*dim;
par_pos[0]=pos[index];
par_pos[1]=pos[index+1];
par_pos[2]=pos[index+2];
for(i=0;i<np;i++){
if(i!=particle){
for(k=0;k<dim;k++) dr[k]=pos[k]-par_pos[k];
MIC(dr,L,dim);
r2inv=1/distSQ(dr);
foo=sig*sig*r2inv;
bar=foo*foo*foo;
*potential+=bar*(bar-1);
}
pos+=dim;
}
*potential*=4*e; //scale and give energy units
}//POT_ONE
int main(){
int D=np*dim;
double* pos=malloc(D*sizeof(double));
double potential=0; //calculated with POT
double U=0; ////calculated with POT_ONE
double tempU=0;
pos[0]=0;pos[1]=0;pos[2]=0;
pos[3]=4;pos[4]=0;pos[5]=0;
pos[6]=0;pos[7]=4;pos[8]=0;
pos[9]=0;pos[10]=0;pos[11]=4;
pos[12]=1;pos[13]=1;pos[14]=1;
POT(pos,&potential);
printf("POT: %f\n", potential);
int i,j;
for(i=0;i<np;i++){
POT_ONE(i,pos,&tempU);
U+=tempU;
}
U=U/2;
printf("POT_ONE: %f\n\n", U);
return 0;
}

Answer 1

Your error is in POT, where you forgot to update x2 at the end of the inner loop.
for (i = 0; i < np - 1; i++) {
double *x2 = x1 + dim;
for (j = i + 1; j < np; j++) {
// ... calculate stuff ..
x2 += dim;
}
x1 += dim;
}
An easier and arguably more readable variant is to forgo pointer arithmetic altogether and use boring old indices:
for (k = 0; k < dim; k++) {
dr[k] = x[j * dim + k] - x[i * dim + k];
}
Further observations:
Please make your variables local to the scope where they are used. A large list of uninitialized variables at the top of the function makes it very hard to track variables, even in a short function like yours.
Please consider returning single values from functions instead of passing in pointers. In my opinion, that makes functions like the square of the distance more readable.
The structure of your code is hard to see, because everything is run togeher very tightly, even the comments.