Off-Lattice MC algorithm for Lennard-Jones 6-12 fluid

1.

Prepare the initial configuration of the system with the desired density (box size and number of particles). Usually just a simple cubic lattice will work.

2.

Loop through the particles, trying to make a MC loop

• Pick up a particle and decide it's new position by choosing the displacement components at random $\mathbf{d}_i = (\ensuremath{\text{\texttt{rand()}}}-0.5)\times\mathbf{x}_{max}$. ( is a random number from 0 to 1, $\mathbf{x}_{max}$ is the maximum allowed displacement magnitude).
• Calculate the energy change induced by displacement $\delta U = \sum_j\left(U_{ij}(\mathbf{r}_i+\mathbf{d}_i-\mathbf{r}_j) - U_{ij}(\mathbf{r}_i-\mathbf{r}_j)\right)$ and decide whether accept it or not according to the Metropolis criterium.
• if accepted, update position, energy, etc.
• Pick the next particle, etc.

3.

Calculate necessary averages, printout the results, etc. Go back to step 2.

Fortran code Example 5 

Here is an example of the Fortran code for the 2D Lennard-Jones fluid
Code.