Download the file LJ.tgz that contains a code to perform NEV simulation of a Lennard-Jones fluid. Once unpacked, the LJ directory will contain two sub-directories: Source (contaning code MD to perform molecular dynamics and code block to perform some statistical processing of the data) and Run that contains a couple of scripts.

Compile the two codes using the provided Makefile (just type make in the Source directory... but you may need to edit the Makefile in order to specify a different compiler name and/or compiler options). Make an effort to understand the two codes (not in all details but at least their general structure).

Run code MD at reduced temperature $T=1.5$ and reduced density $\rho=0.8442$ . Make a plot of the time evolution of the kinetic, potential and total energy. HINT: the file lj.prt generated by the script "run" contains the istantaneous values of temperature, pressure and potential energy per particle for each time step. These information is sufficient to generate the required data.

Check that the time step used in the provided script is sufficiently small to conserve the total energy without significant fluctuation or drift.

Increase gradually the value of the time step (delt) until the integration scheme brakes down and energy conservation is lost. For the rest of your simulations set the time step to a safe value.

Make a plot of the radial distributionn function, $g(r)$ , for a few temperatures (for instance T=0.7, 1.5, 2.5 in reduced units) and verify how atomic shell structure is washed out by temperature.

Study the self diffusion of the atoms in the system for the same set of temperatures by looking to velocity autocorrelation function and the time dependence of mean-square displacement (use and modify script run-vacf). Are the examined simulation conditions tipical of a fluid or of a solid.

Modify the routine lattice.f that set initial configuration of the simulation distributing atoms on the sites of a simple-cubic lattice (a very unlikely configuration for LJ potential that likes compact structures) in such a way that the particles are distributed on a face-centered-cubic lattice (corresponding to low temperature crystalline structure of LJ potential).

Verify that for density close to the equilibrium volume and low enough temperatures the mean-square displacement does not grow indefinitely with increasing time, and self-diffusion vanishes inidicating a crystalline behaviour.