Write an MD NPT program for a simple system of Lennard$-$

Jones particles. These are the main steps:

a$.$ Create a box and fill it with a given number of particles $($the box size and number of

particles should be variable$).$

b$.$ Assign an intermolecular potential $($L$-$J$)$ between the particles in the box.

c$.$ Calculate the potential energy of the system using the L$-$J potential. The cutoff distance

of the L interactions should be variable.

d$.$ You should provide long$-$range corrections for the potential energy beyond the cutoff

distance.

e$.$ You should be able to calculate the forces acting on each particle in the system.

f$.$ You should be able to use the force acting on each particle to predict the velocity and

the next position of each particle $($using a standard integration scheme$).$

g$.$ You should update all positions in the system, based on the integration $($the time step

should be variable$).$

h$.$ You should be able to calculate the kinetic energy and the temperature of the system.

i$.$ You should be able to calculate the pressure in the system $($using the virial$).$

j$.$ You should be able to calculate the diffusion coefficient $($from the mean$-$squared

displacement or from the velocity$-$autocorrelation function$).$

k$.$ You should be able to output a movie of the system trajectory.

I. You should be able to output a plot of the potential energy, the kinetic energy, and the

total energy $($as a function of time$).$

m$.$ You should be able to apply a thermostat to the system to perform an NVT simulation.

n$.$ You should be able to apply a barostat to the system to perform an NPT simulation.

o$.$ You should be able to benchmark your results $($energy$,$ pressure, temperature etc.$)$

against the Lennard$-$Jones Equation of state: