Lennard-Jones Molecules Using the Monte Carlo Simulations with Optimum Maximum Allowed Displacement رسالة ماجستير

Abstract

In this thesis, a periodic systems of N-point particles with Lennard-Jones potential are simulated by using Monte Carlo technique in three dimensional space. Since Lennard-Jones is a short range potential, it is considered to be zero beyond some cut o radius r cut. The optimum r cut found is 2.5. The maximum allowed displacement used in a Monte Carlo simulation of any N- particles system controls the convergence to the potential energy of the system at equilibrium. The optimum maximum allowed displacement is found to be associated with 50% acceptance rate; which is the ratio of accepted Monte Carlo moves to the total number of moves. An explicit mathematical formulas for the optimum maximum allowed displacement (O-dmax) are obtained as a function of both temperature and density. Those formulas are calculated at di erent values of temperature and density by tting the Monte Carlo simulation results, using the tting tool in Matlab.