Evaluation of the translational free energy in a melting temperature calculation by simulation.

We present two methods suitable for controlling the translational degrees of freedom of a system when evaluating directly the free energy difference between the liquid and the solid phases by thermodynamic integration along a reversible path connecting these two phases. Such a constraint is crucial for an accurate prediction of the melting point by means of simulation. In one of the methods, the free energy difference was calculated by fixing one of the particles of the system at the center of the simulation box. In the second method, the free energy difference was calculated by constraining the center of mass of the system to a small region taken around the center of the simulation box. The correction to the free energy difference due to each constraint must be evaluated by a direct simulation. Both methods give consistent results when applied to a truncated and shifted Lennard-Jones system with cutoff radius of 2.5sigma. However, the fixed particle constraint method is found to be more efficient computationally.