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

Abstract

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 2.5. However, the fixed particle constraint method is found to be more efficient computationally.

Direct calculation of solid-vapor coexistence points by thermodynamic integration: Application to single component and binary systems

“…We chose = 0.9 following the earlier work, 14,15,20 while ⌬P was selected such that the density of the fluid phase obtained at the end of the second stage is in the range of 0.7-0.8 in reduced units. We chose = 0.9 following the earlier work, 14,15,20 while ⌬P was selected such that the density of the fluid phase obtained at the end of the second stage is in the range of 0.7-0.8 in reduced units.…”

“…The external potential grid is made to expand or contract isotropically with V, 15 and hence U ext depends on the instantaneous value of V. The Gibbs free energy difference for the third stage is given by The cutoff distance reduces the computation required to calculate the external potential and should be chosen so that the effect of the Gaussian well on a particle is negligible beyond this distance.…”

“…15 For each of the states along the reversible path, the system was equilibrated for 20 000 Monte Carlo ͑MC͒ cycles followed by a production run of 60 000 cycles with block average taken over every 500 cycles. In the first and second stages of the reversible path, we started the simulation with a random configuration while in the third and fourth stages, we started with a perfect fcc configuration.…”

“…15 The core feature of this methodology, i.e., introducing a set of Gaussian potential wells to impart a translational order to the fluid phase, remains useful for the present method. In an earlier work, 14 a TDI path was employed to connect the liquid and solid phases reversibly in a canonical ensemble, which was later adapted to the isothermal-isobaric ensemble.…”

Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method

“…This problem has been reported to occur in many TDI methods including the Einstein crystal method, 1,5 the constrained fluid -integration method, 6,7 the surface free energy calculation of crystal phases, 4 and the direct computation of crystal-melt interfacial energy by the cleaving wall method. 7 A fixed particle constraint was also proposed for this method. In the Einstein crystal method, CM is fixed during TDI along the path.…”