Melting line of the Lennard-Jones system, infinite size, and full potential

Literature estimates of the melting curve of the Lennard-Jones system vary by as much as 10%. The origin of such discrepancies remains unclear. We present precise values for the Lennard-Jones melting temperature, and we examine possible sources of systematic errors in the prediction of melting points, including finite-size and interaction-cutoff effects. A hypothetical thermodynamic integration path is used to find the relative free energies of the solid and liquid phases, for various system sizes, at constant cutoff radius. The solid-liquid relative free energy and melting temperature scale linearly as the inverse of the number of particles, and it is shown that finite-size effects can account for deviations in the melting temperature (from the infinite-size limit) of up to 5%. An extended-ensemble density-of-states method is used to determine free energy changes for each phase as a continuous function of the cutoff radius. The resulting melting temperature predictions exhibit an oscillatory behavior as the cutoff radius is increased. Deviations in the melting temperature (from the full potential limit) arising from a finite cutoff radius are shown to be of comparable magnitude as those resulting from finite-size effects. This method is used to identify melting temperatures at five different pressures, for the infinite-size and full potential Lennard-Jones system. We use our simulation results as references to connect the Lennard-Jones solid equation of state of van der Hoef with the Lennard-Jones fluid equation of state of Johnson. Once the references are applied the two equations of state are used to identify a melting curve. An empirical equation that fits this melting curve is provided. We also report a reduced triple point temperature T(tr)=0.694.