The calculation of the melting temperature by means of molecular simulation poses significant challenges. To this date, estimates of the melting curve of the simple Lennard Jones system vary by as much as 10%. The origin of such discrepancies, and whether it is methodological or numerical, remains unclear. In this work we present precise values for the Lennard Jones melting temperature, and we examine in considerable detail sources of systematic error in prediction of melting points including, finite-size and cutoff radius effects.

A hypothetical integration path is used to find the relative free energies of the solid and liquid phases, of various system sizes, at constant cutoff radius. The solid-liquid relative free energy and melting temperature are shown to exhibit a 1/N scaling, where N is the system size. It is shown that finite-size effects can account for melting temperature errors of up to 5%. An extended-ensemble density-of-states method is used to find free energy change in each phase as a continuous function of the cutoff radius. This study shows that melting temperature predictions display decreasing oscillations as the cutoff radius is increased. Melting temperature prediction errors due to cutoff radius are of the same magnitude as finite-size effects and in some cases lead to errors of as much as 5%.