Figure 1: Ab initio PIMD simulations of solid–liquid coexistence and melting.

Snapshots of the PIMD simulations at 700 GPa showing (a) the starting structure, (b) the final state at 100 K and (c) the final state at 125 K. Thirty-two beads (green balls) were used to represent the imaginary-time path integral for each atom. The grey balls in the insets of b and c correspond to the centroid of each atom. (d) The angularly averaged pair-distribution function g(r) for the same two simulations at 100 and 125 K. At 100 K, the solid state persists (black solid line) as indicated by the relatively sharp peaks. At 125 K (red dashed line), these peaks are much broader and the g(r) is characteristic of a liquid. This is further supported by the data in e, where the mean square displacements (MSD) as a function of time from separate adiabatic centroid MD simulations within the path-integral framework are shown³⁴. The MSD for the 100 K solid phase saturates rapidly, whereas for the liquid phase at 125 K it rises approximately linearly with time, resulting in a finite diffusion coefficient.