Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing density functional theory (DFT) and quantum Monte Carlo (QMC) treatments. The method is applied to address the longstanding discrepancy between DFT calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, in contrast to DAC data.

Figure 1

Energy of a unit cell of fcc xenon calculated with DFT and DMC. The dotted lines correspond to Vinet fits to the DFT calculations. The solid lines correspond to Vinet fits to the DMC calculations. The triangles correspond to DFT or DMC simulations based on the LDA and the circles DFT or DMC based on AM05.

Figure 2

Top: DMC energies corresponding to configurations representative of solid (blue triangles) and liquid (red squares) xenon, generated with quantum molecular dynamics (QMD) on 108-atom systems. The solid lines connect DFT energies calculated on the same configurations. An independent offset is added to the DMC and DFT calculations so that the average energy of the solid snapshots in each method is 0. Bottom: DMC-DFT energy differences for the same configurations. The average DMC-DFT energy difference for the solid is subtracted from all points. Lines represent the average of the energy differences between DMC and DFT in the solid and the liquid.

Figure 3

Relative Helmholtz free energy of the solid and liquid phases at 5600 K determined by DFT calculations to establish the melt pressure and thermodynamic integration to find the relative free energies. A common tangent to the QMC curves is also shown, establishing a melt pressure of 66 GPa.

Figure 4

Melting of xenon as a function of pressure obtained with various theoretical [6, 24, 25, 26] and experimental [5, 27] techniques. Experimental points are solid squares, classical molecular dynamics circles, DFT based molecular dynamics triangles, and QMC diamonds. A correction of the experimental points including an estimate of thermal pressure from SESAME 5191 [28] is shown with solid pentagons. Horizontal error bars on the QMC points include the statistical uncertainty in the pressure shift technique, and the vertical error bars from the temperature shift technique.