| We combine two algorithms recently proposed for the calculation of free energies (the adiabatic switch and the reversible scaling methods) with an improved description of the exchange and correlation functional (meta-GGA) to revisit the problem of calculating melting temperatures from density functional theory. We apply the scheme to the determination of the melting temperature of silicon and obtain Tm = 1700 +/- 50 (experimental Tm = 1687 K), a remarkable improvement over previous DFT determinations based on the local-density or generalized-gradient approximation. We also provide the first DFT-based determination of the melting temperature of germanium, Tm = 1120 +/- 40 K (experimental Tm = 1211 K), in the met-GGA approximation. The results highlight the important role played by the exchange and correlation functional in the determination of melting temperatures, and suggest that the newer generations of functionals are indeed much more accurate in this respect.; We have also calculated the P-T melting curve of diamond from first principles. Our calculated melting curve is in excellent agreement with the experimental estimate of the graphite-diamond-liquid triple point and is consistent with shock wave experiments. We predict the phase diagram of diamond at pressures and temperatures that are difficult to access experimentally. We confirm early speculations on the presence of a re-entrant point in the diamond melting line but find no evidence for a first order liquid-liquid phase transition near the re-entrant point.; We also present the implementation of the adiabatic switch and the reversible scaling methods within Car-Parrinello molecular dynamics simulation, as well as the implementation of metaGGA within the plane-wave and norm-conserving pseudo-potentials based electronic structure theory. |
