Structural phase transitions in Si and SiO2 crystals via the random phase approximation

We have assessed the performance of the non-self-consistent random phase approximation (RPA) on two pressure-induced structural phase transitions, diamond to beta-Sn Si in Si and alpha-quartz to stishovite in SiO2. The calculated equilibrium lattice properties of the four structures are in better agreement with experimental results than are those from several semilocal functionals. The energy differences between the high-and low-pressure phases are found to be 0.37 eV/Si and 0.39 eV/SiO2, respectively. The transition pressure obtained from our RPA calculations for diamond to beta-Sn in Si is 12.2 GPa, in excellent agreement with the experimental value 11.3-12.6 GPa. However, the alpha-quartz to stishovite phase-transition pressure in SiO2 is found to be 5.6 GPa, lower than the experimental 7.46 GPa; the Perdew-Burke-Ernzerhof (PBE) semilocal functional gives the transition pressure closest to experiment in this case. We conclude that the non-self-consistent, nonlocal RPA accurately describes the insulator-to-metal transition in Si, where semilocal density functionals tend to fail. But the RPA error cancellation that is nearly perfect in many solids, including Si, may be less perfect in solid SiO2, as it is in many molecules.