The high-pressure phase transitions of silicon and gallium nitride: a comparative study of Hartree–Fock and density functional calculations

All-electron Hartree–Fock and density functional calculations are performed to study the high-pressure phase transitions in gallium nitride and silicon within the framework of the linear combination of atomic orbitals using the Gaussian basis sets. Under high pressure, GaN makes a transition from the wurtzite (semiconducting) to the rock-salt (semiconducting) phase, whereas Si makes a transition from the cubic (semiconducting) to the β-tin (metallic) phase. The calculated results suggest that the lattice constants and the bulk moduli can be accurately described by both the methodologies for GaN and Si. Furthermore, both the calculations yield a phase transition pressure for GaN which is in reasonable agreement with the experimental data. However, the transition pressure for Si calculated in the closed-shell (restricted) Hartree–Fock approximation differs significantly from the one calculated using the density functional theory and the experimental data. This is primarily due to the fact that the energy difference between a semiconducting and a metallic state of Si is not well produced in the closed-shell Hartree–Fock approximation.