Pressure-induced phase transitions in solid Si,SiO2,and Fe: Performance of local-spin-density and generalized-gradient-approximation density functionals

We focus on a particular shortcoming of the local-spin-density (LSD) approximation for the exchange-correlation energy of a many-electron system: underestimation of the transition pressure $p_t$ at pressure-induced structural phase transitions in solids. We have performed self-consistent full-potential LAPW calculations, with full structure optimization, for three cases—silicon (Si), silica $\left({\mathrm{SiO}}_2\right),$ and iron (Fe). In agreement with previous calculations, we find that gradient corrections to LSD over-correct the equilibrium volumes in Si and ${\mathrm{SiO}}_2,$ but correct or slightly under-correct the volume in Fe and the transition pressures in all three materials. We apply a thermodynamiclike inequality [A. Zupan et al., J. Chem. Phys. 106, 10 184 (1997)] to our results to explain why the generalized gradient approximation expands the equilibrium volume and increases the value of $p_t$ over LSD. In all three cases, gradient corrections to LSD tend to stabilize the low-pressure phase because of its more inhomogeneous electron density.