From semilocal density functionals to random phase approximation renormalized perturbation theory: A methodological assessment of structural phase transitions

The structural phase transitions of different materials, including metal to metal, metal to semiconductor, and semiconductor to semiconductor transitions, were explored using methods based on the random phase approximation. Transition pressures for Si, Ge, SiC, GaAs, ${\mathrm{SiO}}_{2}$, Pb, C, and BN from their stable low-pressure phases to certain high-pressure phases were computed with several semilocal density functionals and from the adiabatic connection fluctuation-dissipation formulation of density functional theory at zero temperature. In addition to the random phase approximation (RPA), three approximate beyond-RPA methods were also investigated to determine the impact of exchange-correlation kernel corrections. Results at finite temperature were obtained with the inclusion of zero-point energy contributions from the phonon spectra. We find that including temperature effects is most important for systems with nearly degenerate phases such as for boron nitride and carbon. In combination with thermal corrections, the kernel-corrected correlation methods deliver high accuracy compared to experimental data and can serve as a useful benchmark method in place of more expensive correlated calculations.