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

Abstract

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, SiO2, 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 termperature 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.

Rationalizing accurate structure prediction in the meta-GGA SCAN functional

“…Compared to other non-empirical semi-local density functionals, SCAN has been shown to yield a significantly more accurate representation of the bulk properties of many semiconducting solids, including but not limited to formation enthalpy [24], bulk modulus, lattice parameter and volume [16], and reaction energies [17], transition pressures [39,40]. However, while SCAN yields accurate properties for strongly-bound compounds [18] and ionic systems, it is moderately worse for weakly-bound intermetallic compounds [19] and significantly worse than PBE in overestimating of magnetic energies in metallic phases [15].…”

Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies

“…(1) in ref. 131 In general, all bRPA methods deliver an overestimation of the equilibrium and transition volumes by about the same amount as the LDA underestimates them. bRPA approximations yielded an overall improvement compared to the bare RPA and semilocal functionals for the transition pressures, as shown in Table 6, although the behavior is less systematic than for RPA.…”

“…In combination with the rAPBE and rALDA kernels, the RPAr approximation was investigated for the structural phase transitions of a small but representative group of materials. 131 The examples were chosen to incorporate several changes in band structure, including from semiconductor to semiconductor, semiconductor to metal, and metal to metal transitions. The assessment includes the phase transitions of the diamond phase of Si to the metallic beta-tin form, the zinc-blende (ZB) to rocksalt transition of SiC, the ZB to Cmcm phase transition of GaAs, the quartz to stishovite transition of SiO 2 , the transition from fcc to hcp structure of Pb, and finally the phase transition of the hexagonal to cubic structures of BN.…”

“…(9) in ref. 131 Compared to zero Kelvin, the addition of thermal corrections introduces a rigid shift in the performance of all the methods for most of the materials in the assessment, and the agreement typically improves with experiment when the thermal corrections are included.…”

“…17 Energy-volume curves for the quartz and stishovite phases of SiO 2 with RPA and rAPBE (within the HOT approximation) per functional unit. 131 The negative slope of the common tangent line corresponds to the transition pressure. The kernel corrections for SiO 2 increase the equilibrium energy difference between phases and correct the large underestimation of the transition pressure by RPA as a result.…”