Zero-Point Energies prevent a Trigonal to Simple Cubic Transition in High-Pressure Sulfur

Abstract

Recently published Density Functional Theory results from Whaley-Baldwin et. al. [New J. Phys. 22 023020, Feb 2020] using the PBE functional suggest that elemental sulfur does not adopt the simple-cubic (SC) $Pm\bar{3}m$ phase at high pressures, in disagreement with previous works on this system [Phys. Rev. Lett. 83, 3049, Oct 1999]. We carry out an extensive set of calculations using a variety of different XC-functionals, pseudopotentials and the all-electron code ELK, and we are now able to show that even though under LDA and PW91 a high-pressure simple-cubic phase does indeed become favourable at the static lattice level, when zero-point energies (ZPEs) are included, the transition to the simple-cubic phase is suppressed in every case, owing to the larger ZPE of the SC phase. We reproduce these findings with pseudopotentials that explicitly include deep core and semicore states, and show that even at these high pressures, only the $n=3$ valence shell contributes to bonding in sulfur. We further show that the $Pm\bar{3}m$ phase becomes even more unfavourable at finite temperatures. We finally investigate whether anharmonic corrections to the zero-point energies could make the $Pm\bar{3}m$ phase favourable, and find that these corrections are several orders of magnitude smaller than the ZPEs and are thus negligable. These results therefore confirm the original findings of Whaley-Baldwin et. al.; that the high pressure transition sequence of sulfur is $R\bar{3}m \rightarrow$ BCC, with no intervening SC phase.