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

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