  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.
