Recently published density functional theory results using the PBE functional (Whaley-Baldwin and Needs 2020 New J. Phys. 22 023020) suggest that elemental sulfur does not adopt the simple-cubic (SC) phase at high pressures, in disagreement with previous works (Rudin and Liu 1999 Phys. Rev. Lett. 83 3049--52; Gavryushkin et al 2017 Phys. Status Solidi B 254 1600857). We carry out an extensive set of calculations using a variety of different exchange–correlation functionals (both local and non-local), and show that even though under LDA and PW91 a high-pressure SC phase does indeed become favourable at the static lattice level, when zero-point energies (ZPEs) are included, the transition to the SC phase is suppressed in every case, owing to the larger ZPE of the SC phase; thus confirming the transition sequence as BCC, with no intervening SC phase. We reproduce these findings with pseudopotentials that explicitly include core electronic states, and show that even at these high pressures, only the n = 3 valence shell contributes to bonding in sulfur. We then compare our findings against the all-electron code ELK, which is in excellent agreement with our pseudopotential results, and examine the roles of the exchange and correlation contributions to the total energy. We further calculate anharmonic vibrational corrections to the ZPEs of the two phases, and find that such corrections are several orders of magnitude smaller than the ZPEs and are thus negligible. The effect of finite temperatures is also considered, and we show that the phase becomes even more unfavourable with an increase in temperature. Finally, the experimental consequences of our results on the equation of state of sulfur and its superconducting critical temperature are explicitly calculated.

最近发表的使用PBE泛函的密度泛函理论结果（Whaley-Baldwin and Needs 2020 New J.Phys.22 023020）表明，元素硫在高压下不采用简单立方（SC）相，这与之前的工作有所不同（鲁丁和Liu 1999 。物理学快报修订版。 83 3049--52; Gavryushkin等人2017和。物理学1.166乙2541600857）。我们使用各种不同的交换相关函数（局部和非局部）进行了广泛的计算，结果表明，即使在LDA和PW91下，高压SC相在静态晶格水平上确实变得有利。 ，当包含零点能量（ZPE）时，由于SC相的ZPE较大，在每种情况下都抑制了向SC相的转变；因此确认过渡序列为BCC，无中间SC相。我们用明确包括核心电子状态的伪电位来再现这些发现，并表明即使在这些高压下，只有n = 3价壳对硫键合起作用。然后，我们将我们的发现与全电子代码ELK进行比较，与我们的准势结果非常吻合，并研究了交换和相关贡献对总能量的作用。我们进一步计算了两相ZPE的非谐振动校正，发现这种校正比ZPE小几个数量级，因此可以忽略不计。还考虑了有限温度的影响，并且我们表明，随着温度的升高，相变得更加不利。最后，明确计算了我们的结果对硫及其超导临界温度方程的实验结果。