论文标题
零点的能量防止在高压硫中的简单立方过渡到三角
Zero-Point Energies prevent a Trigonal to Simple Cubic Transition in High-Pressure Sulfur
论文作者
论文摘要
最近发表的密度功能理论来自Whaley-Baldwin等。 al。 [New J. Phys。 22 023020，2020年2月]使用PBE功能，表明元素硫不采用Simple-Cibic（SC）$ PM \ bar \ bar \ bar {3} m $相位，在高压下，与以前在该系统上的作品不同意[Phys [phys]。莱特牧师。 83，3049，1999年10月]。 We carry out an extensive set of calculations using a variety of different XC-functionals, pseudopotentials and the all-electron code ELK, and we are now able to show that even though under LDA and PW91 a high-pressure simple-cubic phase does indeed become favourable at the static lattice level, when zero-point energies (ZPEs) are included, the transition to the simple-cubic phase is suppressed in every case, owing到SC阶段的较大ZPE。我们用明确包括深核和半核心状态的伪电量来重现这些发现，并表明即使在这些高压力下，也只有$ n = 3 $ valence shell有助于硫磺中的粘合。我们进一步表明，在有限温度下，$ pm \ bar {3} m $相位变得更加不利。我们最终研究了对零点能量的非谐校正是否可以使$ pm \ bar \ bar {3} m $相位有利，并发现这些校正比ZPE小几个数量级，因此可忽略不可忽视。因此，这些结果证实了Whaley-Baldwin等人的原始发现。 Al。;硫的高压过渡顺序为$ r \ bar {3} m \ rightarrow $ bcc，没有中间的SC阶段。
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.
