Lattice dynamics and structural phase stability of group IV elemental solids with the r²SCAN functional

The strongly constrained and appropriately normed (SCAN) meta-GGA functional is a milestone achievement of electronic structure theory. Recently, a revised and restored form (r²SCAN) has been suggested as a replacement for SCAN in high-throughput applications. Here, we assess the accuracy and reliability of the r²SCAN meta-GGA functional for the group IV elemental solids carbon (C), silicon (Si), germanium (Ge), and tin (Sn). We show that the r²SCAN functional agrees closely with its parent functional SCAN for elastic constants, bulk moduli, and phonon dispersions, but the numerical stability of r²SCAN is superior. Both meta-GGA functionals outperform standard GGA (Perdew-Burke-Ernzerhof) in terms of accuracy and approach the level of common hybrid functionals (Heyd-Scuseria-Ernzerhof). However, we find that r²SCAN performs much worse than SCAN for the α ↔ β phase transition of both Ge and Sn, yielding larger phase energy differences and transition pressures.Here we make available the raw phonon dispersion data and VASP input files for an example phonon calculation.

强约束恰当归一化（strongly constrained and appropriately normed, SCAN）meta广义梯度近似（meta-GGA）泛函是电子结构理论领域的里程碑式成果。近期，一种修正重构版本（r²SCAN）被提出，可在高通量计算场景中替代SCAN泛函。本文针对第四族单质固体：碳（C）、硅（Si）、锗（Ge）以及锡（Sn），评估了r²SCAN meta-GGA泛函的准确性与可靠性。研究表明，在弹性常数、体积模量与声子色散的计算上，r²SCAN泛函与其母泛函SCAN结果吻合度极高，但r²SCAN的数值稳定性更优。两种meta-GGA泛函在计算精度上均优于标准广义梯度近似（Perdew-Burke-Ernzerhof）泛函，且精度接近主流杂化泛函（Heyd-Scuseria-Ernzerhof）。但本文发现，针对锗与锡的α↔β相变，r²SCAN的计算表现远差于SCAN，其给出的相能量差与转变压力均偏大。本文公开了本次声子计算示例的原始声子色散数据与VASP输入文件。