AI 中文总结
研究针对元广义梯度近似泛函中等轨道指标在低密度尾部发散问题，通过采用物理动机的泡利KED取代分母消除发散，测试两个增强因子，在不同交换泛函中改进效果显著，推动了相关泛函进一步发展。
AI 中文摘要
等轨道指标α=（τ-τ^vW）/τ^UEG是元广义梯度近似（meta-GGA）泛函的关键成分，但在低密度尾部发散，导致非物理交换势和系统带隙误差。我们用源于无轨道密度泛函理论文献的具有物理动机的泡利KED取代α的分母，消除了低密度原子尾部的发散。在r^2SCAN和MS2交换泛函中测试了两个增强因子LKT和PGS，发现修改后的指标抑制了半局域交换势中的虚假振荡并恢复了原子尾部正确的电子定位。对于十个成员的立方半导体基准，r^2SCAN@PGS的带隙平均绝对误差降低了41.1%，MS2@PGS降低了48.8%，同时凝聚能精度基本保持。两种不同结构的泛函都有一致改进，证实了其物理而非泛函特定的起源，并推动了具有满足约束的等轨道指标的元GGA泛函的进一步发展。
英文摘要
The iso-orbital indicator $α= (τ- τ^\mathrm{vW})/τ^\mathrm{UEG}$ is a key ingredient of meta-generalized gradient approximation (meta-GGA) functionals, but diverges in low-density tails , causing unphysical exchange potentials and systematic band gap errors as noted in [J. Chem. Phys. 150, 161101 (2019)]. We replace the denominator of $α$ with a physically motivated Pauli KED drawn from the orbital-free DFT literature, eliminating the divergence in the low density atomic tail without any empirical regularization parameter. Testing two such enhancement factors: LKT and PGS, within the r$^2$SCAN and MS2 exchange functionals, we find that the modified indicators suppress spurious oscillations in the semilocal exchange potential and restore correct electron localization in atomic tails. For a ten-member cubic semiconductor benchmark, the band gap mean absolute error is reduced by 41.1 % for r$^2$SCAN@PGS and 48.8 % for MS2@PGS, while cohesive energy accuracy is largely preserved. The consistent improvement across two functionals with distinct constructions confirms a physical rather than functional specific origin, and motivates further development of meta-GGA functionals with constraint satisfying iso-orbital indicators.
Comments11 pages, 9 Figures
