观点：HSE屏蔽杂化泛函与带隙问题：起源、影响与竞争者

中文摘要 AI 辅助

屏蔽杂化泛函HSE背后的想法形成于21世纪初，距今约四分之一个世纪。HSE并非明确为预测带隙而设计，尽管当时我们确实认识到杂化泛函有助于解决带隙问题。它的设计目的是在扩展体系中使精确交换变得可负担且在物理上站得住脚。在短程保留精确交换并在长程将其屏蔽掉，这颠倒了为分子制定的方案。当HSE对普通半导体和选定金属氧化物的带隙计算结果比传统半局域近似明显更接近实验值时，我们感到惊喜，并对自己所走的道路受到鼓舞。从HSE03到HSE06的修订改善了分子热化学，同时保持了对半导体带隙的良好精度。四分之一交换比例原封不动地继承了用于分子的成功未屏蔽PBE杂化泛函，而非针对固体拟合。HSE确立了一种实用的屏蔽杂化方法用于精确带隙计算，扩展了缺陷物理、光伏、电力电子和量子信息等领域的第一性原理工作。本观点第一部分回顾了HSE诞生时所做的决策及其对后续发展的影响。第二部分基于固体集合的基准评估了半局域和杂化泛函的最新进展。最近的meta-GGA对选定的半导体达到了HSE06级别的精度，而介电常数依赖型和调谐型杂化泛函解决了固定屏蔽的局限性。这些杂化泛函的发展与我们早期关于局域杂化和局域范围分离的工作共享一个目标，即让精确交换适应电子环境。这些比较在评估带隙的同时，也考察了结构、能量学、计算成本和可迁移性。

英文摘要

The ideas behind the screened hybrid functional HSE took shape in the early 2000s, about a quarter century ago. HSE was not explicitly designed to predict band gaps, although at the time we did recognize that hybrids could help address the band-gap problem. It was designed to make exact exchange affordable and physically defensible in extended systems. Keeping exact exchange at short range and screening it away at long range inverted the prescription developed for molecules. When HSE band gaps for ordinary semiconductors and selected metal oxides came out substantially closer to experiment than those obtained with conventional semilocal approximations, we were pleasantly surprised and encouraged by the path we had taken. The revision from HSE03 to HSE06 improved molecular thermochemistry while preserving the good accuracy for semiconductor gaps. The one-quarter exchange fraction was inherited unchanged from the successful unscreened PBE hybrid for molecules, rather than fitted to solids. HSE established a practical screened-hybrid approach for accurate band-gap calculations, expanding first-principles work in defect physics, photovoltaics, power electronics, and quantum information, among other areas. The first part of this Perspective recounts the decisions made at HSE's birth and their influence on subsequent developments. The second part assesses recent advances in semilocal and hybrid functionals against benchmarks on sets of solids. Recent meta-GGAs achieve HSE06-level accuracy for selected semiconductors, while dielectric-dependent and tuned hybrids address the limitations of fixed screening. These hybrid developments share with our early work on local hybrids and local range separation the aim of adapting exact exchange to the electronic environment. The comparisons assess band gaps alongside structures, energetics, computational cost, and transferability.

发表机构

• Rice University（莱斯大学）

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