DFT+U+V等同于具有密度依赖混合投影算符的DFT+U
DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors
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中文总结 AI 辅助
研究哈伯德修正密度泛函理论中，位间$+V$修正与在位DFT+$U$的关系。通过密度依赖的哈伯德投影算符重新定义，证明二者等价，为$V$影响共价性提供见解，还提出了关于$V$计算及哈伯德子空间的问题。
中文摘要 AI 辅助
哈伯德修正密度泛函理论（DFT+$U$）是用于具有局域化$d$或$f$电子材料的第一性原理建模的常用工具，但其在位修正往往使电荷过度局域化并破坏共价键。引入了位间$+V$修正来解决此问题，目前已被广泛使用，但缺乏形式上的论证。本文表明，在位间修正与在位DFT+$U$在密度依赖的哈伯德投影算符重新定义下精确等价，该投影算符与相邻位点的投影算符混合，这为$V$影响共价性的明确机制提供了见解。如果投影算符保持冻结，这是常见做法，等价性会部分失效。这些结果不仅重新解释了形式主义，还尖锐地提出了如何计算$V$以及哈伯德子空间本质上是什么的问题。
英文摘要
Hubbard-corrected density-functional theory (DFT+$U$) is a popular tool for first-principles modeling of materials with localized $d$ or $f$ electrons, but its on-site corrections tend to over-localize charge and break covalent bonds. Inter-site $+V$ corrections were introduced to counter this and are now widely used, but a formal justification has been lacking. Here we show that -- to first order in $V/U$ -- inter-site corrections are exactly equivalent to on-site DFT+$U$ evaluated on a density-matrix-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites, providing insight into the explicit mechanism by which $V$ affects covalency. If the projectors are held frozen, as is common practice, the equivalence partially breaks down. Beyond reinterpreting the formalism, these results sharpen the questions of how $V$ should be computed and what the Hubbard subspaces fundamentally are.
发表机构
- Paul Scherrer Institute（保罗谢尔研究所）
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), Paul Scherrer Institute（保罗谢尔研究所新型材料计算设计与发现国家中心（MARVEL））
- École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
- University of Cambridge（剑桥大学）
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