Ganoe Brad, Shee James
Department of Chemistry, Rice University, Houston, TX, 77005, USA.
Faraday Discuss. 2024 Nov 6;254(0):53-75. doi: 10.1039/d4fd00066h.
Strong correlation has been said to have many faces, and appears to have many synonyms of questionable suitability. In this work we aim not to define the term once and for all, but to highlight one possibility that is both rigorously defined and physically transparent, and remains so in reference to molecules and quantum lattice models. We survey both molecular examples - hydrogen systems (H, = 2, 4, 6), Be, H-He-H, and benzene - and the half-filled Hubbard model over a range of correlation regimes. Various quantities are examined including the extent of spin symmetry breaking in correlated single-reference wave functions, energetic ratios inspired by the Hubbard model and the Virial theorem, and metrics derived from the one- and two-electron reduced density matrices (RDMs). The trace and the square norm of the cumulant of the two-electron reduced density matrix capture what may well be defined as strong correlation. Accordingly, strong correlation is understood as a statistical dependence between two electrons, and is distinct from the concepts of "correlation energy" and more general than entanglement quantities that require a partitioning of a quantum system into distinguishable subspaces. This work enables us to build a bridge between a rigorous and quantifiable regime of strong electron correlation and more familiar chemical concepts such as anti-aromaticity in the context of Baird's rule.
人们常说强关联具有多种表现形式，而且似乎有许多适用性存疑的同义词。在这项工作中，我们的目的不是一劳永逸地定义这个术语，而是强调一种既经过严格定义又具有物理透明度的可能性，并且在涉及分子和量子晶格模型时依然如此。我们考察了分子实例——氢体系（H₂、H₄、H₆）、BeH₂、H-He-H以及苯——以及在一系列关联区域内的半填充哈伯德模型。研究了各种量，包括相关单参考波函数中自旋对称性破缺的程度、受哈伯德模型和维里定理启发的能量比，以及从单电子和双电子约化密度矩阵（RDM）导出的度量。双电子约化密度矩阵累积量的迹和平方范数捕捉到了很可能被定义为强关联的东西。因此，强关联被理解为两个电子之间的统计依赖性，它不同于“关联能”的概念，并且比需要将量子系统划分为可区分子空间的纠缠量更具普遍性。这项工作使我们能够在严格且可量化的强电子关联机制与更熟悉的化学概念（如在贝尔德规则背景下的反芳香性）之间架起一座桥梁。
