Evangelista Francesco A
Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States.
J Chem Theory Comput. 2025 Aug 12;21(15):7471-7484. doi: 10.1021/acs.jctc.5c00766. Epub 2025 Jul 29.
Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, , based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. To assess the ability of mutual correlation to identify orbital interactions, we performed benchmark studies on model systems, including H, N, and -benzyne, and performed a formal and numerical comparison with orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states.
量化量子多体状态中的相关性和复杂性是推动理论和计算化学、物理学以及量子信息科学发展的核心。这项工作引入了一个基于两体约化密度矩阵累积量的弗罗贝尼乌斯范数平方的新颖框架。通过对累积量范数进行系统划分，互相关量化了相互作用子系统之间的非加性相关性。为了评估互相关识别轨道相互作用的能力，我们对包括H、N和 - 苯炔在内的模型系统进行了基准研究，并与轨道互信息进行了形式上和数值上的比较。通过最大化互相关的非线性代价函数获得的最大相关轨道，也被用于识别相关性的与基无关的划分。这项研究表明，互相关是一种广泛适用的度量，在活性空间选择和电子态解释中很有用。
