Weflen Kaila E, Bentley Megan R, Thorpe James H, Franke Peter R, Martin Jan M L, Matthews Devin A, Stanton John F
Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States.
Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States.
J Phys Chem Lett. 2025 May 22;16(20):5121-5127. doi: 10.1021/acs.jpclett.5c00885. Epub 2025 May 14.
The fundamental non-Hermitian nature of the forms of the coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present paper shows how this can be used to an advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of the full coupled-cluster theory [which is equivalent to full configuration interaction (FCI)], the electronic wave function and correlation energy are exact within a given one-particle basis set, and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of "how difficult the problem is" (like the well-known diagnostic), but its variation with the level of theory also gives information about "how well this particular method works", irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be). Future application of this idea to excited states, open-shell systems, and symmetry-breaking problems and an extension of the method to the two-particle density are then proposed.
量子化学中广泛使用的耦合簇（CC）理论形式的基本非厄米性质通常被视为不利因素，但本文展示了如何将其转化为优势。具体而言，还原的单粒子密度矩阵（在分子轨道基组中）的非对称性质被倡导作为计算质量的诊断指标。在完全耦合簇理论（等同于完全组态相互作用（FCI））的极限情况下，电子波函数和相关能在给定的单粒子基组内是精确的，并且精确密度矩阵的对称特征得以恢复。密度矩阵不对称的程度被证明可提供一种衡量“问题有多难”的方法（类似于著名的诊断方法），但其随理论水平的变化也给出了关于“这种特定方法效果如何”的信息，而与手头问题的难度无关。所提出的诊断方法被描述并应用于一组选定的小分子，通过将其应用于铍二聚体（Be）展示了其对量子化学从业者的整体实用性示例。然后提出了该想法在激发态、开壳层系统和对称性破缺问题上的未来应用，以及将该方法扩展到双粒子密度的内容。
