Earth Mover’s Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities,Journal of Chemical Theory and Computation

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Earth Mover’s Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2023-11-03 , DOI: 10.1021/acs.jctc.3c00894
Zhe Wang ₁ , Jiashu Liang ₁ , Martin Head-Gordon _{1,

2}

Affiliation

This paper presents a novel theoretical measure, μ^EMD, based on the earth mover’s distance (EMD), for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground- and excited-state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron–hole separation in a wide range of excited states (valence, Rydberg, charge transfer, etc.). The results showcase the EMD metric’s effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that μ^EMD can function as a promising diagnostic tool for predicting the failure of pure exchange–correlation functionals. Specifically, we show statistical relationships among the functional-driven errors, the exact exchange content within the functional, and the magnitude of μ^EMD values.

中文翻译：

使用离散实空间密度将推土机距离作为衡量激励中电荷转移程度的指标

本文提出了一种基于推土机距离 (EMD) 的新颖理论测量 μ ^{EMD ，用于量化分子中电子激发引起的密度变化。}作为输入，EMD 度量仅使用真实空间中的离散基态和激发态电子密度，使其与几乎所有用于计算激发态的电子结构方法兼容。EMD 度量与其他流行的理论度量进行比较，用于描述各种激发态（价态、里德伯态、电荷转移等）下电子-空穴分离的程度。结果展示了 EMD 指标在所有激励类型中的有效性，并表明它可作为表征电子激励的附加工具。该研究还表明，μ ^EMD可以作为一种很有前景的诊断工具，用于预测纯交换相关泛函的失效。具体来说，我们展示了函数驱动误差、函数内的确切交换内容以及 μ ^EMD值的大小之间的统计关系。

更新日期：2023-11-03

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