{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/earth-mover-s-distance-as-a-metric-to","title":"Earth Mover's Distance as a metric to evaluate the extent of charge transfer in excitations using discretized real-space densities","arxiv_id":"2308.07544","date":"2023-08-15","proceeding":null,"authors":["Zhe Wang","Jiashu Liang","Martin Head-Gordon"],"abstract":"This paper presents a novel theoretical measure, $\\mu^{\\text{EMD}}$, based on the Earth Mover's Distance, 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 $\\mu^{\\text{EMD}}$ can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships between the functional-driven errors, the exact exchange content within the functional, and the magnitude of $\\mu^{\\text{EMD}}$ values.","url_abs":"https://arxiv.org/abs/2308.07544v2","url_pdf":"https://arxiv.org/pdf/2308.07544v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"earth-mover-s-distance-as-a-metric-to","repo_url":"https://github.com/zhewang233/chargeemd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}