Using topology for understanding your computational results
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Ángel Martín Pendás
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Julia Contreras-García
Abstract
The integration of quantum theory (QT) into chemistry has significantly enhanced computational accuracy, yet challenges remain in translating quantum mechanical results into intuitive chemical concepts. Traditional atomic and molecular models, while empirically effective, lack direct representation in Hilbert space, leading to ambiguities in chemical interpretation. Here, we present a summary of topological methods as a bridge between QT and chemical reasoning, focusing on the quantum theory of atoms in molecules (QTAIM) and the electron localization function (ELF). These approaches provide rigorous frameworks for defining atomic and bonding regions, enabling additive decompositions of quantum mechanical observables. By analyzing critical points of the electron density and other scalar fields, we demonstrate how the QTAIM and the ELF offer complementary insights into molecular bonding. As a case study, we examine the electronic structure of carbon suboxide (C3O2), revealing that a combined QTAIM-ELF approach resolves discrepancies between two bonding descriptions.
Funding source: Emergence-SU
Award Identifier / Grant number: H2Ox S23JR31014
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: Fisciency S23JRAR060
Award Identifier / Grant number: TcPredictor S22JRAR036
Funding source: MICIU
Award Identifier / Grant number: PID2021-122763NB-I00
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None used.
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Conflict of interest: The author states no conflict of interest.
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Research funding: JCG thanks ANR TcPredictor S22JRAR036, ANR Fisciency S23JRAR060 and Emergence-SU H2Ox S23JR31014 for funding. AMP thanks grant PID2021-122763NB-I00 funded by the Spanish MICIU (https://dx.doi.org/10.13039/501100011033) and by “ERDF A way of making Europe”, for financial support.
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Data availability: All data are contained in the manuscript.
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Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/pac-2025-0466).
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