Topology and geometry of molecular conformational spaces and energy landscapes

Solis, Ingrid Membrillo; Pirashvili, Mariam; Steinberg, Lee; Brodzki, Jacek; Frey, Jérémy

doi:10.48550/arxiv.1907.07770

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…In practice, it allows users to discriminate important features from non-significant configurations and provides the necessary basis for multi-scale data analysis. Recent years have witnessed some successful applications of TDA to chemistry, where it helped to understand hydrogen-bonding networks in ion aggregates, 86,88 aqueous solubility of molecules, 56,85 stability of fullerenes, 87 molecular transition pathways, 14 conformational spaces of molecules 44 or the bonding patterns in molecular systems. 15,33,36,82 In this letter we focus on the use of TDA to investigate non-covalent interactions (NCIs) for systems containing heavy elements.…”

mentioning

confidence: 99%

A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

Olejniczak

Gomes

Tierny

2019

Int J of Quantum Chemistry

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Topological Data Analysis (TDA) is a powerful mathematical theory, largely unexplored in theoretical chemistry. In this work we demonstrate how TDA provides new insights into topological features of electron densities and reduced density gradients, by investigating the effects of relativity on the bonding of the Au4‐S‐C6H4‐S′‐Au′4 molecule. Whereas recent analyses of this species carried out with the Quantum Theory of Atoms‐In‐Molecules (a previous study) concluded, from the emergence of new topological features in the electron density, that relativistic effects yielded noncovalent interactions between gold and hydrogen atoms, we show from their low persistence values (which decrease with increased basis set size) these features are not significant. Further analysis of the reduced density gradient confirms no relativity‐induced noncovalent interactions in Au4‐S‐C6H4‐S′‐Au′4. We argue TDA should be integrated into electronic structure analysis methods, and be considered as a basis for the development of new topology‐based approaches.

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mentioning

confidence: 99%

A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

Olejniczak

Gomes

Tierny

2019

Int J of Quantum Chemistry

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“…Persistent homology already has several interesting chemistry applications. In the analysis of point cloud data (e.g., Cartesian coordinates of atoms) it has helped characterize different conformations of molecules, 19,20 solution phase organization [21][22][23] , and to identify chemical reactivity 24 using filtration values based upon Euclidean distance. In the case of manifolds, sublevelset persistent homology has been applied to the probability surfaces of activated processes 25 and in the characterization of energy landscapes.…”

Section: Sublevelset Persistent Homologymentioning

confidence: 99%

Additive energy functions have predictable landscape topologies

Story

Sadhu

Adams

et al. 2023

The Journal of Chemical Physics

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Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features—such as the number of sublevelset persistence bars—could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

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Additive energy functions have predictable landscape topologies

Story

Sadhu

Adams

et al. 2022

Preprint

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Recent work (J. Chem. Phys. 154, 114114) has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in $3N$-dimensions. This includes information about all transition paths between local minima (connected by critical points of index > 1), and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations like disconnectivity graphs using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features --- such as the number of sublevelset persistence bars --- could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

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Topology and geometry of molecular conformational spaces and energy landscapes

Cited by 3 publications

References 25 publications

A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

Additive energy functions have predictable landscape topologies

Additive energy functions have predictable landscape topologies

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