1
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Cignoni E, Suman D, Nigam J, Cupellini L, Mennucci B, Ceriotti M. Electronic Excited States from Physically Constrained Machine Learning. ACS Cent Sci 2024; 10:637-648. [PMID: 38559300 PMCID: PMC10979507 DOI: 10.1021/acscentsci.3c01480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2023] [Revised: 01/16/2024] [Accepted: 01/30/2024] [Indexed: 04/04/2024]
Abstract
Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or combined explicitly with physically grounded operations. We present an example of an integrated modeling approach in which a symmetry-adapted ML model of an effective Hamiltonian is trained to reproduce electronic excitations from a quantum-mechanical calculation. The resulting model can make predictions for molecules that are much larger and more complex than those on which it is trained and allows for dramatic computational savings by indirectly targeting the outputs of well-converged calculations while using a parametrization corresponding to a minimal atom-centered basis. These results emphasize the merits of intertwining data-driven techniques with physical approximations, improving the transferability and interpretability of ML models without affecting their accuracy and computational efficiency and providing a blueprint for developing ML-augmented electronic-structure methods.
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Affiliation(s)
- Edoardo Cignoni
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, 56126 Pisa, Italy
| | - Divya Suman
- Laboratory
of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale
de Lausanne, 1015 Lausanne, Switzerland
| | - Jigyasa Nigam
- Laboratory
of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale
de Lausanne, 1015 Lausanne, Switzerland
| | - Lorenzo Cupellini
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, 56126 Pisa, Italy
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, 56126 Pisa, Italy
| | - Michele Ceriotti
- Laboratory
of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale
de Lausanne, 1015 Lausanne, Switzerland
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
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2
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Gigli L, Tisi D, Grasselli F, Ceriotti M. Mechanism of Charge Transport in Lithium Thiophosphate. Chem Mater 2024; 36:1482-1496. [PMID: 38370276 PMCID: PMC10870718 DOI: 10.1021/acs.chemmater.3c02726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Revised: 01/10/2024] [Accepted: 01/10/2024] [Indexed: 02/20/2024]
Abstract
Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.
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Affiliation(s)
| | | | - Federico Grasselli
- Laboratory of Computational
Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational
Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
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3
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Back S, Aspuru-Guzik A, Ceriotti M, Gryn'ova G, Grzybowski B, Gu GH, Hein J, Hippalgaonkar K, Hormázabal R, Jung Y, Kim S, Kim WY, Moosavi SM, Noh J, Park C, Schrier J, Schwaller P, Tsuda K, Vegge T, von Lilienfeld OA, Walsh A. Accelerated chemical science with AI. Digit Discov 2024; 3:23-33. [PMID: 38239898 PMCID: PMC10793638 DOI: 10.1039/d3dd00213f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 12/06/2023] [Indexed: 01/22/2024]
Abstract
In light of the pressing need for practical materials and molecular solutions to renewable energy and health problems, to name just two examples, one wonders how to accelerate research and development in the chemical sciences, so as to address the time it takes to bring materials from initial discovery to commercialization. Artificial intelligence (AI)-based techniques, in particular, are having a transformative and accelerating impact on many if not most, technological domains. To shed light on these questions, the authors and participants gathered in person for the ASLLA Symposium on the theme of 'Accelerated Chemical Science with AI' at Gangneung, Republic of Korea. We present the findings, ideas, comments, and often contentious opinions expressed during four panel discussions related to the respective general topics: 'Data', 'New applications', 'Machine learning algorithms', and 'Education'. All discussions were recorded, transcribed into text using Open AI's Whisper, and summarized using LG AI Research's EXAONE LLM, followed by revision by all authors. For the broader benefit of current researchers, educators in higher education, and academic bodies such as associations, publishers, librarians, and companies, we provide chemistry-specific recommendations and summarize the resulting conclusions.
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Affiliation(s)
- Seoin Back
- Department of Chemical and Biomolecular Engineering, Institute of Emergent Materials, Sogang University Seoul Republic of Korea
| | - Alán Aspuru-Guzik
- Departments of Chemistry, Computer Science, University of Toronto St. George Campus Toronto ON Canada
- Acceleration Consortium and Vector Institute for Artificial Intelligence Toronto ON M5S 1M1 Canada
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling (COSMO), École Polytechnique Fédérale de Lausanne Lausanne Switzerland
| | - Ganna Gryn'ova
- Heidelberg Institute for Theoretical Studies (HITS gGmbH) 69118 Heidelberg Germany
- Interdisciplinary Center for Scientific Computing, Heidelberg University 69120 Heidelberg Germany
| | - Bartosz Grzybowski
- Center for Algorithmic and Robotized Synthesis (CARS), Institute for Basic Science (IBS) Ulsan Republic of Korea
- Institute of Organic Chemistry, Polish Academy of Sciences Warsaw Poland
- Department of Chemistry, Ulsan National Institute of Science and Technology Ulsan Republic of Korea
| | - Geun Ho Gu
- Department of Energy Engineering, Korea Institute of Energy Technology (KENTECH) Naju 58330 Republic of Korea
| | - Jason Hein
- Department of Chemistry, University of British Columbia Vancouver BC V6T 1Z1 Canada
| | - Kedar Hippalgaonkar
- School of Materials Science and Engineering, Nanyang Technological University 50 Nanyang Avenue Singapore 639798 Singapore
- Institute of Materials Research and Engineering, Agency for Science Technology and Research 2 Fusionopolis Way, 08-03 Singapore 138634 Singapore
| | | | - Yousung Jung
- Department of Chemical and Biomolecular Engineering, KAIST Daejeon Republic of Korea
- School of Chemical and Biological Engineering, Interdisciplinary Program in Artificial Intelligence, Seoul National University 1 Gwanak-ro, Gwanak-gu Seoul 08826 Republic of Korea
| | - Seonah Kim
- Department of Chemistry, Colorado State University 1301 Center Avenue Fort Collins CO 80523 USA
| | - Woo Youn Kim
- Department of Chemistry, KAIST Daejeon Republic of Korea
| | - Seyed Mohamad Moosavi
- Chemical Engineering & Applied Chemistry, University of Toronto Toronto Ontario M5S 3E5 Canada
| | - Juhwan Noh
- Chemical Data-Driven Research Center, Korea Research Institute of Chemical Technology Daejeon 34114 Republic of Korea
| | | | - Joshua Schrier
- Department of Chemistry, Fordham University The Bronx NY 10458 USA
| | - Philippe Schwaller
- Laboratory of Artificial Chemical Intelligence (LIAC) & National Centre of Competence in Research (NCCR) Catalysis, École Polytechnique Fédérale de Lausanne Lausanne Switzerland
| | - Koji Tsuda
- Graduate School of Frontier Sciences, The University of Tokyo Kashiwa Chiba 277-8561 Japan
- Center for Basic Research on Materials, National Institute for Materials Science Tsukuba Ibaraki 305-0044 Japan
- RIKEN Center for Advanced Intelligence Project Tokyo 103-0027 Japan
| | - Tejs Vegge
- Department of Energy Conversion and Storage, Technical University of Denmark 301 Anker Engelunds vej, Kongens Lyngby Copenhagen 2800 Denmark
| | - O Anatole von Lilienfeld
- Acceleration Consortium and Vector Institute for Artificial Intelligence Toronto ON M5S 1M1 Canada
- Departments of Chemistry, Materials Science and Engineering, and Physics, University of Toronto, St George Campus Toronto ON Canada
- Machine Learning Group, Technische Universität Berlin and Berlin Institute for the Foundations of Learning and Data 10587 Berlin Germany
| | - Aron Walsh
- Department of Materials, Imperial College London London SW7 2AZ UK
- Department of Physics, Ewha Women's University Seoul Republic of Korea
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4
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Chong S, Grasselli F, Ben Mahmoud C, Morrow JD, Deringer VL, Ceriotti M. Robustness of Local Predictions in Atomistic Machine Learning Models. J Chem Theory Comput 2023; 19:8020-8031. [PMID: 37948446 PMCID: PMC10688186 DOI: 10.1021/acs.jctc.3c00704] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 10/12/2023] [Accepted: 10/12/2023] [Indexed: 11/12/2023]
Abstract
Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.
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Affiliation(s)
- Sanggyu Chong
- Laboratory
of Computational Science and Modeling, Institute
of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Federico Grasselli
- Laboratory
of Computational Science and Modeling, Institute
of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Chiheb Ben Mahmoud
- Laboratory
of Computational Science and Modeling, Institute
of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Joe D. Morrow
- Department
of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, Oxford OX1 3QR, U.K.
| | - Volker L. Deringer
- Department
of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, Oxford OX1 3QR, U.K.
| | - Michele Ceriotti
- Laboratory
of Computational Science and Modeling, Institute
of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
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5
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Huguenin-Dumittan K, Loche P, Haoran N, Ceriotti M. Physics-Inspired Equivariant Descriptors of Nonbonded Interactions. J Phys Chem Lett 2023; 14:9612-9618. [PMID: 37862712 PMCID: PMC10626632 DOI: 10.1021/acs.jpclett.3c02375] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 10/13/2023] [Indexed: 10/22/2023]
Abstract
One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects such as electrostatic or dispersion interactions. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body nonbonded interactions in the data-driven modeling of matter.
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Affiliation(s)
- Kevin
K. Huguenin-Dumittan
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Philip Loche
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Ni Haoran
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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6
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Goscinski A, Principe VP, Fraux G, Kliavinek S, Helfrecht BA, Loche P, Ceriotti M, Cersonsky RK. scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science. Open Res Eur 2023; 3:81. [PMID: 38234865 PMCID: PMC10792272 DOI: 10.12688/openreseurope.15789.2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 09/01/2023] [Indexed: 01/19/2024]
Abstract
Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.
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Affiliation(s)
- Alexander Goscinski
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Victor Paul Principe
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Sergei Kliavinek
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Benjamin Aaron Helfrecht
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
- Pacific Northwest National Laboratory, Richland, WA, 99352, USA
| | - Philip Loche
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
| | - Rose Kathleen Cersonsky
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Federale de Lausanne, Lausanne, Vaud, 1015, Switzerland
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin, 53706, USA
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7
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Bigi F, Fraux G, Browning NJ, Ceriotti M. Fast evaluation of spherical harmonics with sphericart. J Chem Phys 2023; 159:064802. [PMID: 37551818 DOI: 10.1063/5.0156307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/12/2023] [Indexed: 08/09/2023] Open
Abstract
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from geology and atmospheric sciences to signal processing and computer graphics. More recently, they have become a key component of rotationally equivariant models in geometric machine learning, including applications to atomic-scale modeling of molecules and materials. We present an elegant and efficient algorithm for the evaluation of the real-valued spherical harmonics. Our construction features many of the desirable properties of existing schemes and allows us to compute Cartesian derivatives in a numerically stable and computationally efficient manner. To facilitate usage, we implement this algorithm in sphericart, a fast C++ library that also provides C bindings, a Python API, and a PyTorch implementation that includes a GPU kernel.
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Affiliation(s)
- Filippo Bigi
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Guillaume Fraux
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | | | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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8
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Ceriotti M, Jensen L, Manolopoulos DE, Martinez T, Reichman DR, Sciortino F, Sherrill CD, Shi Q, Vega C, Wang LS, Weiss EA, Zhu X, Stein J, Lian T. 2021 JCP Emerging Investigator Special Collection. J Chem Phys 2023; 158:060401. [PMID: 36792492 DOI: 10.1063/5.0143234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
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9
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Cersonsky RK, Pakhnova M, Engel EA, Ceriotti M. A data-driven interpretation of the stability of organic molecular crystals. Chem Sci 2023; 14:1272-1285. [PMID: 36756329 PMCID: PMC9891366 DOI: 10.1039/d2sc06198h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 12/06/2022] [Indexed: 01/17/2023] Open
Abstract
Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning of their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals, exploiting its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.
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Affiliation(s)
- Rose K. Cersonsky
- Laboratory of Computational Science and Modeling (COSMO), École Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Maria Pakhnova
- Laboratory of Computational Science and Modeling (COSMO), École Polytechnique Fédérale de Lausanne Lausanne Switzerland
| | - Edgar A. Engel
- TCM Group, Trinity College, Cambridge UniversityCambridgeUK
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling (COSMO), École Polytechnique Fédérale de Lausanne Lausanne Switzerland
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10
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Bigi F, Huguenin-Dumittan KK, Ceriotti M, Manolopoulos DE. A smooth basis for atomistic machine learning. J Chem Phys 2022; 157:234101. [PMID: 36550032 DOI: 10.1063/5.0124363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to expand the angular dependence of this density, but there is, as of yet, no clear rationale to choose one radial basis over another. Here, we investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates a basis of controllable smoothness within the sphere (in the same sense as plane waves provide a basis with controllable smoothness for a problem with periodic boundaries) and that a tensor product of Laplacian eigenstates also provides a smooth basis for expanding any higher-order correlation of the atomic density within the appropriate hypersphere. We consider several unsupervised metrics of the quality of a basis for a given dataset and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets and competitive with data-driven bases that numerically optimize each metric. Finally, we investigate the role of the basis in building models of the potential energy. In these tests, we find that a combination of the Laplacian eigenstate basis and target-oriented heuristics leads to equal or improved regression performance when compared to both heuristic and data-driven bases in the literature. We conclude that the smoothness of the basis functions is a key aspect of successful atomic density representations.
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Affiliation(s)
- Filippo Bigi
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Kevin K Huguenin-Dumittan
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
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11
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Helfrecht BA, Pireddu G, Semino R, Auerbach SM, Ceriotti M. Ranking the synthesizability of hypothetical zeolites with the sorting hat. Digit Discov 2022; 1:779-789. [PMID: 36561986 PMCID: PMC9721151 DOI: 10.1039/d2dd00056c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 10/10/2022] [Indexed: 12/12/2022]
Abstract
Zeolites are nanoporous alumino-silicate frameworks widely used as catalysts and adsorbents. Even though millions of siliceous networks can be generated by computer-aided searches, no new hypothetical framework has yet been synthesized. The needle-in-a-haystack problem of finding promising candidates among large databases of predicted structures has intrigued materials scientists for decades; yet, most work to date on the zeolite problem has been limited to intuitive structural descriptors. Here, we tackle this problem through a rigorous data science scheme-the "Zeolite Sorting Hat"-that exploits interatomic correlations to discriminate between real and hypothetical zeolites and to partition real zeolites into compositional classes that guide synthetic strategies for a given hypothetical framework. We find that, regardless of the structural descriptor used by the Zeolite Sorting Hat, there remain hypothetical frameworks that are incorrectly classified as real ones, suggesting that they might be good candidates for synthesis. We seek to minimize the number of such misclassified frameworks by using as complete a structural descriptor as possible, thus focusing on truly viable synthetic targets, while discovering structural features that distinguish real and hypothetical frameworks as an output of the Zeolite Sorting Hat. Further ranking of the candidates can be achieved based on thermodynamic stability and/or their suitability for the desired applications. Based on this workflow, we propose three hypothetical frameworks differing in their molar volume range as the top targets for synthesis, each with a composition suggested by the Zeolite Sorting Hat. Finally, we analyze the behavior of the Zeolite Sorting Hat with a hierarchy of structural descriptors including intuitive descriptors reported in previous studies, finding that intuitive descriptors produce significantly more misclassified hypothetical frameworks, and that more rigorous interatomic correlations point to second-neighbor Si-O distances around 3.2-3.4 Å as the key discriminatory factor.
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Affiliation(s)
- Benjamin A. Helfrecht
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne1015 LausanneSwitzerland
| | - Giovanni Pireddu
- PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS24 rue Lhomond75005 ParisFrance,Sorbonne Université, CNRS, Physico-chimie des Electrolytes et Nanosystèmes InterfaciauxPHENIXF-75005 ParisFrance
| | - Rocio Semino
- Sorbonne Université, CNRS, Physico-chimie des Electrolytes et Nanosystèmes InterfaciauxPHENIXF-75005 ParisFrance,ICGM, Univ. Montpellier, CNRS, ENSCMMontpellierFrance
| | - Scott M. Auerbach
- Department of Chemistry and Department of Chemical Engineering, University of Massachusetts AmherstAmherstMA 01003USA
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne1015 LausanneSwitzerland
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12
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Grisafi A, Lewis AM, Rossi M, Ceriotti M. Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density. J Chem Theory Comput 2022. [PMID: 36453538 DOI: 10.1021/acs.jctc.2c00850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multicentered atomic basis analogous to that routinely used in density fitting approximations. However, the nonorthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex data sets, obtaining very accurate predictions using a comparatively small training set. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark data set, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.
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Affiliation(s)
- Andrea Grisafi
- PASTEUR, Département de chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - Alan M. Lewis
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Mariana Rossi
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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13
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Pozdnyakov S, Ceriotti M. Incompleteness of graph neural networks for points clouds in three dimensions. Mach Learn : Sci Technol 2022. [DOI: 10.1088/2632-2153/aca1f8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there exist graphs that are distinct but appear identical when seen through the lens of the GNN. More complicated schemes have thus been designed to increase their resolving power. Applications to molecules (and more generally, point clouds), however, add a geometric dimension to the problem. The most straightforward and prevalent approach to construct graph representation for molecules regards atoms as vertices in a graph and draws a bond between each pair of atoms within a chosen cutoff. Bonds can be decorated with the distance between atoms, and the resulting ``distance graph NNs'' (dGNN) have empirically demonstrated excellent resolving power and are widely used in chemical ML, {with all known indistinguishable configurations being resolved in the fully-connected limit, which is equivalent to infinite or sufficiently large cutoff.} Here we {present a counterexample that proves that dGNNs are not complete even for the restricted case of fully-connected graphs induced by 3D atom clouds.} We construct pairs of distinct point clouds whose associated graphs are, for any cutoff radius, equivalent based on a first-order Weisfeiler-Lehman test. This class of degenerate structures includes chemically-plausible configurations, {both for isolated structures and for infinite structures that are periodic in 1, 2, and 3 dimensions.} The existence of indistinguishable configurations sets an ultimate limit to the expressive power of some of the well-established GNN architectures for atomistic machine learning. Models that explicitly use angular or directional information in the description of atomic environments can resolve this class of degeneracies.
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14
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Pozdnyakov S, Willatt MJ, Bartok-Partay A, Ortner C, Csanyi G, Ceriotti M. Comment on "Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four body interactions". J Chem Phys 2022; 157:177101. [DOI: 10.1063/5.0088404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The "quasi-constant' SOAP and ACSF fingerprint manifolds recently discovered by Parsaeifard and Goedecker[J. Chem. Phys. 156, 034302 (2022)] are closely related to the degenerate pairs of configurations, that are a known shortcoming of all low-body-order atom-density correlation representations of molecular structures. Configurations that are rigorously singular -- that we demonstrate can only occur in finite, discrete sets, and not as a continuous manifolds -- determine the complete failure of machine-learning models built on this class of descriptors. The ``quasi-constant' manifolds, on the other hand, exhibit low but non-zero sensitivity to atomic displacements. As a consequence, for any such manifold, it is possible to optimize the model parameters and the training set to mitigate their impact on learning, even though this is often impractical and it is preferable to use descriptors that avoid both the exact singularities and the associated numerical instability.
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Affiliation(s)
| | | | - Albert Bartok-Partay
- Scientific Computing Department, Science and Technology Facilities Council, United Kingdom
| | - Christoph Ortner
- UBC, University of British Columbia Department of Mathematics, Canada
| | - Gabor Csanyi
- Engineering Laboratory, University of Cambridge Department of Engineering, United Kingdom
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15
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Cordova M, Engel EA, Stefaniuk A, Paruzzo F, Hofstetter A, Ceriotti M, Emsley L. A Machine Learning Model of Chemical Shifts for Chemically and Structurally Diverse Molecular Solids. J Phys Chem C Nanomater Interfaces 2022; 126:16710-16720. [PMID: 36237276 PMCID: PMC9549463 DOI: 10.1021/acs.jpcc.2c03854] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 08/24/2022] [Indexed: 06/16/2023]
Abstract
Nuclear magnetic resonance (NMR) chemical shifts are a direct probe of local atomic environments and can be used to determine the structure of solid materials. However, the substantial computational cost required to predict accurate chemical shifts is a key bottleneck for NMR crystallography. We recently introduced ShiftML, a machine-learning model of chemical shifts in molecular solids, trained on minimum-energy geometries of materials composed of C, H, N, O, and S that provides rapid chemical shift predictions with density functional theory (DFT) accuracy. Here, we extend the capabilities of ShiftML to predict chemical shifts for both finite temperature structures and more chemically diverse compounds, while retaining the same speed and accuracy. For a benchmark set of 13 molecular solids, we find a root-mean-squared error of 0.47 ppm with respect to experiment for 1H shift predictions (compared to 0.35 ppm for explicit DFT calculations), while reducing the computational cost by over four orders of magnitude.
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Affiliation(s)
- Manuel Cordova
- Laboratory
of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
- National
Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
| | - Edgar A. Engel
- Theory
of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, U.K.
| | - Artur Stefaniuk
- Laboratory
of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
| | - Federico Paruzzo
- Laboratory
of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
| | - Albert Hofstetter
- Laboratory
of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
| | - Michele Ceriotti
- National
Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
- Laboratory
of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
| | - Lyndon Emsley
- Laboratory
of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
- National
Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
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16
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Nigam J, Pozdnyakov S, Fraux G, Ceriotti M. Unified theory of atom-centered representations and message-passing machine-learning schemes. J Chem Phys 2022; 156:204115. [DOI: 10.1063/5.0087042] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, which are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), which are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes that gather information on the relationship between neighboring atoms using “message-passing” ideas cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provide a coherent foundation to systematize our understanding of both atom-centered and message-passing and invariant and equivariant machine-learning schemes.
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Affiliation(s)
- Jigyasa Nigam
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Sergey Pozdnyakov
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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17
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Fabregat R, Fabrizio A, Engel EA, Meyer B, Juraskova V, Ceriotti M, Corminboeuf C. Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides. J Chem Theory Comput 2022; 18:1467-1479. [PMID: 35179897 PMCID: PMC8908737 DOI: 10.1021/acs.jctc.1c00813] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
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The application of
machine learning to theoretical chemistry has
made it possible to combine the accuracy of quantum chemical energetics
with the thorough sampling of finite-temperature fluctuations. To
reach this goal, a diverse set of methods has been proposed, ranging
from simple linear models to kernel regression and highly nonlinear
neural networks. Here we apply two widely different approaches to
the same, challenging problem: the sampling of the conformational
landscape of polypeptides at finite temperature. We develop a local
kernel regression (LKR) coupled with a supervised sparsity method
and compare it with a more established approach based on Behler-Parrinello
type neural networks. In the context of the LKR, we discuss how the
supervised selection of the reference pool of environments is crucial
to achieve accurate potential energy surfaces at a competitive computational
cost and leverage the locality of the model to infer which chemical
environments are poorly described by the DFTB baseline. We then discuss
the relative merits of the two frameworks and perform Hamiltonian-reservoir
replica-exchange Monte Carlo sampling and metadynamics simulations,
respectively, to demonstrate that both frameworks can achieve converged
and transferable sampling of the conformational landscape of complex
and flexible biomolecules with comparable accuracy and computational
cost.
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Affiliation(s)
| | | | - Edgar A Engel
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | | | | | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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18
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Nigam J, Willatt MJ, Ceriotti M. Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties. J Chem Phys 2022; 156:014115. [PMID: 34998321 DOI: 10.1063/5.0072784] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most cases, the models rely on a description of atom-centered environments and are suitable to learn atomic properties or global observables that can be decomposed into atomic contributions. Many quantities that are relevant for quantum mechanical calculations, however-most notably the single-particle Hamiltonian matrix when written in an atomic orbital basis-are not associated with a single center, but with two (or more) atoms in the structure. We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-center case and show, in particular, how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis. These N-center features are fully equivariant-not only in terms of translations and rotations but also in terms of permutations of the indices associated with the atoms-and are suitable to construct symmetry-adapted machine-learning models of new classes of properties of molecules and materials.
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Affiliation(s)
- Jigyasa Nigam
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michael J Willatt
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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19
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Ceriotti M, Jensen L, Manolopoulos DE, Martinez TJ, Michaelides A, Ogilvie JP, Reichman DR, Shi Q, Straub JE, Vega C, Wang LS, Weiss E, Zhu X, Stein JL, Lian T. 2020 JCP Emerging Investigator Special Collection. J Chem Phys 2021; 155:230401. [PMID: 34937385 DOI: 10.1063/5.0078934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Lasse Jensen
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Todd J Martinez
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Angelos Michaelides
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jennifer P Ogilvie
- Department of Physics and Biophysics, University of Michigan, 450 Church St., Ann Arbor, Michigan 48109, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - John E Straub
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Carlos Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Lai-Sheng Wang
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Emily Weiss
- Departments of Chemistry, Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Xiaoyang Zhu
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | | | - Tianquan Lian
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
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20
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Cheng B, Mazzola G, Pickard CJ, Ceriotti M. Reply to: On the liquid-liquid phase transition of dense hydrogen. Nature 2021; 600:E15-E16. [PMID: 34912081 DOI: 10.1038/s41586-021-04079-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 09/30/2021] [Indexed: 11/09/2022]
Affiliation(s)
- Bingqing Cheng
- Department of Computer Science and Technology, University of Cambridge, Cambridge, UK.
| | | | - Chris J Pickard
- Department of Materials Science & Metallurgy, University of Cambridge, Cambridge, UK
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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21
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Cordova M, Balodis M, Simões de Almeida B, Ceriotti M, Emsley L. Bayesian probabilistic assignment of chemical shifts in organic solids. Sci Adv 2021; 7:eabk2341. [PMID: 34826232 PMCID: PMC8626066 DOI: 10.1126/sciadv.abk2341] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
A prerequisite for NMR studies of organic materials is assigning each experimental chemical shift to a set of geometrically equivalent nuclei. Obtaining the assignment experimentally can be challenging and typically requires time-consuming multidimensional correlation experiments. An alternative solution for determining the assignment involves statistical analysis of experimental chemical shift databases, but no such database exists for molecular solids. Here, by combining the Cambridge Structural Database with a machine learning model of chemical shifts, we construct a statistical basis for probabilistic chemical shift assignment of organic crystals by calculating shifts for more than 200,000 compounds, enabling the probabilistic assignment of organic crystals directly from their two-dimensional chemical structure. The approach is demonstrated with the 13C and 1H assignment of 11 molecular solids with experimental shifts and benchmarked on 100 crystals using predicted shifts. The correct assignment was found among the two most probable assignments in more than 80% of cases.
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Affiliation(s)
- Manuel Cordova
- Laboratory of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Martins Balodis
- Laboratory of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Bruno Simões de Almeida
- Laboratory of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Michele Ceriotti
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Lyndon Emsley
- Laboratory of Magnetic Resonance, Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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22
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Abstract
![]()
We introduce a local
machine-learning method for predicting the
electron densities of periodic systems. The framework is based on
a numerical, atom-centered auxiliary basis, which enables an accurate
expansion of the all-electron density in a form suitable for learning
isolated and periodic systems alike. We show that, using this formulation,
the electron densities of metals, semiconductors, and molecular crystals
can all be accurately predicted using symmetry-adapted Gaussian process
regression models, properly adjusted for the nonorthogonal nature
of the basis. These predicted densities enable the efficient calculation
of electronic properties, which present errors on the order of tens
of meV/atom when compared to ab initio density-functional
calculations. We demonstrate the key power of this approach by using
a model trained on ice unit cells containing only 4 water molecules
to predict the electron densities of cells containing up to 512 molecules
and see no increase in the magnitude of the errors of derived electronic
properties when increasing the system size. Indeed, we find that these
extrapolated derived energies are more accurate than those predicted
using a direct machine-learning model. Finally, on heterogeneous data
sets SALTED can predict electron densities with errors below 4%.
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Affiliation(s)
- Alan M Lewis
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Andrea Grisafi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Mariana Rossi
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
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23
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Pozdnyakov SN, Zhang L, Ortner C, Csányi G, Ceriotti M. Local invertibility and sensitivity of atomic structure-feature mappings. Open Res Eur 2021; 1:126. [PMID: 37645092 PMCID: PMC10445828 DOI: 10.12688/openreseurope.14156.1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/07/2021] [Indexed: 08/31/2023]
Abstract
Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety of representations that can be used to convert them into a finite set of symmetric descriptors or features. Methods: Here, we analyze the sensitivity of the mapping to atomic displacements, using a singular value decomposition of the Jacobian of the transformation to quantify the sensitivity for different configurations, choice of representations and implementation details. Results: We show that the combination of symmetry and smoothness leads to mappings that have singular points at which the Jacobian has one or more null singular values (besides those corresponding to infinitesimal translations and rotations). This is in fact desirable, because it enforces physical symmetry constraints on the values predicted by regression models constructed using such representations. However, besides these symmetry-induced singularities, there are also spurious singular points, that we find to be linked to the incompleteness of the mapping, i.e. the fact that, for certain classes of representations, structurally distinct configurations are not guaranteed to be mapped onto different feature vectors. Additional singularities can be introduced by a too aggressive truncation of the infinite basis set that is used to discretize the representations. Conclusions: These results exemplify the subtle issues that arise when constructing symmetric representations of atomic structures, and provide conceptual and numerical tools to identify and investigate them in both benchmark and realistic applications.
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Affiliation(s)
- Sergey N. Pozdnyakov
- Laboratory of Computational Science and Modelling, Institute of Materials, Federal Institute of Technology (EPFL) CH-1015 Lausanne, Lausanne, 1015, Switzerland
| | - Liwei Zhang
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
| | - Christoph Ortner
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Federal Institute of Technology (EPFL) CH-1015 Lausanne, Lausanne, 1015, Switzerland
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24
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Abstract
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here, we take a different, unsupervised viewpoint, aiming to determine the basis that encodes in the most compact way possible the structural information that is relevant for the dataset at hand. For each training dataset and number of basis functions, one can build a unique basis that is optimal in this sense and can be computed at no additional cost with respect to the primitive basis by approximating it with splines. We demonstrate that this construction yields representations that are accurate and computationally efficient, particularly when working with representations that correspond to high-body order correlations. We present examples that involve both molecular and condensed-phase machine-learning models.
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Affiliation(s)
- Alexander Goscinski
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Félix Musil
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Sergey Pozdnyakov
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Jigyasa Nigam
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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25
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Abstract
We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.
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Affiliation(s)
- Volker L. Deringer
- Department
of Chemistry, Inorganic Chemistry Laboratory, University of Oxford, Oxford OX1 3QR, United Kingdom
| | - Albert P. Bartók
- Department
of Physics and Warwick Centre for Predictive Modelling, School of
Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Noam Bernstein
- Center
for Computational Materials Science, U.S.
Naval Research Laboratory, Washington D.C. 20375, United States
| | - David M. Wilkins
- Atomistic
Simulation Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom
| | - Michele Ceriotti
- Laboratory
of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
- National
Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale
de Lausanne, Lausanne, Switzerland
| | - Gábor Csányi
- Engineering
Laboratory, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
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26
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Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Cecilia Clementi
- Freie Universität Berlin, Department of Physics, Arnimallee 14, 14195 Berlin, Germany
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Abstract
The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for 1H, 13C, and 15N shieldings in polymorphs of three paradigmatic molecular crystals: benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion improves the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.
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Affiliation(s)
- Edgar A Engel
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Venkat Kapil
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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28
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Abstract
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.
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Affiliation(s)
- Felix Musil
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Andrea Grisafi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Albert P Bartók
- Department of Physics and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Christoph Ortner
- University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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29
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Affiliation(s)
- C David Sherrill
- School of Chemistry and Biochemistry and School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Angelos Michaelides
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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30
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Cersonsky RK, Helfrecht BA, Engel EA, Kliavinek S, Ceriotti M. Improving sample and feature selection with principal covariates regression. Mach Learn : Sci Technol 2021. [DOI: 10.1088/2632-2153/abfe7c] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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31
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Abstract
Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite their popularity, it is well known that they have constraints that hinder their application to complex problems. The core issue lies in the need to describe the system using a small number of collective variables (CVs). Any slow degree of freedom that is not properly described by the chosen CVs will hinder sampling efficiency. However, the exploration of configuration space is also hampered by including variables that are not relevant for the activated process under study. This paper presents the Adaptive Topography of Landscape for Accelerated Sampling (ATLAS), a new biasing method capable of working with many CVs. The root idea of ATLAS is to apply a divide-and-conquer strategy, where the high-dimensional CVs space is divided into basins, each of which is described by an automatically determined, low-dimensional set of variables. A well-tempered metadynamics-like bias is constructed as a function of these local variables. Indicator functions associated with the basins switch on and off the local biases so that the sampling is performed on a collection of low-dimensional CV spaces that are smoothly combined to generate an effectively high-dimensional bias. The unbiased Boltzmann distribution is recovered through reweighing, making the evaluation of conformational and thermodynamic properties straightforward. The decomposition of the free-energy landscape in local basins can be updated iteratively as the simulation discovers new (meta)stable states.
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Affiliation(s)
- F Giberti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - G A Tribello
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT14 7EN, United Kingdom
| | - M Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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32
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Abstract
Over recent years, the use of statistical learning techniques applied to chemical problems has gained substantial momentum. This is particularly apparent in the realm of physical chemistry, where the balance between empiricism and physics-based theory has traditionally been rather in favor of the latter. In this guest Editorial for the special topic issue on "Machine Learning Meets Chemical Physics," a brief rationale is provided, followed by an overview of the topics covered. We conclude by making some general remarks.
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Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Cecilia Clementi
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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34
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Musil F, Veit M, Goscinski A, Fraux G, Willatt MJ, Stricker M, Junge T, Ceriotti M. Efficient implementation of atom-density representations. J Chem Phys 2021; 154:114109. [DOI: 10.1063/5.0044689] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Félix Musil
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Center for Computational Design and Discovery of Novel Materials (MARVEL), Lausanne, Switzerland
| | - Max Veit
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Center for Computational Design and Discovery of Novel Materials (MARVEL), Lausanne, Switzerland
| | - Alexander Goscinski
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michael J. Willatt
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Markus Stricker
- Laboratory for Multiscale Mechanics Modeling, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany
| | - Till Junge
- Laboratory for Multiscale Mechanics Modeling, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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35
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Dakhchoune M, Villalobos LF, Semino R, Liu L, Rezaei M, Schouwink P, Avalos CE, Baade P, Wood V, Han Y, Ceriotti M, Agrawal KV. Gas-sieving zeolitic membranes fabricated by condensation of precursor nanosheets. Nat Mater 2021; 20:362-369. [PMID: 33020610 DOI: 10.1038/s41563-020-00822-2] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Accepted: 09/03/2020] [Indexed: 06/11/2023]
Abstract
The synthesis of molecular-sieving zeolitic membranes by the assembly of building blocks, avoiding the hydrothermal treatment, is highly desired to improve reproducibility and scalability. Here we report exfoliation of the sodalite precursor RUB-15 into crystalline 0.8-nm-thick nanosheets, that host hydrogen-sieving six-membered rings (6-MRs) of SiO4 tetrahedra. Thin films, fabricated by the filtration of a suspension of exfoliated nanosheets, possess two transport pathways: 6-MR apertures and intersheet gaps. The latter were found to dominate the gas transport and yielded a molecular cutoff of 3.6 Å with a H2/N2 selectivity above 20. The gaps were successfully removed by the condensation of the terminal silanol groups of RUB-15 to yield H2/CO2 selectivities up to 100. The high selectivity was exclusively from the transport across 6-MR, which was confirmed by a good agreement between the experimentally determined apparent activation energy of H2 and that computed by ab initio calculations. The scalable fabrication and the attractive sieving performance at 250-300 °C make these membranes promising for precombustion carbon capture.
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Affiliation(s)
- Mostapha Dakhchoune
- Laboratory of Advanced Separations (LAS), École Polytechnique Fédérale de Lausanne (EPFL), Sion, Switzerland
| | - Luis Francisco Villalobos
- Laboratory of Advanced Separations (LAS), École Polytechnique Fédérale de Lausanne (EPFL), Sion, Switzerland
| | - Rocio Semino
- Laboratory of Computational Science and Modelling (COSMO), EPFL, Lausanne, Switzerland
- ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France
| | - Lingmei Liu
- Advanced Membranes and Porous Materials Center, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
| | - Mojtaba Rezaei
- Laboratory of Advanced Separations (LAS), École Polytechnique Fédérale de Lausanne (EPFL), Sion, Switzerland
| | - Pascal Schouwink
- Institut des Sciences et Ingénierie Chimiques (ISIC), EPFL, Lausanne, Switzerland
| | | | - Paul Baade
- Department of Information Technology and Electrical Engineering, ETH, Zürich, Switzerland
| | - Vanessa Wood
- Department of Information Technology and Electrical Engineering, ETH, Zürich, Switzerland
| | - Yu Han
- Advanced Membranes and Porous Materials Center, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling (COSMO), EPFL, Lausanne, Switzerland
| | - Kumar Varoon Agrawal
- Laboratory of Advanced Separations (LAS), École Polytechnique Fédérale de Lausanne (EPFL), Sion, Switzerland.
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36
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Imbalzano G, Zhuang Y, Kapil V, Rossi K, Engel EA, Grasselli F, Ceriotti M. Uncertainty estimation for molecular dynamics and sampling. J Chem Phys 2021; 154:074102. [DOI: 10.1063/5.0036522] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Giulio Imbalzano
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Yongbin Zhuang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen 361005, China
| | - Venkat Kapil
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Kevin Rossi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Laboratory of Nanochemistry for Energy, ISIC, École Polytechnique Fédérale de Lausanne, 1950 Sion, Switzerland
| | - Edgar A. Engel
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Federico Grasselli
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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37
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Lan J, Kapil V, Gasparotto P, Ceriotti M, Iannuzzi M, Rybkin VV. Simulating the ghost: quantum dynamics of the solvated electron. Nat Commun 2021; 12:766. [PMID: 33536410 PMCID: PMC7859219 DOI: 10.1038/s41467-021-20914-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 01/04/2021] [Indexed: 01/13/2023] Open
Abstract
The nature of the bulk hydrated electron has been a challenge for both experiment and theory due to its short lifetime and high reactivity, and the need for a high-level of electronic structure theory to achieve predictive accuracy. The lack of a classical atomistic structural formula makes it exceedingly difficult to model the solvated electron using conventional empirical force fields, which describe the system in terms of interactions between point particles associated with atomic nuclei. Here we overcome this problem using a machine-learning model, that is sufficiently flexible to describe the effect of the excess electron on the structure of the surrounding water, without including the electron in the model explicitly. The resulting potential is not only able to reproduce the stable cavity structure but also recovers the correct localization dynamics that follow the injection of an electron in neat water. The machine learning model achieves the accuracy of the state-of-the-art correlated wave function method it is trained on. It is sufficiently inexpensive to afford a full quantum statistical and dynamical description and allows us to achieve accurate determination of the structure, diffusion mechanisms, and vibrational spectroscopy of the solvated electron.
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Affiliation(s)
- Jinggang Lan
- Department of Chemistry, University of Zurich, Zürich, Switzerland.
| | - Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Piero Gasparotto
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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38
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Abstract
Electronic nearsightedness is one of the fundamental principles that governs the behavior of condensed matter and supports its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables - such as the cohesive energy, the electron density, or a variety of response properties - as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.
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Affiliation(s)
- Andrea Grisafi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland
| | - Jigyasa Nigam
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland .,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland.,Indian Institute of Space Science and Technology Thiruvananthapuram 695547 India
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland .,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne 1015 Lausanne Switzerland
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39
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Helfrecht BA, Cersonsky RK, Fraux G, Ceriotti M. Structure-property maps with Kernel principal covariates regression. Mach Learn : Sci Technol 2020. [DOI: 10.1088/2632-2153/aba9ef] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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40
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Pozdnyakov SN, Willatt MJ, Bartók AP, Ortner C, Csányi G, Ceriotti M. Incompleteness of Atomic Structure Representations. Phys Rev Lett 2020; 125:166001. [PMID: 33124874 DOI: 10.1103/physrevlett.125.166001] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 09/09/2020] [Indexed: 05/26/2023]
Abstract
Many-body descriptors are widely used to represent atomic environments in the construction of machine-learned interatomic potentials and more broadly for fitting, classification, and embedding tasks on atomic structures. There is a widespread belief in the community that three-body correlations are likely to provide an overcomplete description of the environment of an atom. We produce several counterexamples to this belief, with the consequence that any classifier, regression, or embedding model for atom-centered properties that uses three- (or four)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centered contributions mitigates the impact of this fundamental deficiency-explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.
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Affiliation(s)
- Sergey N Pozdnyakov
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Michael J Willatt
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Albert P Bartók
- Department of Physics and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Christoph Ortner
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
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41
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Abstract
Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible N-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different order (generalizations of N-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically improvable, symmetry adapted representations for atomistic machine learning.
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Affiliation(s)
- Jigyasa Nigam
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Sergey Pozdnyakov
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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42
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Cheng B, Mazzola G, Pickard CJ, Ceriotti M. Evidence for supercritical behaviour of high-pressure liquid hydrogen. Nature 2020; 585:217-220. [PMID: 32908269 DOI: 10.1038/s41586-020-2677-y] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 07/10/2020] [Indexed: 11/09/2022]
Abstract
Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression1. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago2, several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism1,3-5, an anomalous melting line6 and the possible transition to a superconducting state7. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to 'learn' potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.
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Affiliation(s)
- Bingqing Cheng
- Department of Chemistry, University of Cambridge, Cambridge, UK. .,TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK. .,Trinity College, Cambridge, UK.
| | | | - Chris J Pickard
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, UK.,Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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43
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Zamani M, Imbalzano G, Tappy N, Alexander DTL, Martí-Sánchez S, Ghisalberti L, Ramasse QM, Friedl M, Tütüncüoglu G, Francaviglia L, Bienvenue S, Hébert C, Arbiol J, Ceriotti M, Fontcuberta I Morral A. 3D Ordering at the Liquid-Solid Polar Interface of Nanowires. Adv Mater 2020; 32:e2001030. [PMID: 32762011 DOI: 10.1002/adma.202001030] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Revised: 06/29/2020] [Indexed: 06/11/2023]
Abstract
The nature of the liquid-solid interface determines the characteristics of a variety of physical phenomena, including catalysis, electrochemistry, lubrication, and crystal growth. Most of the established models for crystal growth are based on macroscopic thermodynamics, neglecting the atomistic nature of the liquid-solid interface. Here, experimental observations and molecular dynamics simulations are employed to identify the 3D nature of an atomic-scale ordering of liquid Ga in contact with solid GaAs in a nanowire growth configuration. An interplay between the liquid ordering and the formation of a new bilayer is revealed, which, contrary to the established theories, suggests that the preference for a certain polarity and polytypism is influenced by the atomic structure of the interface. The conclusions of this work open new avenues for the understanding of crystal growth, as well as other processes and systems involving a liquid-solid interface.
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Affiliation(s)
- Mahdi Zamani
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Giulio Imbalzano
- Laboratory of Computational Science and Modeling, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Nicolas Tappy
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Duncan T L Alexander
- Electron Spectrometry and Microscopy Laboratory, Institute of Physics, Faculty of Basic Sciences, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
- Interdisciplinary Centre for Electron Microscopy (CIME), École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Sara Martí-Sánchez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Barcelona, Catalonia, 08193, Spain
| | - Lea Ghisalberti
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Quentin M Ramasse
- SuperSTEM Laboratory, SciTech Daresbury Campus, Keckwick Lane, Daresbury, WA4 4AD, UK
- School of Chemical and Process Engineering and School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK
| | - Martin Friedl
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Gözde Tütüncüoglu
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Luca Francaviglia
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Sebastien Bienvenue
- Laboratory of Computational Science and Modeling, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Cécile Hébert
- Electron Spectrometry and Microscopy Laboratory, Institute of Physics, Faculty of Basic Sciences, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
- Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Jordi Arbiol
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Barcelona, Catalonia, 08193, Spain
- ICREA, Pg. Lluís Companys 23, Barcelona, Catalonia, 08010, Spain
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
| | - Anna Fontcuberta I Morral
- Laboratory of Semiconductor Materials, Institute of Materials, Faculty of Engineering, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
- Institute of Physics, Faculty of Basic Sciences, École Polytechnique Fédérale de Lausanne, EPFL, Lausanne, 1015, Switzerland
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44
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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45
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Veit M, Wilkins DM, Yang Y, DiStasio RA, Ceriotti M. Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles. J Chem Phys 2020; 153:024113. [DOI: 10.1063/5.0009106] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Max Veit
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - David M. Wilkins
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Yang Yang
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Robert A. DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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46
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Rossi K, Jurásková V, Wischert R, Garel L, Corminbœuf C, Ceriotti M. Simulating Solvation and Acidity in Complex Mixtures with First-Principles Accuracy: The Case of CH 3SO 3H and H 2O 2 in Phenol. J Chem Theory Comput 2020; 16:5139-5149. [PMID: 32567854 DOI: 10.1021/acs.jctc.0c00362] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
We present a generally applicable computational framework for the efficient and accurate characterization of molecular structural patterns and acid properties in an explicit solvent using H2O2 and CH3SO3H in phenol as an example. To address the challenges posed by the complexity of the problem, we resort to a set of data-driven methods and enhanced sampling algorithms. The synergistic application of these techniques makes the first-principle estimation of the chemical properties feasible without renouncing to the use of explicit solvation, involving extensive statistical sampling. Ensembles of neural network (NN) potentials are trained on a set of configurations carefully selected out of preliminary simulations performed at a low-cost density functional tight-binding (DFTB) level. The energy and forces of these configurations are then recomputed at the hybrid density functional theory (DFT) level and used to train the neural networks. The stability of the NN model is enhanced by using DFTB energetics as a baseline, but the efficiency of the direct NN (i.e., baseline-free) is exploited via a multiple-time-step integrator. The neural network potentials are combined with enhanced sampling techniques, such as replica exchange and metadynamics, and used to characterize the relevant protonated species and dominant noncovalent interactions in the mixture, also considering nuclear quantum effects.
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Affiliation(s)
- Kevin Rossi
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland
| | - Veronika Jurásková
- Laboratory for Computational Molecular Design (LCMD), Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland
| | - Raphael Wischert
- Eco-Efficient Products and Processes Laboratory, Solvay, RIC Shanghai, Shanghai 201108, China
| | - Laurent Garel
- Aroma Performance Laboratory, Solvay, RIC Lyon, 69190 Saint-Fons, France
| | - Clémence Corminbœuf
- Laboratory for Computational Molecular Design (LCMD), Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling (COSMO), Institute of Materials, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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47
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Abstract
At room temperature, the quantum contribution to the kinetic energy of a water molecule exceeds the classical contribution by an order of magnitude. The quantum kinetic energy (QKE) of a water molecule is modulated by its local chemical environment and leads to uneven partitioning of isotopes between different phases in thermal equilibrium, which would not occur if the nuclei behaved classically. In this work, we use ab initio path integral simulations to show that QKEs of the water molecules and the equilibrium isotope fractionation ratios of the oxygen and hydrogen isotopes are sensitive probes of the hydrogen bonding structures in aqueous ionic solutions. In particular, we demonstrate how the QKE of water molecules in path integral simulations can be decomposed into translational, rotational and vibrational degrees of freedom, and use them to determine the impact of solvation on different molecular motions. By analyzing the QKEs and isotope fractionation ratios, we show how the addition of the Na+, Cl- and HPO42- ions perturbs the competition between quantum effects in liquid water and impacts their local solvation structures.
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Affiliation(s)
- Lu Wang
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA.
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48
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Liu M, Zhang L, Little MA, Kapil V, Ceriotti M, Yang S, Ding L, Holden DL, Balderas-Xicohténcatl R, He D, Clowes R, Chong SY, Schütz G, Chen L, Hirscher M, Cooper AI. Barely porous organic cages for hydrogen isotope separation. Science 2020; 366:613-620. [PMID: 31672893 DOI: 10.1126/science.aax7427] [Citation(s) in RCA: 140] [Impact Index Per Article: 35.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Accepted: 10/10/2019] [Indexed: 01/18/2023]
Abstract
The separation of hydrogen isotopes for applications such as nuclear fusion is a major challenge. Current technologies are energy intensive and inefficient. Nanoporous materials have the potential to separate hydrogen isotopes by kinetic quantum sieving, but high separation selectivity tends to correlate with low adsorption capacity, which can prohibit process scale-up. In this study, we use organic synthesis to modify the internal cavities of cage molecules to produce hybrid materials that are excellent quantum sieves. By combining small-pore and large-pore cages together in a single solid, we produce a material with optimal separation performance that combines an excellent deuterium/hydrogen selectivity (8.0) with a high deuterium uptake (4.7 millimoles per gram).
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Affiliation(s)
- Ming Liu
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Linda Zhang
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
| | - Marc A Little
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Venkat Kapil
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Siyuan Yang
- Department of Chemistry, Xi'an JiaoTong-Liverpool University, 111 Ren'ai Road, Suzhou Dushu Lake Higher Education Town, Jiangsu Province, 215123, China
| | - Lifeng Ding
- Department of Chemistry, Xi'an JiaoTong-Liverpool University, 111 Ren'ai Road, Suzhou Dushu Lake Higher Education Town, Jiangsu Province, 215123, China
| | - Daniel L Holden
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | | | - Donglin He
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Rob Clowes
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Samantha Y Chong
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Gisela Schütz
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
| | - Linjiang Chen
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK.,Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
| | - Michael Hirscher
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany.
| | - Andrew I Cooper
- Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK. .,Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory and Department of Chemistry, University of Liverpool, 51 Oxford Street, Liverpool, L7 3NY, UK
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49
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Kapil V, Wilkins DM, Lan J, Ceriotti M. Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats. J Chem Phys 2020; 152:124104. [PMID: 32241150 DOI: 10.1063/1.5141950] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Accurate modeling of these quantum nuclear effects requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here, we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, which makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems that have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.
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Affiliation(s)
- Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - David M Wilkins
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
| | - Jinggang Lan
- Department of Chemistry, University of Zürich, Zürich, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
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50
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Poltavsky I, Kapil V, Ceriotti M, Kim KS, Tkatchenko A. Accurate Description of Nuclear Quantum Effects with High-Order Perturbed Path Integrals (HOPPI). J Chem Theory Comput 2020; 16:1128-1135. [PMID: 31913625 DOI: 10.1021/acs.jctc.9b00881] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Imaginary time path-integral (PI) simulations that account for nuclear quantum effects (NQE) beyond the harmonic approximation are increasingly employed together with modern electronic-structure calculations. Existing PI methods are applicable to molecules, liquids, and solids; however, the computational cost of such simulations increases dramatically with decreasing temperature. To address this challenge, here, we propose to combine high-order PI factorization with perturbation theory (PT). Already for conventional second-order PI simulations, the PT ansatz increases the accuracy 2-fold compared to fourth-order schemes with the same settings. In turn, applying PT to high-order path integrals (HOPI) further improves the efficiency of simulations for molecular and condensed matter systems especially at low temperatures. We present results for bulk liquid water, the aspirin molecule, and the CH5+ molecule. Perturbed HOPI simulations remain both efficient and accurate down to 20 K and provide a convenient method to estimate the convergence of quantum-mechanical observables.
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Affiliation(s)
- Igor Poltavsky
- Physics and Materials Science Research Unit , University of Luxembourg , L-1511 Luxembourg City , Luxembourg
| | - Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials , Ecole Polytechnique Fédérale de Lausanne , Lausanne , Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials , Ecole Polytechnique Fédérale de Lausanne , Lausanne , Switzerland
| | - Kwang S Kim
- Department of Chemistry, School of Natural Science , Ulsan National Institute of Science and Technology , Ulsan 44919 , Korea
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit , University of Luxembourg , L-1511 Luxembourg City , Luxembourg
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