1
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Mészáros BB, Szabó A, Daru J. Short-Range Δ-Machine Learning: A Cost-Efficient Strategy to Transfer Chemical Accuracy to Condensed Phase Systems. J Chem Theory Comput 2025; 21:5372-5381. [PMID: 40434991 DOI: 10.1021/acs.jctc.5c00367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2025]
Abstract
DFT-based machine-learning potentials (MLPs) are now routinely trained for condensed-phase systems, but surpassing DFT accuracy remains challenging due to the cost or unavailability of periodic reference calculations. Our previous work ( Phys. Rev. Lett. 2022, 129, 226001) demonstrated that high-accuracy periodic MLPs can be trained within the CCMD framework using extended yet finite reference calculations. Here, we introduce short-range Δ-Machine Learning (srΔML), a method that starts from a baseline MLP trained on low-level periodic data and adds a Δ-MLP correction based on high-level cluster calculations at the CC level. Applied to liquid water, srΔML reduces the required cluster size from (H2O)64 to (H2O)15 and significantly lowers the number of clusters needed, resulting in a 50-200× reduction in computational cost. The resulting potential closely reproduces the target CC potential and accurately captures both two- and three-body structural descriptors.
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Affiliation(s)
- Bence Balázs Mészáros
- Hevesy György PhD School of Chemistry Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
- Department of Organic Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - András Szabó
- Department of Organic Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - János Daru
- Department of Organic Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
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2
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Ji X, Li TE. Selective Excitation of IR-Inactive Modes via Vibrational Polaritons: Insights from Atomistic Simulations. J Phys Chem Lett 2025; 16:5034-5042. [PMID: 40356572 DOI: 10.1021/acs.jpclett.5c00848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2025]
Abstract
Vibrational polaritons, hybrid light-matter states formed between molecular vibrations and infrared (IR) cavity modes, provide a novel approach for modifying chemical reaction pathways and energy transfer processes. For vibrational polaritons involving condensed-phase molecules, the short polariton lifetime raises a debate over whether pumping polaritons may produce different effects on molecules compared to directly exciting the molecules in free space or under weak coupling. Here, for liquid methane under vibrational strong coupling, classical cavity molecular dynamics simulations show that pumping the upper polariton (UP) formed by the asymmetric bending mode of methane can sometimes selectively excite the IR-inactive symmetric bending mode. This finding is validated when the molecular system is described using both empirical force fields and machine-learning potentials, also in qualitative agreement with analytical theory of polariton energy transfer rates based on Fermi's golden rule calculations. Additionally, our study suggests that polariton-induced energy transfer to IR-inactive modes reaches maximal efficiency when the UP has significant contributions from both photons and molecules, underscoring the importance of light-matter hybridization. As IR-inactive vibrational modes are generally inaccessible to direct IR excitation, our study highlights the unique role of polariton formation in selectively controlling IR-inactive vibrations. Since this polariton-induced process occurs after the polariton decays, it may impact IR photochemistry on a time scale longer than the polariton lifetime, as observed in experiments.
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Affiliation(s)
- Xinwei Ji
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
| | - Tao E Li
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, United States
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3
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Gross E, Driver MD, Saif A, Evans ON, Hunter CA. Solvation energies from atomic surface site interaction points. Phys Chem Chem Phys 2025; 27:8844-8855. [PMID: 40202218 DOI: 10.1039/d5cp00635j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2025]
Abstract
The surface site interaction model for liquids at equilibrium (SSIMPLE) is a method for calculating thermodynamic properties in a fluid phase based on the use of surface site interaction points (SSIP) to represent all of the non-covalent interactions that molecules make with the environment. Interactions between the SSIPs of two different molecules are governed by a non-polar term and a polar term. Here the formulation originally made for room temperature liquids is generalized to any temperature. We show that the non-polar interaction term is temperature independent while the polar interaction term depends on temperature. This formulation was used to develop a description of the temperature dependence of fluid phase density in terms of an expansion energy, which is based on net intermolecular SSIP interactions. The method is shown to accurately model the temperature dependence of experimentally measured association constants for the formation of 1 : 1 H-bonded complexes in carbon tetrachloride. The atomic interaction point (AIP) version of the SSIP descripiton of 171 different compounds was used in SSIMPLE to calculate room temperature liquid densities that are in good agreement with experimental data. Since non-covalent interactions in the vapour phase can be treated in the same way as liquid phase interactions, SSIMPLE can also be used to calcuate vapour-liquid equilibria (VLE). Experimental VLE data for 196 binary mixtures of 30 miscible compounds was collected, and SSIMPLE was shown to reproduce the experimental behaviour well.
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Affiliation(s)
- Emily Gross
- Department of Chemistry, University of Regensburg, Universitaetsstrasse 31, 93053 Regensburg, Germany
| | - Mark D Driver
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Areesha Saif
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Oliver N Evans
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Christopher A Hunter
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
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4
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Abedi M, Behler J, Goldsmith CF. High-Dimensional Neural Network Potentials for Accurate Prediction of Equation of State: A Case Study of Methane. J Chem Theory Comput 2023; 19:7825-7832. [PMID: 37902963 DOI: 10.1021/acs.jctc.3c00469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2023]
Abstract
Machine learning-based interatomic potentials, such as those provided by neural networks, are increasingly important in molecular dynamics simulations. In the present work, we consider the applicability and robustness of machine learning molecular dynamics to predict the equation of state properties of methane by using high-dimensional neural network potentials (HDNNPs). We investigate two different strategies for generating training data: one strategy based upon bulk representations using periodic cells and another strategy based upon clusters of molecules. We assess the accuracy of the trained potentials by predicting the equilibrium mass density for a wide range of thermodynamic conditions to characterize the liquid phase, supercritical fluid, and gas phase, as well as the liquid-vapor coexistence curve. Our results show an excellent agreement with reference phase diagrams, with an average error below ∼2% for all studied phases. Moreover, we confirm the applicability of models trained on cluster data sets for producing accurate and reliable results.
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Affiliation(s)
- Mostafa Abedi
- School of Engineering, Brown University, Providence, Rhode Island 02906, United States
| | - Jörg Behler
- Lehrstuhl für Theoretische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany
- Research Center Chemical Sciences and Sustainability, Research Alliance Ruhr, 44780 Bochum, Germany
| | - C Franklin Goldsmith
- School of Engineering, Brown University, Providence, Rhode Island 02906, United States
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5
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Thermodynamics of diamond formation from hydrocarbon mixtures in planets. Nat Commun 2023; 14:1104. [PMID: 36843123 PMCID: PMC9968715 DOI: 10.1038/s41467-023-36841-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 02/15/2023] [Indexed: 02/28/2023] Open
Abstract
Hydrocarbon mixtures are extremely abundant in the Universe, and diamond formation from them can play a crucial role in shaping the interior structure and evolution of planets. With first-principles accuracy, we first estimate the melting line of diamond, and then reveal the nature of chemical bonding in hydrocarbons at extreme conditions. We finally establish the pressure-temperature phase boundary where it is thermodynamically possible for diamond to form from hydrocarbon mixtures with different atomic fractions of carbon. Notably, here we show a depletion zone at pressures above 200 GPa and temperatures below 3000 K-3500 K where diamond formation is thermodynamically favorable regardless of the carbon atomic fraction, due to a phase separation mechanism. The cooler condition of the interior of Neptune compared to Uranus means that the former is much more likely to contain the depletion zone. Our findings can help explain the dichotomy of the two ice giants manifested by the low luminosity of Uranus, and lead to a better understanding of (exo-)planetary formation and evolution.
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6
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Sauceda HE, Gálvez-González LE, Chmiela S, Paz-Borbón LO, Müller KR, Tkatchenko A. BIGDML-Towards accurate quantum machine learning force fields for materials. Nat Commun 2022; 13:3733. [PMID: 35768400 PMCID: PMC9243122 DOI: 10.1038/s41467-022-31093-x] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 06/01/2022] [Indexed: 12/16/2022] Open
Abstract
Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene-graphene dynamics induced by nuclear quantum effects and their strong contributions to the hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.
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Affiliation(s)
- Huziel E Sauceda
- Departamento de Materia Condensada, Instituto de Física, Universidad Nacional Autónoma de México, Cd. de México C.P., 04510, Mexico.
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany.
- BASLEARN - TU Berlin/BASF Joint Lab for Machine Learning, Technische Universität Berlin, 10587, Berlin, Germany.
| | - Luis E Gálvez-González
- Programa de Doctorado en Ciencias (Física), División de Ciencias Exactas y Naturales, Universidad de Sonora, Blvd. Luis Encinas & Rosales, Hermosillo, C.P., 83000, Mexico
| | - Stefan Chmiela
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Berlin, Germany
| | - Lauro Oliver Paz-Borbón
- Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Cd. de México C.P., 04510, Mexico
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Berlin, Germany.
- Google Research, Brain team, Berlin, Germany.
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, 02841, Seoul, Korea.
- Max Planck Institute for Informatics, Stuhlsatzenhausweg, 66123, Saarbrücken, Germany.
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg.
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7
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Graham RS, Wheatley RJ. Machine learning for non-additive intermolecular potentials: quantum chemistry to first-principles predictions. Chem Commun (Camb) 2022; 58:6898-6901. [PMID: 35642644 DOI: 10.1039/d2cc01820a] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Prediction of thermophysical properties from molecular principles requires accurate potential energy surfaces (PES). We present a widely-applicable method to produce first-principles PES from quantum chemistry calculations. Our approach accurately interpolates three-body non-additive interaction data, using the machine learning technique, Gaussian Processes (GP). The GP approach needs no bespoke modification when the number or type of molecules is changed. Our method produces highly accurate interpolation from significantly fewer training points than typical approaches, meaning ab initio calculations can be performed at higher accuracy. As an exemplar we compute the PES for all three-body cross interactions for CO2-Ar mixtures. From these we calculate the CO2-Ar virial coefficients up to 5th order. The resulting virial equation of state (EoS) is convergent for densities up to the critical density. Where convergent, the EoS makes accurate first-principles predictions for a range of thermophysical properties for CO2-Ar mixtures, including the compressibility factor, speed of sound and Joule-Thomson coefficient. Our method has great potential to make wide-ranging first-principles predictions for mixtures of comparably sized molecules. Such predictions can replace the need for expensive, laborious and repetitive experiments and inform the continuum models required for applications.
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Affiliation(s)
- Richard S Graham
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.
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8
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Abstract
Computational methods in fluid research have been progressing during the past few years, driven by the incorporation of massive amounts of data, either in textual or graphical form, generated from multi-scale simulations, laboratory experiments, and real data from the field. Artificial Intelligence (AI) and its adjacent field, Machine Learning (ML), are about to reach standardization in most fields of computational science and engineering, as they provide multiple ways for extracting information from data that turn into knowledge, with the aid of portable software implementations that are easy to adopt. There is ample information on the historical and mathematical background of all aspects of AI/ML in the literature. Thus, this review article focuses mainly on their impact on fluid research at present, highlighting advances and opportunities, recognizing techniques and methods having been proposed, tabulating, and testing some of the most popular algorithms that have shown significant accuracy and performance on fluid applications. We also investigate algorithmic accuracy on several fluid datasets that correspond to simulation results for the transport properties of fluids and suggest that non-linear, decision tree-based methods have shown remarkable performance on reproducing fluid properties.
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9
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Deringer VL, Bartók AP, Bernstein N, Wilkins DM, Ceriotti M, Csányi G. Gaussian Process Regression for Materials and Molecules. Chem Rev 2021; 121:10073-10141. [PMID: 34398616 PMCID: PMC8391963 DOI: 10.1021/acs.chemrev.1c00022] [Citation(s) in RCA: 324] [Impact Index Per Article: 81.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Indexed: 12/18/2022]
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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10
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Westermayr J, Marquetand P. Machine Learning for Electronically Excited States of Molecules. Chem Rev 2021; 121:9873-9926. [PMID: 33211478 PMCID: PMC8391943 DOI: 10.1021/acs.chemrev.0c00749] [Citation(s) in RCA: 198] [Impact Index Per Article: 49.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Indexed: 12/11/2022]
Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data
Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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11
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Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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12
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Young TA, Johnston-Wood T, Deringer VL, Duarte F. A transferable active-learning strategy for reactive molecular force fields. Chem Sci 2021; 12:10944-10955. [PMID: 34476072 PMCID: PMC8372546 DOI: 10.1039/d1sc01825f] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 07/04/2021] [Indexed: 11/25/2022] Open
Abstract
Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels-Alder reaction in the gas phase and non-equilibrium dynamics (a model SN2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems.
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Affiliation(s)
- Tom A Young
- Chemistry Research Laboratory, University of Oxford Mansfield Road Oxford OX1 3TA UK
| | - Tristan Johnston-Wood
- Chemistry Research Laboratory, University of Oxford Mansfield Road Oxford OX1 3TA UK
| | - Volker L Deringer
- Department of Chemistry, Inorganic Chemistry Laboratory, University of Oxford Oxford OX1 3QR UK
| | - Fernanda Duarte
- Chemistry Research Laboratory, University of Oxford Mansfield Road Oxford OX1 3TA UK
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13
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Musil F, Grisafi A, Bartók AP, Ortner C, Csányi G, Ceriotti M. Physics-Inspired Structural Representations for Molecules and Materials. Chem Rev 2021; 121:9759-9815. [PMID: 34310133 DOI: 10.1021/acs.chemrev.1c00021] [Citation(s) in RCA: 183] [Impact Index Per Article: 45.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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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14
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Inguva PK, Walker PJ, Yew HW, Zhu K, Haslam AJ, Matar OK. Continuum-scale modelling of polymer blends using the Cahn-Hilliard equation: transport and thermodynamics. SOFT MATTER 2021; 17:5645-5665. [PMID: 34095939 DOI: 10.1039/d1sm00272d] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The Cahn-Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn-Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid-liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.
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Affiliation(s)
- Pavan K Inguva
- Department of Chemical Engineering, Massachusetts Institute of Technology, 25 Ames Street, Cambridge, MA 02142, USA and Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
| | - Pierre J Walker
- Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
| | - Hon Wa Yew
- Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
| | - Kezheng Zhu
- Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
| | - Andrew J Haslam
- Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
| | - Omar K Matar
- Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK.
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15
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Laurens G, Rabary M, Lam J, Peláez D, Allouche AR. Infrared spectra of neutral polycyclic aromatic hydrocarbons based on machine learning potential energy surface and dipole mapping. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02773-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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16
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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: 5.8] [Reference Citation Analysis] [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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17
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Allen AEA, Dusson G, Ortner C, Csányi G. Atomic permutationally invariant polynomials for fitting molecular force fields. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abd51e] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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18
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Benoit M, Amodeo J, Combettes S, Khaled I, Roux A, Lam J. Measuring transferability issues in machine-learning force fields: the example of gold–iron interactions with linearized potentials. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/abc9fd] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Machine-learning force fields have been increasingly employed in order to extend the possibility of current first-principles calculations. However, the transferability of the obtained potential cannot always be guaranteed in situations that are outside the original database. To study such limitation, we examined the very difficult case of the interactions in gold–iron nanoparticles. For the machine-learning potential, we employed a linearized formulation that is parameterized using a penalizing regression scheme which allows us to control the complexity of the obtained potential. We showed that while having a more complex potential allows for a better agreement with the training database, it can also lead to overfitting issues and a lower accuracy in untrained systems.
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19
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Grisafi A, Nigam J, Ceriotti M. Multi-scale approach for the prediction of atomic scale properties. Chem Sci 2020; 12:2078-2090. [PMID: 34163971 PMCID: PMC8179303 DOI: 10.1039/d0sc04934d] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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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20
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Abstract
We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.
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Affiliation(s)
- Janus J Eriksen
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
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21
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Abstract
A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.
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Affiliation(s)
- Peng Xu
- Department of Chemistry, Iowa State University, Ames, Iowa 50014, United States
| | - Melisa Alkan
- Department of Chemistry, Iowa State University, Ames, Iowa 50014, United States
| | - Mark S Gordon
- Department of Chemistry, Iowa State University, Ames, Iowa 50014, United States
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22
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Riera M, Hirales A, Ghosh R, Paesani F. Data-Driven Many-Body Models with Chemical Accuracy for CH4/H2O Mixtures. J Phys Chem B 2020; 124:11207-11221. [DOI: 10.1021/acs.jpcb.0c08728] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Alan Hirales
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Raja Ghosh
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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23
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Liu YB, Yang JY, Xin GM, Liu LH, Csányi G, Cao BY. Machine learning interatomic potential developed for molecular simulations on thermal properties of β-Ga 2O 3. J Chem Phys 2020; 153:144501. [PMID: 33086840 DOI: 10.1063/5.0027643] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The thermal properties of β-Ga2O3 can significantly affect the performance and reliability of high-power electronic devices. To date, due to the absence of a reliable interatomic potential, first-principles calculations based on density functional theory (DFT) have been routinely used to probe the thermal properties of β-Ga2O3. DFT calculations can only tackle small-scale systems due to the huge computational cost, while the thermal transport processes are usually associated with large time and length scales. In this work, we develop a machine learning based Gaussian approximation potential (GAP) for accurately describing the lattice dynamics of perfect crystalline β-Ga2O3 and accelerating atomic-scale simulations. The GAP model shows excellent convergence, which can faithfully reproduce the DFT potential energy surface at a training data size of 32 000 local atomic environments. The GAP model is then used to predict ground-state lattice parameters, coefficients of thermal expansion, heat capacity, phonon dispersions at 0 K, and anisotropic thermal conductivity of β-Ga2O3, which are all in excellent agreement with either the DFT results or experiments. The accurate predictions of phonon dispersions and thermal conductivities demonstrate that the GAP model can well describe the harmonic and anharmonic interactions of phonons. Additionally, the successful application of our GAP model to the phonon density of states of a 2500-atom β-Ga2O3 structure at elevated temperature indicates the strength of machine learning potentials to tackle large-scale atomic systems in long molecular simulations, which would be almost impossible to generate with DFT-based molecular simulations at present.
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Affiliation(s)
- Yuan-Bin Liu
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Jia-Yue Yang
- School of Energy and Power Engineering, Shandong University, Jinan, Shandong 250061, China
| | - Gong-Ming Xin
- School of Energy and Power Engineering, Shandong University, Jinan, Shandong 250061, China
| | - Lin-Hua Liu
- School of Energy and Power Engineering, Shandong University, Jinan, Shandong 250061, China
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
| | - Bing-Yang Cao
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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24
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Jablonka K, Ongari D, Moosavi SM, Smit B. Big-Data Science in Porous Materials: Materials Genomics and Machine Learning. Chem Rev 2020; 120:8066-8129. [PMID: 32520531 PMCID: PMC7453404 DOI: 10.1021/acs.chemrev.0c00004] [Citation(s) in RCA: 176] [Impact Index Per Article: 35.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Indexed: 12/16/2022]
Abstract
By combining metal nodes with organic linkers we can potentially synthesize millions of possible metal-organic frameworks (MOFs). The fact that we have so many materials opens many exciting avenues but also create new challenges. We simply have too many materials to be processed using conventional, brute force, methods. In this review, we show that having so many materials allows us to use big-data methods as a powerful technique to study these materials and to discover complex correlations. The first part of the review gives an introduction to the principles of big-data science. We show how to select appropriate training sets, survey approaches that are used to represent these materials in feature space, and review different learning architectures, as well as evaluation and interpretation strategies. In the second part, we review how the different approaches of machine learning have been applied to porous materials. In particular, we discuss applications in the field of gas storage and separation, the stability of these materials, their electronic properties, and their synthesis. Given the increasing interest of the scientific community in machine learning, we expect this list to rapidly expand in the coming years.
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Affiliation(s)
- Kevin
Maik Jablonka
- Laboratory of Molecular Simulation
(LSMO), Institut des Sciences et Ingénierie Chimiques (ISIC), École Polytechnique Fédérale
de Lausanne (EPFL), Sion, Switzerland
| | - Daniele Ongari
- Laboratory of Molecular Simulation
(LSMO), Institut des Sciences et Ingénierie Chimiques (ISIC), École Polytechnique Fédérale
de Lausanne (EPFL), Sion, Switzerland
| | - Seyed Mohamad Moosavi
- Laboratory of Molecular Simulation
(LSMO), Institut des Sciences et Ingénierie Chimiques (ISIC), École Polytechnique Fédérale
de Lausanne (EPFL), Sion, Switzerland
| | - Berend Smit
- Laboratory of Molecular Simulation
(LSMO), Institut des Sciences et Ingénierie Chimiques (ISIC), École Polytechnique Fédérale
de Lausanne (EPFL), Sion, Switzerland
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25
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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: 101] [Impact Index Per Article: 20.2] [Reference Citation Analysis] [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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26
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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: 7.8] [Reference Citation Analysis] [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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27
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Cheng Z, Zhao D, Ma J, Li W, Li S. An On-the-Fly Approach to Construct Generalized Energy-Based Fragmentation Machine Learning Force Fields of Complex Systems. J Phys Chem A 2020; 124:5007-5014. [DOI: 10.1021/acs.jpca.0c04526] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- Zheng Cheng
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Dongbo Zhao
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
- Kuang Yaming Honors School, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Jing Ma
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Wei Li
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Shuhua Li
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
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28
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Neufeld VA, Thom AJW. Accelerating Convergence in Fock Space Quantum Monte Carlo Methods. J Chem Theory Comput 2020; 16:1503-1510. [DOI: 10.1021/acs.jctc.9b01023] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Verena A. Neufeld
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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29
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Proppe J, Gugler S, Reiher M. Gaussian Process-Based Refinement of Dispersion Corrections. J Chem Theory Comput 2019; 15:6046-6060. [PMID: 31603673 DOI: 10.1021/acs.jctc.9b00627] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections. We refer to the associated, statistically improved model as D3-GP. It is trained on differences between interaction energies obtained from PBE-D3(BJ)/ma-def2-QZVPP and DLPNO-CCSD(T)/CBS calculations. We generated a data set containing interaction energies for 1248 molecular dimers, which resemble the dispersion-dominated systems contained in the S66 data set. Our systems represent not only equilibrium structures but also dimers with various relative orientations and conformations at both shorter and longer distances. A reparametrization of the D3(BJ) model based on 66 of these dimers suggests that two of its three empirical parameters, a1 and s8, are zero, whereas a2 = 5.6841 bohr. For the remaining 1182 dimers, we find that this new set of parameters is superior to all previously published D3(BJ) parameter sets. To train our D3-GP model, we engineered two different vectorial representations of (supra-)molecular systems, both derived from the matrix of atom-pairwise D3(BJ) interaction terms: (a) a distance-resolved interaction energy histogram, histD3(BJ), and (b) eigenvalues of the interaction matrix ordered according to their decreasing absolute value, eigD3(BJ). Hence, the GP learns a mapping from D3(BJ) information only, which renders D3-GP-type dispersion corrections comparable to those obtained with the original D3 approach. They improve systematically if the underlying training set is selected carefully. Here, we harness the prediction variance obtained from GP regression to select optimal training sets in an automated fashion. The larger the variance, the more information the corresponding data point may add to the training set. For a given set of molecular systems, variance-based sampling can approximately determine the smallest subset being subjected to reference calculations such that all dispersion corrections for the remaining systems fall below a predefined accuracy threshold. To render the entire D3-GP workflow as efficient as possible, we present an improvement over our variance-based, sequential active-learning scheme [ J. Chem. Theory Comput. 2018 , 14 , 5238 ]. Our refined learning algorithm selects multiple (instead of single) systems that can be subjected to reference calculations simultaneously. We refer to the underlying selection strategy as batchwise variance-based sampling (BVS). BVS-guided active learning is an essential component of our D3-GP workflow, which is implemented in a black-box fashion. Once provided with reference data for new molecular systems, the underlying GP model automatically learns to adapt to these and similar systems. This approach leads overall to a self-improving model (D3-GP) that predicts system-focused and GP-refined D3-type dispersion corrections for any given system of reference data.
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Affiliation(s)
- Jonny Proppe
- Department of Chemistry , and Department of Computer Science , University of Toronto , Toronto , Ontario M5S , Canada.,Laboratory of Physical Chemistry , ETH Zurich , Vladimir-Prelog-Weg 2 , 8093 Zurich , Switzerland
| | - Stefan Gugler
- Laboratory of Physical Chemistry , ETH Zurich , Vladimir-Prelog-Weg 2 , 8093 Zurich , Switzerland
| | - Markus Reiher
- Laboratory of Physical Chemistry , ETH Zurich , Vladimir-Prelog-Weg 2 , 8093 Zurich , Switzerland
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30
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Kapil V, Wieme J, Vandenbrande S, Lamaire A, Van Speybroeck V, Ceriotti M. Modeling the Structural and Thermal Properties of Loaded Metal–Organic Frameworks. An Interplay of Quantum and Anharmonic Fluctuations. J Chem Theory Comput 2019; 15:3237-3249. [DOI: 10.1021/acs.jctc.8b01297] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Jelle Wieme
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Steven Vandenbrande
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Aran Lamaire
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Veronique Van Speybroeck
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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