1
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Bigi F, Pozdnyakov SN, Ceriotti M. Wigner kernels: Body-ordered equivariant machine learning without a basis. J Chem Phys 2024; 161:044116. [PMID: 39056390 DOI: 10.1063/5.0208746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Accepted: 06/10/2024] [Indexed: 07/28/2024] Open
Abstract
Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their discretized neighbor densities has been used widely and very successfully. We propose a novel density-based method, which involves computing "Wigner kernels." These are fully equivariant and body-ordered kernels that can be computed iteratively at a cost that is independent of the basis used to discretize the density and grows only linearly with the maximum body-order considered. Wigner kernels represent the infinite-width limit of feature-space models, whose dimensionality and computational cost instead scale exponentially with the increasing order of correlations. We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching an accuracy that is competitive with state-of-the-art deep-learning architectures. We discuss the broader relevance of these findings to equivariant geometric machine-learning.
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Affiliation(s)
- Filippo Bigi
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Sergey N Pozdnyakov
- 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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2
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Wan K, He J, Shi X. Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2305758. [PMID: 37640376 DOI: 10.1002/adma.202305758] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 08/24/2023] [Indexed: 08/31/2023]
Abstract
The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.
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Affiliation(s)
- Kaiwei Wan
- Laboratory of Theoretical and Computational Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China
| | - Jianxin He
- Laboratory of Theoretical and Computational Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China
| | - Xinghua Shi
- Laboratory of Theoretical and Computational Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China
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3
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Telari E, Tinti A, Settem M, Maragliano L, Ferrando R, Giacomello A. Charting Nanocluster Structures via Convolutional Neural Networks. ACS NANO 2023; 17:21287-21296. [PMID: 37856254 PMCID: PMC10655179 DOI: 10.1021/acsnano.3c05653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 10/13/2023] [Indexed: 10/21/2023]
Abstract
A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.
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Affiliation(s)
- Emanuele Telari
- Dipartimento
di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome 00184, Italy
| | - Antonio Tinti
- Dipartimento
di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome 00184, Italy
| | - Manoj Settem
- Dipartimento
di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome 00184, Italy
| | - Luca Maragliano
- Dipartimento
Scienze della Vita e dell’Ambiente, Università Politecnica delle Marche, Ancona 60131, Italy
- Center
for Synaptic Neuroscience and Technology, Istituto Italiano di Tecnologia, Genova 16132, Italy
| | | | - Alberto Giacomello
- Dipartimento
di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome 00184, Italy
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4
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Broad J, Wheatley RJ, Graham RS. Parallel Implementation of Nonadditive Gaussian Process Potentials for Monte Carlo Simulations. J Chem Theory Comput 2023. [PMID: 37368843 DOI: 10.1021/acs.jctc.3c00113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
A strategy is presented to implement Gaussian process potentials in molecular simulations through parallel programming. Attention is focused on the three-body nonadditive energy, though all algorithms extend straightforwardly to the additive energy. The method to distribute pairs and triplets between processes is general to all potentials. Results are presented for a simulation box of argon, including full box and atom displacement calculations, which are relevant to Monte Carlo simulation. Data on speed-up are presented for up to 120 processes across four nodes. A 4-fold speed-up is observed over five processes, extending to 20-fold over 40 processes and 30-fold over 120 processes.
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Affiliation(s)
- Jack Broad
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Richard J Wheatley
- School of Chemistry, University of Nottingham, Nottingham, NG7 2RD, England
| | - Richard S Graham
- School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, England
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5
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Ashraf M, Ahmad MS, Inomata Y, Ullah N, Tahir MN, Kida T. Transition metal nanoparticles as nanocatalysts for Suzuki, Heck and Sonogashira cross-coupling reactions. Coord Chem Rev 2023. [DOI: 10.1016/j.ccr.2022.214928] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
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6
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Nguyen NTK, Lebastard C, Wilmet M, Dumait N, Renaud A, Cordier S, Ohashi N, Uchikoshi T, Grasset F. A review on functional nanoarchitectonics nanocomposites based on octahedral metal atom clusters (Nb 6, Mo 6, Ta 6, W 6, Re 6): inorganic 0D and 2D powders and films. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2022; 23:547-578. [PMID: 36212682 PMCID: PMC9542349 DOI: 10.1080/14686996.2022.2119101] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 08/10/2022] [Accepted: 08/24/2022] [Indexed: 05/29/2023]
Abstract
This review is dedicated to various functional nanoarchitectonic nanocomposites based on molecular octahedral metal atom clusters (Nb6, Mo6, Ta6, W6, Re6). Powder and film nanocomposites with two-dimensional, one-dimensional and zero-dimensional morphologies are presented, as well as film matrices from organic polymers to inorganic layered oxides. The high potential and synergetic effects of these nanocomposites for biotechnology applications, photovoltaic, solar control, catalytic, photonic and sensor applications are demonstrated. This review also provides a basic level of understanding how nanocomposites are characterized and processed using different techniques and methods. The main objective of this review would be to provide guiding significance for the design of new high-performance nanocomposites based on transition metal atom clusters.
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Affiliation(s)
- Ngan T. K. Nguyen
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- International Center for Young Scientists, ICYS-Sengen, Global Networking Division, NIMS, Tsukuba, Japan
| | - Clément Lebastard
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- Université Rennes, CNRS, ISCR, UMR6226, Rennes, France
| | - Maxence Wilmet
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- Université Rennes, CNRS, ISCR, UMR6226, Rennes, France
- Saint Gobain Research Paris, Aubervilliers, France
| | - Noée Dumait
- Université Rennes, CNRS, ISCR, UMR6226, Rennes, France
| | - Adèle Renaud
- Université Rennes, CNRS, ISCR, UMR6226, Rennes, France
| | | | - Naoki Ohashi
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- Research Center for Functional Materials, NIMS, Tsukuba, Japan
| | - Tetsuo Uchikoshi
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- Research Center for Functional Materials, NIMS, Tsukuba, Japan
| | - Fabien Grasset
- CNRS-Saint Gobain-NIMS, IRL3629, Laboratory for Innovative Key Materials and Structures (LINK), National Institute for Materials Science (NIMS), Tsukuba, Japan
- Université Rennes, CNRS, ISCR, UMR6226, Rennes, France
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7
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Teng C, Wang Y, Huang D, Martin K, Tristan JB, Bao JL. Dual-Level Training of Gaussian Processes with Physically Inspired Priors for Geometry Optimizations. J Chem Theory Comput 2022; 18:5739-5754. [PMID: 35939760 DOI: 10.1021/acs.jctc.2c00546] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Gaussian process (GP) regression has been recently developed as an effective method in molecular geometry optimization. The prior mean function is one of the crucial parts of the GP. We design and validate two types of physically inspired prior mean functions: force-field-based priors and posterior-type priors. In this work, we implement a dual-level training (DLT) optimizer for the posterior-type priors. The DLT optimizers can be considered as a class of optimization algorithms that belong to the delta-machine learning paradigm but with several major differences compared to the previously proposed algorithms in the same paradigm. In the first level of the DLT, we incorporate the classical mechanical descriptions of the equilibrium geometries into the prior function, which enhances the performance of the GP optimizer as compared to the one using a constant (or zero) prior. In the second level, we utilize the surrogate potential energy surfaces (PESs), which incorporate the physics learned in the first-level training, as the prior function to refine the model performance further. We find that the force-field-based priors and posterior-type priors reduce the overall optimization steps by a factor of 2-3 when compared to the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer as well as the constant-prior GP optimizer proposed in previous works. We also demonstrate the potential of recovering the real PESs with GP with a force-field prior. This work shows the importance of including domain knowledge as an ingredient in the GP, which offers a potentially robust learning model for molecular geometry optimization and for exploring molecular PESs.
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Affiliation(s)
- Chong Teng
- Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02467, United States
| | - Yang Wang
- Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02467, United States
| | - Daniel Huang
- Department of Computer Science, San Francisco State University, San Francisco, California 94132, United States
| | - Katherine Martin
- Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02467, United States
| | - Jean-Baptiste Tristan
- Department of Computer Science, Boston College, Chestnut Hill, Massachusetts 02467, United States
| | - Junwei Lucas Bao
- Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02467, United States
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8
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Winkler L, Müller KR, Sauceda HE. High-fidelity molecular dynamics trajectory reconstruction with bi-directional neural networks. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac6ec6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Molecular dynamics (MD) simulations are a cornerstone in science, enabling the investigation of a system’s thermodynamics all the way to analyzing intricate molecular interactions. In general, creating extended molecular trajectories can be a computationally expensive process, for example, when running ab-initio simulations. Hence, repeating such calculations to either obtain more accurate thermodynamics or to get a higher resolution in the dynamics generated by a fine-grained quantum interaction can be time- and computational resource-consuming. In this work, we explore different machine learning methodologies to increase the resolution of MD trajectories on-demand within a post-processing step. As a proof of concept, we analyse the performance of bi-directional neural networks (NNs) such as neural ODEs, Hamiltonian networks, recurrent NNs and long short-term memories, as well as the uni-directional variants as a reference, for MD simulations (here: the MD17 dataset). We have found that Bi-LSTMs are the best performing models; by utilizing the local time-symmetry of thermostated trajectories they can even learn long-range correlations and display high robustness to noisy dynamics across molecular complexity. Our models can reach accuracies of up to 10−4 Å in trajectory interpolation, which leads to the faithful reconstruction of several unseen high-frequency molecular vibration cycles. This renders the comparison between the learned and reference trajectories indistinguishable. The results reported in this work can serve (1) as a baseline for larger systems, as well as (2) for the construction of better MD integrators.
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9
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Lee JD, Miller JB, Shneidman AV, Sun L, Weaver JF, Aizenberg J, Biener J, Boscoboinik JA, Foucher AC, Frenkel AI, van der Hoeven JES, Kozinsky B, Marcella N, Montemore MM, Ngan HT, O'Connor CR, Owen CJ, Stacchiola DJ, Stach EA, Madix RJ, Sautet P, Friend CM. Dilute Alloys Based on Au, Ag, or Cu for Efficient Catalysis: From Synthesis to Active Sites. Chem Rev 2022; 122:8758-8808. [PMID: 35254051 DOI: 10.1021/acs.chemrev.1c00967] [Citation(s) in RCA: 28] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
The development of new catalyst materials for energy-efficient chemical synthesis is critical as over 80% of industrial processes rely on catalysts, with many of the most energy-intensive processes specifically using heterogeneous catalysis. Catalytic performance is a complex interplay of phenomena involving temperature, pressure, gas composition, surface composition, and structure over multiple length and time scales. In response to this complexity, the integrated approach to heterogeneous dilute alloy catalysis reviewed here brings together materials synthesis, mechanistic surface chemistry, reaction kinetics, in situ and operando characterization, and theoretical calculations in a coordinated effort to develop design principles to predict and improve catalytic selectivity. Dilute alloy catalysts─in which isolated atoms or small ensembles of the minority metal on the host metal lead to enhanced reactivity while retaining selectivity─are particularly promising as selective catalysts. Several dilute alloy materials using Au, Ag, and Cu as the majority host element, including more recently introduced support-free nanoporous metals and oxide-supported nanoparticle "raspberry colloid templated (RCT)" materials, are reviewed for selective oxidation and hydrogenation reactions. Progress in understanding how such dilute alloy catalysts can be used to enhance selectivity of key synthetic reactions is reviewed, including quantitative scaling from model studies to catalytic conditions. The dynamic evolution of catalyst structure and composition studied in surface science and catalytic conditions and their relationship to catalytic function are also discussed, followed by advanced characterization and theoretical modeling that have been developed to determine the distribution of minority metal atoms at or near the surface. The integrated approach demonstrates the success of bridging the divide between fundamental knowledge and design of catalytic processes in complex catalytic systems, which can accelerate the development of new and efficient catalytic processes.
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Affiliation(s)
- Jennifer D Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Jeffrey B Miller
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Anna V Shneidman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Lixin Sun
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Jason F Weaver
- Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States
| | - Joanna Aizenberg
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States.,John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States.,Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Juergen Biener
- Nanoscale Synthesis and Characterization Laboratory, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - J Anibal Boscoboinik
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Alexandre C Foucher
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Anatoly I Frenkel
- Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, New York 11794, United States.,Division of Chemistry, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Jessi E S van der Hoeven
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States.,John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Boris Kozinsky
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Nicholas Marcella
- Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, New York 11794, United States
| | - Matthew M Montemore
- Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States
| | - Hio Tong Ngan
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Christopher R O'Connor
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Cameron J Owen
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States.,John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Dario J Stacchiola
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Eric A Stach
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Robert J Madix
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Philippe Sautet
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States.,Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Cynthia M Friend
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States.,John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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10
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Bissuel D, Albaret T, Niehaus TA. Critical assessment of machine-learned repulsive potentials for the Density Functional based Tight-Binding method: a case study for pure silicon. J Chem Phys 2022; 156:064101. [DOI: 10.1063/5.0081159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Zeni C, Rossi K, Pavloudis T, Kioseoglou J, de Gironcoli S, Palmer RE, Baletto F. Data-driven simulation and characterisation of gold nanoparticle melting. Nat Commun 2021; 12:6056. [PMID: 34663814 PMCID: PMC8523526 DOI: 10.1038/s41467-021-26199-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 09/07/2021] [Indexed: 11/09/2022] Open
Abstract
The simulation and analysis of the thermal stability of nanoparticles, a stepping stone towards their application in technological devices, require fast and accurate force fields, in conjunction with effective characterisation methods. In this work, we develop efficient, transferable, and interpretable machine learning force fields for gold nanoparticles based on data gathered from Density Functional Theory calculations. We use them to investigate the thermodynamic stability of gold nanoparticles of different sizes (1 to 6 nm), containing up to 6266 atoms, concerning a solid-liquid phase change through molecular dynamics simulations. We predict nanoparticle melting temperatures in good agreement with available experimental data. Furthermore, we characterize the solid-liquid phase change mechanism employing an unsupervised learning scheme to categorize local atomic environments. We thus provide a data-driven definition of liquid atomic arrangements in the inner and surface regions of a nanoparticle and employ it to show that melting initiates at the outer layers.
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Affiliation(s)
- Claudio Zeni
- Department of Physics, King's College London, London, WC2R 2LS, UK.
- International School for Advanced Studies, Via Bonomea, 265, 34136, Trieste, Italy.
| | - Kevin Rossi
- Department of Physics, King's College London, London, WC2R 2LS, UK
- Laboratory of Nanochemistry, Institute of Chemistry and Chemical Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Theodore Pavloudis
- College of Engineering, Swansea University, Bay Campus, Fabian Way, Swansea, SA1 8EB, UK
- Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece
| | - Joseph Kioseoglou
- Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece
| | - Stefano de Gironcoli
- International School for Advanced Studies, Via Bonomea, 265, 34136, Trieste, Italy
| | - Richard E Palmer
- College of Engineering, Swansea University, Bay Campus, Fabian Way, Swansea, SA1 8EB, UK
| | - Francesca Baletto
- Department of Physics, King's College London, London, WC2R 2LS, UK
- DIPC, Paseo Manuel de Lardizabal, 20018, San Sebastian, Spain
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12
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Broad J, Preston S, Wheatley RJ, Graham RS. Gaussian process models of potential energy surfaces with boundary optimization. J Chem Phys 2021; 155:144106. [PMID: 34654292 DOI: 10.1063/5.0063534] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A strategy is outlined to reduce the number of training points required to model intermolecular potentials using Gaussian processes, without reducing accuracy. An asymptotic function is used at a long range, and the crossover distance between this model and the Gaussian process is learnt from the training data. The results are presented for different implementations of this procedure, known as boundary optimization, across the following dimer systems: CO-Ne, HF-Ne, HF-Na+, CO2-Ne, and (CO2)2. The technique reduces the number of training points, at fixed accuracy, by up to ∼49%, compared to our previous work based on a sequential learning technique. The approach is readily transferable to other statistical methods of prediction or modeling problems.
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Affiliation(s)
- Jack Broad
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Simon Preston
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Richard J Wheatley
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Richard S Graham
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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13
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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: 229] [Impact Index Per Article: 76.3] [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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14
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Zeni C, Rossi K, Glielmo A, de Gironcoli S. Compact atomic descriptors enable accurate predictions via linear models. J Chem Phys 2021; 154:224112. [PMID: 34241204 DOI: 10.1063/5.0052961] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.
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Affiliation(s)
- Claudio Zeni
- Physics Area, International School for Advanced Studies, Trieste, Italy
| | - Kevin Rossi
- Laboratory of Nanochemistry, Institute of Chemistry and Chemical Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, CH, Switzerland
| | - Aldo Glielmo
- Physics Area, International School for Advanced Studies, Trieste, Italy
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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: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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16
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Han R, Rodríguez-Mayorga M, Luber S. A Machine Learning Approach for MP2 Correlation Energies and Its Application to Organic Compounds. J Chem Theory Comput 2021; 17:777-790. [DOI: 10.1021/acs.jctc.0c00898] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ruocheng Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | | | - Sandra Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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17
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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: 1.8] [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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18
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Ernst WE, Hauser AW. Metal clusters synthesized in helium droplets: structure and dynamics from experiment and theory. Phys Chem Chem Phys 2020; 23:7553-7574. [PMID: 33057510 DOI: 10.1039/d0cp04349d] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Metal clusters have drawn continuous interest because of their high potential for the assembly of matter with special properties that may significantly differ from the corresponding bulk. Controlled combination of particular elements in one nanoparticle can increase the options for the creation of new materials for photonic, catalytic, or electronic applications. Superfluid helium droplets provide confinement and ultralow temperature, i.e. an ideal environment for the atom-by-atom aggregation of a new nanoparticle. This perspective presents a review of the current research progress on the synthesis of tailored metal and metal oxide clusters including core-shell designs, their characterization within the helium droplet beam, deposition on various solid substrates, and analysis via surface diagnostics. Special attention is given to the thermal properties of mixed metal clusters and questions about alloy formation on the nanoscale. Experimental results are accompanied by theoretical approaches employing computational chemistry, molecular dynamics simulations and He density functional theory.
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Affiliation(s)
- Wolfgang E Ernst
- Institute of Experimental Physics, Graz University of Technology, Petersgasse 16, A-8010 Graz, Austria.
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19
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Yanxon H, Zagaceta D, Wood BC, Zhu Q. Neural network potential from bispectrum components: A case study on crystalline silicon. J Chem Phys 2020; 153:054118. [PMID: 32770884 DOI: 10.1063/5.0014677] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we present a systematic study on developing machine learning force fields (MLFFs) for crystalline silicon. While the main-stream approach of fitting a MLFF is to use a small and localized training set from molecular dynamics simulations, it is unlikely to cover the global features of the potential energy surface. To remedy this issue, we used randomly generated symmetrical crystal structures to train a more general Si-MLFF. Furthermore, we performed substantial benchmarks among different choices of material descriptors and regression techniques on two different sets of silicon data. Our results show that neural network potential fitting with bispectrum coefficients as descriptors is a feasible method for obtaining accurate and transferable MLFFs.
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Affiliation(s)
- Howard Yanxon
- Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154, USA
| | - David Zagaceta
- Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154, USA
| | - Brandon C Wood
- Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Qiang Zhu
- Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154, USA
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Pattnaik P, Raghunathan S, Kalluri T, Bhimalapuram P, Jawahar CV, Priyakumar UD. Machine Learning for Accurate Force Calculations in Molecular Dynamics Simulations. J Phys Chem A 2020; 124:6954-6967. [DOI: 10.1021/acs.jpca.0c03926] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Punyaslok Pattnaik
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India
| | - Shampa Raghunathan
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India
| | - Tarun Kalluri
- Center for Visual Information Technology, KCIS, International Institute of Information Technology, Hyderabad 500 032, India
| | - Prabhakar Bhimalapuram
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India
| | - C. V. Jawahar
- Center for Visual Information Technology, KCIS, International Institute of Information Technology, Hyderabad 500 032, India
| | - U. Deva Priyakumar
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India
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21
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Han R, Luber S. Trajectory-based machine learning method and its application to molecular dynamics. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1788189] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- R. Han
- Department of Chemistry A, University of Zurich, Zurich, Switzerland
| | - S. Luber
- Department of Chemistry A, University of Zurich, Zurich, Switzerland
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22
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Pihlajamäki A, Hämäläinen J, Linja J, Nieminen P, Malola S, Kärkkäinen T, Häkkinen H. Monte Carlo Simulations of Au 38(SCH 3) 24 Nanocluster Using Distance-Based Machine Learning Methods. J Phys Chem A 2020; 124:4827-4836. [PMID: 32412747 DOI: 10.1021/acs.jpca.0c01512] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present an implementation of distance-based machine learning (ML) methods to create a realistic atomistic interaction potential to be used in Monte Carlo simulations of thermal dynamics of thiolate (SR) protected gold nanoclusters. The ML potential is trained for Au38(SR)24 by using previously published, density functional theory (DFT) based, molecular dynamics (MD) simulation data on two experimentally characterized structural isomers of the cluster and validated against independent DFT MD simulations. This method opens a door to efficient probing of the configuration space for further investigations of thermal-dependent electronic and optical properties of Au38(SR)24. Our ML implementation strategy allows for generalization and accuracy control of distance-based ML models for complex nanostructures having several chemical elements and interactions of varying strength.
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Affiliation(s)
- Antti Pihlajamäki
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Joonas Hämäläinen
- Faculty of Information Technology, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Joakim Linja
- Faculty of Information Technology, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Paavo Nieminen
- Faculty of Information Technology, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Sami Malola
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Tommi Kärkkäinen
- Faculty of Information Technology, University of Jyväskylä, FI-40014 Jyväskylä, Finland
| | - Hannu Häkkinen
- Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland.,Department of Chemistry, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
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23
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Building Nonparametric n-Body Force Fields Using Gaussian Process Regression. MACHINE LEARNING MEETS QUANTUM PHYSICS 2020. [DOI: 10.1007/978-3-030-40245-7_5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
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24
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A fast neural network approach for direct covariant forces prediction in complex multi-element extended systems. NAT MACH INTELL 2019. [DOI: 10.1038/s42256-019-0098-0] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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25
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Baletto F. Structural properties of sub-nanometer metallic clusters. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:113001. [PMID: 30562724 DOI: 10.1088/1361-648x/aaf989] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.
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Affiliation(s)
- Francesca Baletto
- Physics Department, King's College London, WC2R 2LS, London, United Kingdom
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26
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Rupp M, von Lilienfeld OA, Burke K. Guest Editorial: Special Topic on Data-Enabled Theoretical Chemistry. J Chem Phys 2018; 148:241401. [DOI: 10.1063/1.5043213] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Matthias Rupp
- Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - O. Anatole von Lilienfeld
- Department of Chemistry, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, University of Basel, 4056 Basel, Switzerland
| | - Kieron Burke
- Departments of Chemistry and Physics, University of California, Irvine, California 92697, USA
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27
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Li W, Ando Y. Comparison of different machine learning models for the prediction of forces in copper and silicon dioxide. Phys Chem Chem Phys 2018; 20:30006-30020. [DOI: 10.1039/c8cp04508a] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Recently, the machine learning (ML) force field has emerged as a powerful atomic simulation approach because of its high accuracy and low computational cost.
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Affiliation(s)
- Wenwen Li
- Research Center for Computational Design of Advanced Functional Materials
- National Institute of Advanced Industrial Science and Technology
- Tsukuba
- Japan
| | - Yasunobu Ando
- Research Center for Computational Design of Advanced Functional Materials
- National Institute of Advanced Industrial Science and Technology
- Tsukuba
- Japan
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