1
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Friede M, Hölzer C, Ehlert S, Grimme S. dxtb-An efficient and fully differentiable framework for extended tight-binding. J Chem Phys 2024; 161:062501. [PMID: 39120026 DOI: 10.1063/5.0216715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 07/18/2024] [Indexed: 08/10/2024] Open
Abstract
Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.
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Affiliation(s)
- Marvin Friede
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
| | - Christian Hölzer
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
| | - Sebastian Ehlert
- AI4Science, Microsoft Research, Evert van de Beekstraat 354, 1118CZ Schiphol, Netherlands
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, University of Bonn, Bonn 53115, Germany
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2
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Aldossary A, Campos-Gonzalez-Angulo JA, Pablo-García S, Leong SX, Rajaonson EM, Thiede L, Tom G, Wang A, Avagliano D, Aspuru-Guzik A. In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2402369. [PMID: 38794859 DOI: 10.1002/adma.202402369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 04/28/2024] [Indexed: 05/26/2024]
Abstract
Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.
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Affiliation(s)
- Abdulrahman Aldossary
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | | | - Sergio Pablo-García
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
| | - Shi Xuan Leong
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Ella Miray Rajaonson
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Luca Thiede
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Gary Tom
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Andrew Wang
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Davide Avagliano
- Chimie ParisTech, PSL University, CNRS, Institute of Chemistry for Life and Health Sciences (iCLeHS UMR 8060), Paris, F-75005, France
| | - Alán Aspuru-Guzik
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
- Department of Materials Science & Engineering, University of Toronto, 184 College St., Toronto, ON, M5S 3E4, Canada
- Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5, Canada
- Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 66118 University Ave., Toronto, M5G 1M1, Canada
- Acceleration Consortium, 80 St George St, Toronto, M5S 3H6, Canada
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3
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Schwade M, Schilcher MJ, Reverón Baecker C, Grumet M, Egger DA. Temperature-transferable tight-binding model using a hybrid-orbital basis. J Chem Phys 2024; 160:134102. [PMID: 38557853 DOI: 10.1063/5.0197986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/13/2024] [Indexed: 04/04/2024] Open
Abstract
Finite-temperature calculations are relevant for rationalizing material properties, yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many explicit first-principles calculations, tight-binding and machine-learning models for the electronic structure emerged as promising alternatives, but transferability of such methods to elevated temperatures in a data-efficient way remains a great challenge. In this work, we suggest a tight-binding model for efficient and accurate calculations of temperature-dependent properties of semiconductors. Our approach utilizes physics-informed modeling of the electronic structure in the form of hybrid-orbital basis functions and numerically integrating atomic orbitals for the distance dependence of matrix elements. We show that these design choices lead to a tight-binding model with a minimal amount of parameters that are straightforwardly optimized using density functional theory or alternative electronic-structure methods. The temperature transferability of our model is tested by applying it to existing molecular-dynamics trajectories without explicitly fitting temperature-dependent data and comparison with density functional theory. We utilize it together with machine-learning molecular dynamics and hybrid density functional theory for the prototypical semiconductor gallium arsenide. We find that including the effects of thermal expansion on the onsite terms of the tight-binding model is important in order to accurately describe electronic properties at elevated temperatures in comparison with experiment.
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Affiliation(s)
- Martin Schwade
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Maximilian J Schilcher
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Christian Reverón Baecker
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - Manuel Grumet
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
| | - David A Egger
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
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4
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Fedik N, Nebgen B, Lubbers N, Barros K, Kulichenko M, Li YW, Zubatyuk R, Messerly R, Isayev O, Tretiak S. Synergy of semiempirical models and machine learning in computational chemistry. J Chem Phys 2023; 159:110901. [PMID: 37712780 DOI: 10.1063/5.0151833] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 07/11/2023] [Indexed: 09/16/2023] Open
Abstract
Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.
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Affiliation(s)
- Nikita Fedik
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Benjamin Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Maksim Kulichenko
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Ying Wai Li
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Roman Zubatyuk
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Richard Messerly
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Olexandr Isayev
- Department of Chemistry, Mellon College of Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Integrated Nanotechnologies Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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5
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Huang B, von Rudorff GF, von Lilienfeld OA. The central role of density functional theory in the AI age. Science 2023; 381:170-175. [PMID: 37440654 DOI: 10.1126/science.abn3445] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 05/30/2023] [Indexed: 07/15/2023]
Abstract
Density functional theory (DFT) plays a pivotal role in chemical and materials science because of its relatively high predictive power, applicability, versatility, and computational efficiency. We review recent progress in machine learning (ML) model developments, which have relied heavily on DFT for synthetic data generation and for the design of model architectures. The general relevance of these developments is placed in a broader context for chemical and materials sciences. DFT-based ML models have reached high efficiency, accuracy, scalability, and transferability and pave the way to the routine use of successful experimental planning software within self-driving laboratories.
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Affiliation(s)
- Bing Huang
- University of Vienna, Faculty of Physics, AT1090 Wien, Austria
| | - Guido Falk von Rudorff
- University Kassel, Department of Chemistry, 34132 Kassel, Germany
- Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), 34132 Kassel, Germany
| | - O Anatole von Lilienfeld
- Vector Institute for Artificial Intelligence, Toronto, Ontario M5S 1M1, Canada
- Department of Chemistry, University of Toronto, St. George Campus, Toronto, Ontario M5S 3H6, Canada
- Department of Materials Science and Engineering, University of Toronto, St. George Campus, Toronto, Ontario M5S 3E4, Canada
- Department of Physics, University of Toronto, St. George Campus, Toronto, Ontario M5S 1A7, Canada
- Machine Learning Group, Technische Universität Berlin and Berlin Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
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6
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Goldman N, Fried LE, Lindsey RK, Pham CH, Dettori R. Enhancing the accuracy of density functional tight binding models through ChIMES many-body interaction potentials. J Chem Phys 2023; 158:144112. [PMID: 37061479 DOI: 10.1063/5.0141616] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of these models can require lengthy effort due to the lack of a systematic approach for their development. In this work, we discuss the use of the Chebyshev Interaction Model for Efficient Simulation (ChIMES) to create rapidly parameterized DFTB models, which exhibit strong transferability due to the inclusion of many-body interactions that might otherwise be inaccurate. We apply our modeling approach to silicon polymorphs and review previous work on titanium hydride. We also review the creation of a general purpose DFTB/ChIMES model for organic molecules and compounds that approaches hybrid functional and coupled cluster accuracy with two orders of magnitude fewer parameters than similar neural network approaches. In all cases, DFTB/ChIMES yields similar accuracy to the underlying quantum method with orders of magnitude improvement in computational cost. Our developments provide a way to create computationally efficient and highly accurate simulations over varying extreme thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly, and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.
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Affiliation(s)
- Nir Goldman
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Laurence E Fried
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Rebecca K Lindsey
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - C Huy Pham
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - R Dettori
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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7
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Negre CFA, Wall ME, Niklasson AMN. Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics. J Chem Phys 2023; 158:074108. [PMID: 36813723 DOI: 10.1063/5.0137119] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.
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Affiliation(s)
- Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Michael E Wall
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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8
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Nakai H, Kobayashi M, Yoshikawa T, Seino J, Ikabata Y, Nishimura Y. Divide-and-Conquer Linear-Scaling Quantum Chemical Computations. J Phys Chem A 2023; 127:589-618. [PMID: 36630608 DOI: 10.1021/acs.jpca.2c06965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.
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Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
| | - Masato Kobayashi
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido060-0810, Japan.,Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido001-0021, Japan
| | - Takeshi Yoshikawa
- Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba274-8510, Japan
| | - Junji Seino
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
| | - Yasuhiro Ikabata
- Information and Media Center, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi441-8580, Japan.,Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi441-8580, Japan
| | - Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
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9
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Fan G, McSloy A, Aradi B, Yam CY, Frauenheim T. Obtaining Electronic Properties of Molecules through Combining Density Functional Tight Binding with Machine Learning. J Phys Chem Lett 2022; 13:10132-10139. [PMID: 36269857 DOI: 10.1021/acs.jpclett.2c02586] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
We have introduced a machine learning workflow that allows for optimizing electronic properties in the density functional tight binding method (DFTB). The workflow allows for the optimization of electronic properties by generating two-center integrals, either by training basis function parameters directly or by training a spline model for the diatomic integrals, which are then used to build the Hamiltonian and the overlap matrices. Using our workflow, we have managed to obtain improved electronic properties, such as charge distributions, dipole moments, and approximated polarizabilities. While both machine learning approaches enabled us to improve on the electronic properties of the molecules as compared with existing DFTB parametrizations, only by training on the basis function parameters we were able to obtain consistent Hamiltonians and overlap matrices in the physically reasonable ranges or to improve on multiple electronic properties simultaneously.
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Affiliation(s)
- Guozheng Fan
- Bremen Center for Computational Materials Science, University of Bremen, 28359Bremen, Germany
| | - Adam McSloy
- Bremen Center for Computational Materials Science, University of Bremen, 28359Bremen, Germany
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, 28359Bremen, Germany
| | - Chi-Yung Yam
- Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China, Shenzhen, 518000China
| | - Thomas Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, 28359Bremen, Germany
- Beijing Computational Science Research Center, 100193Beijing, China
- Shenzhen JL Computational Science and Applied Research Institute, 518110Shenzhen, China
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10
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Fedik N, Zubatyuk R, Kulichenko M, Lubbers N, Smith JS, Nebgen B, Messerly R, Li YW, Boldyrev AI, Barros K, Isayev O, Tretiak S. Extending machine learning beyond interatomic potentials for predicting molecular properties. Nat Rev Chem 2022; 6:653-672. [PMID: 37117713 DOI: 10.1038/s41570-022-00416-3] [Citation(s) in RCA: 25] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/15/2022] [Indexed: 11/09/2022]
Abstract
Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry.
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11
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Mocci F, de Villiers Engelbrecht L, Olla C, Cappai A, Casula MF, Melis C, Stagi L, Laaksonen A, Carbonaro CM. Carbon Nanodots from an In Silico Perspective. Chem Rev 2022; 122:13709-13799. [PMID: 35948072 PMCID: PMC9413235 DOI: 10.1021/acs.chemrev.1c00864] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.
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Affiliation(s)
- Francesca Mocci
- Department
of Chemical and Geological Sciences, University
of Cagliari, I-09042 Monserrato, Italy,
| | | | - Chiara Olla
- Department
of Physics, University of Cagliari, I-09042 Monserrato, Italy
| | - Antonio Cappai
- Department
of Physics, University of Cagliari, I-09042 Monserrato, Italy
| | - Maria Francesca Casula
- Department
of Mechanical, Chemical and Materials Engineering, University of Cagliari, Via Marengo 2, IT 09123 Cagliari, Italy
| | - Claudio Melis
- Department
of Physics, University of Cagliari, I-09042 Monserrato, Italy
| | - Luigi Stagi
- Department
of Chemistry and Pharmacy, Laboratory of Materials Science and Nanotechnology, University of Sassari, Via Vienna 2, 07100 Sassari, Italy
| | - Aatto Laaksonen
- Department
of Chemical and Geological Sciences, University
of Cagliari, I-09042 Monserrato, Italy,Department
of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden,State Key
Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 210009, P. R. China,Centre
of Advanced Research in Bionanoconjugates and Biopolymers, PetruPoni Institute of Macromolecular Chemistry, Aleea Grigore Ghica-Voda 41A, 700487 Iasi, Romania,Division
of Energy Science, Energy Engineering, Luleå
University of Technology, Luleå 97187, Sweden,
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12
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Pham CH, Lindsey RK, Fried LE, Goldman N. High-Accuracy Semiempirical Quantum Models Based on a Minimal Training Set. J Phys Chem Lett 2022; 13:2934-2942. [PMID: 35343698 DOI: 10.1021/acs.jpclett.2c00453] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A great need exists for computationally efficient quantum simulation approaches that can achieve an accuracy similar to high-level theories at a fraction of the computational cost. In this regard, we have leveraged a machine-learned interaction potential based on Chebyshev polynomials to improve density functional tight binding (DFTB) models for organic materials. The benefit of our approach is two-fold: (1) many-body interactions can be corrected for in a systematic and rapidly tunable process, and (2) high-level quantum accuracy for a broad range of compounds can be achieved with ∼0.3% of data required for one advanced deep learning potential. Our model exhibits both transferability and extensibility through comparison to quantum chemical results for organic clusters, solid carbon phases, and molecular crystal phase stability rankings. Our efforts thus allow for high-throughput physical and chemical predictions with up to coupled-cluster accuracy for systems that are computationally intractable with standard approaches.
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Affiliation(s)
- Cong Huy Pham
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Rebecca K Lindsey
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Laurence E Fried
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Nir Goldman
- Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
- Department of Chemical Engineering, University of California, Davis, California 95616, United States
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13
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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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14
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Abstract
Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.
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Affiliation(s)
- Bing Huang
- Faculty
of Physics, University of Vienna, 1090 Vienna, Austria
| | - O. Anatole von Lilienfeld
- Faculty
of Physics, University of Vienna, 1090 Vienna, Austria
- Institute
of Physical Chemistry and National Center for Computational Design
and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, 4056 Basel, Switzerland
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15
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Cawkwell MJ, Burch AC, Ferreira SR, Lease N, Manner VW. Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory. J Chem Inf Model 2021; 61:3337-3347. [PMID: 34252276 DOI: 10.1021/acs.jcim.1c00312] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005-1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2-3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.
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Affiliation(s)
- Marc J Cawkwell
- Los Alamos National Laboratory, Mail Stop B221 Los Alamos, New Mexico 87545, United States
| | - Alexandra C Burch
- Los Alamos National Laboratory, Mail Stop B221 Los Alamos, New Mexico 87545, United States
| | - Suyana R Ferreira
- Los Alamos National Laboratory, Mail Stop B221 Los Alamos, New Mexico 87545, United States
| | - Nicholas Lease
- Los Alamos National Laboratory, Mail Stop B221 Los Alamos, New Mexico 87545, United States
| | - Virginia W Manner
- Los Alamos National Laboratory, Mail Stop B221 Los Alamos, New Mexico 87545, United States
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16
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Ammothum Kandy AK, Wadbro E, Aradi B, Broqvist P, Kullgren J. Curvature Constrained Splines for DFTB Repulsive Potential Parametrization. J Chem Theory Comput 2021; 17:1771-1781. [PMID: 33606527 PMCID: PMC8023658 DOI: 10.1021/acs.jctc.0c01156] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
The Curvature Constrained
Splines (CCS) methodology has been used
for fitting repulsive potentials to be used in SCC-DFTB calculations.
The benefit of using CCS is that the actual fitting of the repulsive
potential is performed through quadratic programming on a convex objective
function. This guarantees a unique (for strictly convex) and optimum
two-body repulsive potential in a single shot, thereby making the
parametrization process robust, and with minimal human effort. Furthermore,
the constraints in CCS give the user control to tune the shape of
the repulsive potential based on prior knowledge about the system
in question. Herein, we developed the method further with new constraints
and the capability to handle sparse data. We used the method to generate
accurate repulsive potentials for bulk Si polymorphs and demonstrate
that for a given Slater-Koster table, which reproduces the experimental
band structure for bulk Si in its ground state, we are unable to find
one single two-body repulsive potential that can accurately describe
the various bulk polymorphs of silicon in our training set. We further
demonstrate that to increase transferability, the repulsive potential
needs to be adjusted to account for changes in the chemical environment,
here expressed in the form of a coordination number. By training a
near-sighted Atomistic Neural Network potential, which includes many-body
effects but still essentially within the first-neighbor shell, we
can obtain full transferability for SCC-DFTB in terms of describing
the energetics of different Si polymorphs.
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Affiliation(s)
| | - Eddie Wadbro
- Department of Computing Science, Umeå University, Umeå SE-901 87, Sweden
| | - Bálint Aradi
- Bremen Center for Computational Materials Science, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
| | - Peter Broqvist
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 538, 751 21 Uppsala, Sweden
| | - Jolla Kullgren
- Department of Chemistry - Ångström Laboratory, Uppsala University, Box 538, 751 21 Uppsala, Sweden
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17
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Jenness GR, Bresnahan CG, Shukla MK. Adventures in DFTB: Toward an Automatic Parameterization Scheme. J Chem Theory Comput 2020; 16:6894-6903. [PMID: 33119287 DOI: 10.1021/acs.jctc.0c00842] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
As we push forward on understanding the fate of chemicals in the environment, we need a method that will allow for the simulation of the inherent heterogeneity. Density functional tight binding (DFTB) is a methodology that allows for a detailed electronic description and would be ideal for this problem. While many parameters can be derived directly from DFT, empirical parameters still exist in the confinement and repulsion potentials. In this manuscript, we examine these potentials and present solutions that will minimize the degree of empiricism. Our results show that it is possible to construct confinement potentials from examining the atomic radial wavefunctions. Moreover, we found that the heterogeneous repulsion potentials can be derived from using only homogeneous repulsion curves.
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Affiliation(s)
- Glen R Jenness
- Environmental Laboratory, US Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180, United States
| | - Caitlin G Bresnahan
- Environmental Laboratory, US Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180, United States
| | - Manoj K Shukla
- Environmental Laboratory, US Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180, United States
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18
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Stöhr M, Medrano Sandonas L, Tkatchenko A. Accurate Many-Body Repulsive Potentials for Density-Functional Tight Binding from Deep Tensor Neural Networks. J Phys Chem Lett 2020; 11:6835-6843. [PMID: 32787209 DOI: 10.1021/acs.jpclett.0c01307] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We combine density-functional tight binding (DFTB) with deep tensor neural networks (DTNN) to maximize the strengths of both approaches in predicting structural, energetic, and vibrational molecular properties. The DTNN is used to construct a nonlinear model for the localized many-body interatomic repulsive energy, which so far has been treated in an atom-pairwise manner in DFTB. Substantially improving upon standard DFTB and DTNN, the resulting DFTB-NNrep model yields accurate predictions of atomization and isomerization energies, equilibrium geometries, vibrational frequencies, and dihedral rotation profiles for a large variety of organic molecules compared to the hybrid DFT-PBE0 functional. Our results highlight the potential of combining semiempirical electronic-structure methods with physically motivated machine learning approaches for predicting localized many-body interactions. We conclude by discussing future advancements of the DFTB-NNrep approach that could enable chemically accurate electronic-structure calculations for systems with tens of thousands of atoms.
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Affiliation(s)
- Martin Stöhr
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Leonardo Medrano Sandonas
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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19
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Manzhos S. Machine learning for the solution of the Schrödinger equation. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/ab7d30] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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20
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Hourahine B, Aradi B, Blum V, Bonafé F, Buccheri A, Camacho C, Cevallos C, Deshaye MY, Dumitrică T, Dominguez A, Ehlert S, Elstner M, van der Heide T, Hermann J, Irle S, Kranz JJ, Köhler C, Kowalczyk T, Kubař T, Lee IS, Lutsker V, Maurer RJ, Min SK, Mitchell I, Negre C, Niehaus TA, Niklasson AMN, Page AJ, Pecchia A, Penazzi G, Persson MP, Řezáč J, Sánchez CG, Sternberg M, Stöhr M, Stuckenberg F, Tkatchenko A, Yu VWZ, Frauenheim T. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. J Chem Phys 2020; 152:124101. [PMID: 32241125 DOI: 10.1063/1.5143190] [Citation(s) in RCA: 409] [Impact Index Per Article: 102.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.
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Affiliation(s)
- B Hourahine
- SUPA, Department of Physics, The University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - B Aradi
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - V Blum
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - F Bonafé
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - A Buccheri
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| | - C Camacho
- School of Chemistry, University of Costa Rica, San José 11501-2060, Costa Rica
| | - C Cevallos
- School of Chemistry, University of Costa Rica, San José 11501-2060, Costa Rica
| | - M Y Deshaye
- Department of Chemistry and Advanced Materials Science and Engineering Center, Western Washington University, Bellingham, Washington 98225, USA
| | - T Dumitrică
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - A Dominguez
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - S Ehlert
- University of Bonn, Bonn, Germany
| | - M Elstner
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - T van der Heide
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - J Hermann
- Freie Universität Berlin, Berlin, Germany
| | - S Irle
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - J J Kranz
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - C Köhler
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - T Kowalczyk
- Department of Chemistry and Advanced Materials Science and Engineering Center, Western Washington University, Bellingham, Washington 98225, USA
| | - T Kubař
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - I S Lee
- Department of Chemistry, Ulsan National Institute of Science and Technology, Ulsan, South Korea
| | - V Lutsker
- Institut I - Theoretische Physik, University of Regensburg, Regensburg, Germany
| | - R J Maurer
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - S K Min
- Department of Chemistry, Ulsan National Institute of Science and Technology, Ulsan, South Korea
| | - I Mitchell
- Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), Ulsan 44919, South Korea
| | - C Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - T A Niehaus
- Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - A M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - A J Page
- School of Environmental and Life Sciences, University of Newcastle, Callaghan, Australia
| | - A Pecchia
- CNR-ISMN, Via Salaria km 29.300, 00015 Monterotondo Stazione, Rome, Italy
| | - G Penazzi
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - M P Persson
- Dassault Systemes, Cambridge, United Kingdom
| | - J Řezáč
- Institute of Organic Chemistry and Biochemistry AS CR, Prague, Czech Republic
| | - C G Sánchez
- Instituto Interdisciplinario de Ciencias Básicas, Universidad Nacional de Cuyo, CONICET, Facultad de Ciencias Exactas y Naturales, Mendoza, Argentina
| | - M Sternberg
- Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - M Stöhr
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - F Stuckenberg
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
| | - A Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - V W-Z Yu
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - T Frauenheim
- Bremen Center for Computational Materials Science, University of Bremen, Bremen, Germany
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21
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Abstract
The world needs new materials to stimulate the chemical industry in key sectors of our economy: environment and sustainability, information storage, optical telecommunications, and catalysis. Yet, nearly all functional materials are still discovered by "trial-and-error", of which the lack of predictability affords a major materials bottleneck to technological innovation. The average "molecule-to-market" lead time for materials discovery is currently 20 years. This is far too long for industrial needs, as highlighted by the Materials Genome Initiative, which has ambitious targets of up to 4-fold reductions in average molecule-to-market lead times. Such a large step change in progress can only be realistically achieved if one adopts an entirely new approach to materials discovery. Fortunately, a fundamentally new approach to materials discovery has been emerging, whereby data science with artificial intelligence offers a prospective solution to speed up these average molecule-to-market lead times.This approach is known as data-driven materials discovery. Its broad prospects have only recently become a reality, given the timely and major advances in "big data", artificial intelligence, and high-performance computing (HPC). Access to massive data sets has been stimulated by government-regulated open-access requirements for data and literature. Natural-language processing (NLP) and machine-learning (ML) tools that can mine data and find patterns therein are becoming mainstream. Exascale HPC capabilities that can aid data mining and pattern recognition and also generate their own data from calculations are now within our grasp. These timely advances present an ideal opportunity to develop data-driven materials-discovery strategies to systematically design and predict new chemicals for a given device application.This Account shows how data science can afford materials discovery via a four-step "design-to-device" pipeline that entails (1) data extraction, (2) data enrichment, (3) material prediction, and (4) experimental validation. Massive databases of cognate chemical and property information are first forged from "chemistry-aware" natural-language-processing tools, such as ChemDataExtractor, and enriched using machine-learning methods and high-throughput quantum-chemical calculations. New materials for a bespoke application can then be predicted by mining these databases with algorithmic encodings of relationships between chemical structures and physical properties that are known to deliver functional materials. These may take the form of classification, enumeration, or machine-learning algorithms. A data-mining workflow short-lists these predictions to a handful of lead candidate materials that go forward to experimental validation. This design-to-device approach is being developed to offer a roadmap for the accelerated discovery of new chemicals for functional applications. Case studies presented demonstrate its utility for photovoltaic, optical, and catalytic applications. While this Account is focused on applications in the physical sciences, the generic pipeline discussed is readily transferable to other scientific disciplines such as biology and medicine.
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Affiliation(s)
- Jacqueline M. Cole
- Cavendish Laboratory, Department of Physics, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, U.K
- ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0QX, U.K
- Department of Chemical Engineering and Biotechnology, University of Cambridge, West Cambridge Site, Philippa Fawcett Drive, Cambridge CB3 0AS, U.K
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, U.K
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22
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Panosetti C, Engelmann A, Nemec L, Reuter K, Margraf JT. Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression. J Chem Theory Comput 2020; 16:2181-2191. [DOI: 10.1021/acs.jctc.9b00975] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Chiara Panosetti
- Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Artur Engelmann
- Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Lydia Nemec
- Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Johannes T. Margraf
- Chair for Theoretical Chemistry, Technical University of Munich, Lichtenbergstr. 4, D-85747 Garching, Germany
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23
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Spiegelman F, Tarrat N, Cuny J, Dontot L, Posenitskiy E, Martí C, Simon A, Rapacioli M. Density-functional tight-binding: basic concepts and applications to molecules and clusters. ADVANCES IN PHYSICS: X 2020; 5:1710252. [PMID: 33154977 PMCID: PMC7116320 DOI: 10.1080/23746149.2019.1710252] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 12/19/2019] [Indexed: 06/10/2023] Open
Abstract
The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.
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Affiliation(s)
- Fernand Spiegelman
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
| | - Nathalie Tarrat
- CEMES, Université de Toulouse (UPS), CNRS, UPR8011, Toulouse, Toulouse, France
| | - Jérôme Cuny
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
| | - Leo Dontot
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
| | - Evgeny Posenitskiy
- Laboratoire Collisions Agrégats et Réactivité LCAR/IRSAMC, UMR5589, Université de Toulouse (UPS) and CNRS, Toulouse, France
| | - Carles Martí
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
- Laboratoire de Chimie, UMR5182, Ecole Normale Supérieure de Lyon, Université de Lyon and CNRS, Lyon, France
| | - Aude Simon
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
| | - Mathias Rapacioli
- Laboratoire de Chimie et Physique Quantiques LCPQ/IRSAMC, UMR5626, Université de Toulouse (UPS)and CNRS, Toulouse, France
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24
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Lu X, Duchimaza-Heredia J, Cui Q. Analysis of Density Functional Tight Binding with Natural Bonding Orbitals. J Phys Chem A 2019; 123:7439-7453. [PMID: 31373822 DOI: 10.1021/acs.jpca.9b05072] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
The description of chemical bonding by the density functional tight binding (DFTB) model is analyzed using natural bonding orbitals (NBOs) and compared to results from density functional theory (B3LYP/aug-cc-pVTZ) calculations. Several molecular systems have been chosen to represent fairly diverse bonding scenarios that include standard covalent bonds, hypervalent interactions, multicenter bonds, metal-ligand interactions (with and without the pseudo-Jahn-Teller effect), and through-space donor-acceptor interactions. Overall, the results suggest that DFTB3/3OB provides physically sound descriptions for the different bonding scenarios analyzed here, as reflected by the general agreement between DFTB3 and B3LYP NBO properties, such as the nature of the NBOs, the magnitudes of natural charges and bond orders, and the dominant donor-acceptor interactions. The degree of ligand-to-metal charge transfer and the ionic nature of pentavalent phosphate are overestimated, likely reflecting the minimal-basis nature of DFTB3/3OB. Moreover, certain orbital interactions, such as geminal interactions, are observed to be grossly overestimated by DFTB3 for hypervalent phosphate and several transition metal compounds that involve copper and nickel. The study indicates that results from NBO analysis can be instructive for identifying electronic structure descriptions at the approximate quantum-mechanical level that require improvement and thus for guiding the systematic improvement of these methods.
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Affiliation(s)
- Xiya Lu
- Department of Chemistry and Theoretical Chemistry Institute , University of Wisconsin-Madison , 1101 University Avenue , Madison , Wisconsin 53706 , United States
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25
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Smith JS, Nebgen BT, Zubatyuk R, Lubbers N, Devereux C, Barros K, Tretiak S, Isayev O, Roitberg AE. Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning. Nat Commun 2019; 10:2903. [PMID: 31263102 PMCID: PMC6602931 DOI: 10.1038/s41467-019-10827-4] [Citation(s) in RCA: 299] [Impact Index Per Article: 59.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2018] [Accepted: 05/29/2019] [Indexed: 01/01/2023] Open
Abstract
Computational modeling of chemical and biological systems at atomic resolution is a crucial tool in the chemist's toolset. The use of computer simulations requires a balance between cost and accuracy: quantum-mechanical methods provide high accuracy but are computationally expensive and scale poorly to large systems, while classical force fields are cheap and scalable, but lack transferability to new systems. Machine learning can be used to achieve the best of both approaches. Here we train a general-purpose neural network potential (ANI-1ccx) that approaches CCSD(T)/CBS accuracy on benchmarks for reaction thermochemistry, isomerization, and drug-like molecular torsions. This is achieved by training a network to DFT data then using transfer learning techniques to retrain on a dataset of gold standard QM calculations (CCSD(T)/CBS) that optimally spans chemical space. The resulting potential is broadly applicable to materials science, biology, and chemistry, and billions of times faster than CCSD(T)/CBS calculations.
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Affiliation(s)
- Justin S Smith
- Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Benjamin T Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Roman Zubatyuk
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- Department of Chemistry, Physics, and Atmospheric Science, Jackson State University, Jackson, MS, 39217, USA
| | - Nicholas Lubbers
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Christian Devereux
- Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Olexandr Isayev
- UNC Eshelman School of Pharmacy, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA.
| | - Adrian E Roitberg
- Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA.
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26
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Podeszwa R, Jankiewicz W, Krzuś M, Witek HA. Correcting long-range electrostatics in DFTB. J Chem Phys 2019; 150:234110. [DOI: 10.1063/1.5099694] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rafał Podeszwa
- Institute of Chemistry, University of Silesia, Szkolna 9, 41-006 Katowice, Poland
| | - Wojciech Jankiewicz
- Institute of Chemistry, University of Silesia, Szkolna 9, 41-006 Katowice, Poland
| | - Magdalena Krzuś
- Institute of Chemistry, University of Silesia, Szkolna 9, 41-006 Katowice, Poland
- Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Kraków, Poland
| | - Henryk A. Witek
- Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, 1001 University Rd., Hsinchu 30010, Taiwan
- Center for Emergent Functional Matter Science, National Chiao Tung University, 1001 University Rd., Hsinchu 30010, Taiwan
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27
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Pun GPP, Batra R, Ramprasad R, Mishin Y. Physically informed artificial neural networks for atomistic modeling of materials. Nat Commun 2019; 10:2339. [PMID: 31138813 PMCID: PMC6538760 DOI: 10.1038/s41467-019-10343-5] [Citation(s) in RCA: 75] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Accepted: 04/26/2019] [Indexed: 11/30/2022] Open
Abstract
Large-scale atomistic computer simulations of materials heavily rely on interatomic potentials predicting the energy and Newtonian forces on atoms. Traditional interatomic potentials are based on physical intuition but contain few adjustable parameters and are usually not accurate. The emerging machine-learning (ML) potentials achieve highly accurate interpolation within a large DFT database but, being purely mathematical constructions, suffer from poor transferability to unknown structures. We propose a new approach that can drastically improve the transferability of ML potentials by informing them of the physical nature of interatomic bonding. This is achieved by combining a rather general physics-based model (analytical bond-order potential) with a neural-network regression. This approach, called the physically informed neural network (PINN) potential, is demonstrated by developing a general-purpose PINN potential for Al. We suggest that the development of physics-based ML potentials is the most effective way forward in the field of atomistic simulations.
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Affiliation(s)
- G P Purja Pun
- Department of Physics and Astronomy, MSN 3F3, George Mason University, Fairfax, VA, 22030, USA
| | - R Batra
- School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - R Ramprasad
- School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - Y Mishin
- Department of Physics and Astronomy, MSN 3F3, George Mason University, Fairfax, VA, 22030, USA.
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28
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Ceriotti M. Unsupervised machine learning in atomistic simulations, between predictions and understanding. J Chem Phys 2019; 150:150901. [PMID: 31005087 DOI: 10.1063/1.5091842] [Citation(s) in RCA: 82] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods-that are geared toward classification and coarse-graining of molecular simulations-seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.
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Affiliation(s)
- Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute des Materiaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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29
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Chou CP, Sakti AW, Nishimura Y, Nakai H. Development of Divide-and-Conquer Density-Functional Tight-Binding Method for Theoretical Research on Li-Ion Battery. CHEM REC 2019; 19:746-757. [PMID: 30462370 DOI: 10.1002/tcr.201800141] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Revised: 10/25/2018] [Accepted: 10/26/2018] [Indexed: 01/24/2023]
Abstract
The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.
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Affiliation(s)
- Chien-Pin Chou
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo, 169-8555, Japan
| | - Aditya Wibawa Sakti
- Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto, 615-8520, Japan
| | - Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo, 169-8555, Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, Tokyo, 169-8555, Japan.,Element Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyotodaigaku-Katsura, Kyoto, 615-8520, Japan.,Department of Chemistry and Biochemistry, School of Advanced Science and Enigineering, Waseda University, Tokyo, 169-8555, Japan
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30
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Chakraborty S, Kayastha P, Ramakrishnan R. The chemical space of B, N-substituted polycyclic aromatic hydrocarbons: Combinatorial enumeration and high-throughput first-principles modeling. J Chem Phys 2019; 150:114106. [PMID: 30902009 DOI: 10.1063/1.5088083] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Combinatorial introduction of heteroatoms in the two-dimensional framework of aromatic hydrocarbons opens up possibilities to design compound libraries exhibiting desirable photovoltaic and photochemical properties. Exhaustive enumeration and first-principles characterization of this chemical space provide indispensable insights for rational compound design strategies. Here, for the smallest seventy-seven Kekulean-benzenoid polycyclic systems, we reveal combinatorial substitution of C atom pairs with the isosteric and isoelectronic B, N pairs to result in 7 453 041 547 842 (7.4 tera) unique molecules. We present comprehensive frequency distributions of this chemical space, analyze trends, and discuss a symmetry-controlled selectivity manifestable in synthesis product yield. Furthermore, by performing high-throughput ab initio density functional theory calculations of over thirty-three thousand (33k) representative molecules, we discuss quantitative trends in the structural stability and inter-property relationships across heteroarenes. Our results indicate a significant fraction of the 33k molecules to be electronically active in the 1.5-2.5 eV region, encompassing the most intense region of the solar spectrum, indicating their suitability as potential light-harvesting molecular components in photo-catalyzed solar cells.
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Affiliation(s)
- Sabyasachi Chakraborty
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Prakriti Kayastha
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Raghunathan Ramakrishnan
- Tata Institute of Fundamental Research, Centre for Interdisciplinary Sciences, Hyderabad 500107, India
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31
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Cawkwell MJ, Perriot R. Transferable density functional tight binding for carbon, hydrogen, nitrogen, and oxygen: Application to shock compression. J Chem Phys 2019; 150:024107. [DOI: 10.1063/1.5063385] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- M. J. Cawkwell
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - R. Perriot
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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32
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Li H, Collins C, Tanha M, Gordon GJ, Yaron DJ. A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians. J Chem Theory Comput 2018; 14:5764-5776. [PMID: 30351008 DOI: 10.1021/acs.jctc.8b00873] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize nonmonotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15 700 hydrocarbons by comparing the root-mean-square error in energy and dipole moment, on test molecules with eight heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to seven heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59%, respectively. Training on molecules with up to four heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.
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33
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Schütt O, VandeVondele J. Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation. J Chem Theory Comput 2018; 14:4168-4175. [PMID: 29957943 PMCID: PMC6096449 DOI: 10.1021/acs.jctc.8b00378] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
It is chemically intuitive that an optimal atom centered basis set must adapt to its atomic environment, for example by polarizing toward nearby atoms. Adaptive basis sets of small size can be significantly more accurate than traditional atom centered basis sets of the same size. The small size and well conditioned nature of these basis sets leads to large saving in computational cost, in particular in a linear scaling framework. Here, it is shown that machine learning can be used to predict such adaptive basis sets using local geometrical information only. As a result, various properties of standard DFT calculations can be easily obtained at much lower costs, including nuclear gradients. In our approach, a rotationally invariant parametrization of the basis is obtained by employing a potential anchored on neighboring atoms to ultimately construct a rotation matrix that turns a traditional atom centered basis set into a suitable adaptive basis set. The method is demonstrated using MD simulations of liquid water, where it is shown that minimal basis sets yield structural properties in fair agreement with basis set converged results, while reducing the computational cost in the best case by a factor of 200 and the required flops by 4 orders of magnitude. Already a very small training set yields satisfactory results as the variational nature of the method provides robustness.
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Affiliation(s)
- Ole Schütt
- Department of Materials , ETH Zürich , 8093 Zürich , Switzerland
| | - Joost VandeVondele
- Department of Materials , ETH Zürich , 8093 Zürich , Switzerland.,Swiss National Supercomputing Centre (CSCS) , 6900 Lugano , Switzerland
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