1
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Pandey P, Arandhara M, Houston PL, Qu C, Conte R, Bowman JM, Ramesh SG. Assessing Permutationally Invariant Polynomial and Symmetric Gradient Domain Machine Learning Potential Energy Surfaces for H 3O 2. J Phys Chem A 2024; 128:3212-3219. [PMID: 38624168 PMCID: PMC11056970 DOI: 10.1021/acs.jpca.4c01044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Revised: 03/15/2024] [Accepted: 03/20/2024] [Indexed: 04/17/2024]
Abstract
The singly hydrated hydroxide anion OH-(H2O) is of central importance to a detailed molecular understanding of water; therefore, there is strong motivation to develop a highly accurate potential to describe this anion. While this is a small molecule, it is necessary to have an extensive data set of energies and, if possible, forces to span several important stationary points. Here, we assess two machine-learned potentials, one using the symmetric gradient domain machine learning (sGDML) method and one based on permutationally invariant polynomials (PIPs). These are successors to a PIP potential energy surface (PES) reported in 2004. We describe the details of both fitting methods and then compare the two PESs with respect to precision, properties, and speed of evaluation. While the precision of the potentials is similar, the PIP PES is much faster to evaluate for energies and energies plus gradient than the sGDML one. Diffusion Monte Carlo calculations of the ground vibrational state, using both potentials, produce similar large anharmonic downshift of the zero-point energy compared to the harmonic approximation of the PIP and sGDML potentials. The computational time for these calculations using the sGDML PES is roughly 300 times greater than using the PIP one.
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Affiliation(s)
- Priyanka Pandey
- Department
of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Mrinal Arandhara
- Department
of Inorganic and Physical Chemistry, Indian
Institute of Science, Bangalore 560012, India
| | - Paul L. Houston
- Department
of Chemistry and Chemical Biology, Cornell
University, Ithaca, New York 14853, United States
- Department
of Chemistry and Biochemistry, Georgia Institute
of Technology, Atlanta, Georgia 30332, United States
| | - Chen Qu
- Independent
Researcher, Toronto, Ontario M9B0E3, Canada
| | - Riccardo Conte
- Dipartimento
di Chimica, Università degli Studi
di Milano, Milano 20133, Italy
| | - Joel M. Bowman
- Department
of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Sai G. Ramesh
- Department
of Inorganic and Physical Chemistry, Indian
Institute of Science, Bangalore 560012, India
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2
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Arandhara M, Ramesh SG. Nuclear Quantum Effects in Hydroxide Hydrate Along the H-Bond Bifurcation Pathway. J Phys Chem A 2024; 128:1600-1610. [PMID: 38393819 DOI: 10.1021/acs.jpca.3c08027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2024]
Abstract
Path integral (PI) simulations are used to explore nuclear quantum effects (NQEs) in hydroxide hydrate and its perdeuterated isotopomer along the H-bond bifurcation pathway. Toward this, a new potential energy surface using the symmetric gradient domain machine learning method with ab initio data at the CCSD(T)/aug-cc-pVTZ level is built. From PI umbrella sampling (US) simulations, free energy profiles along the bifurcation coordinate are explored as a function of temperature. At ambient temperature, the bifurcation barrier is increased upon inclusion of NQEs. At low temperatures in the deep tunneling regime, the barrier is strongly decreased and flattened. These trends are examined, and the role of the O-O distance is also investigated through two-dimensional US simulations.
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Affiliation(s)
- Mrinal Arandhara
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
| | - Sai G Ramesh
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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3
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Lederer J, Gastegger M, Schütt KT, Kampffmeyer M, Müller KR, Unke OT. Automatic identification of chemical moieties. Phys Chem Chem Phys 2023; 25:26370-26379. [PMID: 37750554 PMCID: PMC10548786 DOI: 10.1039/d3cp03845a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 08/18/2023] [Indexed: 09/27/2023]
Abstract
In recent years, the prediction of quantum mechanical observables with machine learning methods has become increasingly popular. Message-passing neural networks (MPNNs) solve this task by constructing atomic representations, from which the properties of interest are predicted. Here, we introduce a method to automatically identify chemical moieties (molecular building blocks) from such representations, enabling a variety of applications beyond property prediction, which otherwise rely on expert knowledge. The required representation can either be provided by a pretrained MPNN, or be learned from scratch using only structural information. Beyond the data-driven design of molecular fingerprints, the versatility of our approach is demonstrated by enabling the selection of representative entries in chemical databases, the automatic construction of coarse-grained force fields, as well as the identification of reaction coordinates.
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Affiliation(s)
- Jonas Lederer
- Berlin Institute of Technology (TU Berlin), 10587 Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Germany
| | - Michael Gastegger
- Berlin Institute of Technology (TU Berlin), 10587 Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Germany
| | - Kristof T Schütt
- Berlin Institute of Technology (TU Berlin), 10587 Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Germany
| | - Michael Kampffmeyer
- Department of Physics and Technology, UiT The Arctic University of Norway, 9019 Tromsø, Norway
| | - Klaus-Robert Müller
- Berlin Institute of Technology (TU Berlin), 10587 Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Germany
- Google Deepmind, Germany
- Department of Artificial Intelligence, Korea University, Seoul 136-713, Korea
- Max Planck Institut für Informatik, 66123 Saarbrücken, Germany
| | - Oliver T Unke
- Berlin Institute of Technology (TU Berlin), 10587 Berlin, Germany.
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Germany
- Google Deepmind, Germany
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4
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Gandolfi M, Ceotto M. Molecular Dynamics of Artificially Pair-Decoupled Systems: An Accurate Tool for Investigating the Importance of Intramolecular Couplings. J Chem Theory Comput 2023; 19:6093-6108. [PMID: 37698951 PMCID: PMC10536992 DOI: 10.1021/acs.jctc.3c00553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Indexed: 09/14/2023]
Abstract
We propose a numerical technique to accurately simulate the vibrations of organic molecules in the gas phase, when pairs of atoms (or, in general, groups of degrees of freedom) are artificially decoupled, so that their motion is instantaneously decorrelated. The numerical technique we have developed is a symplectic integration algorithm that never requires computation of the force but requires estimates of the Hessian matrix. The theory we present to support our technique postulates a pair-decoupling Hamiltonian function, which parametrically depends on a decoupling coefficient α ∈ [0, 1]. The closer α is to 0, the more decoupled the selected atoms. We test the correctness of our numerical method on small molecular systems, and we apply it to study the vibrational spectroscopic features of salicylic acid at the Density Functional Theory ab initio level on a fitted potential. Our pair-decoupled simulations of salicylic acid show that decoupling hydrogen-bonded atoms do not significantly influence the frequencies of stretching modes, but enhance enormously the out-of-plane wagging and twisting motions of the hydroxyl and carboxyl groups to the point that the carboxyl and hydroxyl groups may overcome high potential energy barriers and change the salicylic acid conformation after a short simulation time. In addition, we found that the acidity of salicylic acid is more influenced by the dynamical couplings of the proton of the carboxylic group with the carbon ring than with the hydroxyl group.
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Affiliation(s)
- Michele Gandolfi
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
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5
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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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Unke O, Chmiela S, Sauceda HE, Gastegger M, Poltavsky I, Schütt KT, Tkatchenko A, Müller KR. Machine Learning Force Fields. Chem Rev 2021; 121:10142-10186. [PMID: 33705118 PMCID: PMC8391964 DOI: 10.1021/acs.chemrev.0c01111] [Citation(s) in RCA: 371] [Impact Index Per Article: 123.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Indexed: 12/27/2022]
Abstract
In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.
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Affiliation(s)
- Oliver
T. Unke
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
- DFG
Cluster of Excellence “Unifying Systems in Catalysis”
(UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
| | - Stefan Chmiela
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
| | - Huziel E. Sauceda
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
- BASLEARN,
BASF-TU Joint Lab, Technische Universität
Berlin, 10587 Berlin, Germany
| | - Michael Gastegger
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
- DFG
Cluster of Excellence “Unifying Systems in Catalysis”
(UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
- BASLEARN,
BASF-TU Joint Lab, Technische Universität
Berlin, 10587 Berlin, Germany
| | - Igor Poltavsky
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Kristof T. Schütt
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
| | - Alexandre Tkatchenko
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Klaus-Robert Müller
- Machine
Learning Group, Technische Universität
Berlin, 10587 Berlin, Germany
- BIFOLD−Berlin
Institute for the Foundations of Learning and Data, Berlin, Germany
- Department
of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul 02841, Korea
- Max Planck
Institute for Informatics, Stuhlsatzenhausweg, 66123 Saarbrücken, Germany
- Google
Research, Brain Team, Berlin, Germany
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7
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Poltavsky I, Tkatchenko A. Machine Learning Force Fields: Recent Advances and Remaining Challenges. J Phys Chem Lett 2021; 12:6551-6564. [PMID: 34242032 DOI: 10.1021/acs.jpclett.1c01204] [Citation(s) in RCA: 41] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In chemistry and physics, machine learning (ML) methods promise transformative impacts by advancing modeling and improving our understanding of complex molecules and materials. Each ML method comprises a mathematically well-defined procedure, and an increasingly larger number of easy-to-use ML packages for modeling atomistic systems are becoming available. In this Perspective, we discuss the general aspects of ML techniques in the context of creating ML force fields. We describe common features of ML modeling and quantum-mechanical approximations, so-called global and local ML models, and the physical differences behind these two classes of approaches. Finally, we describe the recent developments and emerging directions in the field of ML-driven molecular modeling. This Perspective aims to inspire interdisciplinary collaborations crossing the borders between physical chemistry, chemical physics, computer science, and data science.
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Affiliation(s)
- Igor Poltavsky
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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8
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Sauceda HE, Vassilev-Galindo V, Chmiela S, Müller KR, Tkatchenko A. Dynamical strengthening of covalent and non-covalent molecular interactions by nuclear quantum effects at finite temperature. Nat Commun 2021; 12:442. [PMID: 33469007 PMCID: PMC7815839 DOI: 10.1038/s41467-020-20212-1] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 11/12/2020] [Indexed: 11/08/2022] Open
Abstract
Nuclear quantum effects (NQE) tend to generate delocalized molecular dynamics due to the inclusion of the zero point energy and its coupling with the anharmonicities in interatomic interactions. Here, we present evidence that NQE often enhance electronic interactions and, in turn, can result in dynamical molecular stabilization at finite temperature. The underlying physical mechanism promoted by NQE depends on the particular interaction under consideration. First, the effective reduction of interatomic distances between functional groups within a molecule can enhance the n → π* interaction by increasing the overlap between molecular orbitals or by strengthening electrostatic interactions between neighboring charge densities. Second, NQE can localize methyl rotors by temporarily changing molecular bond orders and leading to the emergence of localized transient rotor states. Third, for noncovalent van der Waals interactions the strengthening comes from the increase of the polarizability given the expanded average interatomic distances induced by NQE. The implications of these boosted interactions include counterintuitive hydroxyl-hydroxyl bonding, hindered methyl rotor dynamics, and molecular stiffening which generates smoother free-energy surfaces. Our findings yield new insights into the versatile role of nuclear quantum fluctuations in molecules and materials.
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Affiliation(s)
- Huziel E Sauceda
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg.
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany.
- BASLEARN, BASF-TU joint Lab, Technische Universität Berlin, 10587, Berlin, Germany.
| | - Valentin Vassilev-Galindo
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg
| | - Stefan Chmiela
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587, Berlin, Germany.
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Korea.
- Max Planck Institute for Informatics, Stuhlsatzenhausweg, 66123, Saarbrücken, Germany.
- Google Research, Brain team, Berlin, Germany.
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg.
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9
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Sauceda HE, Gastegger M, Chmiela S, Müller KR, Tkatchenko A. Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields. J Chem Phys 2020; 153:124109. [DOI: 10.1063/5.0023005] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Huziel E. Sauceda
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- BASLEARN, BASF-TU Joint Lab, Technische Universität Berlin, 10587 Berlin, Germany
| | - Michael Gastegger
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- BASLEARN, BASF-TU Joint Lab, Technische Universität Berlin, 10587 Berlin, Germany
- DFG Cluster of Excellence “Unifying Systems in Catalysis” (UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
| | - Stefan Chmiela
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul 136-713, South Korea
- Max Planck Institute for Informatics, Stuhlsatzenhausweg, 66123 Saarbrücken, Germany
- Google Research, Brain Team, Berlin, Germany
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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