1
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Liu Y, Guo H. A Gaussian Process Based Δ-Machine Learning Approach to Reactive Potential Energy Surfaces. J Phys Chem A 2023; 127:8765-8772. [PMID: 37815868 DOI: 10.1021/acs.jpca.3c05318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/12/2023]
Abstract
The Gaussian process (GP) is an efficient nonparametric machine learning (ML) method. A distinct advantage of the GP is its ability to provide an estimate of statistical uncertainties. This is particularly useful in constructing high-dimensional potential energy surfaces (PESs) from ab initio data as it offers an optimal way to add new geometries to reduce the overall error. In this work, GP is employed in the context of Δ-machine learning (Δ-ML), in which a correction PES to an inaccurate low-level PES is constructed using a small number of high-level ab initio calculations. This new method is tested in three prototypical reactive systems, namely, the H + H2 → H + H2, OH + H2 → H2O + H, and H + CH4 → H2 + CH3 reactions. The results show that the GP-based Δ-ML approach is more efficient than its direct application in constructing high-level PESs. We also compare the new method to a previously proposed neural-network-based Δ-ML approach [Liu and Li J. Phys. Chem. Lett. 2022, 13, 4729-4738]. The results indicate that the two Δ-ML methods have comparable efficiencies in constructing accurate PESs.
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Affiliation(s)
- Yang Liu
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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2
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Liu X, Wang W, Pérez-Ríos J. Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer. J Chem Phys 2023; 159:144103. [PMID: 37811831 DOI: 10.1063/5.0169080] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2023] [Accepted: 09/20/2023] [Indexed: 10/10/2023] Open
Abstract
In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on ab initio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated ab initio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.
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Affiliation(s)
- Xiangyue Liu
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Weiqi Wang
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Jesús Pérez-Ríos
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
- Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794-3800, USA
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3
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Schmitz G, Schnieder B. Adaptive regularized Gaussian process regression for application in the context of hydrogen adsorption on graphene sheets. J Comput Chem 2023; 44:732-744. [PMID: 36382688 DOI: 10.1002/jcc.27035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 09/21/2022] [Accepted: 09/28/2022] [Indexed: 11/17/2022]
Abstract
We present a Gaussian process regression (GPR) scheme with an adaptive regularization scheme applied to the QM7 and QM9 test set, several protonated water clusters and specifically to the problem of atomic hydrogen adsorption on graphene sheets. For the last system our goal is to achieve good predictive accuracy with only a few training points. Therefore, we assess for these systems a self-correcting multilayer GPR model, in which the prediction is corrected by a chain of additional GPR models. In our adaptive regularization scheme, we impose no noise on the training data, but use an approach based on the data itself to account for its impurity. The strength of this strategy is that the data points are treated differently based on their importance and that the regularization can still be controlled by a single parameter. We assess how the accuracy of the prediction depends on this parameter. We can show that the new regularization scheme as well as the multilayer approach results in more robust predictors. Furthermore, we demonstrate that the predictor can be in good agreement with the density-functional theory results.
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Affiliation(s)
- Gunnar Schmitz
- Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
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4
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The adiabatic potential energy surfaces and photodissociation mechanisms for highly excited states of H 2O. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2111241] [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]
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5
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Yang Z, Chen H, Chen M. Representing Globally Accurate Reactive Potential Energy Surfaces with Complex Topography by Combining Gaussian Process Regression and Neural Network. Phys Chem Chem Phys 2022; 24:12827-12836. [DOI: 10.1039/d2cp00719c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
There has been increasing attention in using machine learning technologies, such as neural network (NN) and Gaussian process regression (GPR), to model multidimensional potential energy surfaces (PESs). NN PES features...
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6
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Lu D, Chen J, Guo H, Li J. Vibrational energy pooling via collisions between asymmetric stretching excited CO 2: a quasi-classical trajectory study on an accurate full-dimensional potential energy surface. Phys Chem Chem Phys 2021; 23:24165-24174. [PMID: 34671798 DOI: 10.1039/d1cp03687d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In low temperature plasmas, energy transfer between asymmetric stretching excited CO2 molecules can be highly efficient, which leads to further excitation (and de-excitation) of the CO2 molecules: CO2(vas) + CO2(vas) → CO2(vas + 1) + CO2(vas - 1). Through such a vibrational ladder climbing mechanism, CO2 can be activated and eventually dissociates. To gain mechanistic insight of such processes, a full-dimensional accurate potential energy surface (PES) for the CO2 + CO2 system is developed using the permutational invariant polynomial-neural network method based on CCSD(T)-F12a/AVTZ energies at about 39 000 geometries. This PES is used in quasi-classical trajectory (QCT) studies of the vibrational energy transfer between CO2 molecules excited in the asymmetric stretching mode. A machine learning algorithm is used to determine state-specific rate coefficients for the vibrational transfer processes from a limited data set. In addition to the CO2(vas + 1) + CO2(vas - 1) channel, the QCT simulations revealed significant contributions from the CO2(vas + 2,3) + CO2(vas - 2,3) channels, particularly at low collision energies/temperatures. These multi-vibrational-quantum processes are attributed to enhanced energy flow in the collisional complex formed by enhanced dipole-dipole interaction between asymmetric stretching excited CO2 molecules.
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Affiliation(s)
- Dandan Lu
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Theoretical and Computational Chemistry, Chongqing University, Chongqing 401331, China. .,Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico, 87131, USA
| | - Jun Chen
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, China
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico, 87131, USA
| | - Jun Li
- School of Chemistry and Chemical Engineering & Chongqing Key Laboratory of Theoretical and Computational Chemistry, Chongqing University, Chongqing 401331, China.
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7
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Morrow Z, Kwon HY, Kelley CT, Jakubikova E. Reduced-dimensional surface hopping with offline-online computations. Phys Chem Chem Phys 2021; 23:19547-19557. [PMID: 34524324 DOI: 10.1039/d1cp03446d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm known as surface hopping. However, the computational expense of integrating the geometry on a full-dimensional PES and computing the required couplings can quickly become prohibitive as the number of atoms increases. In this work, we describe a method for surface hopping that uses only important reaction coordinates, performs all expensive evaluations of the true PESs and couplings only once before simulating dynamics (offline), and then queries the stored values during the surface hopping simulation (online). Our Python codes are freely available on GitHub. Using photodissociation of azomethane as a test case, this method is able to reproduce experimental results that have thus far eluded ab initio surface hopping studies.
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Affiliation(s)
- Zachary Morrow
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.
| | - Hyuk-Yong Kwon
- Department of Chemistry, North Carolina State University, Box 8204, Raleigh, NC, 27695-8204, USA.
| | - C T Kelley
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.
| | - Elena Jakubikova
- Department of Chemistry, North Carolina State University, Box 8204, Raleigh, NC, 27695-8204, USA.
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8
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Morrow Z, Kwon HY, Kelley CT, Jakubikova E. Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation. J Chem Theory Comput 2021; 17:5673-5683. [PMID: 34351740 DOI: 10.1021/acs.jctc.1c00569] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.
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Affiliation(s)
- Zachary Morrow
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Hyuk-Yong Kwon
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - C T Kelley
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Elena Jakubikova
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States
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9
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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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10
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Deng Z, Tutunnikov I, Averbukh IS, Thachuk M, Krems RV. Bayesian optimization for inverse problems in time-dependent quantum dynamics. J Chem Phys 2020; 153:164111. [DOI: 10.1063/5.0015896] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Z. Deng
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - I. Tutunnikov
- AMOS and Department of Chemical and Biological Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
| | - I. Sh. Averbukh
- AMOS and Department of Chemical and Biological Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
| | - M. Thachuk
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - R. V. Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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11
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Sugisawa H, Ida T, Krems RV. Gaussian process model of 51-dimensional potential energy surface for protonated imidazole dimer. J Chem Phys 2020; 153:114101. [DOI: 10.1063/5.0023492] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Hiroki Sugisawa
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Division of Material Chemistry, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| | - Tomonori Ida
- Division of Material Chemistry, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| | - R. V. Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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12
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Schmitz G, Klinting EL, Christiansen O. A Gaussian process regression adaptive density guided approach for potential energy surface construction. J Chem Phys 2020; 153:064105. [DOI: 10.1063/5.0015344] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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13
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Venturi S, Jaffe RL, Panesi M. Bayesian Machine Learning Approach to the Quantification of Uncertainties on Ab Initio Potential Energy Surfaces. J Phys Chem A 2020; 124:5129-5146. [DOI: 10.1021/acs.jpca.0c02395] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- S. Venturi
- University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - R. L. Jaffe
- NASA Ames Research Center, Moffett Field, California 94035-1000, United States
| | - M. Panesi
- University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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14
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Tschöpe M, Feldmaier M, Main J, Hernandez R. Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems. Phys Rev E 2020; 101:022219. [PMID: 32168686 DOI: 10.1103/physreve.101.022219] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2019] [Accepted: 01/29/2020] [Indexed: 05/21/2023]
Abstract
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition-state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on transition state theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.
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Affiliation(s)
- Martin Tschöpe
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Feldmaier
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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15
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Morrow Z, Liu C, Kelley CT, Jakubikova E. Approximating Periodic Potential Energy Surfaces with Sparse Trigonometric Interpolation. J Phys Chem B 2019; 123:9677-9684. [PMID: 31631663 DOI: 10.1021/acs.jpcb.9b08210] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in computational chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as local minima, maxima, and transition states. Construction of full-dimensional PESs for molecules with more than 10 atoms is computationally expensive and often not feasible. Previous work in our group used sparse interpolation with polynomial basis functions to construct a surrogate reduced-dimensional PESs along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. However, polynomial interpolation does not preserve the periodicity of the PES gradient with respect to angular components of geometry, such as torsion angles, which can lead to nonphysical phenomena. In this work, we construct a surrogate PES using trigonometric basis functions, for a system where the selected reaction coordinates all correspond to the torsion angles, resulting in a periodically repeating PES. We find that a trigonometric interpolation basis not only guarantees periodicity of the gradient but also results in slightly lower approximation error than polynomial interpolation.
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Affiliation(s)
- Zachary Morrow
- Department of Mathematics , North Carolina State University , Raleigh , North Carolina 27695 , United States
| | - Chang Liu
- Department of Chemistry , North Carolina State University , Raleigh , North Carolina 27695 , United States
| | - C T Kelley
- Department of Mathematics , North Carolina State University , Raleigh , North Carolina 27695 , United States
| | - Elena Jakubikova
- Department of Chemistry , North Carolina State University , Raleigh , North Carolina 27695 , United States
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16
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Schmitz G, Godtliebsen IH, Christiansen O. Machine learning for potential energy surfaces: An extensive database and assessment of methods. J Chem Phys 2019; 150:244113. [DOI: 10.1063/1.5100141] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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17
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Liu C, Kelley CT, Jakubikova E. Molecular Dynamics Simulations on Relaxed Reduced-Dimensional Potential Energy Surfaces. J Phys Chem A 2019; 123:4543-4554. [PMID: 31038956 DOI: 10.1021/acs.jpca.9b02298] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Molecular dynamics (MD) simulations with full-dimensional potential energy surfaces (PESs) obtained from high-level ab initio calculations are frequently used to model reaction dynamics of small molecules (i.e., molecules with up to 10 atoms). Construction of full-dimensional PESs for larger molecules is, however, not feasible since the number of ab initio calculations required grows rapidly with the increase of dimension. Only a small number of coordinates are often essential for describing the reactivity of even very large systems, and reduced-dimensional PESs with these coordinates can be built for reaction dynamics studies. While analytical methods based on transition-state theory framework are well established for analyzing the reduced-dimensional PESs, MD simulation algorithms capable of generating trajectories on such surfaces are more rare. In this work, we present a new MD implementation that utilizes the relaxed reduced-dimensional PES for standard microcanonical (NVE) and canonical (NVT) MD simulations. The method is applied to the pyramidal inversion of a NH3 molecule. The results from the MD simulations on a reduced, three-dimensional PES are validated against the ab initio MD simulations, as well as MD simulations on full-dimensional PES and experimental data.
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18
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Brorsen KR. Reproducing global potential energy surfaces with continuous-filter convolutional neural networks. J Chem Phys 2019; 150:204104. [DOI: 10.1063/1.5093908] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Kurt R. Brorsen
- Department of Chemistry, University of Missouri, Columbia, Missouri 65203, USA
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19
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Schmitz G, Artiukhin DG, Christiansen O. Approximate high mode coupling potentials using Gaussian process regression and adaptive density guided sampling. J Chem Phys 2019; 150:131102. [DOI: 10.1063/1.5092228] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | | | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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20
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Feldmaier M, Schraft P, Bardakcioglu R, Reiff J, Lober M, Tschöpe M, Junginger A, Main J, Bartsch T, Hernandez R. Invariant Manifolds and Rate Constants in Driven Chemical Reactions. J Phys Chem B 2019; 123:2070-2086. [DOI: 10.1021/acs.jpcb.8b10541] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Matthias Feldmaier
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Philippe Schraft
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Robin Bardakcioglu
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Johannes Reiff
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Melissa Lober
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Martin Tschöpe
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andrej Junginger
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Thomas Bartsch
- Centre for Nonlinear Mathematics and Applications, Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
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21
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Abstract
This article discusses applications of Bayesian machine learning for quantum molecular dynamics.
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Affiliation(s)
- R. V. Krems
- Department of Chemistry
- University of British Columbia
- Vancouver
- Canada
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22
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Yang Z, Wang S, Yuan J, Chen M. Neural network potential energy surface and dynamical isotope effects for the N+(3P) + H2 → NH+ + H reaction. Phys Chem Chem Phys 2019; 21:22203-22214. [DOI: 10.1039/c9cp02798j] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Dynamical isotope effects are calculated for the N+(3P) + H2 → NH+ + H reaction on a new neural network potential energy surface.
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Affiliation(s)
- Zijiang Yang
- Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams (Ministry of Education)
- School of Physics
- Dalian University of Technology
- Dalian 116024
- P. R. China
| | - Shufen Wang
- Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams (Ministry of Education)
- School of Physics
- Dalian University of Technology
- Dalian 116024
- P. R. China
| | - Jiuchuang Yuan
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Science
- Dalian 116023
- P. R. China
| | - Maodu Chen
- Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams (Ministry of Education)
- School of Physics
- Dalian University of Technology
- Dalian 116024
- P. R. China
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23
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Wiens AE, Copan AV, Schaefer HF. Multi-fidelity Gaussian process modeling for chemical energy surfaces. Chem Phys Lett 2019. [DOI: 10.1016/j.cpletx.2019.100022] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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24
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Schmitz G, Christiansen O. Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation. J Chem Phys 2018; 148:241704. [DOI: 10.1063/1.5009347] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gunnar Schmitz
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
| | - Ove Christiansen
- Department of Chemistry, Aarhus Universitet, DK-8000 Aarhus, Denmark
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25
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Kamath A, Vargas-Hernández RA, Krems RV, Carrington T, Manzhos S. Neural networks vs Gaussian process regression for representing potential energy surfaces: A comparative study of fit quality and vibrational spectrum accuracy. J Chem Phys 2018; 148:241702. [DOI: 10.1063/1.5003074] [Citation(s) in RCA: 108] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Aditya Kamath
- Department of Mechanical Engineering, National University of Singapore, Block EA, #07-08, 9 Engineering Drive 1, Singapore 117576
| | | | - Roman V. Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Chernoff Hall, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
| | - Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore, Block EA, #07-08, 9 Engineering Drive 1, Singapore 117576
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26
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Qu C, Yu Q, Van Hoozen BL, Bowman JM, Vargas-Hernández RA. Assessing Gaussian Process Regression and Permutationally Invariant Polynomial Approaches To Represent High-Dimensional Potential Energy Surfaces. J Chem Theory Comput 2018; 14:3381-3396. [DOI: 10.1021/acs.jctc.8b00298] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Chen Qu
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Qi Yu
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Brian L. Van Hoozen
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Joel M. Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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27
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Schraft P, Junginger A, Feldmaier M, Bardakcioglu R, Main J, Wunner G, Hernandez R. Neural network approach to time-dependent dividing surfaces in classical reaction dynamics. Phys Rev E 2018; 97:042309. [PMID: 29758767 DOI: 10.1103/physreve.97.042309] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Indexed: 05/21/2023]
Abstract
In a dynamical system, the transition between reactants and products is typically mediated by an energy barrier whose properties determine the corresponding pathways and rates. The latter is the flux through a dividing surface (DS) between the two corresponding regions, and it is exact only if it is free of recrossings. For time-independent barriers, the DS can be attached to the top of the corresponding saddle point of the potential energy surface, and in time-dependent systems, the DS is a moving object. The precise determination of these direct reaction rates, e.g., using transition state theory, requires the actual construction of a DS for a given saddle geometry, which is in general a demanding methodical and computational task, especially in high-dimensional systems. In this paper, we demonstrate how such time-dependent, global, and recrossing-free DSs can be constructed using neural networks. In our approach, the neural network uses the bath coordinates and time as input, and it is trained in a way that its output provides the position of the DS along the reaction coordinate. An advantage of this procedure is that, once the neural network is trained, the complete information about the dynamical phase space separation is stored in the network's parameters, and a precise distinction between reactants and products can be made for all possible system configurations, all times, and with little computational effort. We demonstrate this general method for two- and three-dimensional systems and explain its straightforward extension to even more degrees of freedom.
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Affiliation(s)
- Philippe Schraft
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andrej Junginger
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Feldmaier
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Robin Bardakcioglu
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Günter Wunner
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
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28
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Zhang YL, Zhou XY, Jiang B. Accelerating the Construction of Neural Network Potential Energy Surfaces: A Fast Hybrid Training Algorithm. CHINESE J CHEM PHYS 2017. [DOI: 10.1063/1674-0068/30/cjcp1711212] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Yao-long Zhang
- Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xue-yao Zhou
- Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
| | - Bin Jiang
- Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China
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29
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Bertsch GF, Bingham D. Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap. PHYSICAL REVIEW LETTERS 2017; 119:252501. [PMID: 29303311 DOI: 10.1103/physrevlett.119.252501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 06/07/2023]
Abstract
We propose using the frequency-domain bootstrap (FDB) to estimate errors of modeling parameters when the modeling error is itself a major source of uncertainty. Unlike the usual bootstrap or the simple χ^{2} analysis, the FDB can take into account correlations between errors. It is also very fast compared to the Gaussian process Bayesian estimate as often implemented for computer model calibration. The method is illustrated with a simple example, the liquid drop model of nuclear binding energies. We find that the FDB gives a more conservative estimate of the uncertainty in liquid drop parameters than the χ^{2} method, and is in fair accord with more empirical estimates. For the nuclear physics application, there are no apparent obstacles to apply the method to the more accurate and detailed models based on density-functional theory.
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Affiliation(s)
- G F Bertsch
- Department of Physics and Institute of Nuclear Theory, University of Washington, Box 351560, Seattle, Washington 98195, USA
| | - Derek Bingham
- Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V3B 6X5, Canada
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30
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Guan Y, Yang S, Zhang DH. Construction of reactive potential energy surfaces with Gaussian process regression: active data selection. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1407460] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Yafu Guan
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, People's Republic of China
- University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
| | - Shuo Yang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, People's Republic of China
- University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
| | - Dong H. Zhang
- University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
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31
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Bohn JL, Rey AM, Ye J. Cold molecules: Progress in quantum engineering of chemistry and quantum matter. Science 2017; 357:1002-1010. [PMID: 28883071 DOI: 10.1126/science.aam6299] [Citation(s) in RCA: 135] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Cooling atoms to ultralow temperatures has produced a wealth of opportunities in fundamental physics, precision metrology, and quantum science. The more recent application of sophisticated cooling techniques to molecules, which has been more challenging to implement owing to the complexity of molecular structures, has now opened the door to the longstanding goal of precisely controlling molecular internal and external degrees of freedom and the resulting interaction processes. This line of research can leverage fundamental insights into how molecules interact and evolve to enable the control of reaction chemistry and the design and realization of a range of advanced quantum materials.
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Affiliation(s)
- John L Bohn
- JILA, National Institute of Standards and Technology and University of Colorado Boulder, Boulder, CO 80309-0440, USA.
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology and University of Colorado Boulder, Boulder, CO 80309-0440, USA.
| | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado Boulder, Boulder, CO 80309-0440, USA.
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32
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Godsi O, Corem G, Alkoby Y, Cantin JT, Krems RV, Somers MF, Meyer J, Kroes GJ, Maniv T, Alexandrowicz G. A general method for controlling and resolving rotational orientation of molecules in molecule-surface collisions. Nat Commun 2017; 8:15357. [PMID: 28480890 PMCID: PMC5424257 DOI: 10.1038/ncomms15357] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2016] [Accepted: 03/14/2017] [Indexed: 11/23/2022] Open
Abstract
The outcome of molecule–surface collisions can be modified by pre-aligning the molecule; however, experiments accomplishing this are rare because of the difficulty of preparing molecules in aligned quantum states. Here we present a general solution to this problem based on magnetic manipulation of the rotational magnetic moment of the incident molecule. We apply the technique to the scattering of H2 from flat and stepped copper surfaces. We demonstrate control of the molecule's initial quantum state, allowing a direct comparison of differences in the stereodynamic scattering from the two surfaces. Our results show that a stepped surface exhibits a much larger dependence of the corrugation of the interaction on the alignment of the molecule than the low-index surface. We also demonstrate an extension of the technique that transforms the set-up into an interferometer, which is sensitive to molecular quantum states both before and after the scattering event. The rotational orientation of a molecule plays a fundamental role in molecule-surface collisions, yet is difficult to study. Here, the authors present a general approach for controlling and resolving molecular rotational orientation and apply it to study H2 scattering from flat and stepped copper surfaces.
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Affiliation(s)
- Oded Godsi
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
| | - Gefen Corem
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
| | - Yosef Alkoby
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
| | - Joshua T Cantin
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
| | - Roman V Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
| | - Mark F Somers
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, PO Box 9502, 2300 RA Leiden, The Netherlands
| | - Jörg Meyer
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, PO Box 9502, 2300 RA Leiden, The Netherlands
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, PO Box 9502, 2300 RA Leiden, The Netherlands
| | - Tsofar Maniv
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
| | - Gil Alexandrowicz
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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33
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Kolb B, Marshall P, Zhao B, Jiang B, Guo H. Representing Global Reactive Potential Energy Surfaces Using Gaussian Processes. J Phys Chem A 2017; 121:2552-2557. [DOI: 10.1021/acs.jpca.7b01182] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Brian Kolb
- Department
of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
- Department
of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Paul Marshall
- Department
of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Bin Zhao
- Department
of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Bin Jiang
- Department
of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hua Guo
- Department
of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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34
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Kolb B, Luo X, Zhou X, Jiang B, Guo H. High-Dimensional Atomistic Neural Network Potentials for Molecule-Surface Interactions: HCl Scattering from Au(111). J Phys Chem Lett 2017; 8:666-672. [PMID: 28102689 DOI: 10.1021/acs.jpclett.6b02994] [Citation(s) in RCA: 73] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Ab initio molecular dynamics (AIMD) simulations of molecule-surface scattering allow first-principles characterization of the dynamics. However, the large number of density functional theory calculations along the trajectories is very costly, limiting simulations of long-time events and giving rise to poor statistics. To avoid this computational bottleneck, we report here the development of a high-dimensional molecule-surface interaction potential energy surface (PES) with movable surface atoms, using a machine learning approach. With 60 degrees of freedom, this PES allows energy transfer between the energetic impinging molecule and thermal surface atoms. Classical trajectory calculations for the scattering of DCl from Au(111) on this PES are found to agree well with AIMD simulations, with ∼105-fold acceleration. Scattering of HCl from Au(111) is further investigated and compared with available experimental results.
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Affiliation(s)
- Brian Kolb
- Department of Chemistry and Chemical Biology, University of New Mexico , Albuquerque, New Mexico 87131, United States
- Department of Mechanical Engineering, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Xuan Luo
- Department of Chemical Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Xueyao Zhou
- Department of Chemical Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Bin Jiang
- Department of Chemical Physics, University of Science and Technology of China , Hefei, Anhui 230026, China
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico , Albuquerque, New Mexico 87131, United States
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35
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Rate Constants for Fine-structure Excitations in O–H Collisions with Error Bars Obtained by Machine Learning. ACTA ACUST UNITED AC 2017. [DOI: 10.3847/1538-4357/835/2/255] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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36
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Balakrishnan N. Perspective: Ultracold molecules and the dawn of cold controlled chemistry. J Chem Phys 2016; 145:150901. [DOI: 10.1063/1.4964096] [Citation(s) in RCA: 157] [Impact Index Per Article: 19.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- N. Balakrishnan
- Department of Chemistry, University of Nevada, Las Vegas, Nevada 89154, USA
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37
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Jiang B, Li J, Guo H. Potential energy surfaces from high fidelity fitting ofab initiopoints: the permutation invariant polynomial - neural network approach. INT REV PHYS CHEM 2016. [DOI: 10.1080/0144235x.2016.1200347] [Citation(s) in RCA: 210] [Impact Index Per Article: 26.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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38
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Loreau J, van der Avoird A. Scattering of NH3 and ND3 with rare gas atoms at low collision energy. J Chem Phys 2015; 143:184303. [DOI: 10.1063/1.4935259] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. Loreau
- Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles (ULB) CP 160/09, 50 av. F.D. Roosevelt, 1050 Brussels, Belgium
| | - A. van der Avoird
- Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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39
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Cui J, Li Z, Krems RV. Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile. J Chem Phys 2015; 143:154101. [DOI: 10.1063/1.4933137] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jie Cui
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Zhiying Li
- Department of Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Roman V. Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
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