1
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Miao Z, Zhang X, Zhang Y, Wang L, Meng Q. Chemistry-Informed Generative Model for Classical Dynamics Simulations. J Phys Chem Lett 2024; 15:532-539. [PMID: 38194494 DOI: 10.1021/acs.jpclett.3c03114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
In this work, a chemistry-informed generative model was proposed, leading to the chemistry-informed generative adversarial network (CI-GAN) approach. To easily build the input database for complex molecular systems, an image-input algorithm is also implemented, leading to the capability to directly recognize the molecular image. Extensive test calculations and analysis on typical examples, H + H2, OH + HO2, and H2O/TiO2(110), find that the present CI-GAN approach generates distributions of geometry and energy. Calculations on the above examples show that the present CI-GAN approach is able to generate 50%-80% meaningful results among all of the generated data with chemistry constraints. Thus, it has the potential capability to predict classical dynamics simulations as well as ab initio calculations avoiding expensive calculations. These results and the power of CI-GANs in generating ab initio energies and MD trajectories are deeply discussed.
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Affiliation(s)
- Zekai Miao
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China
| | - Xingyu Zhang
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China
| | - Yuyuan Zhang
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China
| | - Lemei Wang
- Ministry-of-Education Engineering Center for Embedded System Integration, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China
| | - Qingyong Meng
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China
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2
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Wang W, Liu X, Pérez-Ríos J. AlF-AlF Reaction Dynamics between 200 K and 1000 K: Reaction Mechanisms and Intermediate Complex Characterization. Molecules 2023; 29:222. [PMID: 38202805 PMCID: PMC10780286 DOI: 10.3390/molecules29010222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Revised: 12/20/2023] [Accepted: 12/22/2023] [Indexed: 01/12/2024] Open
Abstract
AlF is a relevant molecule in astrochemistry as a tracer of F-bearing molecules. Additionally, AlF presents diagonal Franck-Condon factors and can be created very efficiently in the lab, which makes it a prototypical molecular for laser cooling. However, very little is known about the reaction dynamics of AlF. In this work, we report on the reaction dynamics of AlF-AlF between 200 and 1000 K using ab initio molecular dynamics and a highly efficient active learning approach for the potential energy surface, including all degrees of freedom. As a result, we identify the main reaction mechanisms and the lifetime of the intermediate complex AlF-AlF relevant to astrochemistry environments and regions in buffer gas cells.
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Affiliation(s)
- Weiqi Wang
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany; (W.W.); (X.L.)
| | - Xiangyue Liu
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany; (W.W.); (X.L.)
| | - Jesús Pérez-Ríos
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
- Institute for Advanced Computational Science, Stony Brook University, Stony Brook, NY 11794-3800, USA
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3
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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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4
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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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5
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Yang Z, Chen H, Buren B, Chen M. Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies. Molecules 2023; 28:molecules28072938. [PMID: 37049701 PMCID: PMC10096016 DOI: 10.3390/molecules28072938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Revised: 03/22/2023] [Accepted: 03/23/2023] [Indexed: 03/29/2023] Open
Abstract
The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.
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6
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Manzhos S, Ihara M. The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces. J Chem Phys 2023; 158:044111. [PMID: 36725493 DOI: 10.1063/5.0136156] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Kernel-based methods, including Gaussian process regression (GPR) and generally kernel ridge regression, have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family, such as Gaussian-like kernels (basis functions), are often used which allow imparting to them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry. We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.
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Affiliation(s)
- Sergei Manzhos
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Manabu Ihara
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
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7
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Töpfer K, Upadhyay M, Meuwly M. Quantitative molecular simulations. Phys Chem Chem Phys 2022; 24:12767-12786. [PMID: 35593769 PMCID: PMC9158373 DOI: 10.1039/d2cp01211a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2022] [Accepted: 04/30/2022] [Indexed: 11/21/2022]
Abstract
All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.
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Affiliation(s)
- Kai Töpfer
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.
| | - Meenu Upadhyay
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.
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8
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Dai J, Krems RV. Quantum Gaussian process model of potential energy surface for a polyatomic molecule. J Chem Phys 2022; 156:184802. [PMID: 35568545 DOI: 10.1063/5.0088821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.
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Affiliation(s)
- J Dai
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, CanadaStewart Blusson Quantum Matter Institute, Vancouver, British Columbia V6T 1Z4, Canada
| | - R V Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, CanadaStewart Blusson Quantum Matter Institute, Vancouver, British Columbia V6T 1Z4, Canada
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9
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Meuwly M. Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─ Quo Vadis?. J Phys Chem B 2022; 126:2155-2167. [PMID: 35286087 DOI: 10.1021/acs.jpcb.2c00212] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.
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Affiliation(s)
- Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland
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10
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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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11
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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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12
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Asnaashari K, Krems RV. Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/ac3845] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be improved either by increasing the number of training points or by improving the models. In order to build accurate models based on expensive ab initio calculations, much of recent work has focused on the latter. In particular, it has been shown that gradient domain machine learning (GDML) models produce accurate results for high-dimensional molecular systems with a small number of ab initio calculations. The present work extends GDML to models with composite kernels built to maximize inference from a small number of molecular geometries. We illustrate that GDML models can be improved by increasing the complexity of underlying kernels through a greedy search algorithm using Bayesian information criterion as the model selection metric. We show that this requires including anisotropy into kernel functions and produces models with significantly smaller generalization errors. The results are presented for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with composite kernels trained by forces at 1000 randomly sampled molecular geometries produces a global 57-dimensional PES with the mean absolute accuracy 0.177 kcal mol−1 (61.9 cm−1) and FFs with the mean absolute error 0.457 kcal mol−1 Å−1.
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13
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Saleh Y, Sanjay V, Iske A, Yachmenev A, Küpper J. Active learning of potential-energy surfaces of weakly bound complexes with regression-tree ensembles. J Chem Phys 2021; 155:144109. [PMID: 34654290 DOI: 10.1063/5.0057051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Several pool-based active learning (AL) algorithms were employed to model potential-energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be obtained by sampling molecular structures corresponding to large uncertainties in their predictions while at the same time not deviating much from the true distribution of the data. To model PESs in an AL framework, we propose to use a regression version of stochastic query by forest, a hybrid method that samples points corresponding to large uncertainties while avoiding collecting too many points from sparse regions of space. The algorithm is implemented with decision trees that come with relatively small computational costs. We empirically show that this algorithm requires around half the data to converge to the same accuracy in comparison to the uncertainty-based query-by-committee algorithm. Moreover, the algorithm is fully automatic and does not require any prior knowledge of the PES. Simulations on a 6D PES of pyrrole(H2O) show that <15 000 configurations are enough to build a PES with a generalization error of 16 cm-1, whereas the final model with around 50 000 configurations has a generalization error of 11 cm-1.
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Affiliation(s)
- Yahya Saleh
- Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Vishnu Sanjay
- Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Armin Iske
- Department of Mathematics, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
| | - Andrey Yachmenev
- Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
| | - Jochen Küpper
- Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
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14
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Liu Q, Liu L, An F, Huang J, Zhou Y, Xie D. A full-dimensional ab initio intermolecular potential energy surface and rovibrational spectra for OC-HF and OC-DF. J Chem Phys 2021; 155:084302. [PMID: 34470366 DOI: 10.1063/5.0061291] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a full-dimensional ab initio intermolecular potential energy surface (IPES) for the OC-HF van der Waals complex. 3167 ab initio points were computed at the frozen-core (FC) explicitly correlated coupled cluster [FC-CCSD(T)-F12b] level, with the augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. Basis set superposition error correction was also considered by the full counterpoise procedure. Gaussian process regression (GPR) was used to map out the potential energy surface, while a multipole expansion method was employed to smooth the ab initio noise of intermolecular potential in the long range. The global minimum of -1248.364 cm-1 was located at the linear configuration with the C atom pointing toward the H atom of the HF molecule. In addition, a local minimum of -602.026 cm-1 was found at another linear configuration with the O atom pointing toward the H atom of the HF molecule. The eigenstates were calculated on the vibrational averaged four-dimensional IPESs with the mixed radial discrete variable representation/angular finite basis representation method and Lanczos propagation algorithm. The dissociation energy D0 was calculated to be 701.827 cm-1, well reproducing the experimental value of 732 ± 2 cm-1. The dipole moment surfaces were also fitted by GPR from 3132 ab initio points calculated using the coupled cluster method [CCSD(T)] with AVTZ basis set plus bond functions. The frequencies and relative line intensities of rovibrational transitions in the HF (DF) and CO stretching bands were further calculated and compared well with the experimental results. These results indicate the high fidelity of the new IPES.
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Affiliation(s)
- Qiong Liu
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Lu Liu
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Feng An
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Jing Huang
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Yanzi Zhou
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
| | - Daiqian Xie
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China
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15
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Westermayr J, Marquetand P. Machine Learning for Electronically Excited States of Molecules. Chem Rev 2021; 121:9873-9926. [PMID: 33211478 PMCID: PMC8391943 DOI: 10.1021/acs.chemrev.0c00749] [Citation(s) in RCA: 162] [Impact Index Per Article: 54.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Indexed: 12/11/2022]
Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data
Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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16
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Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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17
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Zaverkin V, Kästner J. Exploration of transferable and uniformly accurate neural network interatomic potentials using optimal experimental design. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abe294] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Abstract
Machine learning has been proven to have the potential to bridge the gap between the accuracy of ab initio methods and the efficiency of empirical force fields. Neural networks are one of the most frequently used approaches to construct high-dimensional potential energy surfaces. Unfortunately, they lack an inherent uncertainty estimation which is necessary for efficient and automated sampling through the chemical and conformational space to find extrapolative configurations. The identification of the latter is needed for the construction of transferable and uniformly accurate potential energy surfaces. In this paper, we propose an active learning approach that uses the estimated model’s output variance derived in the framework of the optimal experimental design. This method has several advantages compared to the established active learning approaches, e.g. Query-by-Committee, Monte Carlo dropout, feature and latent distances, in terms of the predictive power and computational efficiency. We have shown that the application of the proposed active learning scheme leads to transferable and uniformly accurate potential energy surfaces constructed using only a small fraction of data points. Additionally, it is possible to define a natural threshold value for the proposed uncertainty metric which offers the possibility to generate highly informative training data on-the-fly.
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18
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Lin Q, Zhang L, Zhang Y, Jiang B. Searching Configurations in Uncertainty Space: Active Learning of High-Dimensional Neural Network Reactive Potentials. J Chem Theory Comput 2021; 17:2691-2701. [PMID: 33904718 DOI: 10.1021/acs.jctc.1c00166] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Neural network (NN) potential energy surfaces (PESs) have been widely used in atomistic simulations with ab initio accuracy. While constructing NN PESs, their training data points are often sampled by molecular dynamics trajectories. This strategy can be however inefficient for reactive systems involving rare events. Here, we develop an uncertainty-driven active learning strategy to automatically and efficiently generate high-dimensional NN-based reactive potentials, taking a gas-surface reaction as an example. The difference between two independent NN models is used as a simple and differentiable uncertainty metric, allowing us to quickly search in the uncertainty space and place new samples at which the PES is less reliable. By interfacing this algorithm with the first-principles simulation package, we demonstrate that a globally accurate NN potential of the H2 + Ag(111) system can be constructed with merely ∼150 data points. This PES can be further refined to describe H2 dissociation on Ag(100) by adding ∼130 more configurations on this facet. The entire process is completely automatic and self-terminated once the relative error criterion is fulfilled. Impressively, data points sampled by this uncertainty-driven strategy are substantially fewer than by the traditional trajectory-based sampling. The final NN PES not only converges well the quantum dissociation probability of the molecule but also well-reproduces the phonon properties of the substrate and is capable of describing surface temperature effects. These results show the potential of this active learning approach in developing high-dimensional NN reactive potentials in gas and condensed phases.
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Affiliation(s)
- Qidong Lin
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Liang Zhang
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yaolong Zhang
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Bin Jiang
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
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19
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Sathyamurthy N, Mahapatra S. Time-dependent quantum mechanical wave packet dynamics. Phys Chem Chem Phys 2020; 23:7586-7614. [PMID: 33306771 DOI: 10.1039/d0cp03929b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Starting from a model study of the collinear (H, H2) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH4. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H2) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.
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20
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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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21
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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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22
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Jiang B, Li J, Guo H. High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning. J Phys Chem Lett 2020; 11:5120-5131. [PMID: 32517472 DOI: 10.1021/acs.jpclett.0c00989] [Citation(s) in RCA: 105] [Impact Index Per Article: 26.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.
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Affiliation(s)
- Bin Jiang
- Hefei National Laboratory for Physical Science at the Microscale, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jun Li
- School of Chemistry and Chemical Engineering and Chongqing Key Laboratory of Theoretical and Computational Chemistry, Chongqing University, Chongqing 401331, China
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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23
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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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24
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Lin Q, Zhang Y, Zhao B, Jiang B. Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy. J Chem Phys 2020; 152:154104. [DOI: 10.1063/5.0004944] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Qidong Lin
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yaolong Zhang
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Bin Zhao
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstraße 25, D-33615 Bielefeld, Germany
| | - Bin Jiang
- Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China
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25
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Song Q, Zhang Q, Meng Q. Revisiting the Gaussian process regression for fitting high-dimensional potential energy surface and its application to the OH + HO2→O2+ H2O reaction. J Chem Phys 2020; 152:134309. [PMID: 32268765 DOI: 10.1063/1.5143544] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qingfei Song
- School of Chemistry and Chemical Engineering, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
- Key Laboratory of Special Functional and Smart Polymer Materials of Ministry of Industry and Information Technology, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
| | - Qiuyu Zhang
- School of Chemistry and Chemical Engineering, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
- Key Laboratory of Special Functional and Smart Polymer Materials of Ministry of Industry and Information Technology, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
| | - Qingyong Meng
- School of Chemistry and Chemical Engineering, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
- Key Laboratory of Special Functional and Smart Polymer Materials of Ministry of Industry and Information Technology, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi’an, China
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26
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Dai J, Krems RV. Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels. J Chem Theory Comput 2020; 16:1386-1395. [DOI: 10.1021/acs.jctc.9b00700] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. Dai
- 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
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27
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Győri T, Czakó G. Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program System. J Chem Theory Comput 2019; 16:51-66. [DOI: 10.1021/acs.jctc.9b01006] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tibor Győri
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
| | - Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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28
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Abbott AS, Turney JM, Zhang B, Smith DGA, Altarawy D, Schaefer HF. PES-Learn: An Open-Source Software Package for the Automated Generation of Machine Learning Models of Molecular Potential Energy Surfaces. J Chem Theory Comput 2019; 15:4386-4398. [DOI: 10.1021/acs.jctc.9b00312] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Adam S. Abbott
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Justin M. Turney
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Boyi Zhang
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
| | - Daniel G. A. Smith
- Molecular Sciences Software Institute, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Doaa Altarawy
- Molecular Sciences Software Institute, Virginia Tech, Blacksburg, Virginia 24061, United States
- Computer and Systems Engineering Department, Alexandria University, Alexandria, Egypt
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, United States
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29
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Polyak I, Richings GW, Habershon S, Knowles PJ. Direct quantum dynamics using variational Gaussian wavepackets and Gaussian process regression. J Chem Phys 2019; 150:041101. [PMID: 30709252 DOI: 10.1063/1.5086358] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The method of direct variational quantum nuclear dynamics in a basis of Gaussian wavepackets, combined with the potential energy surfaces fitted on-the-fly using Gaussian process regression, is described together with its implementation. Enabling exact and efficient analytic evaluation of Hamiltonian matrix elements, this approach allows for black-box quantum dynamics of multidimensional anharmonic molecular systems. Example calculations of intra-molecular proton transfer on the electronic ground state of salicylaldimine are provided, and future algorithmic improvements as well as the potential for multiple-state non-adiabatic dynamics are discussed.
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Affiliation(s)
- Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Gareth W Richings
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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30
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Wang H, Bettens RPA. Modelling potential energy surfaces for small clusters using Shepard interpolation with Gaussian-form nodal functions. Phys Chem Chem Phys 2019; 21:4513-4522. [DOI: 10.1039/c8cp07640e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A new interpolation method based on Gaussian functions to reliably generate potential energy surfaces.
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Affiliation(s)
- Haina Wang
- Department of Chemistry
- Princeton University
- Princeton
- USA
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31
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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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32
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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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33
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Uteva E, Graham RS, Wilkinson RD, Wheatley RJ. Active learning in Gaussian process interpolation of potential energy surfaces. J Chem Phys 2018; 149:174114. [DOI: 10.1063/1.5051772] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Elena Uteva
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Richard S. Graham
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Richard D. Wilkinson
- School of Mathematics and Statistics, University of Sheffield, Sheffield S10 2TN, United Kingdom
| | - Richard J. Wheatley
- School of Chemistry, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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34
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Archibald R, Krogel JT, Kent PRC. Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo. J Chem Phys 2018; 149:164116. [DOI: 10.1063/1.5040584] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- R. Archibald
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - J. T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - P. R. C. Kent
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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35
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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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36
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Guan Y, Yang S, Zhang DH. Application of Clustering Algorithms to Partitioning Configuration Space in Fitting Reactive Potential Energy Surfaces. J Phys Chem A 2018. [DOI: 10.1021/acs.jpca.8b00859] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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
- 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
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