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Fujioka K, Sun R. Interpolating Moving Ridge Regression (IMRR): A machine learning algorithm to predict energy gradients for ab initio molecular dynamics simulations. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111482] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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2
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Du Y, Meng Z, Yan Q, Wang CL, Tian Y, Duan W, Zhang S, Lin P. Deep potential for face-centered cubic Cu system at finite temperatures. Phys Chem Chem Phys 2022; 24:18361-18369. [DOI: 10.1039/d2cp02758e] [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
Potential function is critical for molecular dynamics simulation and the state-of-the-art method generating potential functions used in molecular dynamics is based on machine learning with neural networks. This method provides...
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Manzhos S, Carrington T. Neural Network Potential Energy Surfaces for Small Molecules and Reactions. Chem Rev 2020; 121:10187-10217. [PMID: 33021368 DOI: 10.1021/acs.chemrev.0c00665] [Citation(s) in RCA: 119] [Impact Index Per Article: 29.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.
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Affiliation(s)
- Sergei Manzhos
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650, Boulevard Lionel-Boulet, Varennes, Québec City, Québec J3X 1S2, Canada
| | - Tucker Carrington
- Chemistry Department, Queen's University, Kingston Ontario K7L 3N6, Canada
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Karandashev K, Vaníček J. A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations. J Chem Phys 2019; 151:174116. [PMID: 31703487 DOI: 10.1063/1.5124469] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure that is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of the HCN/DCN equilibrium isotope effect.
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Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Quintas-Sánchez E, Dawes R. AUTOSURF: A Freely Available Program To Construct Potential Energy Surfaces. J Chem Inf Model 2018; 59:262-271. [DOI: 10.1021/acs.jcim.8b00784] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ernesto Quintas-Sánchez
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65401, United States
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65401, United States
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Dawes R, Quintas‐Sánchez E. THE CONSTRUCTION OF AB INITIO‐BASED POTENTIAL ENERGY SURFACES. REVIEWS IN COMPUTATIONAL CHEMISTRY 2018. [DOI: 10.1002/9781119518068.ch5] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Gao T, Kitchin JR. Modeling palladium surfaces with density functional theory, neural networks and molecular dynamics. Catal Today 2018. [DOI: 10.1016/j.cattod.2018.03.045] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Cooper AM, Hallmen PP, Kästner J. Potential energy surface interpolation with neural networks for instanton rate calculations. J Chem Phys 2018. [DOI: 10.1063/1.5015950] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- April M. Cooper
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Philipp P. Hallmen
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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Sandhiya L, Zipse H. OO bond homolysis in hydrogen peroxide. J Comput Chem 2017; 38:2186-2192. [DOI: 10.1002/jcc.24870] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Revised: 05/11/2017] [Accepted: 06/13/2017] [Indexed: 11/08/2022]
Affiliation(s)
| | - Hendrik Zipse
- Department of Chemistry; LMU München; München D-81377 Germany
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Tew DP, Mizukami W. Ab Initio Vibrational Spectroscopy of cis- and trans-Formic Acid from a Global Potential Energy Surface. J Phys Chem A 2016; 120:9815-9828. [DOI: 10.1021/acs.jpca.6b09952] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| | - Wataru Mizukami
- School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
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Dawes R, Ndengué SA. Single- and multireference electronic structure calculations for constructing potential energy surfaces. INT REV PHYS CHEM 2016. [DOI: 10.1080/0144235x.2016.1195102] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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A fast hybrid method for constructing multidimensional potential energy surfaces from ab initio calculations: A new global analytic PES of NH2 system. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.04.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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13
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Su NQ, Chen J, Sun Z, Zhang DH, Xu X. H + H2 quantum dynamics using potential energy surfaces based on the XYG3 type of doubly hybrid density functionals: Validation of the density functionals. J Chem Phys 2015; 142:084107. [DOI: 10.1063/1.4913196] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Jun Chen
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Zhigang Sun
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Dong H. Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
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Mizukami W, Habershon S, Tew DP. A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression. J Chem Phys 2014; 141:144310. [DOI: 10.1063/1.4897486] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wataru Mizukami
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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Behler J. Representing potential energy surfaces by high-dimensional neural network potentials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:183001. [PMID: 24758952 DOI: 10.1088/0953-8984/26/18/183001] [Citation(s) in RCA: 162] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The development of interatomic potentials employing artificial neural networks has seen tremendous progress in recent years. While until recently the applicability of neural network potentials (NNPs) has been restricted to low-dimensional systems, this limitation has now been overcome and high-dimensional NNPs can be used in large-scale molecular dynamics simulations of thousands of atoms. NNPs are constructed by adjusting a set of parameters using data from electronic structure calculations, and in many cases energies and forces can be obtained with very high accuracy. Therefore, NNP-based simulation results are often very close to those gained by a direct application of first-principles methods. In this review, the basic methodology of high-dimensional NNPs will be presented with a special focus on the scope and the remaining limitations of this approach. The development of NNPs requires substantial computational effort as typically thousands of reference calculations are required. Still, if the problem to be studied involves very large systems or long simulation times this overhead is regained quickly. Further, the method is still limited to systems containing about three or four chemical elements due to the rapidly increasing complexity of the configuration space, although many atoms of each species can be present. Due to the ability of NNPs to describe even extremely complex atomic configurations with excellent accuracy irrespective of the nature of the atomic interactions, they represent a general and therefore widely applicable technique, e.g. for addressing problems in materials science, for investigating properties of interfaces, and for studying solvation processes.
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Affiliation(s)
- J Behler
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
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Bender JD, Doraiswamy S, Truhlar DG, Candler GV. Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N4. J Chem Phys 2014; 140:054302. [DOI: 10.1063/1.4862157] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ohkubo Y, Kawano A, Orimoto M, Takahashi O, Yamasaki K. Quasiclassical trajectory study of energy relaxation process in collision of highly vibrationally excited O2 and ground-state N2. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2013.12.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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18
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Fournier R, Orel S. Automated fit of high-dimensional potential energy surfaces using cluster analysis and interpolation over descriptors of chemical environment. J Chem Phys 2013; 139:234110. [DOI: 10.1063/1.4846297] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang CR, Zhang DH. Accuracy of Low-level Surface in Hierarchical Construction of Potential Energy Surface. CHINESE J CHEM PHYS 2012. [DOI: 10.1088/1674-0068/25/02/186-190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Le HM, Dinh TS, Le HV. Molecular Dynamics Investigations of Ozone on an Ab Initio Potential Energy Surface with the Utilization of Pattern-Recognition Neural Network for Accurate Determination of Product Formation. J Phys Chem A 2011; 115:10862-70. [DOI: 10.1021/jp206531s] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hung M. Le
- Faculty of Materials Science, College of Science, Vietnam National University, Ho Chi Minh City, Vietnam 750000
| | - Thach S. Dinh
- Faculty of Materials Science, College of Science, Vietnam National University, Ho Chi Minh City, Vietnam 750000
| | - Hieu V. Le
- Faculty of Materials Science, College of Science, Vietnam National University, Ho Chi Minh City, Vietnam 750000
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Carrington T, Wang XG. Computing ro-vibrational spectra of van der Waals molecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.73] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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22
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Behler J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations. Phys Chem Chem Phys 2011; 13:17930-55. [DOI: 10.1039/c1cp21668f] [Citation(s) in RCA: 477] [Impact Index Per Article: 36.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Braams BJ, Bowman JM. Permutationally invariant potential energy surfaces in high dimensionality. INT REV PHYS CHEM 2009. [DOI: 10.1080/01442350903234923] [Citation(s) in RCA: 535] [Impact Index Per Article: 35.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Malshe M, Pukrittayakamee A, Raff LM, Hagan M, Bukkapatnam S, Komanduri R. Accurate prediction of higher-level electronic structure energies for large databases using neural networks, Hartree–Fock energies, and small subsets of the database. J Chem Phys 2009; 131:124127. [DOI: 10.1063/1.3231686] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Le HM, Huynh S, Raff LM. Molecular dissociation of hydrogen peroxide (HOOH) on a neural network ab initio potential surface with a new configuration sampling method involving gradient fitting. J Chem Phys 2009; 131:014107. [DOI: 10.1063/1.3159748] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Malshe M, Narulkar R, Raff LM, Hagan M, Bukkapatnam S, Agrawal PM, Komanduri R. Development of generalized potential-energy surfaces using many-body expansions, neural networks, and moiety energy approximations. J Chem Phys 2009; 130:184102. [PMID: 19449903 DOI: 10.1063/1.3124802] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A general method for the development of potential-energy hypersurfaces is presented. The method combines a many-body expansion to represent the potential-energy surface with two-layer neural networks (NN) for each M-body term in the summations. The total number of NNs required is significantly reduced by employing a moiety energy approximation. An algorithm is presented that efficiently adjusts all the coupled NN parameters to the database for the surface. Application of the method to four different systems of increasing complexity shows that the fitting accuracy of the method is good to excellent. For some cases, it exceeds that available by other methods currently in literature. The method is illustrated by fitting large databases of ab initio energies for Si(n) (n=3,4,...,7) clusters obtained from density functional theory calculations and for vinyl bromide (C(2)H(3)Br) and all products for dissociation into six open reaction channels (12 if the reverse reactions are counted as separate open channels) that include C-H and C-Br bond scissions, three-center HBr dissociation, and three-center H(2) dissociation. The vinyl bromide database comprises the ab initio energies of 71 969 configurations computed at MP4(SDQ) level with a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (4333/433/4) basis set augmented with split outer s and p orbitals (43321/4321/4) and a polarization f orbital with an exponent of 0.5 for the bromine atom. It is found that an expansion truncated after the three-body terms is sufficient to fit the Si(5) system with a mean absolute testing set error of 5.693x10(-4) eV. Expansions truncated after the four-body terms for Si(n) (n=3,4,5) and Si(n) (n=3,4,...,7) provide fits whose mean absolute testing set errors are 0.0056 and 0.0212 eV, respectively. For vinyl bromide, a many-body expansion truncated after the four-body terms provides fitting accuracy with mean absolute testing set errors that range between 0.0782 and 0.0808 eV. These errors correspond to mean percent errors that fall in the range 0.98%-1.01%. Our best result using the present method truncated after the four-body summation with 16 NNs yields a testing set error that is 20.3% higher than that obtained using a 15-dimensional (15-140-1) NN to fit the vinyl bromide database. This appears to be the price of the added simplicity of the many-body expansion procedure.
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Affiliation(s)
- M Malshe
- Nanotechnology Research Group, Oklahoma State University, 218 Engineering, North Stillwater, Oklahoma 74078, USA
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Pukrittayakamee A, Malshe M, Hagan M, Raff LM, Narulkar R, Bukkapatnum S, Komanduri R. Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks. J Chem Phys 2009; 130:134101. [DOI: 10.1063/1.3095491] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Manzhos S, Carrington T. Using neural networks, optimized coordinates, and high-dimensional model representations to obtain a vinyl bromide potential surface. J Chem Phys 2009; 129:224104. [PMID: 19071904 DOI: 10.1063/1.3021471] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We demonstrate that it is possible to obtain good potentials using high-dimensional model representations (HDMRs) fitted with neural networks (NNs) from data in 12 dimensions and 15 dimensions. The HDMR represents the potential as a sum of lower-dimensional functions and our NN-based approach makes it possible to obtain all of these functions from one set of fitting points. To reduce the number of terms in the HDMR, we use optimized redundant coordinates. By using exponential neurons, one obtains a potential in sum-of-products form, which greatly facilitates quantum dynamics calculations. A 12-dimensional (reference) potential surface for vinyl bromide is first refitted to show that it can be represented as a sum of two-dimensional functions. To fit 3d functions of the original coordinates, to improve the potential, a huge amount of data would be required. Redundant coordinates avoid this problem. They enable us to bypass the combinatorial explosion of the number of terms which plagues all HDMR and multimode-type methods. We also fit to a set of approximately 70,000 ab initio points for vinyl bromide in 15 dimensions [M. Malshe et al., J. Chem. Phys. 127, 134105 (2007)] and show that it is possible to obtain a surface in sum-of-products form of quality similar to the quality of the full-dimensional fit. Although we obtain a full-dimensional surface, we limit the cost of the fitting by building it from fits of six-dimensional functions, each of which requires only a small NN.
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Affiliation(s)
- Sergei Manzhos
- Département de chimie, Université de Montréal, Case postale 6128, succursale Centre-ville Montréal, (Québec) H3C 3J7 Canada.
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Agrawal PM, Malshe M, Narulkar R, Raff LM, Hagan M, Bukkapatnum S, Komanduri R. A Self-Starting Method for Obtaining Analytic Potential-Energy Surfaces from ab Initio Electronic Structure Calculations. J Phys Chem A 2009; 113:869-77. [DOI: 10.1021/jp8085232] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- P. M. Agrawal
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - M. Malshe
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - R. Narulkar
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - L. M. Raff
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - M. Hagan
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - S. Bukkapatnum
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
| | - R. Komanduri
- Mechanical & Aerospace Engineering, Chemistry Department, Electrical and Computer Engineering, and Industrial Engineering, Oklahoma State University, Stillwater, Oklahoma 74078
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Malshe M, Narulkar R, Raff LM, Hagan M, Bukkapatnam S, Komanduri R. Parametrization of analytic interatomic potential functions using neural networks. J Chem Phys 2008; 129:044111. [DOI: 10.1063/1.2957490] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Fu B, Xu X, Zhang DH. A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reaction. J Chem Phys 2008; 129:011103. [DOI: 10.1063/1.2955729] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Le HM, Raff LM. Cis→trans, trans→cis isomerizations and N–O bond dissociation of nitrous acid (HONO) on an ab initio potential surface obtained by novelty sampling and feed-forward neural network fitting. J Chem Phys 2008; 128:194310. [DOI: 10.1063/1.2918503] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dawes R, Thompson DL, Wagner AF, Minkoff M. Interpolating moving least-squares methods for fitting potential energy surfaces: A strategy for efficient automatic data point placement in high dimensions. J Chem Phys 2008; 128:084107. [DOI: 10.1063/1.2831790] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Guo Y, Tokmakov I, Thompson DL, Wagner AF, Minkoff M. Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants. J Chem Phys 2007; 127:214106. [DOI: 10.1063/1.2805084] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Malshe M, Raff LM, Rockley MG, Hagan M, Agrawal PM, Komanduri R. Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feedforward neural networks. II. Numerical application of the method. J Chem Phys 2007; 127:134105. [DOI: 10.1063/1.2768948] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Manzhos S, Carrington T. Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions. J Chem Phys 2007; 127:014103. [PMID: 17627333 DOI: 10.1063/1.2746846] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.
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Affiliation(s)
- Sergei Manzhos
- Département de Chimie, Université de Montréal, CP 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada.
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38
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Tokmakov IV, Wagner AF, Minkoff M, Thompson DL. Gradient incorporation in one-dimensional applications of interpolating moving least-squares methods for fitting potential energy surfaces. Theor Chem Acc 2007. [DOI: 10.1007/s00214-007-0358-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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39
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Dawes R, Thompson DL, Guo Y, Wagner AF, Minkoff M. Interpolating moving least-squares methods for fitting potential energy surfaces: Computing high-density potential energy surface data from low-density ab initio data points. J Chem Phys 2007; 126:184108. [PMID: 17508793 DOI: 10.1063/1.2730798] [Citation(s) in RCA: 79] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.
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Affiliation(s)
- Richard Dawes
- Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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40
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Guo Y, Harding LB, Wagner AF, Minkoff M, Thompson DL. Interpolating moving least-squares methods for fitting potential energy surfaces: An application to the H2CN unimolecular reaction. J Chem Phys 2007; 126:104105. [PMID: 17362059 DOI: 10.1063/1.2698393] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.
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Affiliation(s)
- Yin Guo
- Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
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41
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Fernandez-Ramos A, Miller JA, Klippenstein SJ, Truhlar DG. Modeling the kinetics of bimolecular reactions. Chem Rev 2007; 106:4518-84. [PMID: 17091928 DOI: 10.1021/cr050205w] [Citation(s) in RCA: 393] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Antonio Fernandez-Ramos
- Departamento de Quimica Fisica, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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42
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Manzhos S, Carrington T. A random-sampling high dimensional model representation neural network for building potential energy surfaces. J Chem Phys 2006; 125:084109. [PMID: 16965003 DOI: 10.1063/1.2336223] [Citation(s) in RCA: 158] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We combine the high dimensional model representation (HDMR) idea of Rabitz and co-workers [J. Phys. Chem. 110, 2474 (2006)] with neural network (NN) fits to obtain an effective means of building multidimensional potentials. We verify that it is possible to determine an accurate many-dimensional potential by doing low dimensional fits. The final potential is a sum of terms each of which depends on a subset of the coordinates. This form facilitates quantum dynamics calculations. We use NNs to represent HDMR component functions that minimize error mode term by mode term. This NN procedure makes it possible to construct high-order component functions which in turn enable us to determine a good potential. It is shown that the number of available potential points determines the order of the HDMR which should be used.
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Affiliation(s)
- Sergei Manzhos
- Département de chimie, Université de Montréal, Case postale 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada.
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43
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Agrawal PM, Raff LM, Hagan MT, Komanduri R. Molecular dynamics investigations of the dissociation of SiO2 on an ab initio potential energy surface obtained using neural network methods. J Chem Phys 2006; 124:134306. [PMID: 16613454 DOI: 10.1063/1.2185638] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the SiO(2) system. Unlike other similar NN studies, here, we studied the dissociation of SiO(2) without the initial use of any empirical potential. During the dissociation of SiO(2) into Si+O or Si+O(2), the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociation dynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to occur adiabatically. The dynamics on the NN(STP) surface represent those expected if the reaction follows a minimum-energy pathway. This study on a small system demonstrates the application of NNs for MD studies using ab initio data when the spin multiplicity of the system changes during the dissociation process.
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Affiliation(s)
- Paras M Agrawal
- Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
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44
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Manzhos S, Wang X, Dawes R, Carrington T. A Nested Molecule-Independent Neural Network Approach for High-Quality Potential Fits†. J Phys Chem A 2006; 110:5295-304. [PMID: 16623455 DOI: 10.1021/jp055253z] [Citation(s) in RCA: 131] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
It is shown that neural networks (NNs) are efficient and effective tools for fitting potential energy surfaces. For H2O, a simple NN approach works very well. To fit surfaces for HOOH and H2CO, we develop a nested neural network technique in which we first fit an approximate NN potential and then use another NN to fit the difference of the true potential and the approximate potential. The root-mean-square error (RMSE) of the H2O surface is 1 cm(-1). For the 6-D HOOH and H2CO surfaces, the nested approach does almost as well attaining a RMSE of 2 cm(-1). The quality of the NN surfaces is verified by calculating vibrational spectra. For all three molecules, most of the low-lying levels are within 1 cm(-1) of the exact results. On the basis of these results, we propose that the nested NN approach be considered a method of choice for both simple potentials, for which it is relatively easy to guess a good fitting function, and complicated (e.g., double well) potentials for which it is much harder to deduce an appropriate fitting function. The number of fitting parameters is only moderately larger for the 6-D than for the 3-D potentials, and for all three molecules, decreasing the desired RMSE increases only slightly the number of required fitting parameters (nodes). NN methods, and in particular the nested approach we propose, should be good universal potential fitting tools.
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Affiliation(s)
- Sergei Manzhos
- Département de chimie, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal (Québec) H3C 3J7, Canada.
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45
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Doughan DI, Raff LM, Rockley MG, Hagan M, Agrawal PM, Komanduri R. Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feed-forward neural networks. J Chem Phys 2006; 124:054321. [PMID: 16468883 DOI: 10.1063/1.2162170] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The reaction dynamics of vibrationally excited vinyl bromide have been investigated using classical trajectory methods on a neural network potential surface that is fitted to an ab initio database of 12 122 configuration energies obtained from electronic structure calculations conducted at the MP4(SDQ) level of theory using a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (43334334) basis set augmented with split outer s and p orbitals (4332143214) and a polarization f orbital with an exponent of 0.5 for the bromine atom. The sampling of the 12-dimensional configuration hyperspace of vinyl bromide prior to execution of the electronic structure calculations is accomplished by combining novelty-sampling methods, chemical intuition, and trajectory sampling on empirical and neural network surfaces. The final potential is obtained using a two-layer feed-forward neural network comprising 38 and 1 neurons, respectively, with hyperbolic tangent sigmoid and linear transfer functions in the hidden and output layers, respectively. The fitting is accomplished using the Levenberg-Marquardt algorithm with early stopping and Bayesian regularization methods to avoid overfitting. The interpolated potentials have a standard deviation from the ab initio results of 0.0578 eV, which is within the range generally regarded as "chemical accuracy" for the purposes of electronic structure calculations. It is shown that the potential surface may be easily and conveniently transferred from one research group to another. The files required for transfer of the vinyl bromide surface can be obtained from the Electronic Physics Auxiliary Publication Service. Total dissociation rate coefficients for vinyl bromide are obtained at five different excitation energies between 4.50 and 6.44 eV. Branching ratios into each of the six open reaction channels are computed at 24 vibrational energies in the range between 4.00 and 6.44 eV. The distribution of vibrational energies in HBr formed via three-center dissociation from vinyl bromide is determined and compared with previous theoretical and experimental results. It is concluded that the combination of ab initio electronic structure calculations, novelty sampling with chemical intuition and trajectories on empirical analytic surfaces, and feed-forward neural networks provides a viable framework in which to execute purely ab initio molecular-dynamics studies on complex systems with multiple open reaction channels.
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Affiliation(s)
- D I Doughan
- Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078, USA
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46
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Kawano A, Tokmakov IV, Thompson DL, Wagner AF, Minkoff M. Interpolating moving least-squares methods for fitting potential-energy surfaces: Further improvement of efficiency via cutoff strategies. J Chem Phys 2006; 124:054105. [PMID: 16468849 DOI: 10.1063/1.2162171] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In standard applications of interpolating moving least squares (IMLS) for fitting a potential-energy surface (PES), all available ab initio points are used. Because remote ab initio points negligibly influence IMLS accuracy and increase IMLS time-to-solution, we present two methods to locally restrict the number of points included in a particular fit. The fixed radius cutoff (FRC) method includes ab initio points within a hypersphere of fixed radius. The density adaptive cutoff (DAC) method includes points within a hypersphere of variable radius depending on the point density. We test these methods by fitting a six-dimensional analytical PES for hydrogen peroxide. Both methods reduce the IMLS time-to-solution by about an order of magnitude relative to that when no cutoff method is used. The DAC method is more robust and efficient than the FRC method.
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Affiliation(s)
- Akio Kawano
- Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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47
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Raff LM, Malshe M, Hagan M, Doughan DI, Rockley MG, Komanduri R. Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks. J Chem Phys 2005; 122:84104. [PMID: 15836017 DOI: 10.1063/1.1850458] [Citation(s) in RCA: 110] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.
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Affiliation(s)
- L M Raff
- Department of Chemistry, Oklahoma State University, Stillwater, OK 74078, USA
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48
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Maisuradze GG, Kawano A, Thompson DL, Wagner AF, Minkoff M. Interpolating moving least-squares methods for fitting potential energy surfaces: Analysis of an application to a six-dimensional system. J Chem Phys 2004; 121:10329-38. [PMID: 15549910 DOI: 10.1063/1.1810477] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are applied to a six-dimensional potential energy surface (PES) of the HOOH molecule, for which an analytic ("exact") potential is available in the literature. The results of systematic investigations of the effects of weight function parameters, the degree and partial degree of IMLS, the number of data points allowed, and the optimal automatic point selection of data points up to full third-degree IMLS fits are reported. With partial reduction of cross terms and automatic point selection the full six-dimensional HOOH PES can be fit over a range of 100 kcal/mol to an accuracy of less than 1 kcal/mol with approximately 1350 ab initio points.
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Affiliation(s)
- Gia G Maisuradze
- Department of Chemistry, Oklahoma State University, Stillwater, OK 74078, USA
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