151
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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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152
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Malshe M, Raff LM, Hagan M, Bukkapatnam S, Komanduri R. Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases. J Chem Phys 2010; 132:204103. [PMID: 20515084 DOI: 10.1063/1.3431624] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The variation in the fitting accuracy of neural networks (NNs) when used to fit databases comprising potential energies obtained from ab initio electronic structure calculations is investigated as a function of the number and nature of the elements employed in the input vector to the NN. Ab initio databases for H(2)O(2), HONO, Si(5), and H(2)C[Double Bond]CHBr were employed in the investigations. These systems were chosen so as to include four-, five-, and six-body systems containing first, second, third, and fourth row elements with a wide variety of chemical bonding and whose conformations cover a wide range of structures that occur under high-energy machining conditions and in chemical reactions involving cis-trans isomerizations, six different types of two-center bond ruptures, and two different three-center dissociation reactions. The ab initio databases for these systems were obtained using density functional theory/B3LYP, MP2, and MP4 methods with extended basis sets. A total of 31 input vectors were investigated. In each case, the elements of the input vector were chosen from interatomic distances, inverse powers of the interatomic distance, three-body angles, and dihedral angles. Both redundant and nonredundant input vectors were investigated. The results show that among all the input vectors investigated, the set employed in the Z-matrix specification of the molecular configurations in the electronic structure calculations gave the lowest NN fitting accuracy for both Si(5) and vinyl bromide. The underlying reason for this result appears to be the discontinuity present in the dihedral angle for planar geometries. The use of trigometric functions of the angles as input elements produced significantly improved fitting accuracy as this choice eliminates the discontinuity. The most accurate fitting was obtained when the elements of the input vector were taken to have the form R(ij) (-n), where the R(ij) are the interatomic distances. When the Levenberg-Marquardt procedure was modified to permit error minimization with respect to n as well as the weights and biases of the NN, the optimum powers were all found to lie in the range of 1.625-2.38 for the four systems studied. No statistically significant increase in fitting accuracy was achieved for vinyl bromide when a different value of n was employed and optimized for each bond type. The rate of change in the fitting error with n is found to be very small when n is near its optimum value. Consequently, good fitting accuracy can be achieved by employing a value of n in the middle of the above range. The use of interparticle distances as elements of the input vector rather than the Z-matrix variables employed in the electronic structure calculations is found to reduce the rms fitting errors by factors of 8.86 and 1.67 for Si(5) and vinyl bromide, respectively. If the interparticle distances are replaced with input elements of the form R(ij) (-n) with n optimized, further reductions in the rms error by a factor of 1.31 to 2.83 for the four systems investigated are obtained. A major advantage of using this procedure to increase NN fitting accuracy rather than increasing the number of neurons or the size of the database is that the required increase in computational effort is very small.
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Affiliation(s)
- M Malshe
- Mechanical and Aerospace Engineering, Oklahoma State University, 218 Engineering North Stillwater, Oklahoma 74078, USA
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153
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Martin-Gondre L, Crespos C, Larregaray P, Rayez JC, van Ootegem B, Conte D. Dynamics simulation of N(2) scattering onto W(100,110) surfaces: A stringent test for the recently developed flexible periodic London-Eyring-Polanyi-Sato potential energy surface. J Chem Phys 2010; 132:204501. [PMID: 20515094 DOI: 10.1063/1.3389479] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An efficient method to construct the six dimensional global potential energy surface (PES) for two atoms interacting with a periodic rigid surface, the flexible periodic London-Eyring-Polanyi-Sato model, has been proposed recently. The main advantages of this model, compared to state-of-the-art interpolated ab initio PESs developed in the past, reside in its global nature along with the small number of electronic structure calculations required for its construction. In this work, we investigate to which extent this global representation is able to reproduce the fine details of the scattering dynamics of N(2) onto W(100,110) surfaces reported in previous dynamics simulations based on locally interpolated PESs. The N(2)/W(100) and N(2)/W(110) systems are chosen as benchmarks as they exhibit very unusual and distinct dissociative adsorption dynamics although chemically similar. The reaction pathways as well as the role of dynamic trapping are scrutinized. Besides, elastic/inelastic scattering dynamics including internal state and angular distributions of reflected molecules are also investigated. The results are shown to be in fair agreement with previous theoretical predictions.
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Affiliation(s)
- L Martin-Gondre
- Institut des Sciences Moléculaires, UMR 5255 CNRS-Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France
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154
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Groß A. Ab Initio Molecular Dynamics Simulations of the Adsorption of H2 on Palladium Surfaces. Chemphyschem 2010; 11:1374-81. [DOI: 10.1002/cphc.200900818] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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155
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Marquardt R, Cuvelier F, Olsen RA, Baerends EJ, Tremblay JC, Saalfrank P. A new analytical potential energy surface for the adsorption system CO/Cu(100). J Chem Phys 2010; 132:074108. [DOI: 10.1063/1.3308481] [Citation(s) in RCA: 28] [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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156
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Handley CM, Popelier PLA. Potential Energy Surfaces Fitted by Artificial Neural Networks. J Phys Chem A 2010; 114:3371-83. [DOI: 10.1021/jp9105585] [Citation(s) in RCA: 241] [Impact Index Per Article: 17.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Chris M. Handley
- Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain, School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain, and The University of Warwick, Department of Chemistry, Library Road, Coventry CV4 7AL, Great Britain
| | - Paul L. A. Popelier
- Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain, School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain, and The University of Warwick, Department of Chemistry, Library Road, Coventry CV4 7AL, Great Britain
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157
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Martin-Gondre L, Crespos C, Larrégaray P, Rayez J, Conte D, van Ootegem B. Detailed description of the flexible periodic London–Eyring–Polanyi–Sato potential energy function. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2009.11.012] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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158
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Gross A. Ab initio molecular dynamics study of hot atom dynamics after dissociative adsorption of H2 on Pd(100). PHYSICAL REVIEW LETTERS 2009; 103:246101. [PMID: 20366213 DOI: 10.1103/physrevlett.103.246101] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2009] [Indexed: 05/29/2023]
Abstract
The relaxation of hot hydrogen atoms upon the dissociative adsorption of H2 on Pd(100) was studied by ab initio molecular dynamics simulations based on density functional theory, modeling the full dissociative adsorption process in a consistent manner. In spite of the nonlinear dependence of every single trajectory on the run conditions, on the average it is the energy dissipation to the substrate that determines the mean distance of the two H atoms after adsorption which amounts to three to four lattice units and provides an upper bound for heavier species such as oxygen.
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Affiliation(s)
- Axel Gross
- Institut für Theoretische Chemie, Universität Ulm, 89069 Ulm, Germany
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159
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Le HM, Raff LM. Molecular Dynamics Investigation of the Bimolecular Reaction BeH + H2 → BeH2 + H on an ab Initio Potential-Energy Surface Obtained Using Neural Network Methods with Both Potential and Gradient Accuracy Determination. J Phys Chem A 2009; 114:45-53. [DOI: 10.1021/jp907507z] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hung M. Le
- Chemistry Department, Oklahoma State University, Stillwater, Oklahoma 74078
| | - Lionel M. Raff
- Chemistry Department, Oklahoma State University, Stillwater, Oklahoma 74078
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160
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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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161
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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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162
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Dawes R, Passalacqua A, Wagner AF, Sewell TD, Minkoff M, Thompson DL. Interpolating moving least-squares methods for fitting potential energy surfaces: Using classical trajectories to explore configuration space. J Chem Phys 2009; 130:144107. [DOI: 10.1063/1.3111261] [Citation(s) in RCA: 43] [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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163
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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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164
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Dawes R, Wagner AF, Thompson DL. Ab Initio Wavenumber Accurate Spectroscopy: 1CH2 and HCN Vibrational Levels on Automatically Generated IMLS Potential Energy Surfaces. J Phys Chem A 2009; 113:4709-21. [DOI: 10.1021/jp900409r] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Richard Dawes
- Department of Chemistry, University of Missouri—Columbia, Columbia, Missouri 65211, and Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439
| | - Albert F. Wagner
- Department of Chemistry, University of Missouri—Columbia, Columbia, Missouri 65211, and Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439
| | - Donald L. Thompson
- Department of Chemistry, University of Missouri—Columbia, Columbia, Missouri 65211, and Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439
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165
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Evenhuis CR, Collins MA. Locally Optimized Coordinates in Modified Shepard Interpolation. J Phys Chem A 2009; 113:3979-87. [DOI: 10.1021/jp8103722] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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166
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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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167
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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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168
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Latino DA, Fartaria RP, Freitas FF, Aires-de-Sousa J, Fernandes FMS. Mapping Potential Energy Surfaces by Neural Networks: The ethanol/Au(111) interface. J Electroanal Chem (Lausanne) 2008. [DOI: 10.1016/j.jelechem.2008.07.032] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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169
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Carbogno C, Behler J, Grob A, Reuter K. Fingerprints for spin-selection rules in the interaction dynamics of O2 at Al(111). PHYSICAL REVIEW LETTERS 2008; 101:096104. [PMID: 18851627 DOI: 10.1103/physrevlett.101.096104] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2008] [Indexed: 05/26/2023]
Abstract
We perform mixed quantum-classical molecular dynamics simulations based on first-principles potential-energy surfaces to demonstrate that the scattering of a beam of singlet O2 molecules at Al(111) will enable an unambiguous assessment of the role of spin-selection rules for the adsorption dynamics. At thermal energies we predict a sticking probability that is substantially less than unity, with the repelled molecules exhibiting characteristic kinetic, vibrational and rotational signatures arising from the nonadiabatic spin transition.
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170
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Darley MG, Handley CM, Popelier PLA. Beyond Point Charges: Dynamic Polarization from Neural Net Predicted Multipole Moments. J Chem Theory Comput 2008; 4:1435-48. [DOI: 10.1021/ct800166r] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Michael G. Darley
- Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, United Kingdom
| | - Chris M. Handley
- Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, United Kingdom
| | - Paul L. A. Popelier
- Manchester Interdisciplinary Biocentre (MIB), 131 Princess Street, Manchester M1 7DN, United Kingdom
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171
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Olsen RA, McCormack DA, Luppi M, Baerends EJ. Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface. J Chem Phys 2008; 128:194715. [DOI: 10.1063/1.2920488] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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172
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Behler J, Martonák R, Donadio D, Parrinello M. Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential. PHYSICAL REVIEW LETTERS 2008; 100:185501. [PMID: 18518388 DOI: 10.1103/physrevlett.100.185501] [Citation(s) in RCA: 103] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2007] [Indexed: 05/26/2023]
Abstract
We study in a systematic way the complex sequence of the high-pressure phases of silicon obtained upon compression by combining an accurate high-dimensional neural network representation of the density-functional theory potential-energy surface with the metadynamics scheme. Starting from the thermodynamically stable diamond structure at ambient conditions we are able to identify all structural phase transitions up to the highest-pressure fcc phase at about 100 GPa. The results are in excellent agreement with experiment. The method developed promises to be of great value in the study of inorganic solids, including those having metallic phases.
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Affiliation(s)
- Jörg Behler
- Department of Chemistry and Applied Biosciences, ETH Zurich, USI-Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland
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173
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Bocan GA, Díez Muiño R, Alducin M, Busnengo HF, Salin A. The role of exchange-correlation functionals in the potential energy surface and dynamics of N2 dissociation on W surfaces. J Chem Phys 2008; 128:154704. [DOI: 10.1063/1.2897757] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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174
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Ludwig J, Vlachos DG. Molecular dynamics of hydrogen dissociation on an oxygen covered Pt(111) surface. J Chem Phys 2008; 128:154708. [DOI: 10.1063/1.2902981] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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175
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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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176
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Isotope Effects in Photodissociation: Chemical Reaction Dynamics and Implications for Atmospheres. ADVANCES IN QUANTUM CHEMISTRY 2008. [DOI: 10.1016/s0065-3276(07)00207-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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177
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Ludwig J, Vlachos DG. Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling. J Chem Phys 2007; 127:154716. [PMID: 17949200 DOI: 10.1063/1.2794338] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.
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Affiliation(s)
- Jeffery Ludwig
- Department of Chemical Engineering and Center for Catalytic Science and Technology, University of Delaware, Newark, Delaware 19716-3110, USA
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178
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Behler J, Lorenz S, Reuter K. Representing molecule-surface interactions with symmetry-adapted neural networks. J Chem Phys 2007; 127:014705. [PMID: 17627362 DOI: 10.1063/1.2746232] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The accurate description of molecule-surface interactions requires a detailed knowledge of the underlying potential-energy surface (PES). Recently, neural networks (NNs) have been shown to be an efficient technique to accurately interpolate the PES information provided for a set of molecular configurations, e.g., by first-principles calculations. Here, we further develop this approach by building the NN on a new type of symmetry functions, which allows to take the symmetry of the surface exactly into account. The accuracy and efficiency of such symmetry-adapted NNs is illustrated by the application to a six-dimensional PES describing the interaction of oxygen molecules with the Al(111) surface.
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Affiliation(s)
- Jörg Behler
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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179
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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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180
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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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181
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Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces. PHYSICAL REVIEW LETTERS 2007; 98:146401. [PMID: 17501293 DOI: 10.1103/physrevlett.98.146401] [Citation(s) in RCA: 1525] [Impact Index Per Article: 89.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2006] [Indexed: 05/15/2023]
Abstract
The accurate description of chemical processes often requires the use of computationally demanding methods like density-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.
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Affiliation(s)
- Jörg Behler
- Department of Chemistry and Applied Biosciences, ETH Zurich, USI-Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland
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182
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Manzhos S, Carrington T. Using neural networks to represent potential surfaces as sums of products. J Chem Phys 2007; 125:194105. [PMID: 17129087 DOI: 10.1063/1.2387950] [Citation(s) in RCA: 129] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.
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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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183
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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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184
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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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185
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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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186
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Agrawal PM, Samadh ANA, Raff LM, Hagan MT, Bukkapatnam ST, Komanduri R. Prediction of molecular-dynamics simulation results using feedforward neural networks: Reaction of a C2 dimer with an activated diamond (100) surface. J Chem Phys 2005; 123:224711. [PMID: 16375499 DOI: 10.1063/1.2131069] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A new approach involving neural networks combined with molecular dynamics has been used for the determination of reaction probabilities as a function of various input parameters for the reactions associated with the chemical-vapor deposition of carbon dimers on a diamond (100) surface. The data generated by the simulations have been used to train and test neural networks. The probabilities of chemisorption, scattering, and desorption as a function of input parameters, such as rotational energy, translational energy, and direction of the incident velocity vector of the carbon dimer, have been considered. The very good agreement obtained between the predictions of neural networks and those provided by molecular dynamics and the fact that, after training the network, the determination of the interpolated probabilities as a function of various input parameters involves only the evaluation of simple analytical expressions rather than computationally intensive algorithms show that neural networks are extremely powerful tools for interpolating the probabilities and rates of chemical reactions. We also find that a neural network fits the underlying trends in the data rather than the statistical variations present in the molecular-dynamics results. Consequently, neural networks can also provide a computationally convenient means of averaging the statistical variations inherent in molecular-dynamics calculations. In the present case the application of this method is found to reduce the statistical uncertainty in the molecular-dynamics results by about a factor of 3.5.
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Affiliation(s)
- Paras M Agrawal
- Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
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187
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Behler J, Delley B, Lorenz S, Reuter K, Scheffler M. Dissociation of O2 at Al(111): the role of spin selection rules. PHYSICAL REVIEW LETTERS 2005; 94:036104. [PMID: 15698287 DOI: 10.1103/physrevlett.94.036104] [Citation(s) in RCA: 145] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2004] [Indexed: 05/24/2023]
Abstract
A most basic and puzzling enigma in surface science is the description of the dissociative adsorption of O(2) at the (111) surface of Al. Already for the sticking curve alone, the disagreement between experiment and results of state-of-the-art first-principles calculations can hardly be more dramatic. In this Letter we show that this is caused by hitherto unaccounted spin selection rules, which give rise to a highly nonadiabatic behavior in the O(2)/Al(111) interaction. We also discuss problems caused by the insufficient accuracy of present-day exchange-correlation functionals.
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Affiliation(s)
- Jörg Behler
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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188
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Witkoskie JB, Doren DJ. Neural Network Models of Potential Energy Surfaces: Prototypical Examples. J Chem Theory Comput 2004; 1:14-23. [DOI: 10.1021/ct049976i] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James B. Witkoskie
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
| | - Douglas J. Doren
- Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
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