Interpolating moving least-squares methods for fitting potential energy surfaces: Applications to classical dynamics calculations

Guo, Yin; Kawano, Akio; Thompson, Donald L.; Wagner, Albert F.; Minkoff, Michael

doi:10.1063/1.1777572

Cited by 69 publications

(41 citation statements)

References 15 publications

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“…Fitting potential energy surfaces (PESs) and electrostatic multipole moment surfaces of small molecules to data generated by first principles electronic structure calculations has been a mainstay of computational chemistry for decades 7,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . Typically, when modelling the PES of a small group of atoms, the list of pairwise distances is used or, equivalently, some transformed version of the interatomic distances, e.g.…”

Section: Introductionmentioning

confidence: 99%

On representing chemical environments

2013

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We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

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Section: Introductionmentioning

confidence: 99%

On representing chemical environments

2013

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“…24 In addition, only the most important basis functions should be included in the fitting basis set. 22 There exists also a variant of the IMLS method that does not require to solve the least-squares equations for every evaluation point via local approximants. 27 The local interpolation moving least-squares method (L-IMLS) requires to calculate at every ab initio data point, the set of coefficients {a i }, which results in an N 3 m matrix.…”

Section: Constructing the Potential Energy Surface: Interpolating Movmentioning

confidence: 99%

Haptic quantum chemistry

Marti

Reiher

2009

J Comput Chem

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We present an implementation designed to physically experience quantum mechanical forces between reactants in chemical reactions. This allows one to screen the profile of potential energy surfaces for the study of reaction mechanisms. For this, we have developed a interface between the user and a virtual laboratory by means of a force-feedback haptic device. Potential energy surfaces of chemical reactions can be explored efficiently by rendering in the haptic device the gradients calculated with first-principles methods. The underlying potential energy surface is accurately fitted on the fly by the interpolating moving least-squares (IMLS) scheme to a grid of quantum chemical electronic energies (and geometric gradients). In addition, we introduce a new IMLS-based method to locate minimum-energy paths between two points on a potential energy surface.

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“…͓DOI: 10.1063/1.2955729͔ Accurate potential energy surfaces ͑PESs͒ are a prerequisite for many types of chemical calculations, ranging from spectroscopy to reaction dynamics. In the past decades, many surface generation methods, such as functional fitting, 1-3 spline, 4,5 reproducing kernel Hilbert space ͑RKHS͒, 6 modified Shepard interpolation, 7 interpolating moving least-squares, 8 and neural networks, 9 have been developed to construct global PESs from a set of ab initio data points for particular molecular geometries. The accuracy of a constructed PES depends on the ab initio level used for electronic structure calculations, on the number of ab initio data points calculated to sample the molecular configuration, as well as on the generation method used to construct the PES.…”

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confidence: 99%

A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reaction

Zhang

2008

The Journal of Chemical Physics

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We present a hierarchical construction scheme for accurate ab initio potential energy surface generation. The scheme is based on the observation that when molecular configuration changes, the variation in the potential energy difference between different ab initio methods is much smaller than the variation for potential energy itself. This means that it is easier to numerically represent energy difference to achieve a desired accuracy. Because the computational cost for ab initio calculations increases very rapidly with the accuracy, one can gain substantial saving in computational time by constructing a high accurate potential energy surface as a sum of a low accurate surface based on extensive ab initio data points and an energy difference surface for high and low accuracy ab initio methods based on much fewer data points. The new scheme was applied to construct an accurate ground potential energy surface for the FH(2) system using the coupled-cluster method and a very large basis set. The constructed potential energy surface is found to be more accurate on describing the resonance states in the FH(2) and FHD systems than the existing surfaces.

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Interpolating moving least-squares methods for fitting potential energy surfaces: Applications to classical dynamics calculations

Cited by 69 publications

References 15 publications

On representing chemical environments

On representing chemical environments

Haptic quantum chemistry

A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reaction

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