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A local interpolation scheme using no derivatives in potential sampling: Application to O( 1 D ) + H 2 system
Author(s) -
Ishida Toshimasa,
Schatz George C.
Publication year - 2003
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.10252
Subject(s) - interpolation (computer graphics) , hessian matrix , mathematics , scheme (mathematics) , function (biology) , linear interpolation , bilinear interpolation , second derivative , algorithm , computer science , mathematical analysis , artificial intelligence , statistics , motion (physics) , evolutionary biology , polynomial , biology
We recently proposed a local interpolation scheme, in which interpolant moving least squares (IMLS) and Shepard interpolation are employed to describe potential energy surfaces. This IMLS/Shepard scheme is used to interpolate quantum chemical potential energy surfaces for which analytical derivatives are not available. In this study, we apply the scheme to the highly exothermic O( 1 D ) + H 2 → H + OH reaction and compare it with results based on Shepard interpolation using second‐order Taylor expansions. An analytical surface is used to define the potential function so that errors in the interpolation function may accurately be determined. We find that the present scheme reproduces the correct reactive cross‐sections more accurately than the Shepard scheme, and with rms errors for energy and gradients that are significantly smaller than those from Shepard interpolation. This occurs even though the present scheme does not utilize derivative and Hessian information, whereas the Shepard interpolation does. The Bayesian approach proposed by Bettens and Collins does not improve the IMLS/Shepard results significantly, although it does the Shepard‐only approach. The accuracy of the IMLS/Shepard scheme is surprising, but can be explained by the more global nature of the interpolation. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1077–1086, 2003