A local interpolation scheme using no derivatives in potential sampling: Application to O(1D) + H2 system

Toshimasa Ishida*, George C Schatz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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(1D) + H2 → 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.

Original languageEnglish (US)
Pages (from-to)1077-1086
Number of pages10
JournalJournal of Computational Chemistry
Issue number9
StatePublished - Jul 15 2003


  • Bayesian approach
  • HO
  • Local interpolation
  • O(D)
  • Potential energy surface
  • Reactive cross-section

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics


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