Constructing multidimensional molecular potential energy surfaces from ab initio data

Timothy Hollebeek, Tak San Ho, Herschel Rabitz

Research output: Contribution to journalArticlepeer-review

191 Scopus citations


This paper describes the reproducing kernel Hilbert space (RKHS) method for constructing accurate, smooth, and efficient global potential energy surface (PES) representations for polyatomic systems using high-level ab initio data. The RKHS method provides a rigorous and effective framework for smooth multivariate interpolation of arbitrarily scattered data points and also for incorporating various physical requirements onto the PESs. Smoothness, permutation symmetry, and the asymptotic properties of polyatomic systems can be incorporated into the construction of reproducing kernels to render globally accurate PESs. Tensor products of one-dimensional generalized-spline-reproducing kernels are amenable to a fast algorithm, which makes a single evaluation of RKHS PESs essentially independent of the number of interpolated ab initio data points. This efficient implementation enables the study of the detailed dynamics of polyatomic systems based on high-quality RKHS PESs.

Original languageEnglish (US)
Pages (from-to)537-570
Number of pages34
JournalAnnual Review of Physical Chemistry
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • General Medicine


  • Chemical dynamics
  • Reproducing kernel


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