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Calculation of Global, High-Dimensional Potential Energy Surface Fits in Canonical Decomposition Form Using Monte-Carlo Methods: Application to the Eigen Cation

In: High Performance Computing in Science and Engineering '20

Author

Listed:
  • Markus Schröder

    (Universität Heidelberg, Physikalisch-Chemisches Institut)

  • Hans-Dieter Meyer

    (Universität Heidelberg, Physikalisch-Chemisches Institut)

  • Oriol Vendrell

    (Universität Heidelberg, Physikalisch-Chemisches Institut)

Abstract

We have implemented a Monte-Carlo version of a well-known alternating least squares algorithm to obtain a sum-of-products representation of potential energy surfaces, more precisely a so-called Canonical Polyadic Decomposition, for use in quantum-dynamical simulations. Our modification replaces exact integrals with Monte-Carlo integrals. The incorporation of correlated weights, and hence weighted integrals, is straight forward using importance sampling. Using Monte-Carlo methods allows to efficiently solve high-dimensional integrals that are needed in the original scheme and enables us to treat much larger systems than previously possible. We demonstrate the method with calculations on the 33-dimensional Eigen cation.

Suggested Citation

  • Markus Schröder & Hans-Dieter Meyer & Oriol Vendrell, 2021. "Calculation of Global, High-Dimensional Potential Energy Surface Fits in Canonical Decomposition Form Using Monte-Carlo Methods: Application to the Eigen Cation," Springer Books, in: Wolfgang E. Nagel & Dietmar H. Kröner & Michael M. Resch (ed.), High Performance Computing in Science and Engineering '20, pages 73-86, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-80602-6_5
    DOI: 10.1007/978-3-030-80602-6_5
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