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

Markus Schröder (), Hans-Dieter Meyer () and Oriol Vendrell ()
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Markus Schröder: Universität Heidelberg, Physikalisch-Chemisches Institut
Hans-Dieter Meyer: Universität Heidelberg, Physikalisch-Chemisches Institut
Oriol Vendrell: Universität Heidelberg, Physikalisch-Chemisches Institut

A chapter in High Performance Computing in Science and Engineering '20, 2021, pp 73-86 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-80602-6_5

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DOI: 10.1007/978-3-030-80602-6_5

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