Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

Prashant Rai, Khachik Sargsyan, Habib Najm, So Hirata

Research output: Contribution to journalArticle

Abstract

We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we implement a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work suggest a more efficient scaling of computational cost with molecular size as compared to other methods.

Original languageEnglish (US)
Pages (from-to)1732-1754
Number of pages23
JournalJournal of Mathematical Chemistry
Volume57
Issue number7
DOIs
StatePublished - Aug 15 2019

Fingerprint

Sparse Approximation
Low-rank Approximation
Potential Energy Surface
Potential energy surfaces
Zero Point
Tensors
Tensor
Energy
Compressed sensing
Polynomial Basis
Compressed Sensing
Green's function
Rank Reduction
Molecules
Polynomials
Transition State
Sparse Representation
Quadrature Rules
Evaluation
Local Minima

Keywords

  • Anharmonic vibrations
  • Compressed sensing
  • Green’s function theory
  • High dimensional integration
  • Potential energy surfaces
  • Tensor decomposition

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies. / Rai, Prashant; Sargsyan, Khachik; Najm, Habib; Hirata, So.

In: Journal of Mathematical Chemistry, Vol. 57, No. 7, 15.08.2019, p. 1732-1754.

Research output: Contribution to journalArticle

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