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

doi:10.1007/s10910-019-01034-z

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

Journal Article · Sat Jun 08 00:00:00 EDT 2019 · Journal of Mathematical Chemistry

DOI:https://doi.org/10.1007/s10910-019-01034-z· OSTI ID:1529142

Rai, Prashant ^[1]; Sargsyan, Khachik ^[1]; Najm, Habib ^[1]; Hirata, So ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Univ. of Illinois, Urbana-Champaign, IL (United States)

We introduce 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 establish 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 indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Scientific User Facilities Division

Grant/Contract Number:: AC02-05CH11231; AC04-94AL85000; NA0003525; SC0008692

OSTI ID:: 1529142

Report Number(s):: SAND--2018-9076J; SAND--2019-1537J; 672507

Journal Information:: Journal of Mathematical Chemistry, Journal Name: Journal of Mathematical Chemistry Journal Issue: 7 Vol. 57; ISSN 0259-9791

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Anharmonic vibrations
Compressed sensing
Green’s function theory
High dimensional integration
Potential energy surfaces
Tensor decomposition

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

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