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Title: Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm -1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.
Authors:
 [1] ;  [1] ;  [1] ;  [2] ;  [2]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry
Publication Date:
Report Number(s):
SAND-2017-0642J
Journal ID: ISSN 0026-8976; 650599; TRN: US1702460
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 115; Journal Issue: 17-18; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Potential energy surfaces; tensor decomposition; anharmonic vibrations; Green's function theory
OSTI Identifier:
1361645

Rai, Prashant, Sargsyan, Khachik, Najm, Habib, Hermes, Matthew R., and Hirata, So. Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory. United States: N. p., Web. doi:10.1080/00268976.2017.1288937.
Rai, Prashant, Sargsyan, Khachik, Najm, Habib, Hermes, Matthew R., & Hirata, So. Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory. United States. doi:10.1080/00268976.2017.1288937.
Rai, Prashant, Sargsyan, Khachik, Najm, Habib, Hermes, Matthew R., and Hirata, So. 2017. "Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory". United States. doi:10.1080/00268976.2017.1288937. https://www.osti.gov/servlets/purl/1361645.
@article{osti_1361645,
title = {Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory},
author = {Rai, Prashant and Sargsyan, Khachik and Najm, Habib and Hermes, Matthew R. and Hirata, So},
abstractNote = {Here, a new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm-1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.},
doi = {10.1080/00268976.2017.1288937},
journal = {Molecular Physics},
number = 17-18,
volume = 115,
place = {United States},
year = {2017},
month = {3}
}