Lowrank canonicaltensor decomposition of potential energy surfaces: application to gridbased diagrammatic vibrational Green's function theory
Here, a new method is proposed for a fast evaluation of highdimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical lowrank tensor format, reducing its integral into a relatively short sum of products of lowdimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of singlepoint energy evaluations. Therefore, it eradicates a forceconstant 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 zeropoint and transition energy calculations of molecules using the secondorder diagrammatic vibrational manybody Green's function (XVH2) theory with a harmonicapproximation reference. In this application, high dimensional PES and Green's functions are both subjected to a lowrank decomposition. Evaluating the molecular integrals over a lowrank PES and Green's functions as sums of lowdimensional integrals using the Gauss–Hermite quadrature, this canonicaltensordecompositionbased XVH2 (CTXVH2) 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:

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 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Univ. of Illinois, UrbanaChampaign, IL (United States). Dept. of Chemistry
 Publication Date:
 Report Number(s):
 SAND20170642J
Journal ID: ISSN 00268976; 650599; TRN: US1702460
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Molecular Physics
 Additional Journal Information:
 Journal Volume: 115; Journal Issue: 1718; Journal ID: ISSN 00268976
 Publisher:
 Taylor & Francis
 Research Org:
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 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. Lowrank canonicaltensor decomposition of potential energy surfaces: application to gridbased 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. Lowrank canonicaltensor decomposition of potential energy surfaces: application to gridbased 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.
"Lowrank canonicaltensor decomposition of potential energy surfaces: application to gridbased 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 = {Lowrank canonicaltensor decomposition of potential energy surfaces: application to gridbased 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 highdimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical lowrank tensor format, reducing its integral into a relatively short sum of products of lowdimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of singlepoint energy evaluations. Therefore, it eradicates a forceconstant 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 zeropoint and transition energy calculations of molecules using the secondorder diagrammatic vibrational manybody Green's function (XVH2) theory with a harmonicapproximation reference. In this application, high dimensional PES and Green's functions are both subjected to a lowrank decomposition. Evaluating the molecular integrals over a lowrank PES and Green's functions as sums of lowdimensional integrals using the Gauss–Hermite quadrature, this canonicaltensordecompositionbased XVH2 (CTXVH2) achieves an accuracy of 0.1 cm1 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 = 1718,
volume = 115,
place = {United States},
year = {2017},
month = {3}
}