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Title: Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

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Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
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OSTI Identifier:
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 146; Journal Issue: 3
Country of Publication:
United States

Citation Formats

Song, Chenchen, and Martínez, Todd J. Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction. United States: N. p., 2017. Web. doi:10.1063/1.4973840.
Song, Chenchen, & Martínez, Todd J. Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction. United States. doi:10.1063/1.4973840.
Song, Chenchen, and Martínez, Todd J. Sat . "Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction". United States. doi:10.1063/1.4973840.
title = {Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction},
author = {Song, Chenchen and Martínez, Todd J.},
abstractNote = {},
doi = {10.1063/1.4973840},
journal = {Journal of Chemical Physics},
number = 3,
volume = 146,
place = {United States},
year = {Sat Jan 21 00:00:00 EST 2017},
month = {Sat Jan 21 00:00:00 EST 2017}
  • We present a tensor hypercontracted (THC) scaled opposite spin second order Møller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated atomic orbital-based THC-SOS-MP2 calculations is found to be N{sup 2.6} for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 aremore » less than 0.5 kcal/mol for all systems tested (up to 162 atoms).« less
  • Analytic energy gradients for tensor hyper-contraction (THC) are derived and implemented for second-order Møller-Plesset perturbation theory (MP2), with and without the scaled-opposite-spin (SOS)-MP2 approximation. By exploiting the THC factorization, the formal scaling of MP2 and SOS-MP2 gradient calculations with respect to system size is reduced to quartic and cubic, respectively. An efficient implementation has been developed that utilizes both graphics processing units and sparse tensor techniques exploiting spatial sparsity of the atomic orbitals. THC-MP2 has been applied to both geometry optimization and ab initio molecular dynamics (AIMD) simulations. Furthermore, the resulting energy conservation in micro-canonical AIMD demonstrates that the implementationmore » provides accurate nuclear gradients with respect to the THC-MP2 potential energy surfaces.« less
  • We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.
  • We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N{sup 5}) to O(N{sup 3}) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows tomore » replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.« less