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Tensor Hyper-contraction

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The electron repulsion integral (ERI) tensor is a demanding source of computational complexity in many ab initio methods. In the THC approximation, we reduce this fourth-order tensor to a product of five second-order tensors. This new approximation allows ab initio methods to be evaluated with reduced scaling. We have shown that this reduces the scaling to O(N4) for MP2, MP3, CC2, EOM-CC2, and CCSD. Other efforts to increase computational efficiency include the use of the Hubbard type correction to minimal basis sets.

Related Publications

  • Edward G. Hohenstein, Sara I. L. Kokkila, Robert M. Parrish, and Todd J. Martínez, Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2Journal of Chemical Physics, 138, 124111, 2013[link]
  • Edward G. Hohenstein, Sara I. L. Kokkila, Robert M. Parrish, and Todd J. Martínez, Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N4) TimeJournal of Physical Chemistry B, 117, 12972-12978, 2013[link]
  • Edward G. Hohenstein, Robert M. Parrish, and Todd J. Martínez, Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theoryJournal of Chemical Physics, 137, 044103, 2012[link]
  • Edward G. Hohenstein, Robert M. Parrish, David C. Sherrill, and Todd J. Martínez, Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctionsJournal of Chemical Physics, 137, 221101, 2012[link]
  • Robert M. Parrish, Edward G. Hohenstein, Todd J. Martínez, and David C. Sherrill, Tensor hypercontraction. II. Least-squares renormalizationJournal of Chemical Physics, 137, 224106, 2012[link]
  • Robert M. Parrish, Edward G. Hohenstein, Todd J. Martínez, and David C. Sherrill, Discrete variable representation in electronic structure theory: Quadrature grids for least-squares tensor hypercontractionJournal of Chemical Physics, 138, 194107, 2013[link]
  • Robert M. Parrish, Edward G. Hohenstein, Nicolas F. Schunck, David C. Sherrill, and Todd J. Martínez, Exact Tensor Hypercontraction: A Universal Technique for the Resolution of Matrix Elements of Local Finite-Range N-Body Potentials in Many-Body Quantum ProblemsPhysical Review Letters, 111, 12505, 2013[link]
  • Robert M. Parrish, David C. Sherrill, Edward G. Hohenstein, Sara I. L. Kokkila, and Todd J. Martínez, Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontractionJournal of Chemical Physics, 140, 181102, 2014[link]
  • Sara I. L. Kokkila Schumacher, Edward G. Hohenstein, Robert M. Parrish, Lee-Ping Wang, and Todd J. Martínez, Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction EnergiesJournal of Chemical Theory and Computation, 11, 3042-3052, 2015[link]
  • Robert M. Parrish, Edward G. Hohenstein, and Todd J. Martínez, Comment on “Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure” [J. Chem. Phys. 143, 064103 (2015)]Journal of Chemical Physics, 145, 027101, 2016[link]
  • Chenchen Song and Todd J. Martínez, Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontractionJournal of Chemical Physics, 146, 027101, 2017[link]
  • Chenchen Song and Todd J. Martínez, Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsityJournal of Chemical Physics, 144, 174111, 2016[link]
  • Chenchen Song and Todd J Martínez, Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing unitsJournal of Chemical Physics, 147, 161723, 2017[link]