Stanford
The Martínez Group Bridging the gap between Molecular Dynamics and Quantum Chemistry Bridging the gap between Molecular Dynamics and Quantum Chemistry
Bridging the gap between Molecular Dynamics and Quantum Chemistry

Tensor Hyper-contraction

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-CC2, Journal 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) Time, Journal 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 theory, Journal 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 wavefunctions, Journal 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 renormalization, Journal 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 hypercontraction, Journal 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 Problems, Physical 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 hypercontraction, Journal 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 Energies, Journal 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 hypercontraction, Journal 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 sparsity, Journal 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 units, Journal of Chemical Physics, 147, 161723, 2017. [link]