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

- Hohenstein, Edward G. and Kokkila, Sara I. L. and Parrish, Robert M. and Martinez, Todd J. ,
**Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2**,*Journal of Chemical Physics*, 138 , ,**2013**. [link] - Hohenstein, Edward G. and Kokkila, Sara I. L. and Parrish, Robert M. and Martinez, Todd J. ,
**Tensor Hypercontraction Equation-of-Motion Second-Order Approximate Coupled Cluster: Electronic Excitation Energies in O(N-4) Time**,*Journal of Physical Chemistry B*, 117 , 12972-12978 ,**2013**. [link] - Hohenstein, Edward G. and Parrish, Robert M. and Martinez, Todd J. ,
**Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Moller-Plesset perturbation theory**,*Journal of Chemical Physics*, 137 , ,**2012**. [link] - Hohenstein, Edward G. and Parrish, Robert M. and Sherrill, C. David and Martinez, Todd J. ,
**Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions**,*Journal of Chemical Physics*, 137 , ,**2012**. [link] - Parrish, Robert M. and Hohenstein, Edward G. and Martinez, Todd J. and Sherrill, C. David ,
**Tensor hypercontraction. II. Least-squares renormalization**,*Journal of Chemical Physics*, 137 , ,**2012**. [link] - Parrish, Robert M. and Hohenstein, Edward G. and Martinez, Todd J. and Sherrill, C. David ,
**Discrete variable representation in electronic structure theory: Quadrature grids for least-squares tensor hypercontraction**,*Journal of Chemical Physics*, 138 , ,**2013**. [link] - Parrish, Robert M. and Hohenstein, Edward G. and Schunck, Nicolas F. and Sherrill, C. David and Martinez, Todd J. ,
**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 , ,**2013**. [link] - Parrish, Robert M. and Sherrill, C. David and Hohenstein, Edward G. and Kokkila, Sara I. L. and Martinez, Todd J. ,
**Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction**,*Journal of Chemical Physics*, 140 , ,**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**,*J. Chem. Theory Comput.*, 11,3042–3052,**2015**. [link] - Robert M. Parrish, Edward G. Hohenstein, and Todd J. Martinez,
**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)]**,*J. Chem. Phys.*, 145,,**2016**. [link] - Song, Chenchen and Martinez, Todd J. ,
**Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction**,*Journal of Chemical Physics*, 146 , NULL ,**2017**. [link] - Song, Chenchen and Martinez, Todd J. ,
**Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity**,*The Journal of Chemical Physics*, 144 , 174111 ,**2016**. [link] - Chenchen Song, Todd J Martínez,
**Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units**,*The Journal of Chemical Physics*, 147,161723,**2017**. [link]