Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2 The Journal of Chemical Physics 138, 124111 (2013) 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 6 ) to O(N 5 ), with remarkably low error. Combined with a T 1 -transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation. © 2014 AIP Publishing LLC. [http://dx

The second-order approximate coupled cluster singles and doubles method (CC2) is a valuable tool in electronic structure theory. Although the density fitting approximation has been successful in extending CC2 to larger molecules, it cannot address the steep O(N(5)) scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THC-CC2), which reduces the scaling to O(N(4)) and the storage requirements to O(N(2)). We present an algorithm to efficiently evaluate the THC-CC2 correlation energy and demonstrate its quartic scaling. This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.

The tensor hypercontraction (THC) formalism is applied to equation-of-motion second-order approximate coupled cluster singles and doubles (EOM-CC2). The resulting method, THC-EOM-CC2, is shown to scale as O(N4), a reduction of one order from the formal O(N5) scaling of conventional EOM-CC2. Numerical tests for a variety of molecules show that errors of less than 0.02 eV are introduced into the excitation energies.