Quartic scaling second-order approximate coupled cluster singles and doubles via tensor hypercontraction: THC-CC2

Abstract

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 \documentclass[12pt]{minimal}\begin{document}$\mathcal {O}(N^5)$\end{document}O(N5) 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 \documentclass[12pt]{minimal}\begin{document}$\mathcal {O}(N^4)$\end{document}O(N4) and the storage requirements to \documentclass[12pt]{minimal}\begin{document}$\mathcal {O}(N^2)$\end{document}O(N2). 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.