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

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. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4795514]