  We develop a quartic-scaling implementation of coupled-cluster singles and
doubles based on low-rank tensor hypercontraction (THC) factorizations of both
the electron repulsion integrals (ERIs) and the doubles amplitudes. This
extends our rank-reduced coupled-cluster method to incorporate higher-order
tensor factorizations. The THC factorization of the doubles amplitudes accounts
for most of the gain in computational efficiency as it is sufficient, in
conjunction with a Cholesky decomposition of the ERIs, to reduce the
computational complexity of most contributions to the CCSD amplitude equations.
Further THC factorization of the ERIs reduces the complexity of certain terms
arising from nested commutators between the doubles excitation operator and the
two-electron operator. We implement this new algorithm using graphical
processing units (GPUs) and demonstrate that it enables CCSD calculations for
molecules with 250 atoms and 2500 basis functions using a single computer node.
Further, we show that the new method computes correlation energies with
comparable accuracy to the underlying RR-CCSD method.
