We derive and implement a new way of solving coupled cluster equations with
lower computational scaling. Our method is based on decomposition of both
amplitudes and two electron integrals, using a combination of tensor
hypercontraction and canonical polyadic decomposition. While the original
theory scales as O(N6) with respect to the number of basis functions, we
demonstrate numerically that we achieve sub-millihartree difference from the
original theory with O(N4) scaling. This is accomplished by solving directly
for the factors that decompose the cluster operator. The proposed scheme is
quite general and can be easily extended to other many-body methods