  One method of representing a high-rank tensor as a (hyper-)product of
lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et
al. This strategy has been found to be useful for reducing the polynomial
scaling of coupled-cluster methods by representation of a four dimensional
tensor of electron-repulsion integrals in terms of five two-dimensional
matrices. Pierce et al. have already shown that the application of a robust
form of THC to the particle-particle ladder term (PPL) reduces the cost of this
term in couple-cluster singles and doubles (CCSD) from $\mathcal{O} (N^6)$ to
$\mathcal{O} (N^5)$ with negligible errors in energy with respect to the
density-fitted variant. In this work we have implemented the least-squares
variant of THC (LS-THC) which does not require a non-linear tensor
factorization, including the robust form (R-LS-THC), for the calculation of the
excitation and electron attachment energies using equation-of-motion coupled
cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked
the effect of the R-LS-THC-PPL approximation on excitation energies using the
comprehensive QUEST database and the accuracy of electron attachment energies
using the NAB22 database. We find that errors on the order of 1 meV are
achievable with a reduction in total calculation time of approximately
$5\times$.
