Tensor Hypercontraction of Cluster Perturbation Theory: Quartic Scaling Perturbation Series for the Coupled Cluster Singles and Doubles Ground-State Energies

Even though cluster perturbation theory has been shown
to be a
robust noniterative alternative to coupled cluster theory, it is still
plagued by high order polynomial computational scaling and the storage
of higher order tensors. We present a proof-of-concept strategy for
implementing a cluster perturbation theory ground-state energy series
for the coupled cluster singles and doubles energy with N4 computational scaling using tensor hypercontraction
(THC). The reduction in computational scaling by two orders is achieved
by decomposing two electron repulsion integrals, doubles amplitudes
and multipliers, as well as selected double intermediates to the THC
format. Using the outlined strategy, we showcase that the THC pilot
implementations retain numerical accuracy to within 1 kcal/mol relative
to corresponding conventional and density fitting implementations,
and we empirically verify the N4 scaling.