Tensor Hypercontraction Form of the Perturbative Triples Energy in Coupled-Cluster Theory

Abstract

We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes (tijkabc). Through our method, we can reduce the scaling of the (T) energy from the traditional Formula Presented to a more modest Formula Presented. We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields submillihartree (mEh) differences from CCSD(T) when evaluating absolute energies and sub-0.1 kcal/mol energy differences when evaluating relative energies. Finally, we demonstrate that this method converges to the true CCSD(T) energy through the systematic increasing of the rank or eigenvalue tolerance of the orthogonal projector, as well as exhibiting sublinear to linear error growth with respect to system size.