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

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 (t(ijk)(abc)). Through our method, we can reduce the scaling of the (T) energy from the traditional O(N-7) to a more modest O(N-5). 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.

Automated summary

We propose a reduced scaling method for evaluating the perturbative triples energy in coupled-cluster theory using tensor hypercontraction. Our method reduces the scaling of the energy calculation and exhibits good accuracy compared to CCSD(T). We also demonstrate the convergence of our method and its sublinear to linear error growth with system size.