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We present the working equations for a reduced-scaling method of evaluatingthe perturbative triples (T) energy in coupled-cluster theory, through thetensor hypercontraction (THC) of the triples amplitudes ($t_{ijk}^{abc}$).Through our method we can reduce the scaling of the (T) energy from thetraditional O($N^{7}$) to a more modest O($N^{5}$). We also discussimplementation details to aid future research, development, and softwarerealization of this method. Additionally, we show that this method yieldssub-millihartree (mEh) differences from CCSD(T) when evaluating absoluteenergies, and sub-0.1 kcal/mol energy differences when evaluating relativeenergies. Finally, we demonstrate that this method converges to the trueCCSD(T) energy through the systematic increasing of the rank or eigenvaluetolerance of the orthogonal projector, as well as exhibiting sub-linear tolinear error growth with respect to system size.

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