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 sub-millihartree (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 sub-linear to linear error growth with respect to system size.
Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
Externally corrected CCSD with renormalized perturbative triples (R-ecCCSD(T)) and density matrix renormalization group and selected configuration interaction external sources
Time-dependent optimized coupled-cluster method with doubles and perturbative triples [TD-OCCD(T)] for first principles simulation of multielectron dynamics
Consistent inclusion of triple substitutions within a coupled cluster based static quantum embedding theory
University of California, Berkeley（加州大学伯克利分校）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Berkeley Center for Quantum Information and Computation（伯克利量子信息与计算中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
