The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.
Tensor hypercontraction: A universal technique for the resolution of matrix elements of local, finite-range $N$-body potentials in many-body quantum problems
Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
Technical University of Munich（慕尼黑工业大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to molecules and solids with superexchange
Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
提出了一种基于插值可分密度拟合的张量超压缩（THC）分解方法。我们说明算法的细节，以实现这一目标的框架内，贝克的原子为中心的正交网格。单个ISDF参数$c_\text{ISDF}$控制精度和成本之间的权衡。具体地，$c_\text{ISDF}$设置在THC中使用的内插点的数量，$N_\text{IP} = c_\text{ISDF}\times N_\text{X}$，其中$N_\text{X}$是辅助基函数的数量。结合身份解析（RI）技术，我们开发并研究了用于Hartree-Fock和范围分离混合体（例如，$ω$ B 97 X-V）和四次标度二阶和三阶Møller-Plesset理论（MP2和MP3）。这些算法在W 4 -11热化学（原子化能）集和A24非共价相互作用基准集与标准Dunning基组（cc-pVDZ、cc-pVTZ、aug-cc-pVDZ和aug-cc-pVTZ）上进行了评价。我们证明了收敛的THC-RI算法的数值精确RI结果使用ISDF点。在此基础上，我们对每个基组和方法的$c_\text{ISDF}$提出了建议。我们还演示了THC-RI精确交换和MP2对于水团簇和$\text{C}_{20}$等大型系统的实用性。我们强调，更多的挑战等待在获得准确的和数值稳定的THC分解波函数振幅，以及在大基组的虚拟轨道所跨越的空间，并实现稀疏意识的THC-RI算法。
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
