The extension of least-squares tensor hypercontracted second- and third-order Møller-Plessett perturbation theory (LS-THC-MP2 and LS-THC-MP3) to open-shell systems is an important development due to the scaling reduction afforded by THC and the ubiquity of molecular ions, radicals, and other open-shell reactive species. The complexity of wavefunction-based quantum chemical methods such as Møller-Plessett and coupled cluster theory is reflected in the steep scaling of the computational costs with the molecular size. The least-squares tensor hypercontraction (LS-THC) method is an efficient, single-step factorization for the two-electron integral tensor, but can also be used to factorize the double excitation amplitudes, leading to significant scaling reduction. Here, we extend this promising method to open-shell variants of LS-THC-MP2 and -MP3 using diagrammatic techniques and explicit spin-summation. The accuracy of the resulting methods for open-shell species is benchmarked on standard tests systems such as regular alkanes, as well as realistic systems involving bond breaking, radical stabilization, and other effects. We find that open-shell LS-THC-MP$n$ methods exhibit errors highly comparable to those produced by closed-shell LS-THC-MP$n$, and are highly insensitive to particular chemical interactions, geometries, or even to moderate spin contamination.
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
