Robust Tensor Hypercontraction of the Particle–Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory

One method of representing a high-rank tensor as a (hyper-)product
of lower-rank tensors is the tensor hypercontraction (THC) method
of Hohenstein et al. This strategy has been found to be useful for
reducing the polynomial scaling of coupled-cluster methods by representation
of a four-dimensional tensor of electron-repulsion integrals in terms
of five two-dimensional matrices. Pierce et al. have already shown
that the application of a robust form of THC to the particle–particle
ladder (PPL) term reduces the cost of this term in couple-cluster
singles and doubles (CCSD) from O(N6) to O(N5) with negligible errors in energy with respect
to the density-fitted variant. In this work, we have implemented the
least-squares variant of THC (LS-THC) which does not require a nonlinear
tensor factorization, including the robust form (R-LS-THC), for the
calculation of the excitation and electron attachment energies using
equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD,
respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation
on excitation energies using the comprehensive QUEST database and
the accuracy of electron attachment energies using the NAB22 database.
We find that errors on the order of 1 meV are achievable with a reduction
in total calculation time of approximately 5 ×.

将高阶张量表示为低阶张量（超）乘积的一类方法中，Hohenstein等人提出的张量超收缩（tensor hypercontraction, THC）方法是其中之一。该策略通过将四维电子排斥积分张量表示为五个二维矩阵的形式，已被证实可有效降低耦合簇方法的多项式计算标度。Pierce等人此前已证明，将鲁棒形式的THC应用于粒子-粒子梯（particle–particle ladder, PPL）项，可将耦合簇单双激发（coupled-cluster singles and doubles, CCSD）中该项的计算成本从O(N⁶)降至O(N⁵)，且相较于密度拟合变体，其能量误差可忽略不计。本工作中，我们实现了无需非线性张量分解的最小二乘形式张量超收缩（least-squares variant of THC, LS-THC），包括其鲁棒变体（R-LS-THC），并将其用于分别基于运动方程耦合簇方法EOMEE-CCSD与EOMEA-CCSD计算激发能与电子附着能。我们采用全面的QUEST数据库与NAB22数据库，分别对R-LS-THC-PPL近似在激发能计算中的效果，以及电子附着能的计算精度进行了基准测试。研究发现，该方法可实现约5倍的总计算时间缩减，同时可达到毫电子伏特（meV）量级的计算误差。