耦合簇静态嵌入方法 MPCC 的降标度实现：基于密度拟合

中文摘要 AI 辅助

本文提出了一种改进算法，用于实现我们先前提出的静态量子嵌入方法 MPCC（J. Chem. Phys. 161, 164107 (2024)）。该算法在嵌入方法的所有层中均采用密度拟合（DF）近似来处理电子排斥积分（ERIs），这些层包括低层方法、屏蔽相互作用以及高层方法。此外，对于低层方法，基于拉普拉斯变换采用了 Sylvester 方程的近似因式分解求解方案。为了构建屏蔽相互作用，我们探索了基于 Kats 和 Manby（J. Chem. Phys. 141, 061101 (2014)）提出的可区分簇近似（DCA）的近似构造方法，该方法相当于忽略某些高阶交换图和梯子图。结合所有这些技术，我们获得了低层方法的 $\mathcal{O}(N^4)$ 算法；屏蔽相互作用的非迭代 $N_{\rm frag} \mathcal{O}(N^4)$ 算法；以及碎片求解器的迭代 $\mathcal{O}(N_{\rm frag}^6)$ 算法，其中 $N_{\rm frag}$ 是碎片轨道数，$N$ 是总轨道数。由此得到的 MPCC 方法低标度实现被应用于反式多炔烃，即链长 $n=1-8$ 的 C$_{2n}$H$_{2n+2}$ 分子，并将该方法的计时和精度与原始未因式分解实现进行了比较。此外，通过将该方法应用于 \ce{O3} 分子的势能面，进一步验证了这些近似。最后，我们将该方法应用于 S22 数据集中已知 MP2 方法性能较差的选定分子。结果表明，基于 DF 的 MPCC 方法实现显著降低了计算成本，同时保持了与原始实现相当的精度。

英文摘要

An improved algorithm to implement our previously proposed static quantum embedding method MPCC (J. Chem. Phys. 161, 164107 (2024)) is presented. It uses the density-fitting (DF) approximation for the electron-repulsion integrals (ERIs) across all layers of the embedding method: the low-level method, the screened interaction, and the high-level method. Additionally, an approximate factorized solution of the Sylvester equation is employed based on the Laplace transformation for the low-level method. To build the screened interaction, we have explored an approximate construction of it based on the distinguishable cluster approximation (DCA) by Kats and Manby (J. Chem. Phys. 141, 061101 (2014)), which amounts to neglecting certain higher-order exchange and ladder diagrams. Combining all these techniques, we have obtained an $\mathcal{O}(N^4)$ algorithm for the low-level method; a non-iterative $N_{\rm frag} \mathcal{O}(N^4)$ algorithm for the screened interaction; and an iterative $\mathcal{O}(N_{\rm frag}^6)$ algorithm for the fragment solver, where $N_{\rm frag}$ is the number of fragment orbitals and $N$ is the total number of orbitals. The resulting low-scaling implementation of the MPCC method is applied to trans polyacetylenes, that is, C$_{2n}$H$_{2n+2}$ molecules for chain lengths $n=1-8$, and the timing and accuracy of the method are compared to the original unfactorized implementation. Moreover, the approximations are further validated by applying the method to the potential energy surface of the \ce{O3} molecule. Finally, we apply the method to the selected molecules in the S22 dataset for which the performance of the MP2 method is known to be poor. The results demonstrate that the DF-based implementation of the MPCC method provides a significant reduction in computational cost while maintaining accuracy comparable to that of the original implementation.

发表机构

• University of California, Berkeley（加州大学伯克利分校）
• Rensselaer Polytechnic Institute（伦斯勒理工学院）
• Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）

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