Yeh Chia-Nan, Morales Miguel A
Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.
J Chem Theory Comput. 2023 Sep 26;19(18):6197-6207. doi: 10.1021/acs.jctc.3c00615. Epub 2023 Aug 25.
We present a low-scaling algorithm for the random phase approximation (RPA) with -point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of -points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.
我们提出了一种低标度算法，用于在张量超收缩（THC）框架下对电子排斥积分（ERI）进行具有(n)点采样的随机相位近似（RPA）。通过一种改进的插值可分离密度拟合（ISDF）程序获得THC分解，该程序具有用于一般单粒子布洛赫轨道的与动量相关的辅助基。我们的公式不需要预先优化的插值点或辅助基，并且精度由插值点的数量系统地控制。所得的RPA算法与(n)点的数量成线性比例，与系统大小成三次方比例，而无需对轨道的稀疏性或局部性做任何假设。ERI和RPA能量的误差相对于THC辅助基的大小显示出快速收敛，这为构建大规模系统的高阶多体微扰理论的高效算法指明了一个有前景且稳健的方向。
