距离分离的恒等式随机分解：公式化及其在二阶格林函数理论中的应用
Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory
摘要：
我们开发了一个范围分离的随机分辨率的身份方法的$4$指数电子排斥积分，其中较大的条款（高于预定义的阈值）被视为使用确定性的分辨率的身份和其余条款被视为使用随机分辨率的身份。该方法是在一个二阶格林函数形式主义与改进的$O(N^3)$缩放的基集，$N$的大小。此外，与完全随机版本（{\it J. Chem. Phys.} {\bf 151}，044144（2019）），导致基态和激发态能量的计算加速接近两个数量级，如氢二聚体链所示。
英文摘要：
We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the remaining terms are treated using a stochastic resolution of identity. The approach is implemented within a second-order Greens function formalism with an improved $O(N^3)$ scaling with the size of the basis set, $N$. Moreover, the range-separated approach greatly reduces the statistical error compared to the full stochastic version ({\it J. Chem. Phys.} {\bf 151}, 044144 (2019)), resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains.
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