论文标题
范围分隔的随机分辨率：配方和应用于二阶Green的功能理论
Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory
论文作者
论文摘要
我们为$ 4 $ index电子排斥积分的身份方法开发了范围分隔的随机分辨率，其中使用确定性分辨率来处理较大的术语（高于预定义的阈值），其余术语则使用身份的随机分辨率来处理。该方法是在二阶绿色功能形式主义中实现的，并具有改进的$ O（n^3）$缩放，其大小为基集$ n $。此外，与完整的随机版本相比，范围分离的方法大大降低了统计误差（{\ it J.Chem。Phys。} {\ BF 151}，044144（2019）），从而导致地面的计算加速和近两个幅度的激发状态能量，以示例为水。
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.
