论文标题
四成分相对论二阶多体扰动能的随机评估：一种潜在的二次缩放相关方法
Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method
论文作者
论文摘要
通过整合四组分旋转器和库仑电位的13维产物，可以随机评估对相对论的狄拉克 - 哈特里 - 库克能量的二阶多体扰动校正。电子坐标的真实空间中的整合是通过Monte Carlo（MC）方法与大都市采样的，而假想时间结构域中的MC积分是通过反CDF（累积分布函数）方法执行的。在空间紧凑的情况下达到给定的相对统计误差的计算成本并不比立方体差，并且可能具有电子或基础功能的数量。这是对常规的，确定性的二阶多体扰动方法的五分化缩放量表的巨大改进。该算法也很容易有效地平行，显示出92％的强可伸缩性从64到4096处理器，适用于固定的工作规模。
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.
