Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Graduate School of Science, Technology, and Innovation, Kobe University, Nada-ku, Kobe 657-8501, Japan.
J Chem Phys. 2018 Nov 7;149(17):174112. doi: 10.1063/1.5054610.
A highly scalable stochastic algorithm is proposed and implemented for computing the basis-set-incompleteness correction to the diagonal, frequency-independent self-energy of the second-order many-body Green's function (GF2) theory within the explicitly correlated (F12) formalism. The 6-, 9-, 12-, and 15-dimensional integrals comprising the F12 correction are directly evaluated by the Monte Carlo method using appropriate weight functions for importance sampling. The method is naturally and easily parallelized, involves minimal memory space and no disk I/O, and can use virtually any mathematical form of a correlation factor. Its computational cost to correct all ionization energies (IEs) is observed to increase as the fourth power of system size, as opposed to the fifth power in the case of the deterministic counterparts. The GF2 calculations and their F12 corrections for the first IEs of C and C were executed on 128 graphical processing units (GF2) and 896 central processing units (F12), respectively, to reach the results with statistical errors of 0.04 eV or less. They showed that the basis-set-incompleteness (from aug-cc-pVDZ) accounts for only 50%-60% of the deviations from experiments, suggesting the significance of higher-order perturbation corrections.
本文提出并实现了一种高效的随机算法，用于计算二阶多体格林函数（GF2）理论中对角、频率独立自能的基组不完备校正，该算法基于显式相关（F12）形式。使用适当的权函数进行重要性抽样，直接通过蒙特卡罗方法评估包含 F12 校正的 6、9、12 和 15 维积分。该方法自然且易于并行化，所需内存空间小，无需磁盘 I/O，并且可以使用几乎任何形式的相关因子。校正所有电离能（IEs）的计算成本预计随系统尺寸的四次方而增加，而在确定性对应物的情况下则随尺寸的五次方而增加。GF2 计算及其对 C 和 C 的第一电离能的 F12 校正分别在 128 个图形处理单元（GF2）和 896 个中央处理单元（F12）上执行，以达到统计误差在 0.04eV 或更小的结果。结果表明，基组不完备（从 aug-cc-pVDZ）仅占实验偏差的 50%-60%，表明高阶微扰校正的重要性。
