Department of Chemistry, University of Sheffield, Sheffield S3 7HF, United Kingdom.
J Chem Phys. 2017 Aug 21;147(7):074108. doi: 10.1063/1.4986887.
New, efficient schemes for the prescreening and evaluation of integrals over effective core potentials (ECPs) are presented. The screening is shown to give a rigorous, and close bound, to within on average 10% of the true value. A systematic rescaling procedure is given to reduce this error to approximately 0.1%. This is then used to devise a numerically stable recursive integration routine that avoids expensive quadratures. Tests with coupled clusters with single and double excitations and perturbative triple calculations on small silver clusters demonstrate that the new schemes show no loss in accuracy, while reducing both the power and prefactor of the scaling with system size. In particular, speedups of roughly 40 times can be achieved compared to quadrature-based methods.
本文提出了新的、有效的有效核势（ECP）积分预筛选和评估方案。筛选结果表明，其给出了一个严格的、接近真实值的紧密界限，平均误差在 10%以内。文中还给出了一个系统的重标度过程，可将该误差减小到约 0.1%。然后，利用这一过程设计了一种数值稳定的递归积分程序，避免了昂贵的数值积分。在银团簇上进行的单激发和双激发耦合簇以及微扰三计算的测试表明，新方案在不损失精度的情况下，减少了与系统规模相关的缩放的幂次和前置因子。特别是，与基于数值积分的方法相比，可以实现大约 40 倍的加速。
