Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States.
J Chem Theory Comput. 2020 Mar 10;16(3):1382-1385. doi: 10.1021/acs.jctc.9b01205. Epub 2020 Feb 5.
A new method for generating fitting grids for least-squares tensor hypercontraction (LS-THC) is presented. This method draws inspiration from the related interpolative separable density fitting (ISDF) technique but uses only a pivoted Cholesky decomposition of the metric matrix, , already computed as a matter of course in LS-THC. The size and quality of the resulting grid are controlled by a user-defined cutoff parameter and the size of the starting grid. Additionally, the Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit. The quality of the grids produced is evaluated for LS-DF-THC-MP2 calculations on retinal and benzene, the former with a large starting grid and small cc-pVDZ basis set, and the latter with a wide range of grids and basis sets. The error and grid size are found to be well-controlled by either the cutoff parameter (with a large starting grid) or the starting grid size (with a tight cutoff) and highly predictable. The Cholesky-based method is also able to generate unique grids tailored to different charge distributions, for example the (|, (|, and (| distributions that arise in the molecular orbital integrals. While only the (| grid directly affects the MP2 energy, the relative sizes of the other grids are examined.
提出了一种为最小二乘张量超收缩（LS-THC）生成拟合网格的新方法。该方法从相关的内插可分离密度拟合（ISDF）技术中汲取灵感，但仅使用已经作为 LS-THC 中理所当然的计算得到的度量矩阵的枢轴 Cholesky 分解， 。所得网格的大小和质量由用户定义的截止参数和起始网格的大小控制。此外，基于 Cholesky 的方法为执行最小二乘拟合提供了另一种可能更数值稳定的方法。对于视网膜和苯的 LS-DF-THC-MP2 计算，评估了所生成网格的质量，前者具有较大的起始网格和较小的 cc-pVDZ 基组，后者具有广泛的网格和基组范围。发现误差和网格大小可以通过截止参数（具有较大的起始网格）或起始网格大小（具有紧密的截止）很好地控制，并且高度可预测。基于 Cholesky 的方法还能够生成针对不同电荷分布量身定制的独特网格，例如在分子轨道积分中出现的(|，(|，和(|分布。虽然只有(|网格直接影响 MP2 能量，但还检查了其他网格的相对大小。
