论文标题
对MP3的最小二乘张量超收集的关键分析
A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3
论文作者
论文摘要
最小二乘张量超收集（LS-THC）方法是一种有前途的方法，可以减少波函数方法的高多项式缩放，例如基于多体扰动理论或耦合群集的方法。在这里，我们专注于LS-THC-MP3，并确定四个具有不同误差和效率特征的变体。分析了LS-THC-MP3的性能，用于具有多达40个第一行原子的常规测试系统。我们还分析了LS-THC-MP3的尺寸扩展/尺寸一致性以及网格和基准依赖性。总体而言，与标准密度拟合相比，观察到的误差很小，并且建议通过修剪产生网格的方法更简化。实用的交叉（LS-THC-MP3比规范方法便宜的点）在240个相关电子左右实现。尽管已确定的LS-THC有几个缺点：一个小但非零尺寸的一致性误差，对角相关性的描述较差，并且随着基集大小的误差的可能性很大，但结果表明，LS-THC具有在MP3和其他波浪函数方法上实用的重要潜力。
The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.
