发表机构
Marcus Center for Theoretical Chemistry, California Institute of Technology; Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院马克斯理论化学中心; 加州理工学院化学与化学工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将随机张量收缩（STC）应用于拉普拉斯变换MP2的交换贡献，开发出O(N²)随机成本的STC交换算法，在含约7000个基函数的基准分子上，其随机交换评估耗时仅为DF-MP2的1/270，证实STC可作为量子化学通用张量收缩引擎。
AI 中文摘要
二阶Møller-Plesset微扰理论（MP2）是最简单的关联波函数方法之一，但其传统的O(N^5)计算成本限制了其在大体系中的应用。随机张量收缩（STC）是近来出现的一种用于量子化学中高阶张量收缩计算的通用技术。本研究将STC应用于拉普拉斯变换MP2的交换贡献，该贡献是公式中O(N^5)标度的来源。所得STC交换算法具有O(N^3)的确定性设置成本，以及在固定绝对误差下O(N^2)的随机成本。该估计量是无偏的，并且可以通过在完整计算前估计所需样本数量来指定目标随机误差。我们采用混合确定性-随机评估策略实现该算法，结合分组索引采样以降低计算前置因子。在包含约7000个基函数的一系列基准分子上，随机交换评估的耗时仅为同一体系完整DF-MP2计算的1/270。在拉普拉斯变换公式中，O(N^4)标度的直接贡献因此成为唯一显著成本。我们的结果进一步证实了STC作为量子化学通用张量收缩引擎的强大能力。
英文摘要
Second-order Moller--Plesset perturbation theory (MP2) is one of the simplest correlated wave-function methods, but its conventional $O(N^5)$ cost limits its application to large systems. Stochastic tensor contraction (STC) has recently appeared as a general technique to evaluate high-order tensor contractions in quantum chemistry. Here, we apply STC to the exchange contribution of Laplace-transformed MP2, which is the source of $O(N^5)$ scaling in the formulation. The resulting STC exchange algorithm has an $O(N^3)$ deterministic setup cost and an $O(N^2)$ stochastic cost at fixed absolute error. The estimator is unbiased and provides a way to specify the target stochastic error by estimating the number of required samples before the full calculation. We implement the algorithm using a hybrid deterministic--stochastic evaluation strategy, with grouped index sampling, to reduce the computational prefactor. Over a range of benchmark molecules containing up to $\sim 7000$ basis functions, the stochastic exchange evaluation takes as little as $1/270$ of the time of a complete DF-MP2 calculation on the same system. Within the Laplace-transformed formulation, the $O(N^4)$ scaling direct contribution is thus the only significant cost. Our results further substantiate the power of STC to serve as a general tensor-contraction engine for quantum chemistry.
Comments10 pages, 6 figures
