Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a “pair point kernel” missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.最小二乘张量超收缩（Least-squares tensor hypercontraction, LS-THC）作为一种降低量子化学中基于波函数方法高昂计算成本的手段，近年来受到了学界的一定关注。然而，已有研究表明，LS-THC分解在描述波函数分量（例如团簇振幅T̂₂）时的表现，远差于其在描述哈密顿量分量（例如电子排斥积分（pq|rs））时的表现。本研究开发了新颖的理论方法，在实空间T̂₂核的框架下探究这些误差的来源，并首次报道了在“类交换”关联能E_X与T̂₂的LS-THC表示误差中存在一种“关联特征”，该特征在10类分子、3种关联波函数以及4种基组的测试体系中均表现出显著的一致性。该关联特征预示着，常规的波函数LS-THC表示中缺失了一种“点对核”，而该核关键依赖于位于原子附近且点对间距处于1至2玻尔半径之间的成对网格点。上述发现为未来改进LS-THC方法以弥补其现有缺陷指明了方向。