张量超收缩参数约简密度矩阵算法：O（r^4）尺度下的耦合簇精度
The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling
摘要：
张量超收缩（英语：Tensor hyperconstraction）是一种允许将高阶张量表示为低阶张量的乘积的方法。在本文中，我们展示了如何张量超收缩可以应用到电子排斥积分（ERI）张量和两个粒子的激发振幅中使用的参数约化密度矩阵（pRDM）算法。因为在这两个近似中只需要O（r）个辅助函数，所以我们的整体算法可以被证明为O（r4），其中r是单粒子基函数的数量。我们将我们的算法应用于几个小分子，氢链和烷烃，以证明其低形式的缩放和实际效用。如果我们使用足够的辅助函数，我们获得类似于传统的pRDM算法的精度，在CCSD和CCSD（T）之间。
英文摘要：
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).
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