Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2012 Dec 14;137(22):221101. doi: 10.1063/1.4768241.
The manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In particular, we show how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) (and related methods) by two orders [from O(N(6)) to O(N(4))] and remove the memory bottleneck associated with storage of the doubles amplitudes. The accuracy of correlated methods as integral and amplitude approximations are introduced is examined. For a set of 20 small molecules, single and double-excitation configuration interaction (CISD), quadratic CISD (QCISD), and CCSD correlation energies could be reproduced with millihartree accuracy after the introduction of these approximations. Our approach exploits otherwise hidden factorizable tensor structure in both the electron repulsion integrals and the wavefunction coefficients and should be applicable with suitable modifications to many methods in electronic structure theory.
四阶张量双激发幅度的操纵对许多电子结构方法的有效实现提出了挑战。我们提出了在张量重缩聚（THC）表示中逼近双激发幅度的概念验证。特别是，我们展示了 THC 如何用于降低耦合簇单双（CCSD）（和相关方法）的分子大小的比例[从 O(N(6))到 O(N(4))]，并消除与双激发幅度存储相关的内存瓶颈。还介绍了相关方法的积分和幅度逼近的准确性。对于一组 20 个小分子，在引入这些逼近后，可以以毫哈特精度重现单激发和双激发组态相互作用（CISD）、二次 CISD（QCISD）和 CCSD 相关能量。我们的方法利用了电子排斥积分和波函数系数中隐藏的可分解张量结构，并应通过适当的修改适用于电子结构理论中的许多方法。
