Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Mainz D-55099, Germany.
J Chem Phys. 2010 Nov 7;133(17):174118. doi: 10.1063/1.3496373.
The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducing additional unknown parameters. The explicit expressions are presented and analyzed, and possible simplifications to arrive at a computationally efficient scheme are suggested. Numerical tests based on an implementation obtained by an automated approach are presented. Using a partial wave expansion for the neon atom, we can show that the proposed ansatz indeed leads to the expected (L(max)+1)(-7) convergence of the noniterative triples correction, where L(max) is the maximum angular momentum in the orbital expansion. Further results are reported for a test set of 29 molecules, employing Peterson's F12-optimized basis sets. We find that the customary approach of using the conventional noniterative triples correction on top of a CCSD-F12 calculation leads to significant basis set errors. This, however, is not always directly visible for total CCSD(T) energies due to fortuitous error compensation. The new approach offers a thoroughly explicitly correlated CCSD(T)-F12 method with improved basis set convergence of the triples contributions to both total and relative energies.
耦合簇单双激发加上单 Slater 型相关因子（CCSD-F12）方法，由尖端条件（也表示为 SP 假设）确定，与传统 CCSD 相比，仅需少量开销即可得到接近基组极限的结果。然而，对多电子系统的定量计算至少需要包括连接三激发的影响。在本贡献中，回顾了最近提出的 [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] 扩展 SP 假设及其在非迭代三激发修正 CCSD(T)中的应用。该方法允许在不引入额外未知参数的情况下将显式相关纳入连接三激发中。提出并分析了显式表达式，并提出了可能的简化方案以实现计算效率。基于自动化方法获得的实现，提出了数值测试。使用氖原子的部分波展开，我们可以证明所提出的假设确实导致了非迭代三激发修正的预期（L(max)+1)(-7)收敛，其中 L(max)是轨道展开中的最大角动量。对于使用 Peterson 的 F12 优化基组的 29 个分子的测试集，报告了进一步的结果。我们发现，在 CCSD-F12 计算之上使用传统非迭代三激发修正的惯常方法会导致基组误差显著。然而，由于偶然的误差补偿，这对于总 CCSD(T)能量并不总是直接可见。新方法提供了一种彻底显式相关的 CCSD(T)-F12 方法，改进了总能量和相对能量的三激发贡献的基组收敛性。
