Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
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DOI：
10.1063/1.3496372
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发表时间：
2010-11-07
影响因子：
4.4
通讯作者：
Tew, David P.
中科院分区：
文献类型：
--
作者：
Koehn, Andreas;Tew, David P.
基于slater型相关因子和由尖点条件确定的固定膨胀系数的二元函数，近年来被提出作为一种将显式电子相关引入耦合簇理论的有效且数值稳定的方法。在这项工作中，我们分析了显式相关耦合簇单双（CCSD-F12）理论的方程，并引入了一个基于微扰理论的排序格式，该格式可用于表征和理解文献中发现的各种近似。29个分子测试的数值结果支持我们的分析，并提供了额外的见解。特别是，我们的结果有助于使CCSD（F12）近似的成功合理化，CCSD（F12）近似基于非常系统地消去被忽略的，否则单独大的三阶二项式-二项式耦合项。如果保留传统双聚类振幅和双聚类振幅之间的整个三阶耦合项集，则可以在不牺牲精度的情况下引入CCSD（F12）的进一步近似，从而产生最近提出的CCSD（F12）和CCSD（F12*）模型，与传统CCSD计算相比，它们的开销可以忽略不计。特别指出了环项型贡献的重要性，它可以用来改进其他现有的近似，如CCSD-F12b。对于较小的基集，保留某些导致CCSD-F12*的高阶项可能是有利的，对于SP的情况，只涉及对CCSD（F12*）的非迭代修正。(C) 2010年美国物理研究所。(doi: 10.1063/1.3496372)
Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help rationalize the success of the CCSD(F12) approximation which is based on a very systematic cancellation of the neglected, otherwise individually large third-order geminal-geminal coupling terms. Further approximations to CCSD(F12) can be introduced without sacrificing the accuracy if the entire set of third-order coupling terms between the conventional doubles cluster amplitudes and the geminal doubles amplitudes is retained, leading to the recently proposed CCSD(F12) and CCSD(F12*) models, which have negligible overhead compared to conventional CCSD calculations. Particularly, the importance of the ring-term type contribution is pointed out which may be used to improve on other existing approximations such as CCSD-F12b. For small basis sets, it might be advantageous to keep certain higher-order terms leading to CCSD-F12*, which, for the case of the SP ansatz, merely involves a noniterative correction to CCSD(F12*). (C) 2010 American Institute of Physics. [doi: 10.1063/1.3496372]