Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation
Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation
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DOI：
10.1063/1.4948318
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发表时间：
2016-05-07
影响因子：
4.4
通讯作者：
Sherrill, C. David
中科院分区：
文献类型：
--
作者：
Bozkaya, Ugur;Sherrill, C. David
提出了一种基于密度拟合近似的耦合簇单双（CCSD）方法的解析梯度的有效实现方法，简称DF-CCSD。冻结核心条款也包括在内。当应用于一组烷烃，DF-CCSD分析梯度显着加速相比，传统的CCSD较大的分子。我们的DF-CCSD算法的效率来自于几个不同的术语的加速，这些术语被指定为“梯度术语”：粒子密度矩阵（PDM）的计算，广义Fock矩阵（GFM），Z矢量方程的解，松弛的PDM和GFM的形成，PDM和GFM到原子轨道（AO）基础的反向变换，以及AO基础中的梯度的评估。对于烷烃组的最大成员（C10 H22），梯度项（具有cc-pVTZ基组）的计算时间分别为2582.6（CCSD）和310.7（DF-CCSD）min，加速超过8倍。对于梯度相关项，DF方法避免了使用四指数电子排斥积分。根据我们以前的研究[U。Bozkaya，J.Chem.Phys.141，124108（2014）]，我们的形式完全避免了4指数双粒子密度矩阵（TPDM）的构建或存储，而是使用2指数和3指数TPDM。DF方法引入的平衡键长和谐波振动频率的误差可以忽略不计。出版社：AIP Publishing
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies. Published by AIP Publishing.