Equation-of-Motion Coupled-Cluster Theory for Excitation Energies of Closed-Shell Systems with Spin-Orbit Coupling.
Equation-of-Motion Coupled-Cluster Theory for Excitation Energies of Closed-Shell Systems with Spin-Orbit Coupling.
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DOI：
10.1021/ct500854m
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发表时间：
2014-11
影响因子：
5.5
通讯作者：
Zhifan Wang;Zheyan Tu;Fan Wang
中科院分区：
文献类型：
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作者：
Zhifan Wang;Zheyan Tu;Fan Wang
在后Hartree-Fock处理中，基于运动方程(EOM)耦合团簇理论，计算了考虑自旋-轨道耦合(SOC)的闭壳系统在单、双(CCSD)水平上的激发能.SoC可同时包含在CC和EOM步骤(EOM-SOC-CCSD)中，或仅包含在EOM部分(SOC-EOM-CCSD)中。后一种方法是解释SOC效应的一种经济方法，但这种方法的激发能量不是大小密集型的。当忽略后一种方法中的未连接项(CSOC-EOM-CCSD)时，可以得到尺寸密集的激发能。利用时间反转对称性和空间对称性来减少计算量。施加时间反转对称性得到了相似变换的哈密顿量的实矩阵表示，这有助于Davidson算法中对新的试向量的时间反转对称性的要求。对一些含有重元素的闭壳原子和分子的计算结果表明，EOM-SOC-CCSD方法能够较准确地提供激发能和自旋轨道分裂。另一方面，SOC-EOM-CCSD方法能够准确地估计包含元素到第五行的体系的价电子的SOC效应，而CSOC-EOM-CCSD方法对于涉及p1/2自旋的跃迁的自旋-轨道分裂不太准确，即使对于Kr也是如此。
Excitation energies of closed-shell systems based on the equation-of-motion (EOM) coupled-cluster theory at the singles and doubles (CCSD) level with spin-orbit coupling (SOC) included in the post-Hartree-Fock treatment are implemented in the present work. SOC can be included in both the CC and EOM steps (EOM-SOC-CCSD) or only in the EOM part (SOC-EOM-CCSD). The latter approach is an economical way to account for SOC effects, but excitation energies with this approach are not size-intensive. When the unlinked term in the latter approach is neglected (cSOC-EOM-CCSD), size-intensive excitation energies can be obtained. Time-reversal symmetry and spatial symmetry are exploited to reduce the computational effort. Imposing time-reversal symmetry results in a real matrix representation for the similarity-transformed Hamiltonian, which facilitates the requirement of time-reversal symmetry for new trial vectors in Davidson's algorithm. Results on some closed-shell atoms and molecules containing heavy elements show that EOM-SOC-CCSD can provide excitation energies and spin-orbit splittings with reasonable accuracy. On the other hand, the SOC-EOM-CCSD approach is able to afford accurate estimates of SOC effects for valence electrons of systems containing elements up to the fifth row, while cSOC-EOM-CCSD is less accurate for spin-orbit splittings of transitions involving p1/2 spinors, even for Kr.