Cao Zhanli, Li Zhendong, Wang Fan, Liu Wenjian
Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, P. R. China.
Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
Phys Chem Chem Phys. 2017 Feb 1;19(5):3713-3721. doi: 10.1039/c6cp07588f.
The spin-separated exact two-component (X2C) relativistic Hamiltonian [sf-X2C+so-DKHn, J. Chem. Phys., 2012, 137, 154114] is combined with the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD) for the treatment of spin-orbit splittings of open-shell molecular systems. Scalar relativistic effects are treated to infinite order from the outset via the spin-free part of the X2C Hamiltonian (sf-X2C), whereas the spin-orbit couplings (SOC) are handled at the CC level via the first-order Douglas-Kroll-Hess (DKH) type of spin-orbit operator (so-DKH1). Since the exponential of single excitations, i.e., exp(T), introduces sufficient spin orbital relaxations, the inclusion of SOC at the CC level is essentially the same in accuracy as the inclusion of SOC from the outset in terms of the two-component spinors determined variationally by the sf-X2C+so-DKH1 Hamiltonian, but is computationally more efficient. Therefore, such an approach (denoted as sf-X2C-EOM-CCSD(SOC)) can achieve uniform accuracy for the spin-orbit splittings of both light and heavy elements. For light elements, the treatment of SOC can even be postponed until the EOM step (denoted as sf-X2C-EOM(SOC)-CCSD), so as to further reduce the computational cost. To reveal the efficacy of sf-X2C-EOM-CCSD(SOC) and sf-X2C-EOM(SOC)-CCSD, the spin-orbit splittings of the Π states of monohydrides up to the sixth row of the periodic table are investigated. The results show that sf-X2C-EOM-CCSD(SOC) predicts very accurate results (within 5%) for elements up to the fifth row, whereas sf-X2C-EOM(SOC)-CCSD is useful only for light elements (up to the third row but with some exceptions). For comparison, the sf-X2C-S-TD-DFT-SOC approach [spin-adapted open-shell time-dependent density functional theory, Mol. Phys., 2013, 111, 3741] is applied to the same systems. The overall accuracy (1-10%) is satisfactory.
自旋分离精确二分量（X2C）相对论哈密顿量[sf-X2C+so-DKHn，《化学物理杂志》，2012年，137卷，154114页]与含单双激发的运动方程耦合簇方法（EOM-CCSD）相结合，用于处理开壳层分子体系的自旋轨道分裂。标量相对论效应从一开始就通过X2C哈密顿量的无自旋部分（sf-X2C）处理到无穷阶，而自旋轨道耦合（SOC）则在耦合簇水平上通过一阶道格拉斯-克罗尔-赫斯（DKH）型自旋轨道算符（so-DKH1）处理。由于单激发的指数exp(T)引入了足够的自旋轨道弛豫，在耦合簇水平上包含SOC在精度上与从一开始就在由sf-X2C+so-DKH1哈密顿量变分确定的二分量旋量方面包含SOC基本相同，但计算效率更高。因此，这种方法（记为sf-X2C-EOM-CCSD(SOC)）可以对轻元素和重元素的自旋轨道分裂实现统一的精度。对于轻元素，SOC的处理甚至可以推迟到运动方程步骤（记为sf-X2C-EOM(SOC)-CCSD），以便进一步降低计算成本。为了揭示sf-X2C-EOM-CCSD(SOC)和sf-X2C-EOM(SOC)-CCSD的有效性，研究了周期表第六行之前的单氢化物Π态的自旋轨道分裂。结果表明，sf-X2C-EOM-CCSD(SOC)对第五行之前的元素预测了非常准确的结果（在5%以内），而sf-X2C-EOM(SOC)-CCSD仅对轻元素（第三行之前但有一些例外）有用。作为比较，将sf-X2C-S-TD-DFT-SOC方法[自旋适应开壳层含时密度泛函理论，《分子物理》，2013年，111卷，3741页]应用于相同的体系。总体精度（1 - 10%）是令人满意的。
