Wang Meng, Li Chenyang
Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China.
Molecules. 2025 May 7;30(9):2082. doi: 10.3390/molecules30092082.
We present an economical approach to treat spin-orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit-Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin-orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin-orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme.
我们提出了一种在状态平均驱动相似重整化群二阶微扰理论（SA-DSRG-PT2）中处理自旋轨道耦合（SOC）的经济方法。首先通过构建SA-DSRG-PT2修饰的无自旋哈密顿量来引入电子关联。然后用Breit-Pauli哈密顿量对该哈密顿量进行扩充，并使用纯自旋参考态进行对角化，以获得经SOC修正的能谱。还假定采用自旋轨道平均场近似来降低与双电子自旋轨道积分相关的成本。由此产生的方法被称为BP1-SA-DSRG-PT2c，它具有与非相对论对应方法相同的计算标度，其中仅需单粒子和双粒子密度累积量即可获得垂直跃迁能。在一些原子和小分子上评估了BP1-SA-DSRG-PT2c的准确性，这些原子和小分子包括主族双原子分子、过渡金属原子和二氧化锕阳离子。数值结果表明，BP1-SA-DSRG-PT2c的表现与其他使用态相互作用方案处理SOC的内收缩多参考微扰理论相当。
