Within current electronic structure theory methods, fully relativistic four-component (4c) approaches based on the Dirac Hamiltonian treat spin–orbit coupling with the most rigor. The spin treatment arises naturally from the formulation and does not need to be included ad hoc. Spin–orbit splittings can provide insightful benchmark criteria for the assessment of 4c methods; however, there have not been extensive studies in this respect. Spin–orbit splittings of the p-block elements B–I were computed using the 4c-CASSCF, 4c-CASPT2, and 4c-MR-CISD+Q methods, as recently implemented in BAGEL, with uncontracted Dunning basis sets. Comparison with experiment reveals that the four-component methods yield good results, with most of the computed splittings falling within 15% of the experimental values. A large basis set is needed to obtain accurate splittings of the light elements B–F, while splittings of heavier elements show little basis dependence. The 4c-MR-CISD+Q method gave the best splittings for light elements, while 4c-CASSCF showed the best splittings for elements beyond fluorine. The 4c-CASPT2 method gave the best splittings for group 13 atoms.

中文翻译：

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通过四分量多参考方法进行自旋-轨道耦合：p块元素的基准测试和初步建议

在当前的电子结构理论方法中，基于狄拉克·汉密尔顿理论的完全相对论四分量（4c）方法最严格地对待了自旋-轨道耦合。旋转处理自然是从配方中产生的，不需要临时包括在内。自旋轨道分裂可以为4c方法的评估提供深刻的基准标准。但是，在这方面还没有进行广泛的研究。p块元素B–I的自旋轨道分裂是使用4c-CASSCF，4c-CASPT2和4c-MR-CISD + Q方法计算的，如最近在BAGEL中实施的那样，使用了未签约的邓宁基础集。与实验的比较表明，四组分方法产生了良好的结果，大多数计算的分裂落在实验值的15％之内。需要一个大的基集来获得轻元素B–F的精确分割，而较重的元素的分割几乎没有显示出基依性。4c-MR-CISD + Q方法对轻元素的分离效果最好，而4c-CASSCF对氟以外元素的分离效果最好。4c-CASPT2方法对第13组原子给出了最佳拆分。