Spin–Orbit Coupling via Four-Component Multireference Methods: Benchmarking on p-Block Elements and Tentative Recommendations

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.