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This paper systematically evaluates the accuracy and computational efficiency of single-reference algebraic diagrammatic construction combined with state interaction (SI-ADC) for modeling spin-orbit coupling across molecules, transition-metal complexes, and f-block compounds. Second-order SI-ADC(2) achieves zero-field-splitting and spectroscopic accuracy on par with computationally prohibitive four-component and two-component variational relativistic ADC methods due to beneficial error cancellation between spin-orbit and electron correlation effects. Counterintuitively, the higher-order SI-ADC(3) systematically underperforms SI-ADC(2) on heavy-element systems, establishing the lower-order method as the superior practical framework.
Cheap second-order perturbation theory unexpectedly matches the accuracy of fully relativistic four-component benchmarks for spin-orbit coupling, while outperforming its own third-order counterpart on heavy-element complexes.
Spin-orbit coupling and electron correlation play important roles in a broad range of chemical and physical phenomena. In this work, we systematically assess the performance of single-reference algebraic diagrammatic construction combined with state interaction (SI-ADC) for describing electronic structure in the presence of spin-orbit coupling. We find that second-order SI-ADC methods (SI-ADC(2)) achieve zero-field-splitting accuracies comparable to those of higher-level and more computationally demanding approaches, including variational four-component ADC and two-component ADC methods based on spin-orbit effective Hamiltonians. We further demonstrate the broad applicability of SI-ADC by evaluating a diverse range of spin-orbit-coupled properties, including electron affinities, ionization potentials, neutral excitation energies, core-ionization energies, and magnetic g-tensors, for systems ranging from small molecules to transition-metal complexes and f-block compounds. Across these applications, SI-ADC(2) methods provide consistently accurate results, likely benefiting in part from favorable error cancellation between electron-correlation and spin-orbit effects. In contrast, SI-ADC(3) methods are generally less accurate, particularly for systems containing transition-metal and heavy elements. Overall, these results establish SI-ADC as an efficient and broadly applicable framework for incorporating spin-orbit coupling into ADC calculations of electronic and spectroscopic properties.