Implementation and Validation of Fully Relativistic GW Calculations: Spin–Orbit Coupling in Molecules, Nanocrystals, and Solids

We present an implementation of G₀W₀ calculations including spin–orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G₀W₀ calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G₀W₀ results for a broad class of systems. We also address the use of different root-finding algorithms for the G₀W₀ quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G₀W₀ calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.