Fully relativistic first-principles calculation by using extended Hubbard energy functionals*

The extended Hubbard energy functional has been shown the significantly improvement for the description of electron localization and orbital hybridization on the equal footing. To validate this correction in heavy element systems, we extended the energy functionals to account for noncollinear spin states to include spin-orbit coupling effects. We present band structure results, particularly focusing on Bi₂Se₃, which exhibits substantial spin-orbit coupling. This yields a dramatic change in the low-energy band structure compared to conventional exchange-correlational functionals. Parabolic dispersion in valence and conduction bands is observed as similar as the GW approximation. We also confirm gap reduction depending on the number of layers, in line with topological insulator characteristics. Consequently, accurate high-throughput calculations are expected, even in systems that both spin-orbit coupling and strong interactions are necessarily considered.