Relativistic Self-ConsistentGW: Exact Two-Component Formalism with One-Electron Approximation

We present a formulation of relativistic self-consistent GW based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation. Our all-electron implementation is fully ab initio and requires no pseudopotential constructed from relativistic atomic calculations. We examine the effect of the X2C1e approximation by comparison to DFT calculations and reach excellent agreement with the established four-component theory. The simplicity of X2C1e makes it feasible to construct higher order theories, such as embedding theories, on top of GW.