Relativistic two-component projection-based quantum embedding for open-shell systems

In this work, we present a relativistic quantum embedding formalism capable of variationally treating relativistic effects, including scalar-relativity and spin-orbit coupling. We extend density functional theory (DFT)-in-DFT projection-based quantum embedding to a relativistic two-component formalism, where the full spin magnetization vector form is retained throughout the embedding treatment. To benchmark various relativistic embedding schemes, spin-orbit splitting of the nominally t_2g valence manifold of W(CO)₆, exchange coupling of [(H₃N)₄Cr(OH)₂Cr(NH₃)₄]⁴⁺, and the dissociation potential curve of WF₆ are investigated. The relativistic embedding formalism introduced in this work is well suited for efficient modeling of open-shell systems containing late transition metal, lanthanide, and actinide molecular complexes.