Exact Two-Component Relativistic Polarizable Density Embedding

We have implemented the fragment-based polarizable density embedding (PDE) model within a relativistic framework building on the eXact 2-Component (X2C) relativistic Hamiltonian, thereby taking the PDE method to a relativistic framework. The PDE model provides a robust solution to the electron-leakage problem, and we show that this newly implemented model offers an accurate way to model solvated systems possessing significant relativistic effects. To demonstrate the model's performance, we perform comparative calculations of the K- and L_2,3-edge spectra of water-solvated cysteine (both protonated and deprotonated) with the X2C Hamiltonian. Particularly, with counterions such as Na⁺ in the solvent, electron leakage clearly shows in the older polarizable embedding model through spurious peaks in the spectra. However, when the PDE model is employed, these spurious peaks disappear.