Explicit embedding methods combined with the complex polarization propagator (CPP) enable the modeling of spectroscopy for increasingly complex systems with a high density of states. We present the first derivation and implementation of the CPP in four- and exact-two-component (X2C) polarizable embedding (PE) frameworks. We denote the developed methods PE-4c-CPP and PE-X2C-CPP, respectively. We illustrate the methods by estimating the solvent effect on ultraviolet-visible (UV-vis) and X-ray atomic absorption (XAS) spectra of [Rh(H2O)6]3+ and [Ir(H2O)6]3+ immersed in aqueous solution. We moreover estimate solvent effects on UV-vis spectra of a platinum complex that can be photochemically activated (in water) to kill cancer cells. Our results clearly show that the inclusion of the environment is required: UV-vis and (to a lesser degree) XAS spectra can become qualitatively different from vacuum calculations. Comparison of PE-4c-CPP and PE-X2C-CPP methods shows that X2C essentially reproduces the solvent effect obtained with the 4c methods
