Predictive simulations of core electron binding energies of halogenated species adsorbed on ice surfaces from relativistic quantum embedding calculations

We report an investigation of the suitability of quantum embedding for modeling the effects of the environment on the X-ray photoelectron spectra of hydrogen chloride and the chloride ions adsorbed on ice surfaces, as well as of chloride ions in water droplets. In our approach, we combine a density functional theory (DFT) description of the ice surface with that of the halogen species with the recently developed relativistic core-valence separation equation of motion coupled cluster (CVS-EOM-IP-CCSD) via the frozen density embedding formalism (FDE), to determine the K and L$_{1,2,3}$ edges of chlorine. Our calculations, which incorporate temperature effects through snapshots from classical molecular dynamics simulations, are shown to reproduce the experimental trends for L edges of the species on ice surfaces, with respect to changes in temperature as well as the decrease in core binding energies in Cl$^{-}$ with respect to HCl. Finally, we find that in contrast to the L edges, we strongly underestimate the environmental effects on the K edges. We trace this behavior to the inability of the embedding potential obtained with the FDE approach to faithfully reproduce the Kohn-Sham potential of the analogous DFT calculation on the whole (supermolecular) system, and provide an ad hoc correction to the CVS-EOM-IP-CCSD energies, based on ground-state DFT calculations, that yields binding energies with similar accuracy to that observed for the L edges.