Core Excitations of Uranyl in Cs₂UO₂Cl₄ from Relativistic Embedded Damped Response Time-Dependent Density Functional...

X-ray spectroscopies, by their high selectivity and sensitivity to the chemical environment around the atoms probed, provide significant insights into the electronic structures of molecules and materials. Interpreting experimental results requires reliable theoretical models, accounting for environmental, relativistic, electron correlation, and orbital relaxation effects in a balanced manner. In this work, we present a protocol for the simulation of core excited spectra with damped response time-dependent density functional theory based on the Dirac-Coulomb Hamiltonian (4c-DR-TD-DFT), in which environmental effects are accounted for through the frozen density embedding (FDE) method. We showcase this approach for the uranium M₄- and L₃-edges and oxygen K-edge of the uranyl tetrachloride (UO₂Cl₄^2-) unit as found in a host Cs₂UO₂Cl₄ crystal. We have found that the 4c-DR-TD-DFT simulations yield excitation spectra that very closely match the experiment for the uranium M₄-edge and the oxygen K-edge, with good agreement for the broad experimental spectra for the L₃-edge. By decomposing the complex polarizability in terms of its components, we have been able to correlate our results with angle-resolved spectra. We have observed that for all edges, but in particular the uranium M₄-edge, an embedded model in which the chloride ligands are replaced by an embedding potential reproduces rather well the spectral profile obtained for UO₂Cl₄^2-. Our results underscore the importance of the equatorial ligands to simulating core spectra at both uranium and oxygen edges.