Double core hole valence-to-core x-ray emission spectroscopy: A theoretical exploration using time-dependent density functional theory

With the help of newly developed X-ray free-electron laser (XFEL) sources, creating double core holes (DCHs) simultaneously at the same or different atomic sites in a molecule has now become possible. DCH X-ray emission is a new form of X-ray nonlinear spectroscopy that can be studied with a XFEL. Here in this paper, we computationally explore the metal K-edge valence-to-core (VtC) X-ray emission spectroscopy (XES) of metal/metal and metal/ligand DCH states in a series of transition metal complexes with time-dependent density functional theory. The simulated DCH VtC-XES signals are compared with conventional single core hole (SCH) XES signals. The energy shifts and intensity changes of the DCH emission lines with respect to the corresponding SCH-XES features are fingerprints of the coupling between the second core hole and the occupied orbitals around the DCHs that contain important chemical bonding information of the complex. The difference between delocalized/localized core hole models on DCH VtC-XES is also briefly discussed. We theoretically demonstrate that DCH XES provides subtle information on the local electronic structure around metal centers in transition metal complexes beyond conventional linear XES. In conclusion, our predicted changes from calculations between SCH-XES and DCH-XES features should be detectable with modern XFEL sources.