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With the help of newly developed X-ray free-electron laser (XFEL) sources,creating double core holes simultaneously at the same or different atomic sitesin a molecule has now become possible. Double core hole (DCH) X-ray emission isa new form of X-ray nonlinear spectroscopy that can be studied with a XFEL.Here we computationally explore the metal K-edge valence-to-core (VtC) X-rayemission spectroscopy (XES) of metal/metal and metal/ligand double core holestates in a series of transition metal complexes with time-dependent densityfunctional theory. The simulated DCH VtC-XES signals are compared withconventional single core hole (SCH) XES signals. The energy shifts andintensity changes of the DCH emission lines with respect to the correspondingSCH-XES features are fingerprints of the coupling between the second core holeand the occupied orbitals around the DCHs that contain important chemicalbonding information of the complex. The core hole localization effect on DCHVtC-XES is also briefly discussed. We theoretically demonstrate that DCH XESprovides subtle information on the local electronic structure around metalcenters in transition metal complexes beyond conventional linear XES. Ourpredicted changes from calculations between SCH-XES and DCH-XES features shouldbe detectable with modern XFEL sources.

Double Core Hole Valence-to-Core X-ray Emission Spectroscopy: A Theoretical Exploration Using Time-Dependent Density Functional Theory