  Photochemistry and photophysics processes involve structures far from
equilibrium. In these reactions, there is often strong coupling between nuclear
and electronic degrees of freedom. For first-row transition metals, K$\beta$
X-ray emission spectroscopy (XES) is a sensitive probe of electronic structure
due to the direct overlap between the valence orbitals and the 3p hole in the
final state. Here the sensitivity of K$\beta$ mainline (K$\beta$1,3) XES to
structural dynamics is analyzed by simulating spectral changes along the
excited state dynamics of an iron photosensitizer [FeII(bmip)2]2+ [bmip =
2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine], using both restricted active
space (RAS) multiconfigurational wavefunction theory and a one-electron
orbital-energy approach in density-functional theory (1-DFT). Both methods
predict a spectral blue-shift with increasing metal-ligand distance, which
changes the emission intensity for any given detection energy. These results
support the suggestion that the [FeII(bmip)2]2+ femtosecond K$\beta$ XES signal
shows oscillations due to coherent wavepacket dynamics. Based on the RAS
results, the sensitivity to structural dynamics is twice as high for K$\beta$
compared to K$\alpha$, with the drawback of a lower signal-to-noise ratio.
K$\beta$ sensitivity is favored by a larger spectral blue-shift with increasing
metal-ligand distance and larger changes in spectral shape. Comparing the two
simulations methods, 1-DFT predicts smaller energy shifts and lower
sensitivity, likely due to missing final-state effects. The simulations can be
used to design and interpret XES probes of non-equilibrium structures to gain
mechanistic insights in photocatalysis.
