Continuing the developments of theoretical approaches to X-ray spectroscopy in our group we have recently published an article on the interplay (correlation) of nuclear motions and its implications for absorption (XAS) and resonant inelastic scattering spectra (RIXS):

Despite working with high-energy electronic transitions and very short lifetimes, X-ray spectroscopy demonstrates remarkable sensitivity to nuclear motions which are characterized by much smaller energies and larger timescales. Given the prominent place of X-rays in material science, it is of importance since it broadens the scope of the effects which can be studied.

Until now the coupling between electronic and nuclear degrees of freedom in core-level spectra has been analyzed following two strategies: performing numerically exact wave-packet quantum dynamics and applying analytic Franck-Condon model. The former being actively promoted by F. Gel’mukhanov’s group from Stockholm is in general too complicated for large molecules and needs reduction of complexity which could be a non-trivial task. The latter one, in turn, is too simplistic to recover nuclear effects beyond the harmonic approximation for nuclear vibrations.

In our article, we suggest a trajectory-based approach of intermediate complexity, where a system “decides” itself which regions of the phase space to explore and, thus, saving substantial computational effort for large molecules in comparison to exact quantum dynamics. Moreover, our protocol allows disentangling correlated and uncorrelated nuclear dynamics that opens new perspectives in the analysis of vibrational motion with the help of X-rays. Remarkably, we have demonstrated that second-order RIXS spectroscopy should be much more sensitive to nuclear correlation than the first-order XAS.

However, this is only the first proof-of-the-concept step to establishing a robust and versatile tool. In the process of derivation, implementantion, and discussion with colleagues, we have realized the key points, where the protocol needs to be improved. Now we have a roadmap how to systematically approach the exact dynamics and the development is to be continued.