Nuclear vibrations in X-ray spectra with a fine-tooth comb

One might remember the post where I have written about nuclear correlation effects showing up in absorption and resonant inelastic X-ray scattering spectra. A few days ago we have published a follow-up article, where this effect is scrutinously dissected:

Sven Karsten,  Sergey I. Bokarev,  Saadullah G. Aziz,  Sergei D. Ivanov, Oliver Kühn A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy J. Chem. Phys. 146, 224203 (2017).

X-ray nuclear dynamics

In the article, you can find an explicit derivation of the time-domain working expressions, a detailed description of our protocol, loads of formulas and graphs – the whole nine yards. Fans of math should do appreciate Sven’s efforts. Even more important, it represents a critical view of the method and suggests the route how to improve the main pitfalls of classical approximation with moderate effort.


Photodynamics in ferricyanide revisited

In continuation of our collaboration with Prof. Emad F. Aziz and Dr. Igor Yu. Kiyan from Helmholtz-Zentrum in Berlin, a new investigation has been recently published. In this study, we address the early photodynamics of ferricyanide ion in solution applying transient XUV photoelectron spectroscopy in tandem with theoretical modeling.

Light-induced relaxation dynamics of the ferricyanide ion revisited by ultrafast XUV photoelectron spectroscopy Phys. Chem. Chem. Phys., 2017,19, 14248-14255


This combination has been already applied by us to unravel peculiarities of spin crossover in [Fe(bpy)3]2+ complex. Here, we have addressed the problem of charge localization and symmetry-breaking in the simple prototypical coordination compound – ferricyanide. Upon absorption of UV light, it is excited to the charge-transfer state, which can undergo non-radiative relaxation to the ground state or be involved in further chemical reactions. This is a usual trait of coordination and organometallic compounds, which is often used by nature and chemists in, e.g., photosynthesis or photocatalytic retrieval of ecologic fuels.

In previous UV pump – IR probe spectroscopic study of the photochemical fate of ferricyanide, it was concluded that the initially populated charge-delocalized state relaxes to the localized one and the process is driven by the reorganization of the polar solvent. However, we obtained strong evidence for the spin crossover followed by geometrical distortions due to Jahn–Teller effect, rather than localization/delocalization dynamics, as suggested previously. Remarkably, our interpretation also consistently explains the transient features observed in UV-IR pump-probe experiments along with transient XUV PES.

Nuclear correlation effects viewed by X-ray spectroscopy

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):

S. Karsten, S.D. Ivanov, S.G. Aziz, S.I. Bokarev, O. Kühn Nuclear Dynamical Correlation Effects in X‑ray Spectroscopy from a Theoretical Time-Domain Perspective J. Phys. Chem. Lett., 2017, 8 (5), pp 992–996.

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.