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.


More on spin state dynamics

Recently, I wrote about our ultrafast spin dynamics project. The first publication in Phys. Rev. Lett. was a proof of concept article where we have shown the possibility of soft X-ray light to trigger an unprecedentedly fast change of a spin state. A follow-up article presenting the theoretical method used in this investigation in detail also appeared recently in the issue of Molecular Physics devoted to the anniversary of Andre D. Bandrauk:

Huihui Wang, Sergey I. Bokarev, Saadullah G. Aziz, Oliver Kühn Density matrix-based time-dependent configuration interaction approach to ultrafast spin-flip dynamics Mol. Phys. (2017) 1-10.

In this article, we reformulate the problem in the form of a density matrix which allows one to treat general open quantum systems with energy dissipation. In addition to the more thorough study of the influence of different parameters of an excitation pulse on the dynamics, we also discuss a regime where the strong electron correlation plays a decisive role. It was shown that core-excited electronic states may demonstrate entangled dynamics both due to the strong spin-orbit coupling and electron correlation. This makes them interesting objects for the future studies of the ultimate limits of the ultrafast electron motion in atoms, molecules, and extended systems.

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.

Ultrafast spin-flip dynamics in focus

Nowadays physics and chemistry are intensively developing within the ‘ultrafast paradigm’ addressing processes occurring on the femto- (10-15 s) and attosecond timescales (10-18 s). An outstanding progress has been achieved in understanding molecules in motion with femtosecond resolution including movies of chemical reactions. Going further down to hundreds and even tens of attoseconds, one can explore the fundamental limits of electronic motion in atoms and molecules.


Apart from being of fundamental interest, the peculiarities of intricate electron dynamics in molecules have their practical implications, for instance, for molecular electronics limiting the speed of the signal transmission. That is why it has been extensively studied, although mostly theoretically since experimental observations represent a very non-trivial task and stay scarce.

During last decades, the devices where the spin of the electrons plays a decisive role has been suggested that gave birth to the new field of physics called spintronics. With this respect, the materials which undergo ultrafast spin-flip upon absorption of light attracted much attention. Systems, where such an effect was observed, are mostly transition metal complexes which can exist in low- and high-spin forms.

Recently, an article from the subgroup headed by me appeared on the pages of Physics Reviews Letters suggesting a new mechanism for the ultrafast spin-flip in transition metal complexes. It was demonstrated on the example of the Fe(II) aqua complex where the excitation with the soft X-ray light created a hole in the 2p level of iron. Due to the strong spin-orbit coupling in the core-excited electronic state the spin transition takes only about 2 fs what is about 100 times faster than rates reported for valence excitations before. Moreover, with a modest variation of the excitation pulse length and its carrier frequency one can potentially govern the efficiency of such spin transition. This makes a basis for future manipulations of the spin states using short wavelength light.

The effect in focus, of course, needs experimental verification. However, such an experiment requires intense isolated attosecond X-ray pulses and is very difficult to realize. Nevertheless, we expect the experimental evidence to appear due to the upcoming X-ray free electron lasers and future developments of high-harmonic generation setups.