Review on theoretical X-ray spectroscopy

A review of the theoretical developments to predict various kinds of soft X-ray spectra has been published by us recently. It describes how different observables can be extracted from the theoretical calculations: absorption (XAS), photoionization (PES or XPS), resonant inelastic scattering (RIXS), and Auger. The main focus is on L-edge spectra of transition metals and in particular on multi-reference methods as they appear to be essential for this type of systems. However, the review also contains a brief overview of other methods and applications. Enjoy!

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Huihui Wang is now a doctor

Last Friday Huihui Wang has defended her Ph.D. thesis “Laser-driven electron and spin-state quantum dynamics in transition metal complexes” which has been partially done within the joint project with the King Abdulaziz University in Jeddah and also supported by the DFG grant. I have already briefly written about the details of her work on dynamics triggered by isolated as well as trains of pulses.

Congratulations and we wish her further success in her scientific career!

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Molecular asymmetry and photoelectron spectra

As a result of collaboration between our group and the group of Michael Odelius from Stockholm University an open-access article has been recently published on pages of Physical Chemistry Chemical Physics journal:

Jesper Norell, Gilbert Grell, Oliver Kühn, Michael Odelius, Sergey I. Bokarev Photoelectron shake-ups as a probe of molecular symmetry: 4d XPS analysis of I3 in solution  Phys. Chem. Chem. Phys., 20 (2018) 19916.

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The previous work from Michaels group dealt with the influence of the polarity and proticity of the solvent on the photoelectron spectrum of this model system.  For instance, in water I3 represents a quite asymmetric moiety which can be described as I2—I, whereas in less protic solvents the charge is fairly delocalized [I–I–I]. In present work, we joined our forces and applied a protocol derived by us to the analysis of photoelectron intensities. The main focus was on assignment and relative intensities of different transitions. We have considered the so-called main transitions, when one electron is kicked out of a system, and the shake-ups, when in addition to removal of an electron another one is excited to a bound state. Relative intensities of these two types of bands appeared to be a convenient measure of the asymmetry of the structure. Understanding the interaction of I3 with the solvent may serve for better design of redox systems, e.g., dye-sensitized solar cells.

Repeat until successful

I have already told you about out activity in the field of electron dynamics and namely spin-flip dynamics. To wrap it briefly, we have looked what will happen to a system with the strong coupling of spin and orbital motion of electrons if we prepare a pure spin-state. One can imagine, e.g., a Fe2+ ion with four spin-up electrons forming a so-called quintet state. Now if such a system has a hole in the electronic core, which immediately causes strong spin-orbit coupling, an ultrafast spin-flip of an electron will occur leading to triplet final state with effectively only two spin-up electrons.

Well, sounds easy. However, such a situation is so far pure speculation, and we should ask ourselves, how to practically prepare this particular initial state? It is very special because it corresponds not to an eigenstate of a system but rather to a quantum superposition of such “natural” states. One can, of course, absorb light, but this light should also possess somewhat unusual characteristics. First of all, the light pulse should be very short. According to the uncertainty principle, the shorter is the pulse, the broader is it in energy range which it excites. And we exactly need excitation of lots of eigenstates to resemble the situation with an initially prepared core-excited pure-spin state.

Pulse trains

Out of possible light sources, two candidates would potentially fit: free electron lasers and high harmonic generation (HHG) setups. They are able to produce light with energy that is high enough to excite core states and emerged pulses have temporal durations below 1 femtosecond (10-15 seconds). Free electron lasers provide single isolated pulses, whereas HHG usually gives periodic sequences of pulses. We have already discussed in previous publications, how the transition metal complex reacts on the isolated pulse. I have briefly described it in this blog.

In a recent publication:

Huihui Wang, Tobias Möhle, Oliver Kühn, and Sergey I. Bokarev Ultrafast dissipative spin-state dynamics triggered by x-ray pulse trains, PHYSICAL REVIEW A, 98, 013408 (2018).

we have looked how spin of the system will behave if we subject it to repeated sub-femtosecond pulses as resulting from the HHG source. The key difference to isolated pulses is that the yield of spin-fliped states rises in a stepwise manner after every subpulse in a train as can be seen from a figure. This makes this process to occur faster and more complete. Even more important is that due to stimulated emission the population is dumped from core-excited to spin-flipped valence states. Thus, via a core excitation and stimulated emission, and thus mediated by the strong spin-orbit coupling in the core state, an spin-flip which is faster than few fs can be triggered in the manifold of valence electronic state. Usually such a transition requires up to few hundreds of femtoseconds and might be immensely accelerated in this process. Such dumping also decreases the destructive influence of the Auger decay.

Finally, we have looked at the role of the decoherence caused by nuclear motions. Molecular vibrations have been treated at the level of a heat bath. Essentially, the electron dynamics studied in this work is that fast, that relatively slow vibrational motions do not much influence the result.

We envisage that this effect could be used for clocking ultrafast events. In this respect, it is of core-hole clock type but has a different nature. In case of spin flips, the characteristic timescale may be varied by changing the carrier frequency and bandwidth of the incoming radiation, thus adjusting the strength of the coupling and thereby determining essentially the measured time window.

Deciphering the fingerprints of chemical bonds using X-ray spectroscopy

It is my pleasure to point your attention to our article on theoretical X-ray spectroscopy recently published in the 123th issue of the Research Features magazine. It describes some of our developments and case studies as well as our view on the future of the X-ray spectroscopy and its theoretical description on a popular level. Even if you are not expert in this field, you might find it curious to look inside. The article has open access.

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A new twist on quasi-classical approaches to vibronic spectra

In continuation of our efforts for the description of nuclear vibrational effects in X-ray (or in general in vibronic) spectra, we have recently published an article:

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With this publication we tried to resolve the deficiency of the previously suggested method: while talking about transitions between several electronic states, the actual dynamics follows the ground state potential only. Here, making use of the expertise of Sven Karsten and Sergei Ivanov, we employ imaginary-time path integral technique to formulate a method accounting for the dynamics on multiple potential energy surfaces.
In principle, the quasi-classical approaches to the dynamics in the electronic ground state are well established. They employ the so-called Kubo-transformed time correlation functions. Kubo form is beloved by physicists due to its convenient symmetry properties making it the most classical-like quantum correlation function. In our article, we raised a question whether Kubo correlation function stays the most optimal choice when electronic transitions come into play? The answer is – not really.
If you criticize – suggest a better choice. That is why we introduce a generalized quantum time correlation function. It contains many well-established variants, including the Kubo one, as particular cases. But most importantly, it also provides a way to construct a family of new quantum correlation functions.  On the example of a 1D anharmonic model, we have shown that the new approaches may lead to superior results. This generalized strategy paves the way to seek for the even more optimal formulations.

Bachelor and Master: four at a time

Some time has already passed, and I realized that I have not written about the productive end of summer and beginning of autumn resulted in a two Bachelor and two Master defenses under my supervision. Although this was an interesting experience, the dense defenses together with a number of conferences and workshops kicked me out of balance, and I could barely return to my work during this period. Still trying to come up with the research schedule!

Another reason is that Julius Zimmermann has got on 7th of December the faculty price for his Master studies as the best student from Institute of Physics together with other three students from Biology, Chemistry, and Mathematics. He has given two honorable talks on his Master thesis: one at our institute and one at the annual colloquium of the Faculty of Mathematics and Natural Sciences of University of Rostock.  This is already the second student whom I supervised and who got this price. Lucky coincidence as my boss said 😉 This time I was not able to deliver my laudatory speech as I was in Paris on the X-ray workshop and Oliver Kühn did this job for me. Unfortunately, as the other honored student Marie Preuße, Julius did not stay in our group to get his Ph.D. and continued at Faculty of Engineering.

Überreichung der Fakultätspreise der MNF am 7.12.2017

The Master thesis of Julius entitled “Nuclear Dynamical Effects in Theoretical X-Ray Spectroscopy” goes along the lines of our recent publications on this topic in J. Phys. Chem. Lett. and J. Chem. Phys. He has introduced some improvements to the program written by Sven Karsten resulting in better performance. He has also implemented a protocol to allow for correlated electronic structure methods including the spin-orbit coupling which has appeared to be a major development. As a test system, we have chosen Fe(CO)5 as a prototypical catalytic species. I should acknowledge assistance from Dr. Dimitrios Manganas from the group of Prof. Frank Neese because he adjusted some features of RODFT-CIS module of ORCA package to our needs.

Another Master thesis “First principle trajectory based propagation of vibronic wavepackets in non-adiabatic systems” has been defended by Ludwig Ahrens-Iwers. Here, we have tried to apply direct dynamics variational multi-configurational Gaussian (DD-vMCG) method to describe X-ray time-resolved experimental studies of molecular photoionization in strong laser fields. This work was inspired by Prof. Hans Jakob Wörner from Zürich and his recent publication. We are also thankful to Prof. Gram Worth from Imperial College London for his advice in adjusting Quantics package to our needs. Ludwig has done a good job and suggested a couple of ways how to treat this complicated problem using diabatization of many potential energy surfaces on the fly.

Further, two Bachelor theses have been defended by Andy Kaiser and Otto Geburtig. In his work “Modeling Auger spectra for simple systems” cosupervised by Gilbert Grell, Andy has studied the effects of one- and two-center approximations on the Auger spectra of small molecules and respective speed up of calculations. Within his thesis “X-ray resonant inelastic scattering spectra of complex systems” Otto has implemented a method for calculation of RIXS spectra based on restricted excitation window time-dependent density functional theory.

This was a hard but still nice time. Thank you guys, it was a pleasure to work with you!