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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Matsubara-like dynamics for vibronic spectroscopy

I forgot to write about a publication which appeared at the end of the last year. It is a logical continuation of the previous works of Sven Karsten on the semi-classical description of vibronic spectra. That is when both electronic and nuclear motion of a molecule is excited.

 

This time Sven has elaborated on the imaginary time-shifted  correlation functions and applied a Matsubara approximation to a ring polymer which is residing partly on the excited potential energy surface and partly on the ground state one, as has been described in previous publication. This approximation filters out high-frequency vibrations of the ring polymer, leaving only the low-frequency “smooth” distortions. The idea is that the high-frequency counterpart is anyway cut by the Boltzmann distribution at the finite temperature. However, strictly speaking, one cannot call this approximation just Matsubara as there is an abrupt change in the ring due to different potentials it is evolving according to. That is why we call it Matsubara-like.

I hope that this approach upon the proper generalization to more complicated molecules will be a step towards reliable simulation of vibrionic spectra with semi-classical methods.

Optimal tuning and photoelectron spectra

Density functional theory is an indispensable theoretical method to study moderate to large systems due to its computational efficiency. Being physically sound, it relies on approximations since the explicit form of the density functional is not known. Most of the standard functionals available on the market have an inherent problem – electrons in the system experience spurious self-interaction. In many applications, this is not critical, but in some cases, it does matter.

A way to overcome it is to calculate exchange energy exactly. However, the perspective strategy is to add this “exact” correction only at long distances. The smooth function switching between short- and long-range behavior is density-dependent and thus varies for different systems. We use a purely first principles procedure on how to determine the parameters of the switching function for the particular system. As an end effect, we correct the orbital energies such that they become better estimates of ionization potentials which has immediate implication for the accuracy of the computed photoelectron spectra.

 

PES

We have applied this procedure to the prediction of properties of charge-transfer states of photosensitizers and also to photoelectron spectroscopy before. In the recent publication

T. Möhle, O.S. Bokareva, G. Grell, O. Kühn, S.I. Bokarev Tuned Range-Separated Density Functional Theory and Dyson Orbital Formalism for Photoelectron Spectra J. Chem. Theory Comput. 14 (2018), 5870–5880.

we systematically analyze the performance of a combination of optimally-tuned density functionals with Dyson orbital approach. Thus, this approach relies on two cornerstones: reliable prediction of ionization energies and more accurate treatment of intensities using Dyson orbital formalism together with TDDFT.

We critically discuss the advantages and disadvantages of this procedure. It should be advisable in cases when the system studied with photoelectron spectroscopy has a non-singlet ground state. In this case, one has two non-equivalent ionization spin-channels which are otherwise unsatisfactorily reproduced. Moreover, TDDFT with the Dyson approach even levels the error of conventional functionals, and the results are not much different from more accurate range-sepated functional. Another two issues which might be problematic for our approach are the stability of the ground state with respect to orbital variations and spin-contamination. The latter one is unavoidable as either a non-ionized or ionized system has open electronic shells and needs to be treated by the unrestricted variant of DFT which introduces this undesirable spin mixing.

The recommendations formulated in this publication should facilitate the practical application of the protocol. Some of the unsolved issues warrant further research.

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.

RIXS

 

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.