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.
On the 10th of May, Sven Karsten has got a PhD degree. His thesis was devoted to the “Trajectory-based approaches to vibronic spectroscopy of molecular systems.” I have already written about some of the developments by Sven, see, e.g., here, here or here.
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:
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.
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.
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!
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:
A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy J. Chem. Phys. 146, 224203 (2017).
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.
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.
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.