A review of theoretical approaches to 2p X-ray absorption

As a result of the work of the giant community of authors a comprehensive review of different theoretical approaches to the L-edge X-ray spectroscopy of transition metal compounds appeared. It is available under the open-access license:

Frank MF de Groot, Hebatalla Elnaggar, Federica Frati, Ru-pan Wang, Mario U Delgado-Jaime, Michel van Veenendaal, Javier Fernandez-Rodriguez, Maurits W Haverkort, Robert J Green, Gerrit van der Laan, Yaroslav Kvashnin, Atsushi Hariki, Hidekazu Ikeno, Harry Ramanantoanina, Claude Daul, Bernard Delley, Michael Odelius, Marcus Lundberg, Oliver Kühn, Sergey I Bokarev, Eric Shirley, John Vinson, Keith Gilmore, Mauro Stener, Giovanna Fronzoni, Piero Decleva, Peter Kruger, Marius Retegan, Yves Joly, Christian Vorwerk, Claudia Draxl, John Rehr, Arata Tanaka 2p x-ray absorption spectroscopy of 3d transition metal systems J. Electron Spectros. Relat. Phenomena 249 (2021) 147061.

It covers topics from ligand-field multiplet theory to multi-reference methods for the investigation of molecular complexes in the gas phase and solution to solid-state systems.

Photocatalytic reaction through the lens of X-rays

As a logical continuation of our activities in the field of joint experimental and theoretical study of photocatalytic hydrogen water splitting in the optical regime, we have recently published an extension, where the oxidation state of the central metal atom of a photosensitizer is monitored directly by the ultrafast X-ray absorption spectroscopy.

Alexander Britz, Sergey I. Bokarev, Tadesse A. Assefa, Èva G. Bajnóczi, Zoltán Németh, György Vankó, Nils Rockstroh, Henrik Junge, Matthias Beller, Gilles Doumy, Anne Marie March, Stephen H. Southworth, Stefan Lochbrunner, Oliver Kühn, Christian Bressler, Wojciech Gawelda Site‐Selective Real‐Time Observation of Bimolecular Electron Transfer in a Photocatalytic System Using L‐Edge X‐Ray Absorption Spectroscopy ChemPhysChem 22 (2021) 693-700.

The question of the localization of an additional electron received by the photosensitizer from the reductant has already caused debates. The reason for it was that the EPR method predicts an unusual signal for the ligand-localized unpaired electron suggesting an interpretation where the central iridium ion is reduced. However, other experimental methods and theoretical calculations strongly suggested that iridium stays untouched whereas the redox chemistry happens on the bipyridine-like ligand. X-ray spectroscopy has the advantage that it provides direct access to the local atomic properties of a specific type of atoms in a molecule. Together with proper theoretical treatment and interpretation, it represents one of the most powerful methods to monitor oxidation states.

In photosensitizer, the excitation is followed by relaxation and after about 100 femtoseconds the population resides in a long-living triplet metal-to-ligand charge-transfer state. In this state, there is a hole in the 5d orbital of iridium and an additional electron on the bipyridine ligand. This hole has a distinct signature in the L-edge X-ray spectrum; it is filled in course of the catalytic reaction by another electron. Hence, monitoring the spectral changes allowed to measure the rate of triplet state quenching.

This study is, I hope, a final chord in disentangling the photochemistry of this prototypical photosensitizer. Moreover, it should have more significance in establishing techniques how to perform operando measurements on real photocatalytic reactions with the emergent ultrafast X-ray spectroscopic methods.

Highly excited states and spin dynamics

Nowadays, the ultrafast sciences paradigm is changing from working on the femtosecond to a shorter sub-femtosecond or attosecond timescale. Such research attracts scientists’ attention as it allows studying different atomic and molecular processes on the scale of the fastest electronic motion. I have already touched on the subfemtosecond spin-flip dynamics simulations in the highly excited states in my blog. In a new article, we continued research in this direction and have asked a question: are the ultrafast spin dynamics in the 2p-core-excited states a predominantly atomic process or the chemical environment plays a crucial role?

Vladislav Kochetov, Huihui Wang, Sergey I. Bokarev Effect of chemical structure on the ultrafast spin dynamics in core-excited states J. Chem. Phys. (2020) 153, 044304.

From a general viewpoint, such dynamics are rooted in preparing the superposition of the spin-orbit split states with 2p3/2 and 2p1/2 core holes. Thus, it should be nearly an atomic process, and the strength of the spin-orbit coupling of the hole-bearing atom is decisive. However, the systematic theoretical study of several transition metal complexes of titanium, chromium, iron, and nickel has demonstrated that these simple considerations do not hold.

The ligands attached to the same ion appeared to play only a minor role; of course, if one does not change, e.g., all weak-field ligands to strong-field ones. (In the latter case, the dynamics may change qualitatively.) In turn, the central metal ion’s influence is notably more pronounced but does not correlate with the strength of spin-orbit coupling. For instance, the titanium complex demonstrates an efficient spin-flip, whereas the nickel one does not. It is despite a three times larger coupling constant for nickel.


The dynamics are susceptible to the energetic distribution of states with different multiplicity and their “availability” for the excitation by an ultrashort pulse. The figure above shows that singlet (red) and triplet (blue) states cluster according to spin-orbit interaction and dipole absorption strength. Those nodes which are larger correspond to states which are involved in the dynamics. Those with small nodes are unaffected. Decisive for the efficiency is the ratio between the number of involved states with flipped spin (big blue nodes) and the number of involved states with the ground state spin (big red nodes). The influence of vibrations, which are also inherent to the chemical structure of the complex, was found to be negligible.

This work adds to the understanding of the spin-flip dynamics mechanism and suggests some ways to decrease the computational effort and thus include more states in future simulations.

An approach to the Auger spectra of molecules

Auger spectra continue to attract attention as an informative tool to study the properties of matter. The interest even rises due to the invention and development of new high-energy radiation sources such as free-electron lasers and high harmonic generation setups. To move apace with the experiment, theory also needs to meet new challenges.

I have already briefly described our approach to Auger spectra on the example of a neon atom. Recently, it has also been tested on molecules.

Gilbert Grell and Sergey I. Bokarev Multi-reference protocol for (auto)ionization spectra: Application to molecules J. Chem. Phys. 152, 074108 (2020)

The investigated systems all contain main-group elements but have been selected to represent different classes: starting with methane (CH4) – a closed-shell substantially single-configurational molecule with high symmetry – we also studied oxygen (O2), possessing a triplet ground state, and nitrogen dioxide (NO2), being a radical with strong multi-configurational character. Note that both oxygen and nitrogen dioxide feature two ionization spin-channels. Finally, a pyrimidine (C4H4N2) has been selected as a representative of planar heteroaromatic systems. To perform a thorough test of the protocol, the XAS, PES, and RAES at the carbon, oxygen, and nitrogen K-edges have been evaluated and compared to the experimental data.

Our protocol’s central approximation is that the angular structure of the molecular potential is averaged out, leading to spherically symmetric continuum orbitals that are obtained by numerically solving the radial Schrödinger equation. Such an approach, being natural for atoms, in fact, provides a valuable insight into the nature of molecular photoionization
and autoionization spectral features as well.

From the viewpoint of electronic structure calculations, this protocol can be applied together with any quantum chemistry method, allowing for a CI-like representation of the wave function. Thus it can be easily interfaced with any quantum-chemistry code.

Speciation in aqueous solution

In the recent article, we address the characteristic features in the X-ray absorption (XAS) and resonant inelastic scattering (RIXS) spectra of different species coexisting in the CoCl2 aqueous solution.

H. Allehyani, W.I. Hassan, S.G. Aziz, R.H. Hilal, O. Kühn, S.I. Bokarev Solvation and Speciation of Cobalt (II). A Theoretical X-Ray Absorption and RIXS Study, Chem. Phys., 532 (2020) 110681.

In solution, CoCl2 undergoes electrolytic dissociation. Ideally, this results in a hexaaqua [Co(H2O)6]2+ complex. However, the dissociation may not occur completely. Thus, a considerable number of species can form an equilibrium, which depends on the experimental conditions. The speciation of aqueous Co2+ has a number of practical implications, e.g., in cobalt transport and deposition in ore-forming hydrothermal systems or due to the cytotoxic effects of cobalt on human cells.

Special Issue “Molecular quantum dynamics beyond bound states”

Its my pleasure to announce a special issue “Molecular quantum dynamics beyond bound states” in the open-access journal Molecules which I am guest-editing. Please find further information under

https://www.mdpi.com/journal/molecules/special_issues/Molecular_Quantum_Dynamics_Bound

The photon-in/electron-out processes provide a wealth of information about the electronic structure of the target system, which is encoded in the kinetic energy of the outgoing electron, its angular distribution, spin-polarization, etc. That is why different flavors of steady-state and time-resolved photoemission and Auger spectroscopies enjoy great popularity in studying molecules. This Special Issue will address theoretical methods to describe various aspects of ionization and autoionization spectroscopies from UV/Vis to X-ray domains, the interaction of molecules and atoms with intense laser fields, as well as the electronic and non-adiabatic dynamics following the expulsion of an electron. Articles presenting new methodological developments and applications to molecular spectroscopy and dynamics are welcome.

Looking forward to your submissions!

Dyson orbitals with OpenMolcas

OpenMolcas, a free open-source project branched off the Molcas program package, has now the possibility to calculate Dyson orbitals and photoionization cross-sections in the sudden approximation limit. This means that the capabilities which have been available within our external code written by Gilbert Grell are now inherent to the OpenMolcas. You are welcome to try it!

The details of the implementation can be found in the OpenMolcas article:

I. Fernández Galván, M. Vacher, A. Alavi, C. Angeli, F. Aquilante, J. Autschbach, J.J. Bao,   S.I. Bokarev, N.A. Bogdanov, R.K. Carlson, L.F. Chibotaru, J. Creutzberg, N. Dattani, M.G. Delcey, S.S. Dong, A. Dreuw, L. Freitag, L. M. Frutos, L. Gagliardi, F. Gendron, A. Giussani, L. González, G. Grell, M. Guo, C.E. Hoyer, M. Johansson, S. Keller, S. Knecht, G. Kovačević, E. Källman, G. Li Manni, M. Lundberg, Y. Ma, S. Mai, J.P. Malhado, P.-Å. Malmqvist, P. Marquetand, S.A. Mewes, J. Norell, M. Olivucci, M. Oppel, Q.M. Phung, K. Pierloot, F. Plasser, M. Reiher, A.M. Sand, I. Schapiro, P. Sharma, C.J. Stein, L.K. Sørensen, D.G. Truhlar, M. Ugandi, L. Ungur, A. Valentini, S. Vancoillie, V. Veryazov, O. Weser, T.A. Wesołowski, P.-O. Widmark, S. Wouters, A. Zech, J.P. Zobel, and R. Lindh, OpenMolcas: From Source Code to Insight, J. Chem. Theory Comput. 15, 5925 (2019).

ct9b00532_0022

In the center of the graphical abstract, you can see the L-edge photoelectron spectrum of the Fe(II) aqueous ion – our guinea pig for testing different protocols.

Thanks to Joel Creuzberg and Jesper Norell for implementation and Per-Åke Malmqvist for programming support!