Revealing the bonding of solvated Ru complexes with valence-to-core resonant inelastic X-ray scattering

Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Accessing metal-specific orbital interactions in C-H activation with resonant inelastic X-ray scattering

Photochemically prepared transition-metal complexes are known to be effective at cleaving the strong C-H bonds of organic molecules in room temperature solutions. There is also ample theoretical evidence that the two-way, metal to ligand (MLCT) and ligand to metal (LMCT), charge-transfer between an incoming alkane C-H group and the transition metal is the decisive interaction in the C-H activation reaction. What is missing, however, are experimental methods to directly probe these interactions in order to reveal what determines reactivity of intermediates and the rate of the reaction. Here, using quantum chemical simulations we predict and propose future time-resolved valence-to-core resonant inelastic X-ray scattering (VtC-RIXS) experiments at the transition metal L-edge as a method to provide a full account of the evolution of metal-alkane interactions during transition-metal mediated C-H activation reactions. For the model system cyclopentadienyl rhodium dicarbonyl (CpRh(CO)2), we demonstrate, by simulating the VtC-RIXS signatures of key intermediates in the C-H activation pathway, how the Rh-centered valence-excited states accessible through VtC-RIXS directly reflect changes in donation and back-donation between the alkane C-H group and the transition metal as the reaction proceeds via those intermediates. We benchmark and validate our quantum chemical simulations against experimental steady-state measurements of CpRh(CO)2 and Rh(acac)(CO)2 (where acac is acetylacetonate). Our study constitutes the first step towards establishing VtC-RIXS as a new experimental observable for probing reactivity of C-H activation reactions. More generally, the study further motivates the use of time-resolved VtC-RIXS to follow the valence electronic structure evolution along photochemical, photoinitiated and photocatalytic reactions with transition metal complexes.

Resonant Excitation Unlocks Chemical Selectivity of Platinum Lβ Valence-to-Core X-ray Emission Spectra

Valence-to-core X-ray emission spectroscopy (VtC XES) is an emerging technique that uses hard X-rays to probe the valence electronic structure of an absorbing atom. Despite finding varied applications for light elements and first row transition metals, little work has been done on heavier elements such as second and third row transition metals. This lack of application is at least partially due to the relatively low resolution of the data at the high energies required to measure these elements, which obscures the useful chemical information that can be extracted from the lower energy, higher resolution spectra of lighter elements. Herein, we collect data on a set of platinum-containing compounds and demonstrate that the VtC XES resolution can be dramatically enhanced by exciting the platinum atom in resonance with its L3-edge white line absorption. Whereas spectra excited using standard nonresonant absorption well above the Pt L3-edge display broad, unfeatured VtC regions, resonant XES (RXES) spectra have more than twofold improved resolution and are revealed to be rich in chemical information with the ability to distinguish between even closely related species. We further demonstrate that these RXES spectra may be used to selectively probe individual components of a mixture of Pt-containing compounds, establishing this technique as a viable probe for chemically complex samples. Lastly, it is shown that the spectra are interpretable using a molecular orbital framework and may be calculated using density functional theory, thus suggesting resonant excitation as a general strategy for extracting chemically useful information from heavy element VtC spectra.

R-Group stabilization in methylated formamides observed by resonant inelastic X-ray scattering

The inherent stability of methylated formamides is traced to a stabilization of the deep-lying σ-framework by resonant inelastic X-ray scattering at the nitrogen K-edge. Charge transfer from the amide nitrogen to the methyl groups underlie this stabilization mechanism that leaves the aldehyde group essentially unaltered and explains the stability of secondary and tertiary amides.

The inherent stability of methylated formamides is traced to a stabilization of the deep-lying σ-framework by resonant inelastic X-ray scattering at the nitrogen K-edge.

Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods

The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.

Targeting Individual Tautomers in Equilibrium by Resonant Inelastic X-ray Scattering

Tautomerism is one of the most important forms of isomerism, owing to the facile interconversion between species and the large differences in chemical properties introduced by the proton transfer connecting the tautomers. Spectroscopic techniques are often used for the characterization of tautomers. In this context, separating the overlapping spectral response of coexisting tautomers is a long-standing challenge in chemistry. Here, we demonstrate that by using resonant inelastic X-ray scattering tuned to the core excited states at the site of proton exchange between tautomers one is able to experimentally disentangle the manifold of valence excited states of each tautomer in a mixture. The technique is applied to the prototypical keto-enol equilibrium of 3-hydroxypyridine in aqueous solution. We detect transitions from the occupied orbitals into the LUMO for each tautomer in solution, which report on intrinsic and hydrogen-bond-induced orbital polarization within the π and σ manifolds at the proton-transfer site.

Quantifying the Steric Effect on Metal-Ligand Bonding in Fe Carbene Photosensitizers with Fe 2p3d Resonant Inelastic X-ray Scattering

Understanding the electronic structure and chemical bonding of transition metal complexes is important for improving the function of molecular photosensitizers and catalysts. We have utilized X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) at the Fe L₃ edge to investigate the electronic structure of two Fe N-heterocyclic carbene complexes with similar chemical structures but different steric effects and contrasting excited-state dynamics: [Fe(bmip)₂]²⁺ and [Fe(btbip)₂]²⁺, bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)pyridine and btbip = 2,6-bis(3-tert-butyl-imidazole-1-ylidene)pyridine. In combination with charge transfer multiplet and ab initio calculations, we quantified how changes in Fe-carbene bond length due to steric effects modify the metal-ligand bonding, including σ/π donation and π back-donation. We find that σ donation is significantly stronger in [Fe(bmip)₂]²⁺, whereas the π back-donation is similar in both complexes. The resulting stronger ligand field and nephelauxetic effect in [Fe(bmip)₂]²⁺ lead to approximately 1 eV destabilization of the quintet metal-centered ⁵T_2g excited state compared to [Fe(btbip)₂]²⁺, providing an explanation for the absence of a photoinduced ⁵T_2g population and a longer metal-to-ligand charge-transfer excited-state lifetime in [Fe(bmip)₂]²⁺. This work demonstrates how combined modeling of XAS and RIXS spectra can be utilized to understand the electronic structure of transition metal complexes governed by correlated electrons and donation/back-donation interactions.

Development of an experimental apparatus to observe ultrafast phenomena by tender X-ray absorption spectroscopy at PAL-XFEL

Understanding the ultrafast dynamics of molecules is of fundamental importance. Time-resolved X-ray absorption spectroscopy (TR-XAS) is a powerful spectroscopic technique for unveiling the time-dependent structural and electronic information of molecules that has been widely applied in various fields. Herein, the design and technical achievement of a newly developed experimental apparatus for TR-XAS measurements in the tender X-ray range with X-ray free-electron lasers (XFELs) at the Pohang Accelerator Laboratory XFEL (PAL-XFEL) are described. Femtosecond TR-XAS measurements were conducted at the Ru L3-edge of well known photosensitizer tris(bipyridine)ruthenium(II) chloride ([Ru(bpy)3]2+) in water. The results indicate ultrafast photoinduced electron transfer from the Ru center to the ligand, which demonstrates that the newly designed setup is applicable for monitoring ultrafast reactions in the femtosecond domain.

Ligand-Field Effects in a Ruthenium(II) Polypyridyl Complex Probed by Femtosecond X-ray Absorption Spectroscopy

We employ femtosecond X-ray absorption spectroscopy of [Ru(m-bpy)₃]²⁺ (m-bpy = 6-methyl-2,2'-bipyridine) to elucidate the time evolution of the spin and charge density upon metal-to-ligand charge-transfer (MLCT) excitation. The core-level transitions at the Ru L₃-edge reveal a very short MLCT lifetime of 0.9 ps and relaxation to the lowest triplet metal-centered state (³MC) which exhibits a lifetime of about 300 ps. Time-dependent density functional theory relates ligand methylation to a lower ligand field strength that stabilizes the ³MC state. A quarter of the ³MLCT population appears to be trapped which may be attributed to intramolecular vibrational relaxation or further electron transfer to the solvent. Our results demonstrate that small changes in the ligand field allow control of the photophysical properties. Moreover, this study underscores the high information content of femtosecond L-edge spectroscopy as a probe of valence charge density and spin-state in 4d transition metals.

Resonant X-ray photo-oxidation of light-harvesting iron (II/III) N-heterocyclic carbene complexes

Two photoactive iron N-heterocyclic carbene complexes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\hbox {Fe}^{{{\rm{II}}}}(\hbox {btz})_2(\hbox {bpy})]^{2+}}$$\end{document}[FeII(btz)2(bpy)]2+ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\hbox {Fe}^{{\rm{III}}}(\hbox {btz})_3]^{3+}}$$\end{document}[FeIII(btz)3]3+, where btz is 3,3’-dimethyl-1,1’-bis(p-tolyl)-4,4’-bis(1,2,3-triazol-5-ylidene) and bpy is 2,2’-bipyridine, have been investigated by Resonant Photoelectron Spectroscopy (RPES). Tuning the incident X-ray photon energy to match core-valence excitations provides a site specific probe of the electronic structure properties and ligand-field interactions, as well as information about the resonantly photo-oxidised final states. Comparing measurements of the Fe centre and the surrounding ligands demonstrate strong mixing of the Fe \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {t}_{{\rm{2g}}}}$$\end{document}t2g levels with occupied ligand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π orbitals but weak mixing with the corresponding unoccupied ligand orbitals. This highlights the importance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi$$\end{document}π-accepting and -donating considerations in ligand design strategies for photofunctional iron carbene complexes. Spin-propensity is also observed as a final-state effect in the RPES measurements of the open-shell \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{III}}}$$\end{document}FeIII complex. Vibronic coupling is evident in both complexes, where the energy dispersion hints at a vibrationally hot final state. The results demonstrate the significant impact of the iron oxidation state on the frontier electronic structure and highlights the differences between the emerging class of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{III}}}$$\end{document}FeIII photosensitizers from those of more traditional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}^{{\rm{II}}}$$\end{document}FeII complexes.

Resonant Stimulated X-ray Raman Spectroscopy of Mixed-Valence Manganese Complexes

Resonant stimulated X-ray Raman spectroscopy of the bimetallic [Mn^IIIMn^IV(μ-O)₂(μ-OAC)(tacn)₂]²⁺ manganese complex is investigated in a simulation study. Essential biological processes, including water oxidation in photosynthesis, involve charge transfer between manganese sites of different oxidation states. We study a prototypical binuclear mixed-valence transition-metal complex with two Mn atoms in different oxidation states surrounded by ligand structures and employ a pump-probe sequence of resonant X-ray Raman excitations to follow the charge transfer occurring in the molecule. This allows us to generate and monitor valence-electron wave packets at selected regions in the molecule by exploiting element-specific core-excited states. A two-color protocol is presented, with pump and probe pulses tuned to the Mn and N K-edges. A natural orbital decomposition allows the visualization of the electron dynamics underlying the signal.

Strain and ligand effects in Pt-Ni alloys studied by valence-to-core X-ray emission spectroscopy

Experimental detection of the Pt 5d densities of states in the valence band is conducted on a series of Pt-Ni alloys by high energy resolution valence-to-core X-ray emission spectroscopy (VTC-XES) at the Pt L₃-edge. VTC-XES measurements reveal that the Pt d-band centroid shifts away from the Fermi level upon dilution, accompanied by concentration-dependent Pt d-band width. The competition between the strain effect and ligand effect is observed experimentally for the first time. It is found that the d-band widths in Pt₃Ni and PtNi are broader than that of Pt metal due to compressive strain which overcompensates the effect of dilution, while it is narrower in PtNi₃ where the ligand effect dominates. VTC-XES is demonstrated to be a powerful tool to study the Pt d-band contribution to the valence band of Pt-based bimetallic. The implication for the enhanced activity of Pt-Ni catalysts in oxygen reduction reaction is discussed.

Ultrafast x-ray pump x-ray probe transient absorption spectroscopy: A computational study and proposed experiment probing core-valence electronic correlations in solvated complexes

Femtosecond x-ray pump-x-ray probe experiments are currently possible at free electron lasers such as the linac coherent light source, which opens new opportunities for studying solvated transition metal complexes. In order to make the most effective use of these kinds of experiments, it is necessary to determine which chemical properties an x-ray probe pulse will measure. We have combined electron cascade calculations and excited-state time-dependent density functional theory calculations to predict the initial state prepared by an x-ray pump and the subsequent x-ray probe spectra at the Fe K-edge in the solvated model transition metal complex, K₄Fe^II(CN)₆. We find several key spectral features that report on the ligand-field splitting and the 3p and 3d electron interactions. We then show how these features could be measured in an experiment.

Resonant Inelastic X-ray Scattering Calculations of Transition Metal Complexes Within a Simplified Time-Dependent Density Functional Theory Framework

We present a time-dependent density functional theory (TDDFT) approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state in the context of 4d transition metal systems. These quantities are the necessary ingredients to solve the Kramers-Heisenberg (KH) equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where the solutions of a TDDFT calculation can be used to construct excited-state wavefunctions, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. Thus, the present approach bypasses the need to solve the costly TDDFT quadratic-response equations. We illustrate the applicability of the method to 4d transition metal molecular complexes by calculating the 2p4d RIXS maps of three representative ruthenium complexes and comparing them to experimental results. The method can capture all the experimental features in all three complexes to allow the assignment of the experimental peaks, with relative energies correct to within ∼0.6 eV at the cost of two independent TDDFT calculations.