Photochemical Formation and Electronic Structure of an Alkane σ-Complex from Time-Resolved Optical and X-ray Absorption Spectroscopy.

C-H bond activation reactions with transition metals typically proceed via the formation of alkane σ-complexes, where an alkane C-H σ-bond binds to the metal. Due to the weak nature of metal-alkane bonds, σ-complexes are challenging to characterize experimentally. Here, we establish the complete pathways of photochemical formation of the model σ-complex Cr(CO)5-alkane from Cr(CO)6 in octane solution and characterize the nature of its metal-ligand bonding interactions. Using femtosecond optical absorption spectroscopy, we find photoinduced CO dissociation from Cr(CO)6 to occur within the 100 fs time resolution of the experiment. Rapid geminate recombination by a fraction of molecules is found to occur with a time constant of 150 fs. The formation of bare Cr(CO)5 in its singlet ground state is followed by complexation of an octane molecule from solution with a time constant of 8.2 ps. Picosecond X-ray absorption spectroscopy at the Cr L-edge and O K-edge provides unique information on the electronic structure of the Cr(CO)5-alkane σ-complex from both the metal and ligand perspectives. Based on clear experimental observables, we find substantial destabilization of the lowest unoccupied molecular orbital upon coordination of the C-H bond to the undercoordinated Cr center in the Cr(CO)5-alkane σ-complex, and we define this as a general, orbital-based descriptor of the metal-alkane bond. Our study demonstrates the value of combining optical and X-ray spectroscopic methods as complementary tools to study the stability and reactivity of alkane σ-complexes in their role as the decisive intermediates in C-H bond activation reactions.

Quantum Mechanical Versus Polarizable Embedding Schemes: A Study of the Xray Absorption Spectra of Aqueous Ammonia and Ammonium.

The X-ray absorption spectra of aqueous ammonia and ammonium are computed using a combination of coupled cluster singles and doubles (CCSD) with different quantum mechanical and molecular mechanical embedding schemes. Specifically, we compare frozen Hartree-Fock (HF) density embedding, polarizable embedding (PE), and polarizable density embedding (PDE). Integrating CCSD with frozen HF density embedding is possible within the CC-in-HF framework, which circumvents the conventional system-size limitations of standard coupled cluster methods. We reveal similarities between PDE and frozen HF density descriptions, while PE spectra differ significantly. By including approximate triple excitations, we also investigate the effect of improving the electronic structure theory. The spectra computed using this approach show an improved intensity ratio compared to CCSD-in-HF. Charge transfer analysis of the excitations shows the local character of the pre-edge and main-edge, while the post-edge is formed by excitations delocalized over the first solvation shell and beyond.

Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory.

X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.

Fingerprint of Dipole Moment Orientation of Water Molecules in Cu2+ Aqueous Solution Probed by X-ray Photoelectron Spectroscopy.

The electronic structure and geometrical organization of aqueous Cu2+ have been investigated by using X-ray photoelectron spectroscopy (XPS) at the Cu L-edge combined with state-of-the-art ab initio molecular dynamics and a quantum molecular approach designed to simulate the Cu 2p X-ray photoelectron spectrum. The calculations offer a comprehensive insight into the origin of the main peak and satellite features. It is illustrated how the energy drop of the Cu 3d levels (≈7 eV) following the creation of the Cu 2p core hole switches the nature of the highest singly occupied molecular orbitals (MOs) from the dominant metal to the dominant MO nature of water. It is particularly revealed how the repositioning of the Cu 3d levels induces the formation of new bonding (B) and antibonding (AB) orbitals, from which shakeup mechanisms toward the relaxed H-SOMO operate. As highlighted in this study, the appearance of the shoulder near the main peak corresponds to the characteristic signature of shakeup intraligand (1a1 → H-SOMO(1b1)) excitations in water, providing insights into the average dipole moment distribution (≈36°) of the first-shell water molecules surrounding the metal ion and its direct impact on the broadening of the satellite. It is also revealed that the main satellite at 8 eV from the main peak corresponds to (metal/1b2 → H-SOMO(1b1) of water) excitations due to a bonding/antibonding (B/AB) interaction of Cu 3d levels with the deepest valence O2p/H1s 1b2 orbitals of water. This finding underscores the sensitivity of XPS to the electronic structure and orientation of the nearest water molecules around the central ion.

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.

Parity violation in resonant inelastic soft x-ray scattering at entangled core holes.

Resonant inelastic x-ray scattering (RIXS) is a major method for investigation of electronic structure and dynamics, with applications ranging from basic atomic physics to materials science. In RIXS applied to inversion-symmetric systems, it has generally been accepted that strict parity selectivity applies in the sub-kilo-electron volt region. In contrast, we show that the parity selection rule is violated in the RIXS spectra of the free homonuclear diatomic O2 molecule. By analyzing the spectral dependence on scattering angle, we demonstrate that the violation is due to the phase difference in coherent scattering at the two atomic sites, in analogy with Young's double-slit experiment. The result also implies that the interpretation of x-ray absorption spectra for inversion symmetric molecules in this energy range must be revised.

Electronic Fingerprint of the Protonated Imidazole Dimer Probed by X-ray Absorption Spectroscopy.

Protons in low-barrier superstrong hydrogen bonds are typically delocalized between two electronegative atoms. Conventional methods to characterize such superstrong hydrogen bonds are vibrational spectroscopy and diffraction techniques. We introduce soft X-ray spectroscopy to uncover the electronic fingerprints for proton sharing in the protonated imidazole dimer, a prototypical building block enabling effective proton transport in biology and high-temperature fuel cells. Using nitrogen core excitations as a sensitive probe for the protonation status, we identify the X-ray signature of a shared proton in the solvated imidazole dimer in a combined experimental and theoretical approach. The degree of proton sharing is examined as a function of structural variations that modify the shape of the low-barrier potential in the superstrong hydrogen bond. We conclude by showing how the sensitivity to the quantum distribution of proton motion in the double-well potential is reflected in the spectral signature of the shared proton.

Simulating Non-Adiabatic Dynamics of Photoexcited Phenyl Azide: Investigating Electronic and Structural Relaxation en Route to the Formation of Phenyl Nitrene.

Excited state molecular dynamics simulations of the photoexcited phenyl azide have been performed. The semi-classical surface hopping approximation has enabled an unconstrained analysis of the electronic and nuclear degrees of freedom which contribute to the molecular dissociation of phenyl azide into phenyl nitrene and molecular nitrogen. The significance of the second singlet excited state in leading the photodissociation has been established through electronic structure calculations, based on multi-configurational schemes, and state population dynamics. The investigations on the structural dynamics have revealed the N-N bond separation to be accompanied by synchronous changes in the azide N-N-N bond angle. The 100 fs simulation results in a nitrene fragment that is electronically excited in the singlet manifold.

X-ray induced ultrafast charge transfer in thiophene-based conjugated polymers controlled by core-hole clock spectroscopy.

We explore ultrafast charge transfer (CT) resonantly induced by hard X-ray radiation in organic thiophene-based polymers at the sulfur K-edge. A combination of core-hole clock spectroscopy with real-time propagation time-dependent density functional theory simulations gives an insight into the electron dynamics underlying the CT process. Our method provides control over CT by a selective excitation of a specific resonance in the sulfur atom with monochromatic X-ray radiation. Our combined experimental and theoretical investigation establishes that the dominant mechanism of CT in polymer powders and films consists of electron delocalisation along the polymer chain occurring on the low-femtosecond time scale.

Simulations of the Aqueous "Brown-Ring" Complex Reveal Fluctuations in Electronic Character.

Ab initio molecular dynamics (AIMD) simulations of the aqueous [Fe(H2O)5(NO)]2+ "brown-ring" complex in different spin states, in combination with multiconfigurational quantum chemical calculations, show a structural dependence on the electronic character of the complex. Sampling in the quartet and sextet ground states show that the multiplicity is correlated with the Fe-N distance. This provides a motivation for a rigid Fe-N scan in the isolated "brown-ring" complex to investigate how the multiconfigurational wave function and the electron density change around the FeNO moiety. Our results show that subtle changes in the Fe-N distance produce a large response in the electronic configurations underlying the quartet wave function. However, while changes in spin density and potential energy are pronounced, variations in charge are negligible. These trends within the FeNO moiety are preserved in structural sampling of the AIMD simulations, despite distortions present in other degrees of freedom in the bulk solution.

Wave packet theory for non-resonant x-ray emission and non-resonant Auger electron emission in molecules.

We present a time-dependent theory for non-resonant x-ray emission spectrum (XES) and normal Auger spectrum (NAS) calculation, based on a fully quantum description of nuclear dynamics using the vibrational wave packet concept. We compare two formulations of the time-dependent theory, either employing a two-time propagation scheme or using spectral integration over the electron energy continuum. We find that the latter formulation is more efficient for numerical simulations, providing a reasonable accuracy when the integration step is shorter than the lifetime broadening of the core-ionized state. We demonstrate our approach using the example of non-resonant x-ray emission from a water molecule, considering the lowest core-ionized K-1 and first core-ionized shake-up K-1V-1V1 intermediate states. These channels exemplify the developed theory on bound-bound, bound-continuum, continuum-bound, and continuum-continuum transitions. Our results suggest that the time-dependent approach is efficient for simulating XES involving dissociative states, whereas the time-independent approach, based on Franck-Condon factors, is more efficient for bound-bound transitions expressed as discrete frequency dependence in the energy domain. The methods and discussion have general applicability, including both NAS and more complex systems, such as liquid water.

Tracking C-H activation with orbital resolution.

Transition metal reactivity toward carbon-hydrogen (C-H) bonds hinges on the interplay of electron donation and withdrawal at the metal center. Manipulating this reactivity in a controlled way is difficult because the hypothesized metal-alkane charge-transfer interactions are challenging to access experimentally. Using time-resolved x-ray spectroscopy, we track the charge-transfer interactions during C-H activation of octane by a cyclopentadienyl rhodium carbonyl complex. Changes in oxidation state as well as valence-orbital energies and character emerge in the data on a femtosecond to nanosecond timescale. The x-ray spectroscopic signatures reflect how alkane-to-metal donation determines metal-alkane complex stability and how metal-to-alkane back-donation facilitates C-H bond cleavage by oxidative addition. The ability to dissect charge-transfer interactions on an orbital level provides opportunities for manipulating C-H reactivity at transition metals.

Charge transfer in sodium iodide collisions.

Sodium iodide (NaI) has, over the years, served as a prototype system in studies of non-adiabatic dynamics. Here, the charge transfer collision reactions Na+ + I- ⇆ Na + I (mutual neutralization and ion-pair formation) are studied using an ab initio approach and the total and differential cross sections are calculated for the reactions. This involves electronic structure calculations on NaI to obtain adiabatic potential energy curves, non-adiabatic and spin-orbit couplings, followed by nuclear dynamics, treated fully quantum mechanically in a strictly diabatic representation. A single avoided crossing at 13.22 a0 dominates the reactions, and the total cross sections are well captured by the semi-classical Landau-Zener model. Compared to the measured ion-pair formation cross section, the calculated cross section is about a factor of two smaller, and the overall shape of the calculated differential cross section is in reasonable agreement with the measured ion-pair formation differential cross section. Treating the Landau-Zener coupling as an empirical parameter of 0.05 eV, the measured total and differential cross sections are well captured when performing fully quantum mechanical cross section calculations including rotational coupling. A semi-empirical spin-orbit coupling model is also investigated, giving satisfactory estimation of the effects of spin-orbit interactions for the reactions.

Electronic Structure and Chemical Bonding in Methylammonium Lead Triiodide and Its Precursor Methylammonium Iodide.

A detailed examination of the electronic structures of methylammonium lead triiodide (MAPI) and methylammonium iodide (MAI) is performed with ab initio molecular dynamics (AIMD) simulations based on density functional theory, and the theoretical results are compared to experimental probes. The occupied valence bands of a MAPI single crystal and MAI powder are probed with X-ray photoelectron spectroscopy, and the conduction bands are probed from the perspective of nitrogen K-edge X-ray absorption spectroscopy. Combined, the theoretical simulations and the two experimental techniques allow for a dissection of the electronic structure unveiling the nature of chemical bonding in MAPI and MAI. Here, we show that the difference in band gap between MAPI and MAI is caused chiefly by interactions between iodine and lead but also weaker interactions with the MA+ counterions. Spatial decomposition of the iodine p levels allows for analysis of Pb-I σ bonds and π interactions, which contribute to this effect with the involvement of the Pb 6p levels. Differences in hydrogen bonding between the two materials, seen in the AIMD simulations, are reflected in nitrogen valence orbital composition and in nitrogen K-edge X-ray absorption spectra.

From Local Covalent Bonding to Extended Electric Field Interactions in Proton Hydration.

Seemingly simple yet surprisingly difficult to probe, excess protons in water constitute complex quantum objects with strong interactions with the extended and dynamically changing hydrogen-bonding network of the liquid. Proton hydration plays pivotal roles in energy transport in hydrogen fuel cells and signal transduction in transmembrane proteins. While geometries and stoichiometry have been widely addressed in both experiment and theory, the electronic structure of these specific hydrated proton complexes has remained elusive. Here we show, layer by layer, how utilizing novel flatjet technology for accurate x-ray spectroscopic measurements and combining infrared spectral analysis and calculations, we find orbital-specific markers that distinguish two main electronic-structure effects: Local orbital interactions determine covalent bonding between the proton and neigbouring water molecules, while orbital-energy shifts measure the strength of the extended electric field of the proton.

Spatial microheterogeneity in the valence band of mixed halide hybrid perovskite materials.

The valence band of lead halide hybrid perovskites with a mixed I/Br composition is investigated using electronic structure calculations and complementarily probed with hard X-ray photoelectron spectroscopy. In the latter, we used high photon energies giving element sensitivity to the heavy lead and halide ions and we observe distinct trends in the valence band as a function of the I : Br ratio. Through electronic structure calculations, we show that the spectral trends with overall composition can be understood in terms of variations in the local environment of neighboring halide ions. From the computational model supported by the experimental evidence, a picture of the microheterogeneity in the valence band maximum emerges. The microheterogeneity in the valence band suggests that additional charge transport mechanisms might be active in lead mixed halide hybrid perovskites, which could be described in terms of percolation pathways.

A-site cation influence on the conduction band of lead bromide perovskites.

Hot carrier solar cells hold promise for exceeding the Shockley-Queisser limit. Slow hot carrier cooling is one of the most intriguing properties of lead halide perovskites and distinguishes this class of materials from competing materials used in solar cells. Here we use the element selectivity of high-resolution X-ray spectroscopy and density functional theory to uncover a previously hidden feature in the conduction band states, the σ-π energy splitting, and find that it is strongly influenced by the strength of electronic coupling between the A-cation and bromide-lead sublattice. Our finding provides an alternative mechanism to the commonly discussed polaronic screening and hot phonon bottleneck carrier cooling mechanisms. Our work emphasizes the optoelectronic role of the A-cation, provides a comprehensive view of A-cation effects in the crystal and electronic structures, and outlines a broadly applicable spectroscopic approach for assessing the impact of chemical alterations of the A-cation on perovskite electronic structure.

Spectroscopic Signature of Dynamical Instability of the Aqueous Complex in the Brown-Ring Nitrate Test.

The chemistry of the brown-ring test has been investigated for nearly a century. Though recent studies have focused on solid state structure determination and measurement of spectra, mechanistic details and kinetics, the aspects of solution structure and dynamics remain unknown. We have studied structural fluctuations of the brown-ring complex in aqueous solution with ab-initio molecular dynamics simulations, from which we identified that the classically established pseudo-octahedral [Fe(H2 O)5 (NO)]2+ complex is present along with a square-pyramidal [Fe(H2 O)4 (NO)]2+ complex. Based on the inability in multi-reference calculations to reproduce the experimental UV-vis spectra in aqueous solution by inclusion of thermal fluctuations of the [Fe(H2 O)5 (NO)]2+ complex alone, we propose the existence of an equilibrium between pseudo-octahedral and square-pyramidal complexes. Despite challenges in constructing models reproducing the solid-state UV-vis spectrum, the advanced spectrum simulation tool motivates us to challenge the established picture of a sole pseudo-octahedral complex in solution.

Photoinduced bond oscillations in ironpentacarbonyl give delayed synchronous bursts of carbonmonoxide release.

Early excited state dynamics in the photodissociation of transition metal carbonyls determines the chemical nature of short-lived catalytically active reaction intermediates. However, time-resolved experiments have not yet revealed mechanistic details in the sub-picosecond regime. Hence, in this study the photoexcitation of ironpentacarbonyl Fe(CO)5 is simulated with semi-classical excited state molecular dynamics. We find that the bright metal-to-ligand charge-transfer (MLCT) transition induces synchronous Fe-C oscillations in the trigonal bipyramidal complex leading to periodically reoccurring release of predominantly axial CO. Metaphorically the photoactivated Fe(CO)5 acts as a CO geyser, as a result of dynamics in the potential energy landscape of the axial Fe-C distances and non-adiabatic transitions between manifolds of bound MLCT and dissociative metal-centered (MC) excited states. The predominant release of axial CO ligands and delayed release of equatorial CO ligands are explained in a unified mechanism based on the σ*(Fe-C) anti-bonding character of the receiving orbital in the dissociative MC states.

Electronic Structure Changes of an Aromatic Amine Photoacid along the Förster Cycle.

Photoacids show a strong increase in acidity in the first electronic excited state, enabling real-time studies of proton transfer in acid-base reactions, proton transport in energy storage devices and biomolecular sensor protein systems. Several explanations have been proposed for what determines photoacidity, ranging from variations in solvation free energy to changes in electronic structure occurring along the four stages of the Förster cycle. Here we use picosecond nitrogen K-edge spectroscopy to monitor the electronic structure changes of the proton donating group in a protonated aromatic amine photoacid in solution upon photoexcitation and subsequent proton transfer dynamics. Probing core-to-valence transitions locally at the amine functional group and with orbital specificity, we clearly reveal pronounced electronic structure, dipole moment and energetic changes on the conjugate photobase side. This result paves the way for a detailed electronic structural characterization of the photoacidity phenomenon.