Exploring fingerprints of ultrafast structural dynamics in molecular solutions with an X-ray laser.

We apply ultrashort X-ray laser pulses to track optically excited structural dynamics of [Ir2(dimen)4]2+ molecules in solution. In our exploratory study we determine angular correlations in the scattered X-rays, which comprise a complex fingerprint of the ultrafast dynamics. Model-assisted analysis of the experimental correlation data allows us to elucidate various aspects of the photoinduced changes in the excited molecular ensembles. We unambiguously identify that in our experiment the photoinduced transition dipole moments in [Ir2(dimen)4]2+ molecules are oriented perpendicular to the Ir-Ir bond. The analysis also shows that the ground state conformer of [Ir2(dimen)4]2+ with a larger Ir-Ir distance is mostly responsible for the formation of the excited state. We also reveal that the ensemble of solute molecules can be characterized with a substantial structural heterogeneity due to solvent influence. The proposed X-ray correlation approach offers an alternative path for studies of ultrafast structural dynamics of molecular ensembles in the liquid and gas phases.

Resolving Femtosecond Solvent Reorganization Dynamics in an Iron Complex by Nonadiabatic Dynamics Simulations.

The ultrafast dynamical response of solute-solvent interactions plays a key role in transition metal complexes, where charge transfer states are ubiquitous. Nonetheless, there exist very few excited-state simulations of transition metal complexes in solution. Here, we carry out a nonadiabatic dynamics study of the iron complex [Fe(CN)4(bpy)]2- (bpy = 2,2'-bipyridine) in explicit aqueous solution. Implicit solvation models were found inadequate for reproducing the strong solvatochromism in the absorption spectra. Instead, direct solute-solvent interactions, in the form of hydrogen bonds, are responsible for the large observed solvatochromic shift and the general dynamical behavior of the complex in water. The simulations reveal an overall intersystem crossing time scale of 0.21 ± 0.01 ps and a strong reliance of this process on nuclear motion. A charge transfer character analysis shows a branched decay mechanism from the initially excited singlet metal-to-ligand charge transfer (1MLCT) states to triplet states of 3MLCT and metal-centered (3MC) character. We also find that solvent reorganization after excitation is ultrafast, on the order of 50 fs around the cyanides and slower around the bpy ligand. In contrast, the nuclear vibrational dynamics, in the form of Fe-ligand bond changes, takes place on slightly longer time scales. We demonstrate that the surprisingly fast solvent reorganizing should be observable in time-resolved X-ray solution scattering experiments, as simulated signals show strong contributions from the solute-solvent scattering cross term. Altogether, the simulations paint a comprehensive picture of the coupled and concurrent electronic, nuclear, and solvent dynamics and interactions in the first hundreds of femtoseconds after excitation.

Disentangling the resonant Auger spectra of ozone: overlapping core-hole states and core-excited state dynamics.

We investigate the resonant and non-resonant Auger spectra of ozone with a newly implemented multi-reference protocol based on the one-center approximation [Tenorio et al., J. Chem. Theory Comput. 2022, 18, 4387-4407]. The results of our calculations are compared to existing experimental data, where we elucidate the resonant Auger spectrum measured at 530.8 and 536.7 eV, that correspond to the 1sOT → π*(2b1) and 1sOT → σ*(7a1) resonances, and at 542.3 eV, which lies near the 1sOC → σ*(7a1) excited state and above the 1sOT-1 ionization threshold. Using molecular dynamics simulations, we demonstrate the relevance of few-femtoseconds nuclear dynamics in the resonant Auger spectrum of ozone following the 1sOT → π*(2b1) core-excitation.

Tracking structural solvent reorganization and recombination dynamics following e- photoabstraction from aqueous I- with femtosecond x-ray spectroscopy and scattering.

We present a sub-picosecond resolved investigation of the structural solvent reorganization and geminate recombination dynamics following 400 nm two-photon excitation and photodetachment of a valence p electron from the aqueous atomic solute, I-(aq). The measurements utilized time-resolved X-ray Absorption Near Edge Structure (TR-XANES) spectroscopy and X-ray Solution Scattering (TR-XSS) at the Linac Coherent Light Source x-ray free electron laser in a laser pump/x-ray probe experiment. The XANES measurements around the L1-edge of the generated nascent iodine atoms (I0) yield an average electron ejection distance from the iodine parent of 7.4 ± 1.5 Å with an excitation yield of about 1/3 of the 0.1M NaI aqueous solution. The kinetic traces of the XANES measurement are in agreement with a purely diffusion-driven geminate iodine-electron recombination model without the need for a long-lived (I0:e-) contact pair. Nonequilibrium classical molecular dynamics simulations indicate a delayed response of the caging H2O solvent shell and this is supported by the structural analysis of the XSS data: We identify a two-step process exhibiting a 0.1 ps delayed solvent shell reorganization time within the tight H-bond network and a 0.3 ps time constant for the mean iodine-oxygen distance changes. The results indicate that most of the reorganization can be explained classically by a transition from a hydrophilic cavity with a well-ordered first solvation shell (hydrogens pointing toward I-) to an expanded cavity around I0 with a more random orientation of the H2O molecules in a broadened first solvation shell.

Femtochemistry of bimolecular reactions from weakly bound complexes: computational study of the H + H'OD → H'OH + D or HOD + H' exchange reactions.

A full-dimensional wavepacket propagation describing the bimolecular exchange reactions H + H'OD → H'OH + D or HOD + H' initiated by photolysis of HCl in the hydrogen-bound complex (HCl)⋯(HOD) is reported. The dynamics of this reaction is carried out with the MCTDH method on an ab initio potential energy surface (PES) of H3O and the initial state is derived from the ground state wavefunction of the complex obtained by relaxation on its own electronic ground state ab initio PES. The description of the system makes use of polyspherical coordinates parametrizing a set of Radau and Jacobi vectors. The calculated energy- and time-resolved reaction probabilities show, owing to the large collision energies at play stemming from the (almost full) photolysis of HCl, that the repulsion between oxygen in the H'OD molecule and the incoming hydrogen atom is the main feature of the collision and leads to non-reactive scattering. No abstraction reaction products are observed. However, both exchange processes are still observable, with a preference in O-H' bond dissociation over that of O-D. The selectivity is reversed upon vibrational pre-excitation of the O-D stretching mode in the H'OD molecule. It is shown that, after the collision, the hydrogen atom of HCl does most likely not encounter the almost stationary chlorine atom again but we also consider the limit case where the H atom is forced to collide multiple times against H'OD as a result of being pushed back by the Cl atom.

Trajectory surface-hopping photoinduced dynamics from Rydberg states of trimethylamine.

We present a computational study on nonadiabatic excited-state dynamics initiated from the 3p Rydberg states of trimethylamine (TMA). We utilise a methodology based on full-dimensional (39 D) trajectory surface-hopping (TSH) simulations, in which propagation is carried out on on-the-fly density functional theory (DFT)/time-dependent DFT (TD-DFT) potentials. Both our electronic structure benchmarks to high-level ab initio methods (EOM-CCSD, CASPT2) and TSH simulations demonstrate high-accuracy of the applied CAM-B3LYP functional for the description of Rydberg excited states. Based on our excited-state simulations, we construct the following mechanistic picture: when pumped resonantly to the 3p Rydberg manifold, TMA coherently vibrates along the planarisation mode with a period of 104 fs and an exponential coherence decay time constant of 240 fs. Nonadiabatic dynamics occur on a faster (∼1 ps) and a slower (∼3 ps) timescale, along the N-C stretching mode by mixing with a dissociative σN-C* state. As a minor relaxation channel, 3p → 3s internal conversion occurs via branching at the σN-C*/3s intersection. We find that photodissociaton is hardly observable within 3 ps (1%), which is a failure of the range-separated hybrid CAM-B3LYP functional, as a consequence of its static electron correlation deficiency at long range. In contrast, pure DFT (GGA-BLYP) provides an accurate long-range description (19% dissociation yield), also supported by comparison to recent ultrafast experiments, even if the Rydberg state energies are significantly underestimated (>1 eV). Finally, we reveal the crucial role of vibrational coherence and energy transfer from the planarisation mode for N-C bond activation and resulting nonadiabatic dynamics. The present work illustrates the importance of nuclear-electronic coupling for excited-state dynamics and branching at conical intersections.

Publisher's Note: Femtosecond X-Ray Scattering Study of Ultrafast Photoinduced Structural Dynamics in Solvated [Co(terpy)_{2}]

This corrects the article DOI: 10.1103/PhysRevLett.117.013002.

Hot Branching Dynamics in a Light-Harvesting Iron Carbene Complex Revealed by Ultrafast X-ray Emission Spectroscopy.

Iron N-heterocyclic carbene (NHC) complexes have received a great deal of attention recently because of their growing potential as light sensitizers or photocatalysts. We present a sub-ps X-ray spectroscopy study of an FeII NHC complex that identifies and quantifies the states involved in the deactivation cascade after light absorption. Excited molecules relax back to the ground state along two pathways: After population of a hot 3 MLCT state, from the initially excited 1 MLCT state, 30 % of the molecules undergo ultrafast (150 fs) relaxation to the 3 MC state, in competition with vibrational relaxation and cooling to the relaxed 3 MLCT state. The relaxed 3 MLCT state then decays much more slowly (7.6 ps) to the 3 MC state. The 3 MC state is rapidly (2.2 ps) deactivated to the ground state. The 5 MC state is not involved in the deactivation pathway. The ultrafast partial deactivation of the 3 MLCT state constitutes a loss channel from the point of view of photochemical efficiency and highlights the necessity to screen transition-metal complexes for similar ultrafast decays to optimize photochemical performance.

Electronic Coherence in Ultrafast X-Ray Scattering from Molecular Wave Packets.

Simulations of nonresonant ultrafast x-ray scattering from a molecular wave packet in H_{2} are used to examine and classify the components that contribute to the total scattering signal. The elastic component, which can be used to determine the structural dynamics of the molecule, is also found to carry a strong signature of an adiabatic electron transfer that occurs in the simulated molecule. The inelastic component, frequently assumed to be constant, is found to change with the geometry of the molecule. Finally, a coherent mixed component due to interferences between different inelastic transitions is identified and shown to provide a direct probe of transient electronic coherences.

Ultrafast X-Ray Scattering Measurements of Coherent Structural Dynamics on the Ground-State Potential Energy Surface of a Diplatinum Molecule.

We report x-ray free electron laser experiments addressing ground-state structural dynamics of the diplatinum anion Pt_{2}POP_{4} following photoexcitation. The structural dynamics are tracked with <100 fs time resolution by x-ray scattering, utilizing the anisotropic component to suppress contributions from the bulk solvent. The x-ray data exhibit a strong oscillatory component with period 0.28 ps and decay time 2.2 ps, and structural analysis of the difference signal directly shows this as arising from ground-state dynamics along the PtPt coordinate. These results are compared with multiscale Born-Oppenheimer molecular dynamics simulations and demonstrate how off-resonance excitation can be used to prepare a vibrationally cold excited-state population complemented by a structure-dependent depletion of the ground-state population which subsequently evolves in time, allowing direct tracking of ground-state structural dynamics.

Excited-state solvation structure of transition metal complexes from molecular dynamics simulations and assessment of partial atomic charge methods.

In this work, we investigate the excited-state solute and solvation structure of [Ru(bpy)3]2+, [Fe(bpy)3]2+, [Fe(bmip)2]2+ and [Cu(phen)2]+ (bpy = 2,2'-bipyridine; bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine; phen = 1,10-phenanthroline) transition metal complexes (TMCs) in terms of solute-solvent radial distribution functions (RDFs) and evaluate the performance of some of the most popular partial atomic charge (PAC) methods for obtaining these RDFs by molecular dynamics (MD) simulations. To this end, we compare classical MD of a frozen solute in water and acetonitrile (ACN) with quantum mechanics/molecular mechanics Born-Oppenheimer molecular dynamics (QM/MM BOMD) simulations. The calculated RDFs show that the choice of a suitable PAC method is dependent on the coordination number of the metal, denticity of the ligands, and type of solvent. It is found that this selection is less sensitive for water than ACN. Furthermore, a careful choice of the PAC method should be considered for TMCs that exhibit a free direct coordination site, such as [Cu(phen)2]+. The results of this work show that fast classical MD simulations with ChelpG/RESP or CM5 PACs can produce RDFs close to those obtained by QM/MM MD and thus, provide reliable solvation structures of TMCs to be used, e.g. in the analysis of scattering data.

Simulation of ultrafast excited-state dynamics and elastic x-ray scattering by quantum wavepacket dynamics.

Simulation of the ultrafast excited-state dynamics and elastic X-ray scattering of the [Fe(bmip)2]2+ [bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-4-pyridine] complex is presented and analyzed. We employ quantum wavepacket dynamics simulations on a 5-dimensional potential energy surface (PES) calculated by time-dependent density functional theory with 26 coupled diabatic states. The simulations are initiated by explicit inclusion of a time-dependent electromagnetic field. In the case of resonant excitation into singlet metal-to-ligand charge transfer (1MLCT) states, kinetic (exponential) population dynamics are observed with small nuclear motion. In agreement with transient optical absorption spectroscopy experiments, we observe a subpicosecond 1MLCT → 3MLCT intersystem crossing and a subsequent decay into triplet metal-centered (3MC) states on a picosecond time scale. The simulated time-resolved difference scattering signal is dominated by the 3MC component, for which the structural distortions are significant. On the other hand, excitation into 1MC states leads to ballistic (nonexponential) population dynamics with strong nuclear motion. The reason for these ballistic dynamics is that in this case, the excitation occurs into a nonequilibrium region, i.e., far from the minimum of the 1MC PES. This results in wavepacket dynamics along the principal breathing mode, which is clearly visible in both the population dynamics and difference scattering. Finally, the importance of decomposing the difference scattering into components by electronic states is highlighted, information which is not accessible from elastic X-ray scattering experiments.

Time-resolved near-edge X-ray absorption fine structure of pyrazine from electronic structure and nuclear wave packet dynamics simulations.

As a demonstration of the analysis of the electronic structure and the nuclear dynamics from time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS), we present the TR-NEXAFS spectra of pyrazine following the excitation to the 1B2u(ππ*) state. The spectra are calculated combining the frozen-core/core-valence separated equation-of-motion coupled cluster singles and doubles approach for the spectral signatures and the multiconfiguration time-dependent Hartree method for the wave packet propagation. The population decay from the 1B2u(ππ*) state to the 1B3u(nπ*) and 1Au(nπ*) states, followed by oscillatory flow of population between the 1B3u(nπ*) and 1Au(nπ*) states, is interpreted by means of visualization of the potential energy curves and the reduced nuclear densities. By examining the electronic structure of the three valence-excited states and the final core-excited states, we observe that the population dynamics is explicitly reflected in the TR-NEXAFS spectra, especially when the heteroatoms are selected as the X-ray absorption sites. This work illustrates the feasibility of extracting fine details of molecular photophysical processes from TR-NEXAFS spectra by using currently available theoretical methods.

Anisotropy enhanced X-ray scattering from solvated transition metal complexes.

Time-resolved X-ray scattering patterns from photoexcited molecules in solution are in many cases anisotropic at the ultrafast time scales accessible at X-ray free-electron lasers (XFELs). This anisotropy arises from the interaction of a linearly polarized UV-Vis pump laser pulse with the sample, which induces anisotropic structural changes that can be captured by femtosecond X-ray pulses. In this work, a method for quantitative analysis of the anisotropic scattering signal arising from an ensemble of molecules is described, and it is demonstrated how its use can enhance the structural sensitivity of the time-resolved X-ray scattering experiment. This method is applied on time-resolved X-ray scattering patterns measured upon photoexcitation of a solvated di-platinum complex at an XFEL, and the key parameters involved are explored. It is shown that a combined analysis of the anisotropic and isotropic difference scattering signals in this experiment allows a more precise determination of the main photoinduced structural change in the solute, i.e. the change in Pt-Pt bond length, and yields more information on the excitation channels than the analysis of the isotropic scattering only. Finally, it is discussed how the anisotropic transient response of the solvent can enable the determination of key experimental parameters such as the instrument response function.

Time-resolved X-ray scattering by electronic wave packets: analytic solutions to the hydrogen atom.

Modern pulsed X-ray sources permit time-dependent measurements of dynamical changes in atoms and molecules via non-resonant scattering. The planning, analysis, and interpretation of such experiments, however, require a firm and elaborated theoretical framework. This paper provides a detailed description of time-resolved X-ray scattering by non-stationary electronic wave packets in atomic systems. A consistent application of the Waller-Hartree approximation is discussed and different contributions to the total differential scattering signal are identified and interpreted. Moreover, it is demonstrated how the scattering signal of wave packets in the hydrogen atom can be expressed analytically. This permits simulations without numerical integration and establishes a benchmark for both efficiency and accuracy. Based on that, scattering patterns of an exemplary wave packet in the hydrogen atom are computed for different points in time. In doing so, distinct features of time-resolved X-ray scattering by non-stationary electronic wave packets are illustrated and accentuated in greater detail than it has been done before.

Ultrafast X-ray absorption study of longitudinal-transverse phonon coupling in electrolyte aqueous solution.

Ultrafast X-ray absorption spectroscopy is applied to study the conversion of longitudinal to transverse phonons in aqueous solution. Permanganate solutes serve as X-ray probe molecules that permit the measurement of the conversion of 13.5 GHz, longitudinal phonons to 27 GHz, transverse phonons that propagate with high-frequency sound speed. The experimental results, combined with QM/MM MD simulations, show that the hydrogen bond network around the charged solutes has a glass-like stiffness that persists for at least tens of picoseconds.

Femtosecond X-Ray Scattering Study of Ultrafast Photoinduced Structural Dynamics in Solvated [Co(terpy)_{2}]

We study the structural dynamics of photoexcited [Co(terpy)_{2}]^{2+} in an aqueous solution with ultrafast x-ray diffuse scattering experiments conducted at the Linac Coherent Light Source. Through direct comparisons with density functional theory calculations, our analysis shows that the photoexcitation event leads to elongation of the Co-N bonds, followed by coherent Co-N bond length oscillations arising from the impulsive excitation of a vibrational mode dominated by the symmetrical stretch of all six Co-N bonds. This mode has a period of 0.33 ps and decays on a subpicosecond time scale. We find that the equilibrium bond-elongated structure of the high spin state is established on a single-picosecond time scale and that this state has a lifetime of ∼7 ps.

Electron Transfer and Solvent-Mediated Electronic Localization in Molecular Photocatalysis.

This work provides a detailed mechanism for electron transfer in a heterodinuclear complex designed as a model system in which to study homogeneous molecular photocatalysis. With efficient Born-Oppenheimer molecular dynamics simulations, we show how intermediate, charge-separated states can mediate the electron transfer. We observe how Jahn-Teller distortion effects play out in solution, when the molecule has energetically close-lying states, and how this distortion is averaged out in the thermal sampling. Finally, we demonstrate how the solvent helps stabilize and localize the separated charge. The information on the electronic configuration and separate states is of key importance for designing next-generation photocatalysts.

Butterfly Deformation Modes in a Photoexcited Pyrazolate-Bridged Pt Complex Measured by Time-Resolved X-Ray Scattering in Solution.

Pyrazolate-bridged dinuclear Pt(II) complexes represent a series of molecules with tunable absorption and emission properties that can be directly modulated by structural factors, such as the Pt-Pt distance. However, direct experimental information regarding the structure of the emissive triplet excited state has remained scarce. Using time-resolved wide-angle X-ray scattering (WAXS), the excited triplet state molecular structure of [Pt(ppy)(µ-t-Bu2pz)]2 (ppy = 2-phenylpyridine; t-Bu2pz = 3,5-di-tert-butylpyrazolate), complex 1, was obtained in a dilute (0.5 mM) toluene solution utilizing the monochromatic X-ray pulses at Beamline 11IDD of the Advanced Photon Source. The excited-state structural analysis of 1 was performed based on the results from both transient WAXS measurements and density functional theory calculations to shed light on the primary structural changes in its triplet metal-metal-to-ligand charge-transfer (MMLCT) state, in particular, the Pt-Pt distance and ligand rotation. We found a pronounced Pt-Pt distance contraction accompanied by rotational motions of ppy ligands toward one another in the MMLCT state of 1. Our results suggest that the contraction is larger than what has previously been reported, but they are in good agreement with recent theoretical efforts and suggest the ppy moieties as targets for rational synthesis aimed at tuning the excited-state structure and properties.