Uncovering the 3d and 4d Electronic Interactions in Solvated Ru Complexes with 2p3d Resonant Inelastic X-ray Scattering.

The electronic structure and dynamics of ruthenium complexes are widely studied given their use in catalytic and light-harvesting materials. Here we investigate three model Ru complexes, [RuIII(NH3)6]3+, [RuII(bpy)3]2+, and [RuII(CN)6]4-, with L3-edge 2p3d resonant inelastic X-ray scattering (RIXS) to probe unoccupied 4d valence orbitals and occupied 3d orbitals and to gain insight into the interactions between these levels. The 2p3d RIXS maps contain a higher level of spectral information than the L3 X-ray absorption near edge structure (XANES). This study provides a direct measure of the 3d spin-orbit splittings of 4.3, 4.0, and 4.1 eV between the 3d5/2 and 3d3/2 orbitals of the [RuIII(NH3)6]3+, [RuII(bpy)3]2+, and [RuII(CN)6]4- complexes, respectively.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra.

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity.

Two-dimensional Electronic-Vibrational (2D EV) spectroscopy and two-dimensional Vibrational-Electronic (2D VE) spectroscopy are among the newest additions to the coherent multidimensional spectroscopy toolbox, and they are directly sensitive to vibronic couplings. In this first of two papers, the complete orientational response functions are developed for a model system consisting of two coupled anharmonic oscillators and two electronic states in order to simulate polarization-selective 2D EV and 2D VE spectra with arbitrary combinations of linearly polarized electric fields. Here, we propose analytical methods to isolate desired signals within complicated spectra and to extract the relative orientation between vibrational and vibronic dipole moments of the model system using combinations of polarization-selective 2D EV and 2D VE spectral features. Time-dependent peak amplitudes of coherence peaks are also discussed as means for isolating desired signals within the time-domain. This paper serves as a field guide for using polarization-selective 2D EV and 2D VE spectroscopies to map coupled vibronic coordinates on the molecular frame.

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, K4FeII(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.

Double core hole valence-to-core x-ray emission spectroscopy: A theoretical exploration using time-dependent density functional theory.

With the help of newly developed X-ray free-electron laser (XFEL) sources, creating double core holes (DCHs) simultaneously at the same or different atomic sites in a molecule has now become possible. DCH X-ray emission is a new form of X-ray nonlinear spectroscopy that can be studied with a XFEL. Here, we computationally explore the metal K-edge valence-to-core (VtC) X-ray emission spectroscopy (XES) of metal/metal and metal/ligand DCH states in a series of transition metal complexes with time-dependent density functional theory. The simulated DCH VtC-XES signals are compared with conventional single core hole (SCH) XES signals. The energy shifts and intensity changes of the DCH emission lines with respect to the corresponding SCH-XES features are fingerprints of the coupling between the second core hole and the occupied orbitals around the DCHs that contain important chemical bonding information of the complex. The difference between delocalized/localized core hole models on DCH VtC-XES is also briefly discussed. We theoretically demonstrate that DCH XES provides subtle information on the local electronic structure around metal centers in transition metal complexes beyond conventional linear XES. Our predicted changes from calculations between SCH-XES and DCH-XES features should be detectable with modern XFEL sources.

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies.

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Ultrafast Independent N-H and N-C Bond Deformation Investigated with Resonant Inelastic X-Ray Scattering.

The femtosecond excited-state dynamics following resonant photoexcitation enable the selective deformation of N-H and N-C chemical bonds in 2-thiopyridone in aqueous solution with optical or X-ray pulses. In combination with multiconfigurational quantum-chemical calculations, the orbital-specific electronic structure and its ultrafast dynamics accessed with resonant inelastic X-ray scattering at the N 1s level using synchrotron radiation and the soft X-ray free-electron laser LCLS provide direct evidence for this controlled photoinduced molecular deformation and its ultrashort timescale.

Fourier transform two-dimensional electronic-vibrational spectroscopy using an octave-spanning mid-IR probe.

The development of coherent Fourier transform two-dimensional electronic-vibrational (2D EV) spectroscopy with acousto-optic pulse-shaper-generated near-UV pump pulses and an octave-spanning broadband mid-IR probe pulse is detailed. A 2D EV spectrum of a silicon wafer demonstrates the full experimental capability of this experiment, and a 2D EV spectrum of dissolved hexacyanoferrate establishes the viability of our 2D EV experiment for studying condensed phase molecular ensembles.

Two-dimensional vibrational-electronic spectroscopy.

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([Fe(III)(CN)6](3-) dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5Fe(II)CNRu(III)(NH3)5](-) dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

Investigating vibrational anharmonic couplings in cyanide-bridged transition metal mixed valence complexes using two-dimensional infrared spectroscopy.

Using polarization-selective two-dimensional infrared (2D IR) spectroscopy, we measure anharmonic couplings and angles between the transition dipole moments of the four cyanide stretching (νCN) vibrations found in [(NH3)5Ru(III)NCFe(II)(CN)5](-) (FeRu) dissolved in D2O and formamide and [(NC)5Fe(II)CNPt(IV)(NH3)4NCFe(II)(CN)5](4-) (FePtFe) dissolved in D2O. These cyanide-bridged transition metal complexes serve as model systems for studying the role of high frequency vibrational modes in ultrafast photoinduced charge transfer reactions. Here, we focus on the spectroscopy of the νCN modes in the electronic ground state. The FTIR spectra of the νCN modes of the bimetallic and trimetallic systems are strikingly different in terms of frequencies, amplitudes, and lineshapes. The experimental 2D IR spectra of FeRu and FePtFe and their fits reveal a set of weakly coupled anharmonic νCN modes. The vibrational mode anharmonicities of the individual νCN modes range from 14 to 28 cm(-1). The mixed-mode anharmonicities range from 2 to 14 cm(-1). In general, the bridging νCN mode is most weakly coupled to the radial νCN mode, which involves the terminal CN ligands. Measurement of the relative transition dipole moments of the four νCN modes reveal that the FeRu molecule is almost linear in solution when dissolved in formamide, but it assumes a bent geometry when dissolved in D2O. The νCN modes are modelled as bilinearly coupled anharmonic oscillators with an average coupling constant of 6 cm(-1). This study elucidates the role of the solvent in modulating the molecular geometry and the anharmonic vibrational couplings between the νCN modes in cyanide-bridged transition metal mixed valence complexes.

Integrated Quantum-Classical Protocol for the Realistic Description of Solvated Multinuclear Mixed-Valence Transition-Metal Complexes and Their Solvatochromic Properties.

Linear cyanide-bridged polymetallic complexes, which undergo photoinduced metal-to-metal charge transfer, represent prototypical systems for studying long-range electron-transfer reactions and understanding the role played by specific solute-solvent interactions in modulating the excited-state dynamics. To tackle this problem, while achieving a statistically meaningful description of the solvent and of its relaxation, one needs a computational approach capable of handling large polynuclear transition-metal complexes, both in their ground and excited states, as well as the ability to follow their dynamics in several environments up to nanosecond time scales. Here, we present a mixed quantum classical approach, which combines large-scale molecular dynamics (MD) simulations based on an accurate quantum mechanically derived force field (QMD-FF) and self-consistent QMD polarized point charges, with IR and UV-vis spectral calculations to model the solvation dynamics and optical properties of a cyano-bridged trinuclear mixed-valence compound (trans-[(NC)5FeIII(µ-CN)RuII(pyridine)4(µ-NC)FeIII(CN)5]4-). We demonstrate the reliability of the QMD-FF/MD approach in sampling the solute conformational space and capturing the local solute-solvent interactions by comparing the results with higher-level quantum mechanics/molecular mechanics (QM/MM) MD reference data. The IR spectra calculated along the classical MD trajectories in different solvents correctly predict the red shift of the CN stretching band in the aprotic medium (acetonitrile) and the subtle differences measured in water and methanol, respectively. By explicitly including the solvent molecules around the cyanide ligands and calculating the thermal averaged absorption spectra using time-dependent density functional theory calculations within the Tamm-Dancoff approximation, the experimental solvatochromic shift is quantitatively reproduced going from water to methanol, while it is overestimated for acetonitrile. This discrepancy can likely be traced back to the lack of important dispersion interactions between the solvent cyano groups and the pyridine substituents in our micro solvation model. The proposed protocol is applied to the ground state in water, methanol, and acetonitrile and can be flexibly generalized to study excited-state nonequilibrium solvation dynamics.

Effect of solvent polarity on the vibrational dephasing dynamics of the nitrosyl stretch in an Fe(II) complex revealed by 2D IR spectroscopy.

The vibrational dephasing dynamics of the nitrosyl stretching vibration (ν(NO)) in sodium nitroprusside (SNP, Na2[Fe(CN)5NO]·2H2O) are investigated using two-dimensional infrared (2D IR) spectroscopy. The ν(NO) in SNP acts as a model system for the nitrosyl ligand found in metalloproteins which play an important role in the transportation and detection of nitric oxide (NO) in biological systems. We perform a 2D IR line shape study of the ν(NO) in the following solvents: water, deuterium oxide, methanol, ethanol, ethylene glycol, formamide, and dimethyl sulfoxide. The frequency of the ν(NO) exhibits a large vibrational solvatochromic shift of 52 cm(-1), ranging from 1884 cm(-1) in dimethyl sulfoxide to 1936 cm(-1) in water. The vibrational anharmonicity of the ν(NO) varies from 21 to 28 cm(-1) in the solvents used in this study. The frequency-frequency correlation functions (FFCFs) of the ν(NO) in SNP in each of the seven solvents are obtained by fitting the experimentally obtained 2D IR spectra using nonlinear response theory. The fits to the 2D IR line shape reveal that the spectral diffusion time scale of the ν(NO) in SNP varies from 0.8 to 4 ps and is negatively correlated with the empirical solvent polarity scales. We compare our results with the experimentally determined FFCFs of other charged vibrational probes in polar solvents and in the active sites of heme proteins. Our results suggest that the vibrational dephasing dynamics of the ν(NO) in SNP reflect the fluctuations of the nonhomogeneous electric field created by the polar solvents around the nitrosyl and cyanide ligands. The solute solvent interactions occurring at the trans-CN ligand are sensed through the π-back-bonding network along the Fe-NO bond in SNP.

Simulating Ru L3-edge X-ray absorption spectroscopy with time-dependent density functional theory: model complexes and electron localization in mixed-valence metal dimers.

Ruthenium L3-edge X-ray absorption (XA) spectroscopy probes unoccupied 4d orbitals of the metal atom and is increasingly being used to investigate the local electronic structure in ground and excited electronic states of Ru complexes. The simultaneous development of computational tools for simulating Ru L3-edge spectra is crucial for interpreting the spectral features at a molecular level. This study demonstrates that time-dependent density functional theory (TDDFT) is a viable and predictive tool for simulating ruthenium L3-edge XA spectroscopy. We systematically investigate the effects of exchange correlation functional and implicit and explicit solvent interactions on a series of Ru(II) and Ru(III) complexes in their ground and electronic excited states. The TDDFT simulations reproduce all of the experimentally observed features in Ru L3-edge XA spectra within the experimental resolution (0.4 eV). Our simulations identify ligand-specific charge transfer features in complicated Ru L3-edge spectra of [Ru(CN)6](4-) and Ru(II) polypyridyl complexes illustrating the advantage of using TDDFT in complex systems. We conclude that the B3LYP functional most accurately predicts the transition energies of charge transfer features in these systems. We use our TDDFT approach to simulate experimental Ru L3-edge XA spectra of transition metal mixed-valence dimers of the form [(NC)5M(II)-CN-Ru(III)(NH3)5](-) (where M = Fe or Ru) dissolved in water. Our study determines the spectral signatures of electron delocalization in Ru L3-edge XA spectra. We find that the inclusion of explicit solvent molecules is necessary for reproducing the spectral features and the experimentally determined valencies in these mixed-valence complexes. This study validates the use of TDDFT for simulating Ru 2p excitations using popular quantum chemistry codes and providing a powerful interpretive tool for equilibrium and ultrafast Ru L3-edge XA spectroscopy.

Revealing core-valence interactions in solution with femtosecond X-ray pump X-ray probe spectroscopy.

Femtosecond pump-probe spectroscopy using ultrafast optical and infrared pulses has become an essential tool to discover and understand complex electronic and structural dynamics in solvated molecular, biological, and material systems. Here we report the experimental realization of an ultrafast two-color X-ray pump X-ray probe transient absorption experiment performed in solution. A 10 fs X-ray pump pulse creates a localized excitation by removing a 1s electron from an Fe atom in solvated ferro- and ferricyanide complexes. Following the ensuing Auger-Meitner cascade, the second X-ray pulse probes the Fe 1s → 3p transitions in resultant novel core-excited electronic states. Careful comparison of the experimental spectra with theory, extracts +2 eV shifts in transition energies per valence hole, providing insight into correlated interactions of valence 3d with 3p and deeper-lying electrons. Such information is essential for accurate modeling and predictive synthesis of transition metal complexes relevant for applications ranging from catalysis to information storage technology. This study demonstrates the experimental realization of the scientific opportunities possible with the continued development of multicolor multi-pulse X-ray spectroscopy to study electronic correlations in complex condensed phase systems.

Generation of tunable octave-spanning mid-infrared pulses by filamentation in gas media.

The continued development of femtosecond mid-infrared (IR) sources with ultrabroad spectral width is critical for probing and controlling complex molecular structural dynamics on an ultrafast timescale. We report on a sub-20 fs, coherent mid-IR source with an octave-spanning spectral bandwidth (>2000 cm(-1)) tunable from 2-8 micrometers (37.5-150 THz), with energy >0.4 µJ/pulse at 1 kHz. The mid-IR pulses are generated by four-wave mixing during the filamentation of intense 800 nm and 400 nm pulses in various gas media. Spectral tunability is achieved by the choice of gas, pressure and input 800 nm pulse energy.

Coherent fifth-order visible-infrared spectroscopies: ultrafast nonequilibrium vibrational dynamics in solution.

Obtaining a detailed description of photochemical reactions in solution requires measuring time-evolving structural dynamics of transient chemical species on ultrafast time scales. Time-resolved vibrational spectroscopies are sensitive probes of molecular structure and dynamics in solution. In this work, we develop doubly resonant fifth-order nonlinear visible-infrared spectroscopies to probe nonequilibrium vibrational dynamics among coupled high-frequency vibrations during an ultrafast charge transfer process using a heterodyne detection scheme. The method enables the simultaneous collection of third- and fifth-order signals, which respectively measure vibrational dynamics occurring on electronic ground and excited states on a femtosecond time scale. Our data collection and analysis strategy allows transient dispersed vibrational echo (t-DVE) and dispersed pump-probe (t-DPP) spectra to be extracted as a function of electronic and vibrational population periods with high signal-to-noise ratio (S/N > 25). We discuss how fifth-order experiments can measure (i) time-dependent anharmonic vibrational couplings, (ii) nonequilibrium frequency-frequency correlation functions, (iii) incoherent and coherent vibrational relaxation and transfer dynamics, and (iv) coherent vibrational and electronic (vibronic) coupling as a function of a photochemical reaction.

Communication: Probing non-equilibrium vibrational relaxation pathways of highly excited C≡N stretching modes following ultrafast back-electron transfer.

Fifth-order nonlinear visible-infrared spectroscopy is used to probe coherent and incoherent vibrational energy relaxation dynamics of highly excited vibrational modes indirectly populated via ultrafast photoinduced back-electron transfer in a trinuclear cyano-bridged mixed-valence complex. The flow of excess energy deposited into four C≡N stretching (ν(CN)) modes of the molecule is monitored by performing an IR pump-probe experiment as a function of the photochemical reaction (τ(vis)). Our results provide experimental evidence that the nuclear motions of the molecule are both coherently and incoherently coupled to the electronic charge transfer process. We observe that intramolecular vibrational relaxation dynamics among the highly excited ν(CN) modes change significantly en route to equilibrium. The experiment also measures a 7 cm(-1) shift in the frequency of a ∼57 cm(-1) oscillation reflecting a modulation of the coupling between the probed high-frequency ν(CN) modes for τ(vis) < 500 fs.

Femtosecond X-ray Spectroscopy Directly Quantifies Transient Excited-State Mixed Valency.

Quantifying charge delocalization associated with short-lived photoexcited states of molecular complexes in solution remains experimentally challenging, requiring local element specific femtosecond experimental probes of time-evolving electron transfer. In this study, we quantify the evolving valence hole charge distribution in the photoexcited charge transfer state of a prototypical mixed valence bimetallic iron-ruthenium complex, [(CN)5FeIICNRuIII(NH3)5]-, in water by combining femtosecond X-ray spectroscopy measurements with time-dependent density functional theory calculations of the excited-state dynamics. We estimate the valence hole charge that accumulated at the Fe atom to be 0.6 ± 0.2, resulting from excited-state metal-to-metal charge transfer, on an ∼60 fs time scale. Our combined experimental and computational approach provides a spectroscopic ruler for quantifying excited-state valency in solvated complexes.

Probing the photoinduced metal-nitrosyl linkage isomerism of sodium nitroprusside in solution using transient infrared spectroscopy.

We study photoinduced metal-nitrosyl linkage isomerism in sodium nitroprusside (Na(2)[Fe(II)(CN)(5)NO]·2H(2)O, SNP) dissolved in methanol using picosecond transient infrared (IR) spectroscopy. The high sensitivity of this technique allows the simultaneous observation of two known metastable (MS) iron-nitrosyl linkage isomers of SNP, [Fe(II)(CN)(5)(η(1)-ON)](2-) (MS1) and [Fe(II)(CN)(5)(η(2)-NO)](2-) (MS2), at room temperature. The transient population of free nitrosyl radicals (NO·) is also measured in the sample solution. These three transient species are detected using their distinct nitrosyl stretching frequencies at 1794 cm(-1) (MS1), 1652 cm(-1) (MS2), and 1851 cm(-1) (NO·). The metastable isomers and NO· are formed on a subpicosecond time scale and have lifetimes greater than 100 ns. A UV (400 nm)-pump power dependence study reveals that MS1 can be formed with one photon, while MS2 requires two photons to be populated at room temperature in solution. Other photodissociation products including cyanide ion, Prussian blue, and [Fe(III)(CN)(5)(CH(3)OH)](2-) are observed. We develop a photochemical kinetic scheme to model our data, and the analysis reveals that photoisomerization and photodissociation of the metal-NO moiety are competing photochemical pathways in SNP dissolved in methanol at room temperature. Based on the analysis, the solvent-associated Fe(III) species and Prussian blue form on a 130 and 320 ps time scale, respectively. The simultaneous detection and characterization of photoinduced linkage isomerism (MS1 and MS2) and photodissociation of the metal-NO bond in SNP highlights the importance of understanding the role played by metastable metal-nitrosyl linkage isomers in the photochemistry of metal-nitrosyl compounds in chemistry and biology.