A quantitative model of charge injection by ruthenium chromophores connecting femtosecond to continuous irradiance conditions.

A kinetic framework for the ultrafast photophysics of tris(2,2-bipyridine)ruthenium(II) phosphonated and methyl-phosphonated derivatives is used as a basis for modeling charge injection by ruthenium dyes into a semiconductor substrate. By including the effects of light scattering, dye diffusion, and adsorption kinetics during sample preparation and the optical response of oxidized dyes, quantitative agreement with multiple transient absorption datasets is achieved on timescales spanning femtoseconds to nanoseconds. In particular, quantitative agreement with important spectroscopic handles-the decay of an excited state absorption signal component associated with charge injection in the UV region of the spectrum and the dynamical redshift of a ∼500 nm isosbestic point-validates our kinetic model. Pseudo-first-order rate coefficients for charge injection are estimated in this work, with an order of magnitude ranging from 1011 to 1012 s-1. The model makes the minimalist assumption that all excited states of a particular dye have the same charge injection coefficient, an assumption that would benefit from additional theoretical and experimental exploration. We have adapted this kinetic model to predict charge injection under continuous solar irradiation and find that as many as 68 electron transfer events per dye per second take place, significantly more than prior estimates in the literature.

Ruthenium Dye Excitations and Relaxations in Natural Sunlight.

Solar harvesting devices using dyes convert the sun's energy to usable forms. The photophysics involved are generally investigated using time-resolved spectroscopic experiments with femtosecond to nanosecond resolution. We show that a kinetic framework constructed from transient and linear absorption measurements of metal-ligand charge transfer states for a set of ruthenium complexes in solution can be used to simulate the steady-state dynamics of dyes adsorbed on a substrate under diffuse solar radiation. Even though the intensity of sunlight is relatively low, double excitations to higher excited states can occur. The steady-state populations show that the dyes' triplet state is the main species present besides the ground state. While small, these persistent excited populations can influence reactivity over the extended periods of time that the systems operate. The results show that non-radiative and optical events (dye-1 s-1) within the singlet manifold and from the triplet state exhibit a dependence on ligand substituents.

Susceptibility of two-dimensional resonance Raman spectroscopies to cascades involving solute and solvent molecules.

Two-dimensional resonance Raman (2DRR) spectroscopies have been used to investigate the structural heterogeneity of ensembles and chemical reaction mechanisms in recent years. Our previous work suggests that the intensities of artifacts may be comparable to the desired 2DRR response for some chemical systems and experimental approaches. In a type of artifact known as a "cascade," the four-wave mixing signal field radiated by one molecule induces a four-wave mixing process in a second molecule. We consider the susceptibility of 2DRR spectroscopy to various types of signal cascades in the present work. Calculations are conducted using empirical parameters obtained for a molecule with an intramolecular charge-transfer transition in acetonitrile. For a fully impulsive pulse sequence, it is shown that "parallel" cascades involving two solute molecules are generally more intense than that of the desired 2DRR response when the solute's mode displacements are 1.0 or less. In addition, we find that the magnitudes of parallel cascades involving both solute and solvent molecules (i.e., a solute-solvent cascade) may exceed that of the 2DRR response when the solute possesses small mode displacements. It is tempting to assume that solute-solvent cascades possess negligible intensities because the off-resonant Raman cross sections of solvents are usually 4-6 orders of magnitude smaller than that of the electronically resonant solute; however, the present calculations show that the difference in solute and solvent concentrations can fully compensate for the difference in Raman cross sections under common experimental conditions. Implications for control experiments and alternate approaches for 2DRR spectroscopy are discussed.

Ultrafast Spectroscopic Signatures of Coherent Electron-Transfer Mechanisms in a Transition Metal Complex.

The prevalence of ultrafast electron-transfer processes in light-harvesting materials has motivated a deeper understanding of coherent reaction mechanisms. Kinetic models based on the traditional (equilibrium) form of Fermi's Golden Rule are commonly employed to understand photoinduced electron-transfer dynamics. These models fail in two ways when the electron-transfer process is fast compared to solvation dynamics and vibrational dephasing. First, electron-transfer dynamics may be accelerated if the photoexcited wavepacket traverses the point of degeneracy between donor and acceptor states in the solvent coordinate. Second, traditional kinetic models fail to describe electron-transfer transitions that yield products which undergo coherent nuclear motions. We address the second point in this work. Transient absorption spectroscopy and a numerical model are used to investigate coherent back-electron-transfer mechanisms in a transition metal complex composed of titanium and catechol, [Ti(cat)3](2-). The transient absorption experiments reveal coherent wavepacket motions initiated by the back-electron-transfer process. Model calculations suggest that the vibrationally coherent product states may originate in either vibrational populations or coherences of the reactant. That is, vibrational coherence may be produced even if the reactant does not undergo coherent nuclear motions. The analysis raises a question of broader significance: can a vibrational population-to-coherence transition (i.e., a nonsecular transition) accelerate electron-transfer reactions even when the rate is slower than vibrational dephasing?

Two-dimensional resonance Raman spectroscopy of oxygen- and water-ligated myoglobins.

Two-dimensional resonance Raman (2DRR) spectroscopy has recently been developed as a tool for studies of structural heterogeneity and photochemical dynamics in condensed phases. In this paper, 2DRR spectroscopy is used to investigate line broadening mechanisms of both oxygen- and water-ligated myoglobins. General signatures of anharmonicity and inhomogeneous line broadening are first established with model calculations to facilitate signal interpretation. It is shown that the present quasi-degenerate version of 2DRR spectroscopy is insensitive to anharmonicity, because signal generation is allowed for harmonic modes. Rather, the key information to be gained from 2DRR spectroscopy pertains to the line broadening mechanisms, which are fairly obvious by inspection of the data. 2DRR signals acquired for both heme protein systems reveal significant heterogeneity in the vibrational modes local to the heme's propionic acid side chains. These side chains are known to interact with solvent, because they protrude from the hydrophobic pocket that encloses the heme. Molecular dynamics simulations suggest that the heterogeneity detected in our 2DRR experiments reflects fluctuations in the geometries of the side chains. Knowledge of such thermal motions will be useful for understanding protein function (e.g., ligand binding) because the side chains are an effective "gateway" for the exchange of thermal energy between the heme and solvent.

Perspective: Two-dimensional resonance Raman spectroscopy.

Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in complex systems. The 2DRR method can leverage electronic resonance enhancement to selectively probe chromophores embedded in complex environments (e.g., a cofactor in a protein). In addition, correlations between the two dimensions of the 2DRR spectrum reveal information that is not available in traditional Raman techniques. For example, distributions of reactant and product geometries can be correlated in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this perspective article, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide and myoglobin. We also address key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopies. Most notably, it has been shown that these two techniques are subject to a tradeoff between sensitivity to anharmonicity and susceptibility to artifacts. Overall, recent experimental developments and applications of the 2DRR method suggest great potential for the future of the technique.

Communication: Uncovering correlated vibrational cooling and electron transfer dynamics with multidimensional spectroscopy.

Analogues of 2D photon echo methods in which two population times are sampled have recently been used to expose heterogeneity in chemical kinetics. In this work, the two population times sampled for a transition metal complex are transformed into a 2D rate spectrum using the maximum entropy method. The 2D rate spectrum suggests heterogeneity in the vibrational cooling (VC) rate within the ensemble. In addition, a cross peak associated with VC and back electron transfer (BET) dynamics reveals correlation between the two processes. We hypothesize that an increase in the strength of solute-solvent interactions, which accelerates VC, drives the system toward the activationless regime of BET.

Elucidation of reactive wavepackets by two-dimensional resonance Raman spectroscopy.

Traditional second-order kinetic theories fail to describe sub-picosecond photochemical reactions when solvation and vibrational dephasing undermine the assumption of equilibrium initial conditions. Four-wave mixing spectroscopies may reveal insights into such non-equilibrium processes but are limited by the single "population time" available in these types of experiments. Here, we use two-dimensional resonance Raman (2DRR) spectroscopy to expose correlations between coherent nuclear motions of the reactant and product in the photodissociation reaction of triiodide. It is shown that the transition of a nuclear wavepacket from the reactant (triiodide) to product (diiodide) states gives rise to a unique pattern of 2DRR resonances. Peaks associated with this coherent reaction mechanism are readily assigned, because they are isolated in particular quadrants of the 2DRR spectrum. A theoretical model in which the chemical reaction is treated as a vibronic coherence transfer transition from triiodide to diiodide reproduces the patterns of 2DRR resonances detected in experiments. These signal components reveal correlation between the nonequilibrium geometry of triiodide and the vibrational coherence frequency of diiodide. The 2DRR signatures of coherent reaction mechanisms established in this work may generalize to studies of ultrafast energy and charge transfer processes.

Water oxidation by a dye-catalyst diad in natural sunlight: timing and coordination of excitations and reactions across timescales of picoseconds to hours.

The mechanisms of how dyes and catalysts for solar-driven transformations such as water oxidation to form O2 work have been intensively investigated, however little is known about how their independent photophysical and chemical processes work together. The level of coordination between the dye and the catalyst in time determines the overall water oxidation system's efficiency. In this computational stochastic kinetics study, we have examined coordination and timing for a Ru-based dye-catalyst diad, [P2Ru(4-mebpy-4'-bimpy)Ru(tpy)(OH2)]4+, where P2 is 4,4'-bisphosphonato-2,2'-bipyridine, 4-mebpy-4'-bimpy is 4-(methylbipyridin-4'-yl)-N-benzimid-N'-pyridine, a bridging ligand, and tpy is (2,2':6',2''-terpyridine), taking advantage of the extensive data available for both dye and catalyst, and direct studies of the diads bound to a semiconductor surface. The simulation results for both ensembles of diads and single diads show that progress through the generally accepted water oxidation catalytic cycle is not controlled by the relatively low flux of solar irradiation or by charge or excitation losses, rather is gated by buildup of intermediates whose chemical reactions are not accelerated by photoexcitations. The stochastics of these thermal reactions govern the level of coordination between the dye and the catalyst. This suggests that catalytic efficiency can be improved in these multiphoton catalytic cycles by providing a means for photostimulation of all intermediates so that the catalytic rate is governed by charge injection under solar illumination alone.

Ultrafast Relaxations in Ruthenium Polypyridyl Chromophores Determined by Stochastic Kinetics Simulations.

Maximizing the efficiency of solar energy conversion using dye assemblies rests on understanding where the energy goes following absorption. Transient spectroscopies in solution are useful for this purpose, and the time-resolved data are usually analyzed with a sum of exponentials. This treatment assumes that dynamic events are well separated in time, and that the resulting exponential prefactors and phenomenological lifetimes are related directly to primary physical values. Such assumptions break down for coincident absorption, emission, and excited state relaxation that occur in transient absorption and photoluminescence of tris(2,2'-bipyridine)ruthenium(2+) derivatives, confounding the physical meaning of the reported lifetimes. In this work, we use inductive modeling and stochastic chemical kinetics to develop a detailed description of the primary ultrafast photophysics in transient spectroscopies of a series of Ru dyes, as an alternative to sums of exponential analysis. Commonly invoked three-level schemes involving absorption, intersystem crossing (ISC), and slow nonradiative relaxation and incoherent emission to the ground state cannot reproduce the experimentally measured spectra. The kinetics simulations reveal that ultrafast decay from the singlet excited state manifold to the ground state competes with ISC to the triplet excited state, whose efficiency was determined to be less than unity. The populations predicted by the simulations are used to estimate the magnitudes of transition dipoles for excited state excitations and evaluate the influence of specific ligands. The mechanistic framework and methodology presented here are entirely general, applicable to other dye classes, and can be extended to include charge injection by molecules bound to semiconductor surfaces.

Two-Dimensional Resonance Raman Signatures of Vibronic Coherence Transfer in Chemical Reactions.

Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in condensed phase systems. 2DRR spectroscopy is motivated by knowledge of non-equilibrium effects that cannot be detected with traditional resonance Raman spectroscopy. For example, 2DRR spectra may reveal correlated distributions of reactant and product geometries in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this chapter, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide. We show that signatures of "vibronic coherence transfer" in the photodissociation process can be targeted with particular 2DRR pulse sequences. Key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopy techniques are also addressed. Overall, recent experimental developments and applications of the 2DRR method suggest that it will be a valuable tool for elucidating ultrafast chemical reaction mechanisms.