Recombination of photodissociated iodine: A time-resolved x-ray-diffraction study

Reaction dynamics studied via femtosecond X-ray liquidography at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) provide femtosecond X-ray pulses suitable for pump–probe time-resolved studies with a femtosecond time resolution. Since the advent of the first XFEL in 2009, recent years have witnessed a great number of applications with various pump–probe techniques at XFELs. Among these, time-resolved X-ray liquidography (TRXL) is a powerful method for visualizing structural dynamics in the liquid solution phase. Here, we classify various chemical and biological molecular systems studied via femtosecond TRXL (fs-TRXL) at XFELs, depending on the focus of the studied process, into (i) bond cleavage and formation, (ii) charge distribution and electron transfer, (iii) orientational dynamics, (iv) solvation dynamics, (v) coherent nuclear wavepacket dynamics, and (vi) protein structural dynamics, and provide a brief review on each category. We also lay out a plausible roadmap for future fs-TRXL studies for areas that have not been explored yet.

Femtosecond X-ray liquidography using X-ray free-electron lasers (XFELs) visualizes various aspects of reaction dynamics.

Structural Dynamics of C2F4I2 in Cyclohexane Studied via Time-Resolved X-ray Liquidography

The halogen elimination of 1,2-diiodoethane (C2H4I2) and 1,2-diiodotetrafluoroethane (C2F4I2) serves as a model reaction for investigating the influence of fluorination on reaction dynamics and solute-solvent interactions in solution-phase reactions. While the kinetics and reaction pathways of the halogen elimination reaction of C2H4I2 were reported to vary substantially depending on the solvent, the solvent effects on the photodissociation of C2F4I2 remain to be explored, as its reaction dynamics have only been studied in methanol. Here, to investigate the solvent dependence, we conducted a time-resolved X-ray liquidography (TRXL) experiment on C2F4I2 in cyclohexane. The data revealed that (ⅰ) the solvent dependence of the photoreaction of C2F4I2 is not as strong as that observed for C2H4I2, and (ⅱ) the nongeminate recombination leading to the formation of I2 is slower in cyclohexane than in methanol. We also show that the molecular structures of the relevant species determined from the structural analysis of TRXL data provide an excellent benchmark for DFT calculations, especially for investigating the relevance of exchange-correlation functionals used for the structural optimization of haloalkanes. This study demonstrates that TRXL is a powerful technique to study solvent dependence in the solution phase.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

Monitoring nonadiabatic avoided crossing dynamics in molecules by ultrafast X-ray diffraction

We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information through the transition charge densities (off-diagonal elements of the charge-density operator). Simulations are presented for the nonadiabatic harpooning process in the excited state of sodium fluoride.

SVD-aided pseudo principal-component analysis: A new method to speed up and improve determination of the optimum kinetic model from time-resolved data

Determination of the optimum kinetic model is an essential prerequisite for characterizing dynamics and mechanism of a reaction. Here, we propose a simple method, termed as singular value decomposition-aided pseudo principal-component analysis (SAPPA), to facilitate determination of the optimum kinetic model from time-resolved data by bypassing any need to examine candidate kinetic models. We demonstrate the wide applicability of SAPPA by examining three different sets of experimental time-resolved data and show that SAPPA can efficiently determine the optimum kinetic model. In addition, the results of SAPPA for both time-resolved X-ray solution scattering (TRXSS) and transient absorption (TA) data of the same protein reveal that global structural changes of protein, which is probed by TRXSS, may occur more slowly than local structural changes around the chromophore, which is probed by TA spectroscopy.

Ultrafast X-Ray Crystallography and Liquidography

Time-resolved X-ray diffraction provides direct information on three-dimensional structures of reacting molecules and thus can be used to elucidate structural dynamics of chemical and biological reactions. In this review, we discuss time-resolved X-ray diffraction on small molecules and proteins with particular emphasis on its application to crystalline (crystallography) and liquid-solution (liquidography) samples. Time-resolved X-ray diffraction has been used to study picosecond and slower dynamics at synchrotrons and can now access even femtosecond dynamics with the recent arrival of X-ray free-electron lasers.

Tracking reaction dynamics in solution by pump–probe X-ray absorption spectroscopy and X-ray liquidography (solution scattering)

TRXL and TRXAS are powerful techniques for real-time probing of structural and electronic dynamics of photoinduced reactions in solution phase.

Solvent-dependent structure of molecular iodine probed by picosecond X-ray solution scattering

The effect of solute-solvent interaction on molecular structure and reaction dynamics has been a target of intense studies in solution-phase chemistry, but it is often challenging to characterize the subtle effect of solute-solvent interaction even for the simplest diatomic molecules. Since the I2 molecule has only one structural parameter and exhibits solvatochromism, it is a good model system for investigating the solvent dependence of the solute structure. By using X-rays as a probe, time-resolved X-ray liquidography (TRXL) can directly elucidate the structures of reacting molecules in solution and can thus determine the solvent-dependent structural change with atomic resolution. Here, by applying TRXL, we characterized the molecular structure of I2 in methanol and cyclohexane with sub-angstrom accuracy. Specifically, we found that the I-I bond length of I2 is longer in the polar solvent (methanol) by ∼0.2 Å than in nonpolar solvents (cyclohexane and CCl4). Density functional theory (DFT) using 22 explicit methanol molecules well reproduces the longer I-I bond of molecular iodine in methanol and reveals that the larger bond length originates from partial negative charge filled in an antibonding σ* orbital through solvent-to-solute charge transfer.

Topical Review: Molecular reaction and solvation visualized by time-resolved X-ray solution scattering: Structure, dynamics, and their solvent dependence

Time-resolved X-ray solution scattering is sensitive to global molecular structure and can track the dynamics of chemical reactions. In this article, we review our recent studies on triiodide ion (I3 (-)) and molecular iodine (I2) in solution. For I3 (-), we elucidated the excitation wavelength-dependent photochemistry and the solvent-dependent ground-state structure. For I2, by combining time-slicing scheme and deconvolution data analysis, we mapped out the progression of geminate recombination and the associated structural change in the solvent cage. With the aid of X-ray free electron lasers, even clearer observation of ultrafast chemical events will be made possible in the near future.

Synchrotron ultrafast techniques for photoactive transition metal complexes

In the last decade, the use of time-resolved X-ray techniques has revealed the structure of light-generated transient species for a wide range of samples, from small organic molecules to proteins. Time resolutions of the order of 100 ps are typically reached, allowing one to monitor thermally equilibrated excited states and capture their structure as a function of time. This review aims at providing a general overview of the application of time-resolved X-ray solution scattering (TR-XSS) and time-resolved X-ray absorption spectroscopy (TR-XAS), the two techniques prevalently employed in the investigation of light-triggered structural changes of transition metal complexes. In particular, we herein describe the fundamental physical principles for static XSS and XAS and illustrate the theory of time-resolved XSS and XAS together with data acquisition and analysis strategies. Selected pioneering examples of photoactive transition metal complexes studied by TR-XSS and TR-XAS are discussed in depth.

Structural dynamics of photoinduced molecular switching in the solid state

Fast and ultra-fast time-resolved diffraction is a fantastic tool for directly observing the structural dynamics of a material rearrangement during the transformation induced by an ultra-short laser pulse. The paper illustrates this ability using the dynamics of photoinduced molecular switching in the solid state probed by 100 ps X-ray diffraction. This structural information is crucial for establishing the physical foundations of how to direct macroscopic photoswitching in materials. A key feature is that dynamics follow a complex pathway from molecular to material scales through a sequence of processes. Not only is the pathway indirect, the nature of the dynamical processes along the pathway depends on the timescale. This dictates which types of degrees of freedom are involved in the subsequent dynamics or kinetics and which are frozen or statistically averaged. We present a recent investigation of the structural dynamics in multifunctional spin-crossover materials, which are prototypes of molecular bistability in the solid state. The time-resolved X-ray diffraction results show that the dynamics span from subpicosecond molecular photoswitching followed by volume expansion (on a nanosecond timescale) and additional thermoswitching (on a microsecond timescale).

Ultrafast X-ray diffraction in liquid, solution and gas: present status and future prospects

In recent years, the time-resolved X-ray diffraction technique has been established as an excellent tool for studying reaction dynamics and protein structural transitions with the aid of 100 ps X-ray pulses generated from third-generation synchrotrons. The forthcoming advent of the X-ray free-electron laser (XFEL) will bring a substantial improvement in pulse duration, photon flux and coherence of X-ray pulses, making time-resolved X-ray diffraction even more powerful. This technical breakthrough is envisioned to revolutionize the field of reaction dynamics associated with time-resolved diffraction methods. Examples of candidates for the first femtosecond X-ray diffraction experiments using highly coherent sub-100 fs pulses generated from XFELs are presented in this paper. They include the chemical reactions of small molecules in the gas and solution phases, solvation dynamics and protein structural transitions. In these potential experiments, ultrafast reaction dynamics and motions of coherent rovibrational wave packets will be monitored in real time. In addition, high photon flux and coherence of XFEL-generated X-ray pulses give the prospect of single-molecule diffraction experiments.

Photolysis of Br2in CCl4studied by time-resolved X-ray scattering

A time-resolved X-ray solution scattering study of bromine molecules in CCl4is presented as an example of how to track atomic motions in a simple chemical reaction. The structures of the photoproducts are tracked during the recombination process, geminate and non-geminate, from 100 ps to 10 µs after dissociation. The relaxation of hot Br2*molecules heats the solvent. At early times, from 0.1 to 10 ns, an adiabatic temperature rise is observed, which leads to a pressure gradient that forces the sample to expand. The expansion starts after about 10 ns with the laser beam sizes used here. When thermal artefacts are removed by suitable scaling of the transient solvent response, the excited-state solute structures can be obtained with high fidelity. The analysis shows that 30% of Br2*molecules recombine directly along theXpotential, 60% are trapped in theA/A′ state with a lifetime of 5.5 ns, and 10% recombine non-geminatelyviadiffusive motion in about 25 ns. The Br—Br distance distribution in theA/A′ state peaks at 3.0 Å.

Solvent dependent structural perturbations of chemical reaction intermediates visualized by time-resolved x-ray diffraction

Ultrafast time-resolved wide angle x-ray scattering from chemical reactions in solution has recently emerged as a powerful technique for determining the structural dynamics of transient photochemical species. Here we examine the structural evolution of photoexcited CH(2)I(2) in the nonpolar solvent cyclohexane and draw comparisons with a similar study in the polar solvent methanol. As with earlier spectroscopic studies, our data confirm a common initial reaction pathway in both solvents. After photoexcitation, CH(2)I(2) dissociates to form CH(2)I* + I*. Iodine radicals remaining within the solvent cage recombine with a nascent CH(2)I* radical to form the transient isomer CH(2)I-I, whereas those which escape the solvent cage ultimately combine to form I(2) in cyclohexane. Moreover, the transient isomer has a lifetime approximately 30 times longer in the nonpolar solvent. Of greater chemical significance is the property of time-resolved wide angle x-ray diffraction to accurately determine the structure of the of CH(2)I-I reaction intermediate. Thus we observe that the transient iodine-iodine bond is 0.07 A+/-0.04 A shorter in cyclohexane than in methanol. A longer iodine-iodine bond length for the intermediate arises in methanol due to favorable H-bond interaction with the polar solvent. These findings establish that time-resolved x-ray diffraction has sufficient sensitivity to enable solvent dependent structural perturbations of transient chemical species to be accurately resolved.

Successive dynamical steps of photoinduced switching of a molecular Fe(III) spin-crossover material by time-resolved x-ray diffraction

We investigate the out-of-equilibrium switching dynamics of a molecular Fe(III) spin-crossover solid triggered by a femtosecond laser flash. The time-resolved x-ray diffraction and optical results show that the dynamics span from subpicosecond local photoswitching followed by volume expansion (nanosecond) and thermal switching (microsecond). We present a physical picture of the consecutive steps in the photoswitching of molecular materials.

Probing the hydrogen-bond network of water via time-resolved soft X-ray spectroscopy

We report time-resolved studies of hydrogen bonding in liquid H(2)O, in response to direct excitation of the O-H stretch mode at 3 mum, probed via soft X-ray absorption spectroscopy at the oxygen K-edge. This approach employs a newly developed nanofluidic cell for transient soft X-ray spectroscopy in the liquid phase. Distinct changes in the near-edge spectral region (XANES) are observed, and are indicative of a transient temperature rise of 10 K following transient laser excitation and rapid thermalization of vibrational energy. The rapid heating occurs at constant volume and the associated increase in internal pressure, estimated to be 8 MPa, is manifested by distinct spectral changes that differ from those induced by temperature alone. We conclude that the near-edge spectral shape of the oxygen K-edge is a sensitive probe of internal pressure, opening new possibilities for testing the validity of water models and providing new insight into the nature of hydrogen bonding in water.

Visualizing solution-phase reaction dynamics with time-resolved X-ray liquidography

Most chemical reactions occur in solution, and complex interactions between solute and solvent influence the rich chemistry of these processes. To track time-dependent processes in such reactions, researchers often use time-resolved spectroscopy. In these experiments, an optical pulse (pump) initiates a reaction, and another time-delayed optical pulse (probe) monitors the progress of the reaction. However, because of the wavelength range of the probe light used in these experiments, from infrared to ultraviolet, researchers cannot directly determine detailed structural information such as the bond lengths and bond angles of reaction intermediates. In addition, not all intermediates might be sensitive to the spectroscopic signal chosen for the experiment. This Account describes time-resolved X-ray liquidography (TRXL), a technique that overcomes these problems. In this technique, we replace the optical probe with the diffraction of hard X-ray pulses emitted from a synchrotron source. In TRXL, diffraction signals are sensitive to all chemical species simultaneously. In addition, each chemical species has a characteristic diffraction signal, a fingerprint, that we calculate from its three-dimensional atomic coordinates. Because, X-rays scatter from all atoms in the solution sample, including both the solute and the solvent, the analysis of TRXL data can track not only the reaction pathways of the solute molecules but also the solvent behavior and the solute-solvent arrangement, thus providing a global picture of the reactions. We have used TRXL to study structural dynamics and spatiotemporal kinetics of many molecular systems including diatomic molecules, haloalkanes, organometallic complexes, and protein molecules over timescales from picoseconds to milliseconds. We have observed that TRXL data adds to and, in some cases, contradicts results from time-resolved spectroscopy. For example, TRXL has shown that the reaction intermediates upon C-I bond dissociation in C(2)H(4)I(2) and C(2)F(4)I(2) have completely different structures and corresponding subsequent reaction pathways, underscoring the dramatic effect of the fluorine substitution. We have also used TRXL to identify a new reaction intermediate of the photolysis of Ru(3)(CO)(12) that has no bridging carbonyl groups. Though not detected by time-resolved infrared spectroscopy, this intermediate predominates based on the TRXL data. In looking at the quaternary conformational changes of hemoglobin, TRXL analysis suggests a faster transition than was suggested by optical spectroscopy. The time resolution of TRXL is currently limited by the X-ray pulse width available from synchrotron sources ( approximately 100 ps). The resolution should improve to 100 fs or better with X-ray free electron lasers. With this higher resolution, real time observation of ultrafast chemical events such as bond-breaking and bond-making will be possible.

Chopper system for time resolved experiments with synchrotron radiation

A chopper system for time resolved pump-probe experiments with x-ray beams from a synchrotron is described. The system has three parts: a water-cooled heatload chopper, a high-speed chopper, and a millisecond shutter. The chopper system, which is installed in beamline ID09B at the European Synchrotron Radiation Facility, provides short x-ray pulses for pump-probe experiments with ultrafast lasers. The chopper system can produce x-ray pulses as short as 200 ns in a continuous beam and repeat at frequencies from 0 to 3 kHz. For bunch filling patterns of the synchrotron with pulse separations greater than 100 ns, the high-speed chopper can isolate single 100 ps x-ray pulses that are used for the highest time resolution. A new rotor in the high-speed chopper is presented with a single pulse (100 ps) and long pulse (10 micros) option. In white beam experiments, the heatload of the (noncooled) high-speed chopper is lowered by a heatload chopper, which absorbs 95% of the incoming power without affecting the pulses selected by the high speed chopper.

Photocrystallography

This review describes the development and application of a new crystallographic technique that is starting to enable the three-dimensional structural determination of molecules in their photo-activated states. So called `photocrystallography' has wide applicability, particularly in the currently exciting area of photonics, and a discussion of this applied potential is put into context in this article. Studies are classified into four groups: photo-structural changes that are (i) irreversible; (ii) long-lived but reversible under certain conditions; (iii) transient with photo-active lifetimes of the order of microseconds; (iv) very short lived, existing at the nanosecond or even picosecond level. As photo-structural changes relative to the `ground state' can be subtle, this article necessarily concentrates on small-molecule single-crystal X-ray diffraction given that high atomic resolution is possible. That said, where it is pertinent, references are also made to related major advances in photo-induced macromolecular crystallography. The review concludes with an outlook on this new research area, including the future possibility of studying even more ephemeral, femtosecond-lived, photo-active species.

The problem with determining atomic structure at the nanoscale

Emerging complex functional materials often have atomic order limited to the nanoscale. Examples include nanoparticles, species encapsulated in mesoporous hosts, and bulk crystals with intrinsic nanoscale order. The powerful methods that we have for solving the atomic structure of bulk crystals fail for such materials. Currently, no broadly applicable, quantitative, and robust methods exist to replace crystallography at the nanoscale. We provide an overview of various classes of nanostructured materials and review the methods that are currently used to study their structure. We suggest that successful solutions to these nanostructure problems will involve interactions among researchers from materials science, physics, chemistry, computer science, and applied mathematics, working within a "complex modeling" paradigm that combines theory and experiment in a self-consistent computational framework.

Analyzing solution-phase time-resolved x-ray diffraction data by isolated-solute models

Extracting transient structural information of a solute from time-resolved x-ray diffraction (TRXD) data is not trivial because the signal from a solution contains not only the solute-only term as in the gas phase, but also solvent-related terms. To obtain structural insights, the diffraction signal in q space is often Fourier sine transformed (FT) into r space, and molecular dynamics (MD) simulation-aided signal decomposition into the solute, cage, and solvent terms has so far been indispensable for a clear-cut assignment of structural features. Here we present a convenient method of comparative structural analysis without involving MD simulations by incorporating only isolated-species models for the solute. FT is applied to both the experimental data and candidate isolated-solute models, and comparison of the correlation factors between the experimental FT and the model FTs can distinguish the best candidate among isolated-solute models for the reaction intermediates. The low q region whose influence by solvent-related terms is relatively high can be further excluded, and this mode of truncated Fourier transform (TFT) improves the correlation factors and facilitates the comparison. TFT analysis has been applied to TRXD data on the photodissociation of C(2)H(4)I(2) in two different solvents (methanol and cyclohexane), HgI(2) in methanol, and I(3) (-) in methanol excited at 267 nm. The results are consistent with previous conclusions for C(2)H(4)I(2) in methanol and HgI(2) in methanol, and the new TRXD data reveal that the C(2)H(4)I transient radical has a bridged structure in cyclohexane and I(3) (-) in methanol decomposes into I+I(2) (-) upon irradiation at 267 nm. This TFT method should greatly simplify the analysis because it bypasses MD simulations.

Picosecond calorimetry: Time-resolved x-ray diffraction studies of liquid CH2Cl2

Liquid phase time-resolved x-ray diffraction with 100 ps resolution has recently emerged as a powerful technique for probing the structural dynamics of transient photochemical species in solution. It is intrinsic to the method, however, that a structural signal is observed not only from the photochemical of interest but also from the embedding solvent matrix. To experimentally characterize the x-ray diffraction signal deriving from the solvent alone we performed time-resolved diffraction studies of a pure liquid sample over a time domain from -250 ps to 2.5 micros. Multiphoton excitation was used to rapidly heat liquid CH(2)Cl(2) using UV pulses of 100 fs duration. A significant x-ray diffraction signal is visible prior to the onset of thermal expansion, which characterizes a highly compressed superheated liquid. Liquid CH(2)Cl(2) then expands as a shock wave propagates through the sample and the temporal dependence of this phenomenon is in good agreement with theory. An unexpectedly slow initial release of energy into the liquid as heat is observed from multiphoton excited CH(2)Cl(2), revealing the presence of a metastable state of multiphoton excited CH(2)Cl(2).

Spatiotemporal reaction kinetics of an ultrafast photoreaction pathway visualized by time-resolved liquid x-ray diffraction

We have studied the reaction dynamics for HgI(2) in methanol by using time-resolved x-ray diffraction (TRXD). Although numerous time-resolved spectroscopic studies have provided ample information about the early dynamics of HgI(2), a comprehensive reaction mechanism in the solution phase spanning from picoseconds up to microseconds has been lacking. Here we show that TRXD can provide this information directly and quantitatively. Picosecond optical pulses triggered the dissociation of HgI(2), and 100-ps-long x-ray pulses from a synchrotron probed the evolving structures over a wide temporal range. To theoretically explain the diffracted intensities, the structural signal from the solute, the local structure around the solute, and the hydrodynamics of bulk solvents were considered in the analysis. The results in this work demonstrate that the determination of transient states in solution is strongly correlated with solvent energetics, and TRXD can be used as an ultrafast calorimeter. It also is shown that a manifold of structural channels can be resolved at the same time if the measurements are accurate enough and that global analysis is applied. The rate coefficients for the reactions were obtained by fitting our model against the experimental data in one global fit including all q-values and time delays. The comparison between all putative reaction channels confirms that two-body dissociation is the dominant dissociation pathway. After this primary bond breakage, two parallel channels proceed. Transient HgI associates nongeminately with an iodine atom to form HgI(2), and I(2) is formed by nongeminate association of two iodine atoms.

Impulsive solvent heating probed by picosecond x-ray diffraction

The time-resolved diffraction signal from a laser-excited solution has three principal components: the solute-only term, the solute-solvent cross term, and the solvent-only term. The last term is very sensitive to the thermodynamic state of the bulk solvent, which may change during a chemical reaction due to energy transfer from light-absorbing solute molecules to the surrounding solvent molecules and the following relaxation to equilibrium with the environment around the scattering volume. The volume expansion coefficient alpha for a liquid is typically approximately 1 x 10(-3) K(-1), which is about 1000 times greater than for a solid. Hence solvent scattering is a very sensitive on-line thermometer. The decomposition of the scattered x-ray signal has so far been aided by molecular dynamics (MD) simulations, a method capable of simulating the solvent response as well as the solute term and solute/solvent cross terms for the data analysis. Here we present an experimental procedure, applicable to most hydrogen containing solvents, that directly measures the solvent response to a transient temperature rise. The overtone modes of OH stretching and CH3 asymmetric stretching in liquid methanol were excited by near-infrared femtosecond laser pulses at 1.5 and 1.7 microm and the ensuing hydrodynamics, induced by the transfer of heat from a subset of excited CH3OH* to the bulk and the subsequent thermal expansion, were probed by 100 ps x-ray pulses from a synchrotron. The time-resolved data allowed us to extract two key differentials: the change in the solvent diffraction from a temperature change at constant density, seen at a very short time delay approximately 100 ps, and a term from a change in density at constant temperature. The latter term becomes relevant at later times approximately 1 mus when the bulk of liquid expands to accommodate its new temperature at ambient pressure. These two terms are the principal building blocks in the hydrodynamic equation of state, and they are needed in a self-consistent reconstruction of the solvent response during a chemical reaction. We compare the experimental solvent terms with those from MD simulations. The use of experimentally determined solvent differentials greatly improved the quality of global fits when applied to the time-resolved data for C2H4I2 dissolved in methanol.