Projection to extract the perpendicular component (PEPC) method for extracting kinetics from time-resolved data.

Time-resolved x-ray liquidography (TRXL) is a potent method for investigating the structural dynamics of chemical and biological reactions in the liquid phase. It has enabled the extraction of detailed structural aspects of various dynamic processes, the molecular structures of intermediates, and kinetics of reactions across a wide range of systems, from small molecules to proteins and nanoparticles. Proper data analysis is key to extracting the information of the kinetics and structural dynamics of the studied system encrypted in the TRXL data. In typical TRXL data, the signals from solute scattering, solvent scattering, and solute-solvent cross scattering are mixed in the q-space, and the solute kinetics and solvent hydrodynamics are mixed in the time domain, thus complicating the data analysis. Various methods developed so far generally require prior knowledge of the molecular structures of candidate species involved in the reaction. Because such information is often unavailable, a typical data analysis often involves tedious trial and error. To remedy this situation, we have developed a method named projection to extract the perpendicular component (PEPC), capable of removing the contribution of solvent kinetics from TRXL data. The resulting data then contain only the solute kinetics, and, thus, the solute kinetics can be easily determined. Once the solute kinetics is determined, the subsequent data analysis to extract the structural information can be performed with drastically improved convenience. The application of the PEPC method is demonstrated with TRXL data from the photochemistry of two molecular systems: [Au(CN)2-]3 in water and CHI3 in cyclohexane.

SVD-aided non-orthogonal decomposition (SANOD) method to exploit prior knowledge of spectral components in the analysis of time-resolved data.

Analysis of time-resolved data typically involves discriminating noise against the signal and extracting time-independent components and their time-dependent contributions. Singular value decomposition (SVD) serves this purpose well, but the extracted time-independent components are not necessarily the physically meaningful spectra directly representing the actual dynamic or kinetic processes but rather a mathematically orthogonal set necessary for constituting the physically meaningful spectra. Converting the orthogonal components into physically meaningful spectra requires subsequent posterior analyses such as linear combination fitting (LCF) and global fitting (GF), which takes advantage of prior knowledge about the data but requires that all components are known or satisfactory components are guessed. Since in general not all components are known, they have to be guessed and tested via trial and error. In this work, we introduce a method, which is termed SVD-aided Non-Orthogonal Decomposition (SANOD), to circumvent trial and error. The key concept of SANOD is to combine the orthogonal components from SVD with the known prior knowledge to fill in the gap of the unknown signal components and to use them for LCF. We demonstrate the usefulness of SANOD via applications to a variety of cases.

100 ps time-resolved solution scattering utilizing a wide-bandwidth X-ray beam from multilayer optics.

100 ps time-resolved X-ray solution-scattering capabilities have been developed using multilayer optics at the beamline NW14A, Photon Factory Advanced Ring, KEK. X-ray pulses with an energy bandwidth of DeltaE/E = 1-5% are generated by reflecting X-ray pulses (DeltaE/E = 15%) through multilayer optics, made of W/B(4)C or depth-graded Ru/C on silicon substrate. This tailor-made wide-bandwidth X-ray pulse provides high-quality solution-scattering data for obtaining photo-induced molecular reaction dynamics. The time-resolved solution scattering of CH(2)I(2) in methanol is demonstrated as a typical example.

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.

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

A time-resolved x-ray-diffraction experiment is presented that aims to study the recombination of laser-dissociated iodine molecules dissolved in CCl4. This process is monitored over an extended time interval from pico- to microseconds. The variations of atom-atom distances are probed with a milliangstrom resolution. A recent theory of time-resolved x-ray diffraction is used to analyze the experimental data; it employs the correlation function approach of statistical mechanics. The most striking outcome of this study is the experimental determination of time-dependent I-I atom-atom distribution functions. The structure of the CCl4 solvent changes simultaneously; the solvent thus appears as a reaction partner rather than an inert medium hosting it. Thermal expansion of the system is nonuniform in time, an effect due to the presence of the acoustic horizon. One concludes that a time-resolved x-ray diffraction permits real-time visualization of solvent and solute motions during a chemical reaction.

Ultrafast x-ray diffraction of transient molecular structures in solution.

We report direct structural evidence of the bridged radical (CH2ICH2.) in a polar solution, obtained using time-resolved liquid-phase x-ray diffraction. This transient intermediate has long been hypothesized to explain stereo-chemical control in many association and/or dissociation reactions involving haloalkanes. Ultrashort optical pulses were used to dissociate an iodine atom from the haloethane molecule (C2H4I2) dissolved in methanol, and the diffraction of picosecond x-ray pulses from a synchrotron supports the following structural dynamics, with approximately 0.01 angstrom spatial resolution and approximately 100 picosecond time resolution: The loss of one iodine atom from C2H4I2 leads to the C-I-C triangular geometry of CH2ICH2.. This transient C2H4I then binds to an iodine atom to form a new species, the C2H4I-I isomer, which eventually decays into C2H4 + I2. Solvent dynamics were also extracted from the data, revealing a change in the solvent cage geometry, heating, and thermal expansion.

Ultrafast diffraction and structural dynamics: the nature of complex molecules far from equilibrium.

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown-especially for complex systems-and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of approximately 4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a CC bond distance of over 1.7 A, which is 0.2 A away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Direct imaging of transient molecular structures with ultrafast diffraction.

Ultrafast electron diffraction (UED) has been developed to study transient structures in complex chemical reactions initiated with femtosecond laser pulses. This direct imaging of reactions was achieved using our third-generation apparatus equipped with an electron pulse (1.07 +/- 0.27 picoseconds) source, a charge-coupled device camera, and a mass spectrometer. Two prototypical gas-phase reactions were studied: the nonconcerted elimination reaction of a haloethane, wherein the structure of the intermediate was determined, and the ring opening of a cyclic hydrocarbon containing no heavy atoms. These results demonstrate the vastly improved sensitivity, resolution, and versatility of UED for studying ultrafast structural dynamics in complex molecular systems.

Ultrafast electron diffraction and direct observation of transient structures in a chemical reaction.

Ultrafast electron diffraction is a unique method for the studies of structural changes of complex molecular systems. In this contribution, we report direct ultrafast electron diffraction study of the evolution of short-lived intermediates in the course of a chemical change. Specifically, we observe the transient intermediate in the elimination reaction of 1,2-diiodotetrafluoroethane (C2F4I2) to produce the corresponding ethylene derivative by the breakage of two carbon-iodine, C---I, bonds. The evolution of the ground-state intermediate (C2F4I radical) is directly revealed in the population change of a single chemical bond, namely the second C---I bond. The elimination of two iodine atoms was shown to be nonconcerted, with reaction time of the second C---I bond breakage being 17 +/- 2 ps. The structure of the short-lived C2F4I radical is more favorable to the classical radical structure than to the bridged radical structure. This leap in our ability to record structural changes on the ps and shorter time scales bodes well for many future applications in complex molecular systems.