Femtosecond X-ray Liquidography Visualizes Wavepacket Trajectories in Multidimensional Nuclear Coordinates for a Bimolecular Reaction

Abstract

Conspectus Vibrational wavepacket motions on potential energy surfaces are one of the critical factors that determine the reaction dynamics of photoinduced reactions. The motions of vibrational wavepackets are often discussed in the interpretation of observables measured with various time-resolved vibrational or electronic spectroscopies but mostly in terms of the frequencies of wavepacket motions, which are approximated by normal modes, rather than the actual positions of the wavepacket. Although the time-dependent positions (that is, the trajectory) of wavepackets are hypothesized or drawn in imagined or calculated potential energy surfaces, it is not trivial to experimentally determine the trajectory of wavepackets, especially in multidimensional nuclear coordinates for a polyatomic molecule. Recently, we performed a femtosecond X-ray liquidography (solution scattering) experiment on a gold trimer complex (GTC), [Au­(CN)2 –]3, in water at X-ray free-electron lasers (XFELs) and elucidated the time-dependent positions of vibrational wavepackets from the Franck–Condon region to equilibrium structures on both excited and ground states in the course of the formation of covalent bonds between gold atoms. Bond making is an essential process in chemical reactions, but it is challenging to keep track of detailed atomic movements associated with bond making because of its bimolecular nature that requires slow diffusion of two reaction parties to meet each other. Bond formation in the solution phase has been elusive because the diffusion of the reactants limits the reaction rate of a bimolecular process, making it difficult to initiate and track the bond-making processes with an ultrafast time resolution. In principle, if the bimolecular encounter can be controlled to overcome the limitation caused by diffusion, the bond-making processes can be tracked in a time-resolved manner, providing valuable insight into the bimolecular reaction mechanism. In this regard, GTC offers a good model system for studying the dynamics of bond formation in solution. Au­(I) atoms in GTC exhibit a noncovalent aurophilic interaction, making GTC an aggregate complex without any covalent bond. Upon photoexcitation of GTC, an electron is excited from an antibonding orbital to a bonding orbital, leading to the formation of covalent bonds among Au atoms. Since Au atoms in the ground state of GTC are located in close proximity within the same solvent cage, the formation of Au–Au covalent bonds occurs without its reaction rate being limited by diffusion through the solvent. Femtosecond time-resolved X-ray liquidography (fs-TRXL) data revealed that the ground state has an asymmetric bent structure. From the wavepacket trajectory determined in three-dimensional nuclear coordinates (two internuclear distances and one bond angle), we found that two covalent bonds are formed between three Au atoms of GTC asynchronously. Specifically, one covalent bond is formed first for the shorter Au–Au pair (of the asymmetric and bent ground-state structure) in 35 fs,...

Sensitivity of time‐resolved diffraction data to changes in internuclear distances and atomic positions

“…Then, one-dimensional (1D) scattering curves, S(q, t), are obtained by azimuthal integration of the 2D scattering images as a function of the momentum transfer q = (4π/λ)sin(θ), where λ is the wavelength of x-rays, 2θ is the scattering angle, and t is the time delay between the laser and x-ray pulses. [1][2][3][4] The difference scattering curves, qΔS(q, t), are obtained by subtracting S(q, t) at a negative time delay from S(q, t) at positive time delays and multiplying q to amplify the intensities at high scattering angle.…”

“…Usually, a theoretical ΔS(q, t) with the following three components is considered. [1][2][3][4] ΔS q,t ð Þ¼ΔS solute q,t ð ÞþΔS cage q, t ð ÞþΔS solvent q, t ð Þ ð1Þ…”

“…In a typical experiment of TRXL, an ultrashort optical pulse from a femtosecond laser system is used to initiate a reaction of interest, and an x-ray pulse with a time delay with respect to the laser pulse is used as the probe pulse to interrogate the status of the reaction progress. [1][2][3][4] X-ray scattering pattern is collected as a function of time delay between the pump pulse and the x-ray pulse. The scattering pattern can be expressed as a mathematical function of structural parameters such as bond lengths and angles.…”

“…A typical TRXL signal has three components: (i) the solute-only term, (ii) the solute-solvent cross term (or cage term), and (iii) the solvent-only term (or solvent heating term). [1][2][3][4] Scube also provides the expected noise level as well as the expected signal for each term, and thus the relative magnitudes of the three terms can be easily accessed. 91 Besides these features, it would be ideal if two additional pieces of information are available in advance:…”

“…Another useful information is how sensitively the difference scattering curve changes with regard to the changes of the atomic positions and internuclear distances of the reactant and product molecules. 4 The TRXL signal is affected by diverse factors. For example, the change of the three-dimensional structure of reactant and product molecules contributes to the TRXL signal.…”