Solvent-Dependent Structural Dynamics in the Ultrafast Photodissociation Reaction of Triiodide Observed with Time-Resolved X-ray Solution Scattering

Resolving the structural dynamics of bond breaking, bond formation, and solvation is required for a deeper understanding of solution-phase chemical reactions. In this work, we investigate the photodissociation of triiodide in four solvents using femtosecond time-resolved X-ray solution scattering following 400 nm photoexcitation. Structural analysis of the scattering data resolves the solvent-dependent structural evolution during the bond cleavage, internal rearrangements, solvent-cage escape, and bond reformation in real time. The nature and structure of the reaction intermediates during the recombination are determined, elucidating the full mechanism of photodissociation and recombination on ultrafast time scales. We resolve the structure of the precursor state for recombination as a geminate pair. Further, we determine the size of the solvent cages from the refined structures of the radical pair. The observed structural dynamics present a comprehensive picture of the solvent influence on structure and dynamics of dissociation reactions.

The triiodide ion (I 3 -) was generated in situ by dissolving molecular iodine (I 2 , Wako Pure Chemical Industries) and potassium iodiode (KI, Wako Pure Chemical Industries) in the respective solvent in the amounts according to table S1.   (2-amino-5-[(E)-(4-sulfophenyl)diazenyl]benzenesulfonic acid) was obtained from Sigma-Aldrich. 1 All chemicals were used without further purification. All experiments were performed at room temperature.

Time-Resolved X-ray Solution Scattering Experiment
The pump pulse was generated by second-harmonic generation (SHG) of the 800 nm fundamental from a Legend Elite (Coherent) and an in-house-designed multi-pass amplifier (∼15 mJ pulse energy, <40 fs FWHM pulse duration). The CPA system is synchronized to the XFEL operating frequency and is described elsewhere. 2 The optical pump pulse with a fluence of 80 mJ cm −2 (450 × 450 µm FWHM beam dimension, 400 nm, <100 fs FWHM, 450 µJ pulse energy) and the unfocused XFEL beam (300 µm FWHM diameter, 11.98 ± 0.028 keV, 10 fs FWHM, 30 Hz repetition rate) were spatially overlapped in a near-colinear geometry on a liquid-sheet jet (100 µm thick) and propagated horizontally with respect to the laser table. Overlap (300 µm to 600 µm offset below the nozzle outlet) was assured using two remote-controlled microscope cameras. The distance between the sample jet and the detector (octal MPCCD) 3 was kept at 62 mm throughout the experiment. The detector was vertically offset from the center by 80 mm. A beam stop was positioned between sample and a 50 µm thick Kapton window. With the described parameters a momentum transfer range of q = 0.53Å −1 to 5.98Å −1 was achieved. The sample delivery was mounted such that the X-ray beam was normal to the plane of the liquid jet. The chamber was kept under He atmosphere.

Determination of the Instrument Response Function
The time resolution of the experiment was limited by the pulse widths of optical pump-and X-ray probe pulses and their velocity mismatch when passing the liquid jet. To determine the actual time-resolution of the experiment, the Instrument Response Function (IRF) was determined by a least square fit of the integrated signal in the range of q = 1.5Å −1 to 2.5Å −1 against the following The model and experimental data are presented in Fig. S3 and the resulting values for σ and t 0 are presented in Tab. S2. The presented data are corrected for the t 0 offset.

Data Reduction
The measured scattering patterns were corrected for background, solid angle coverage, X-ray polarization and common mode fluctuations. 1,4 The sample-detector distance calibration was per- Figure S3: Instrument response function fitted to the integrated absolute signal in the range of q = 1.5Å −1 to 2.5Å −1 for all solvents.
formed by comparison of the azimuthally integrated signal with the scattering signal of pure solvent (water, acetonitrile, ethanol or methanol respectively). 4,5 All scattering curves were scaled to the signal from one liquid unit cell known from reference data in order to obtain signals in units of electron units per solute molecule (e.u. molec. −1 ). Fig. S4 shows the scaled experimental absolute scattering curves (blue) to reference curves (red). The reference curves include coherent and incoherent contributions to the solvent scattering, and the coherent scattering from the solvated I 3 -, as well as scattering from the excess I -+ K + . Scaling was optimised by minimising the difference between experimental and scattering curves in the q-range 1.2Å −1 to 2Å −1 .
To measure difference scattering curves, every seventh X-ray shot a scattering pattern without laser excitation was recorded. The nearest ten 'dark' scattering patterns to a 'light' measurement were then averaged and subtracted. Binning of scattering curves for different timepoints was performed differently for early and late times. For <2 ps the timing tool was used to determine the time delay with 10 fs (FWHM) accuracy. 6 After time sorting these scattering patterns were then binned where each bin contained ∼7500 curves. At late times (>2 ps) scattering curves at selected time points up to 500 ps were measured where the bins cover a wider time range than for the early delay times.

Molecular Dynamics simulations
The MD simulations for generating the RDF library for 17,336 I 3 structures were set up as follows: Three iodine atoms with their arrangement described by the structural paramters R were placed into a cuboid simulation box, keeping a distance of 1.6 nm between iodine and the box boundary in water, and a distance of 1.7 nm between iodine and the box boundary in all other solvents. The solvation was modelled by placing the solute molecule in a pre-equilibrated simulation box of water, acetonitrile, ethanol or methanol, respectively. Lennard-Jones parameters  for iodine atoms were set to σ = 0.38 nm and ε = 2.092 kJ mol −1 nm −2 , taken from the General Amber Force Field (GAFF). 7 The partial charges of the three iodine atoms were adapted from the heuristic model by Benjamin and Ruhman. 8 Accordingly, the partial charges of I 3 are: . Parameters for acetonitrile, ethanol and methanol were taken from the GAFF topologies deposited at virtualchemistry.org. 9 Water was modelled with the SPCE model. 10 The energy of each system was minimised, and each system of the 17,336 structures was simulated for 1 ns. During the simulation, the positions of the iodine atoms were frozen, such that the pre-selected arrangement R was maintained.
The simulations were carried out with the GROMACS simulation software, version 4.68. 11 The temperature was fixed at 293.15 K using a stochastic dynamics integration scheme 12 (with a time constant τ = 0.5 ps −1 ), and the pressure was kept at 1 bar using the weak coupling scheme 13 (with a friction constant τ = 0.5 ps −1 ). Bond lengths of the solvent were constrained using LINCS, 14 allowing a time step of 2 fs. Dispersive interactions and short-range repulsion were described by a Lennard-Jones potential with a cut-off at 1.2 nm. Electrostatic interactions were computed with the particle-mesh Ewald method with a Fourier grid spacing of 0.12 nm −1 . 15,16 Fig . S8 show the RDFs around different structures of I 3 throughout the dissociation and recombination with the following structure for the ground state (GS), two geminate pairs (GP1 and GP2) and a solvent-separated structure (NG). GS: R 1 = 3.01Å, R 2 = 2.98Å, α = 3.002, GP1 : R 1 = 2.6Å, R 2 = 6.5Å, α = π, GP2: R 1 = 3.1Å, R 2 = 3.9Å, α = π, and NG R 1 = 3.1Å, R 2 = 100 A, α = π. The solvent structure gradually changes from the GS species over the GP species to the solvent-separated pair. Interestingly, the structure of the GP separated by a layer of solvent molecules (GP2) shows higher similarity to the structure around NG than to the structure around a caged geminate pair. These structures can however still be distinguished by there signatures from the Debye term.

Dynamic vs. equilibrated MD simulations
To investigate the effect of the dynamic solvent rearrangement around the solute compared to the approach using static structures described above, we have performed dynamic MD simulations.
This was done examplary for the dissociation of I 3 in water. The simulations were performed in GROMACS. I 3 in a water box was first equilibrated, and the excitation simulated by applying an LEPS potential simulating the excited state potential. 17 Simulations were run for 30 starting structures and each for 5 ps and sampled every 0.8 fs.  , I and C atoms (middle), and I and N (bottom) describing the solvent structure around a GS structure (blue), a caged GP structure (orange), a contact pair structure (green) and a solvent separated pair structure (red).
When comparing the two time-dependent difference scattering curves, we only observe minor differences between scattering calculated from static and dynamic MD simulations. Hence, we used the library of static solvent cages for modelling the difference scattering in the structural refinement. In the case of the photodissociation of I 3 the strongest contributions to the difference signal are expected from the solute-solute term.

Data Analysis
Calculation of contributions to the modelled scattering curves As described in the main text, we include contributions from a solute-solute term (S solute ), and a cage term (S cage ) when calculating scattering for a specific solute structure. S cage includes contributions from a solvent-solute cross term (S c ), and a displaced volume term (S v ). Calculation of (S solute ) is described in the main text (eqs. 5 and 6). For calculation of S c we used the RDFs between the I atoms and solvent atoms v, g Iv (r), from the above described MD simulations.
S c (q, R) = 2 ρ c (r) sinc(qr)dr = 2 ∑ v F I F v ρ v,0 N I 4π (g Iv (r) − 1)r 2 sinc(qr)dr. 18,19 With the respective form factors F i for solvent (v and solute (I) atoms. In order to calculate the scattering contributions caused by changes in the structure of the solvent cage (S v ), we used the displaced volume approach to model the solvent signal. 20 Dummy atoms described by solvent specific form factors, F DV , are being placed in the position of the iodine atoms. The form factors for these dummy atoms determined from the RDFs: These form factors are then used to determine the solvent scattering using the Debye equation: To minimise truncation errors from the limited box-size in the MD simulations we applied an exponential damping factor (exp(−( r µ − 1) 2 )) to the g Iv (r) used for calculation of S v and S c for r ≥ µ.
The solute contributions to the anisotropic scattering are calculated as: with the atomic form factors F * i including a term describing positional uncertainty (see main text eq. 5), and the Bessel function.
The second order Legendre polynomial is defined as: The anisotropic difference scattering, ∆S 2 , can be calculated as: Since the solvent response due to heating is assumed to be predominantly isotropic, no heat response is included in modelling the anisotropic signal.
As discussed in the main text, in this study the ground state structure of triiodide in the different solvents was not optimised but adapted from previous MD studies. 21 Fig. S10 shows fit between experimental and modelled data at a delay time of 500 ps in acetonitrile using the ground state structure used in the refinement (R 1 = 2.95Å, R 2 = 3.06Å, α = 3.002), the GS structure published by the Ihee group (middle panel, R 1 = 3.01Å, R 2 = 2.98Å, α = π) 22 and a more bent, but symmetric structure (lower panel, R 1 = 3.01Å, R 2 = 2.98Å, α = 2.7). The comparison shows best agreement with experimental data using the structure by Jena et al.

Regularisation
The large number of parameters optimised in the structural refinement (described by the optimisa- The amplitude of the heat signal was normalised to make sure all parameters are in the same order of magnitude. The optimal λ parameter was determined using the L-curve approach. 23 The refinement was performed over a range of λ values (from 10 −4 to 10 4 ), and the resulting penalties f tot were plotted against χ 2 tot with f tot = ∑ t f and χ 2 tot = ∑ t chi 2 , leading to an L-shaped curve   Modelled data for all solvents Figure S12: Comparison of structures obtained from refinement with (circles) and without (crosses) regularisation for data of triiodide in acetonitrile.

Heat response of the solvent
Additionally, to the structural signal, the difference signal cause by solvent heating was included in modelling the data. Using reference difference scattering for a 1 K heat increase in the different solvents, 5 this amplitude could be used to estimate the temperature change of the solution. The time-dependent temperature change is presented in Fig. S17, left. Except for the results in water the changes in temperature obtained from the structural refinement show high uncertainty. This can be explained by the low signal strength of the heat signal compared to the signal caused by structural changes in the solute in MeCN, EtOH, and MeOH. In water the signal caused by solvent heating of 1 K shows a higher amplitude than in the other organic solvents. 5 This is illustrated by From the ∆S ∆T contribution to the difference signals the temperature increase and the total energy released to solvent can also be estimated. 5 The temperature increase ∆T (t) for all solvents is presented in in Fig. S17 and from the maximum temperature increase within the observed 500 ps, the energy deposited into solvent heating was determined (E heating ) and is included in Table S3.   Figure S16: Overview of all paramters refined for the difference scattering data for triiodide in acetonitrile. The top panel shows the amplitudes for the isotropic and anisotropic signal as well as for the fraction of the geminate pair and the amplitude of the heating signal. The lower panel shows the three parameters describing the I 3 structure.
The energy released into solvent heating (600 kJ mol −1 to 1100 kJ mol −1 ) is much higher than the energy of an incident 400 nm photon (299 kJ mol −1 ) for all solvents. One explanation for the large ∆T observed might be two-photon absorption of iodide in solution, abundant in all solutions (see Supporting InformationTab. S1). This process would lead to ionisation of the iodidide and formation of a solvated electron. The structural changes linked to this process (I -−−→ I + e -) are linked to the solvent cage, causing only a weak change in scattering signal compared to signals caused by structural changes in I 3 -. 24 Therefore, this process can be neglected in our analysis.  Anisotropic population dynamics Fig. S18 shows the population dynamics obtained from the refinement of isotropic (left) and anisotropic data (right). The excitation fraction observed for the anisotropic signal is much lower than the excitation fraction for isotropic signal due to only a fraction of the excited molecules being aligned. The decay of the anisotropic signal within tens of picoseconds is due to the rotational dephasing of the initially aligned molecules. Figure S18: Left: Overall amplitude of the isotropic difference scattering signal, right: overall amplitude of the anisotropic difference scattering signal from the structural refinement.

Kinetics of the GP population
The amplitudes of the GP species obtained from the structural refinement were used to estimate the lifetimes with which the population of this state decays. The decay was fit with an biexponential decay, convoluted with a Gaussian function to model the inital increase. The results are presented in the main paper Fig. 5.

Energy partitioning
From the speed of fragment dissociation (v diss ), rotation of the I 2 fragment (ω), we can estimate the energy partitioning into translational, E trans , and rotational energy, E rot , These are calculated as follows: With the reduced mass µ = m 1 m 2 m 1 +m 2 and Avogadro's number N A .
The rotational temperature was estimated as: From the heat released into the solvent (∆T , see previous section), we can further determine the amount of energy released into the solvent, E heat :

Error estimation
Due to the regularised refinement, the uncertainty of the optimised parameters cannot be directly determined using the Hessian output from the fminunc function. Instead, the errors were estimated as follows. The χ 2 landscape was determined in the 7D parameter space. A range of 9 values around the optimised parameter from structural refinement were chosen for each parameter. Then,

Noise estimation
For calculation of χ 2 as part of the structural refinement, we need to determine the standard deviation σ of the difference scattering signal. σ is expected to show q-dependency as the number of pixels measured depends on the respective q-bin. We used difference scattering from time delays below −0.5 ps where no signal should be recorded to estimate the noise.
With the number of time points N t . Fig. S20 shows the σ (q) for anisotropic and isotropic scattering for all solvents. Structural refinement

Three Body Dissociation
In order to exclude possible contributions from three-body dissociation as observed for excitation of I 3 with 266 nm, or in the gas phase, we have simulated difference scattering caused by 3-body dissociation and compared it to simulated difference scattering for two-body dissociation (as assumed in the structural refinement). The results for dissociation in acetonitrile are plotted in Fig. S22. The simulated difference scattering was multiplied with the time-dependent excitation fraction from obtained from the structural refinement, to make the results more comparable.
Dissociation was modelled with 5Å ps −1 for the first 700 fs. The experimental data show a much better agreement with the pattern of the simulated two-body dissociation. Figure S22: Experimental ∆S(q) (left) and simulated ∆S(q) for two-body (middle) and three-body (right) dissociation. Dissociation was modelled with 5Å ps −1 for 700 fs.

Implementation of the Debye-Waller-like factor
As mentioned in the main text we implement a Debye-Waller-like factor (DWF) on the atomic form factors instead of on the molecular form factor as in previous XSS studies. 27,28 Fig. S23 presents a comparison of the results of structural refinement applying both implementations of the DWF. For applying the DWF to the molecular form factor, the solute term was calculated as: S solute (q, R) = ∑ i, j F * I,i (q)F I, j (q) sinc(qd i j ) exp[−q 2 σ 2 i, j /3]. (S18) With σ i, j being the rmsd of the interatomic distance d i, j . For the comparison σ i, j was estimated as √ σ i with σ i the rmsd applied in eq. 3 in the main text. Results of the refinement applying the DWF on the atomic form factor (see eq. 3 in the main text) correspond to the results presented in the main text and are plotted as crosses. Results of the refinement applying the DWF to the molecular form factor are plotted as circles, where apart from the implementation of the DWF factor on the molecular form factor, the refinement was implemented as described in the main text. The left panels show the refined interatomic distances, R(I − 2 ) in red and R(I − 2 − I) in blue. The right panels show the refined amplitudes for the geminate pair (green) and the non-geminate pair (orange). The results are presented for all solvents and only show minor discrepancies in the refined parameters using the two implementations of the DWF showing that the main conclusions of this paper do not depend on the implementation of the DWF. Figure S23: Comparison of the results of structural refinement applying both implementations of the DWF. Results of the refinement applying the DWF on the atomic form factor are plotted as crosses, results of the refinement applying the DWF to the molecular form factor are plotted as circles. The left panels show the refined interatomic distances, R(I − 2 ) in red and R(I − 2 − I) in blue. The right panels show the refined amplitudes for the geminate pair (green) and the non-geminate pair (orange).