Observing the Structural Evolution in the Photodissociation of Diiodomethane with Femtosecond Solution X-Ray Scattering

Matthijs R. Panman , Elisa Biasin , Oskar Berntsson , Markus Hermann , Stephan Niebling, Ashley J. Hughes, Joachim Kübel , Kalina Atkovska, Emil Gustavsson, Amke Nimmrich, Asmus O. Dohn, Mads Laursen, Diana B. Zederkof, Alireza Honarfar , Kensuke Tono, Tetsuo Katayama, Shigeki Owada, Tim B. van Driel, Kasper Kjaer, Martin M. Nielsen, Jan Davidsson, Jens Uhlig , Kristoffer Haldrup, Jochen S. Hub, and Sebastian Westenhoff 1,* Department of Chemistry and Molecular Biology, University of Gothenburg, Box 462, 40530 Gothenburg, Sweden Centre for Molecular Movies, Department of Physics, Technical University of Denmark, DK-2800 Lyngby, Denmark Georg-August-Universität Göttingen, Institute for Microbiology and Genetics, Justus-von-Liebig-Weg 11, 37077 Göttingen, Germany Department of Chemical Physics, Lund University, Box 124, S-2210, Lund, Sweden Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan LCLS, SLAC National Laboratory, Menlo Park, California 94025, USA Department of Chemistry, Ångström Laboratory, Uppsala University, Box 523, SE75120 Uppsala, Sweden

Understanding chemical reactivity requires resolving the reaction mechanism. Fundamental reaction events, such as the breaking, rearrangement, and formation of bonds as well as the interaction with solvent molecules, occur on femtosecond timescales. Femtosecond time-resolved spectroscopy has yielded a wealth of information about these steps. However, most femtosecond spectroscopic methods probe electronic states or vibrational modes, reporting only indirectly on molecular structure [1,2]. In particular, ubiquitous species in solution-state chemistry without covalent or ionic bonds, such as molecular encounter complexes, supramolecular assemblies, or solute-solvent complexes, are difficult to study [3]. Therefore, timeresolved techniques that are sensitive to atomic position are essential to further the understanding of chemical reactivity [4][5][6][7][8][9][10][11][12][13].
The photodissociation of diiodomethane (CH 2 I 2 ) is an ideal model reaction for studying elementary chemical events. In apolar solvents, absorption of light at a wavelength of 266 nm results in impulsive C─I bond scission, yielding (CH 2 I 2 → CH 2 I • þ I • ) [14]. Within picoseconds, the fragments recombine to form a photoisomer (CH 2 I • þ I • → CH 2 I − I) [15][16][17]. On nano-and microsecond timescales, the isomer and radical pair fragments undergo further bimolecular reactions to reform the parent molecule and I 2 [15]. The photoisomer is the methylene transfer agent in the cyclopropanation of olefins with diiodomethane [15,18].
Femtosecond optical spectra have shown that dissociation occurs impulsively within 200 fs [19,20]. However, the translational and rotational trajectories of the fragments cannot be retrieved from the optical spectra. The structure, solvent arrangement, and separation of the formed radical pairs remains unknown. Disagreement persists on whether the isomer is formed with a lifetime of 100 fs [19], 1 ps [20], or biphasically with 1 to 5 ps [15]. This is probably because the spectral signatures of the photoisomer and the vibrational relaxation of CH 2 I • overlap. Nevertheless, the quantum yield of photoisomer formation has been determined to be between ∼70% and 95% for a variety of solvents at 100 ps [15]. The remaining portion of the initial fragments are thought to be separated by solvent molecules so that they cannot recombine into the isomer. Solvent cage escape is a common explanation of incomplete reactions on fast timescales [20][21][22][23]. Even though this is a reasonable assumption, it is untested, as the structure of the radical pair cannot be probed with spectroscopic methods.
Femtosecond time-resolved WAXS.-To resolve the structural evolution of the fragments on femto-and picoseconds after photodissociation of CH 2 I 2 , we used time-resolved wide-angle x-ray scattering (TRWAXS) at an x-ray free electron laser (XFEL). We recorded the data at the Linear Coherent Light Source (LCLS) and Spring-8 Angstrom Compact free electron LAser (SACLA). CH 2 I 2 in cyclohexane (50 mmol L −1 ) was supplied to the experiment in a liquid jet (see Supplemental Material and Fig. S1 [24] for details of the sample preparation and delivery). The reaction was triggered with femtosecond optical laser pulses (266 nm, < 60 fs FWHM duration), which overlapped with the x-ray pulses (9.5 keV photon energy, < 50 fs FWHM duration) in the sample jet. The optical excitation density was 32 mJ cm −2 , comparable to the 20 mJ cm −2 used in past ultrafast optical studies [15] and in the linear excitation regime of the sample (see Supplemental Material Fig. S2 [24]). The x-ray scattering was recorded at defined delay times relative to the laser pulse with an effective time resolution of 90 fs using the timing diagnostic at the beam line [60]. The signal processing of the diffuse 2D scattering images is described in the Supplemental Material [24]. The TRWAXS signal, due to solvent heating, was subtracted from the difference data prior to fitting the difference scattering (see Supplemental Material and Figs. S5-S7 [24]). In the following, we present the data recorded at the LCLS, but the data obtained at SACLA confirms the conclusions drawn (see Supplemental Material Figs. S13, S14, and S16 [24]).
Direct visualization of a dissociating molecule.-The azimuthally integrated difference scattering curves [Fig 1(c)] arise predominantly from the evolution of the distance of the two electron-rich I atoms. The observed momentum transfers (q) range from 0.4 to 4.8 Å −1 , which is sufficient for a high-quality structural determination [61,62]. Figure 1(d) shows the data in real space, which allows inspection of the evolution of the interatomic distances in a model-free fashion [63]. The r 2 ΔSðr; tÞ signal shows a negative feature with a time-dependent minimum between 3 and 4 Å, which is due to the depletion of the I Á Á Á I distance of the CH 2 I 2 ground state. The position of this negative peak ought to be time independent, and the observed shift is due to the overlapping positive signals. A positive difference-scattering feature appears at 100 fs and shifts to large distances within a few hundred femtoseconds (orange band), which we assign to the impulsive (ballistic) separation of the I atom from the parent molecule. Impulsive separation is expected from optical spectra and the timescale is reasonable for the expected time of flight for an atom to hit the neighboring molecule [15,20]. A pronounced positive shoulder arises after ∼1 ps (green band) in between 5 and 6 Å. Both positive peaks correspond to photoinduced structures within the first solvent shell, which has a diameter of approximately 7 Å, as estimated from our molecular dynamics simulations (see Supplemental Material [24] for details). We assign the two distances to I • positioned at the I-and CH 2 -hemisphere of the CH 2 I • fragment due to the rotation of the CH 2 I • fragment. A third positive feature is visible at shorter I Á Á Á I distances compared to the ground state bleach (magenta band). The signal overlaps with the ground state bleach and is first visible as a positive indent of the negative band from around ∼400 fs and more pronounced at later times. This marks the formation of the photoisomer (PI) [16,64,65]. Features associated with the rearrangement of the solvent are found at r ≥ 6.5 Å.
Structural refinement.-We continued our analysis by refining iodine distances (I Á Á Á I) and their time-dependent concentrations [AðtÞ] against the difference scattering in reciprocal space. The fits were obtained by selection from a model library of 124 theoretical scattering curves for two iodine atoms constrained at distances spanning 0 to 15 Å (see Supplemental Material Fig. S17 [24]). The theoretical scattering was computed as ΔS ¼ P i AðtÞ i · ½S i ðI Á Á Á IÞ − S gs ðI Á Á Á IÞ, where three contributions are considered for the calculation of SðI Á Á Á IÞ: the solute, solvent-solute, and solvent scattering terms. The solute term was computed using the Debye equation for two iodine atoms. Following a common approach [16,66], the solvent-solute term was extracted from molecular dynamics trajectories of iodine atoms in cyclohexane. The solvent-solvent term was also extracted from the same molecular dynamics trajectories (see Supplemental Material Eqs. S6, S7, and S10 [24]). The scattering of ground state was assumed to be independent of time. Following our qualitative assignments, we included four I Á Á Á I distances, corresponding to three photoinduced species in the structural refinement. One distance represented the photoisomer and another one a radical pair, which was separated by solvent molecules. We fixed the latter distance to 100 Å, since the difference scattering in our detected range is invariant for I Á Á Á I separation ⪆15 Å. The remaining two I Á Á Á I distances represent the geminate radical pair within the same solvent shell. The I • is most likely distributed continuously around the CH 2 I • , but using the two dominating distances, which describe the I • fragment on either side of the CH 2 I • hemisphere, is a practical approximation. We obtained optimal fits for I Á Á Á I distances of the geminate pair at 4.  [24] for the individual scattering contributions of each species]. The isomer and ground state distances agree with previous synchrotron studies in methanol [16,65] and cyclohexane [64]. There are no significant discrepancies between the fit and data, indicating that the minimal model is sufficient to reproduce the experiment.
Kinetic analysis at t < 1 ps.-In order to describe the initial dissociation of the molecule, the short I Á Á Á I distance of the geminate pair was allowed to increase linearly for t < 500 fs. Figure 2(a) shows that the fragments separate by 0.7 AE 0.1 Å over a period of 300 fs before stopping at the static I Á Á Á I separation of 4.35 AE 0.03 Å. The instrument response function (IRF) as extracted from the anisotropic scattering (see Supplemental Material [24] for details) was shorter than the observed flight of the fragments [ Fig. 2(b)]. Thus, the observation reflects how the I Á Á Á I bond in CH 2 I 2 breaks; how the fragments continue their flight; and how they finally collide with the solvent shell. The fragments travel with a relative velocity of 2.1 AE 0.4 Åps −1 corresponding to 210 AE 40 ms −1 .
Next, we inspect the time-dependent concentrations obtained by the structural refinement [ Fig. 2(b)]. We observe that the short I Á Á Á I distance of the geminate pair rises, limited by the instrument response function (yellow markers). The concentration of the longer distance of the geminate pair rises concomitantly with the decay of the short distance (green markers). This supports our interpretation that the longer distance of the geminate pair is produced by rotation of the CH 2 I • fragment. The rotation of this fragment increases the distance between the two iodine atoms because the CH 2 moiety of the CH 2 I • takes up space between them. A high-level quantum mechanics calculation shows that the distances are reasonable [see Supplemental Material Figs. S11 (a) and (b) [24] ]. Figure 2(b) also reveals a delayed rise of the distance corresponding to the solvent-separated radical pair (black), which reflects the fragments having to travel a longer distance to escape the solvent cage. The relative amplitude of this species is a minor component of the total product species, indicating that the majority of the radical pairs stop at the first solvent shell. The distance corresponding to the photoisomer does not appear within the first picosecond (magenta; see below).
We cast these observations into a comprehensive kinetic model (Eqs. S1-S30, and see Supplemental Material Fig. S15 [24] for a visual representation) and performed a least-squares fit to the time-dependent amplitudes [solid lines, Fig. 2(b)]. We found that the rotational transition from the short to the long distance in the geminate pair occurs with a lifetime of τ r ¼ 0.77 AE 0.07 ps. This τ r corresponds to a rotational lifetime of 0.25 AE 0.02 ps rad −1 and an angular velocity of 4.1 ps −1 , which is many times faster than the predicted rotationalcorrelation lifetime of the steady-state CH 2 I • fragment as estimated from the Stokes-Einstein-Debye equation (16 ps rad −1 , see Supplemental Material Eqs. S31-S34 [24]). Therefore, the rotational motion is photoinduced and not caused by the equilibrium motion of the radicals. Interestingly, τ r is longer than the collision time with the solvent (0.34 AE 0.07 ps), which implies that the rotational energy is not fully dissipated during the initial collision with the solvent shell. This illustrates that the geometry of the solute-solvent interaction is important for determining the dissipation of energy into the solvent.
The partitioning of excess energy.-Photoexcitation of a molecule transfers it into a high-lying electronic state, where the excess energy is partitioned into translational, rotational, and vibrational degrees of freedom, before energy dissipates to the solvent. The separation velocity (2.1 AE 0.4 ps Å −1 ) gives a translational kinetic energy of 0.02 eV (see Supplemental Material Eqs. S35-S36 [24]). This represents ∼0.5% of the 4.66 eV excitation photon energy or ∼7% of the 0.28 eV kinetic energy found in the gas-phase dissociation reaction [67]. The rotational kinetic energy of the CH 2 I • fragment was computed from the angular velocity (4.1 ps −1 ) and is 0.55 eV, representing ∼12% of the 4.66 eV excitation photon energy (see Supplemental Material Eqs. S37-S39 [24]). Thus, the translational energy partition is smaller than the rotational by a factor of 24. In part, this may be due to the choice of photoexcitation energy. It may also be that our measurement rather underestimates the separation velocity, because it is close to the time resolution of the experiment. However, it is consistent that we find that a low amount of solvent separated species as the initial translational energy of the fragments is insufficient to break through the solvent barrier. These considerations also show that the notable portion of the excess excitation energy is held as vibrational energy. Kinetic analysis at t > 1 ps.-Now, inspecting the kinetics at (t > 1 ps), we observe that the two I Á Á Á I distances of the geminate pair decay biphasically and concurrently [ Fig. 2(b)]. The characteristic I Á Á Á I distance of the photoisomer is formed concomitantly with the biphasic decay of the geminate pair (τ 1 ¼ 8 AE 1 ps and τ 2 ¼ 2.8 AE 0.5 ns). This is slower than what was concluded from optical spectroscopy [15,19,20]. We note that optical spectroscopic studies have never reached agreement on the timescale of isomer formation. We consider the results obtained from the TRWAXS experiment to be reliable given that the peaks of the photoisomer are well separated from other peaks in the TRWAXS data [ Fig. 2(b)]. The kinetics of heat generation in the sample also corroborates the biphasic formation of the photoisomer (see Supplemental Material and Fig. S8 [24]).
Observation of a long-lived, but chemically inactive, geminate radical pair.
-Surprisingly, we observe that the geminate pair is present for hundreds of picoseconds [ Figs. 2(b) and 1(b)]. The concentration of the solventseparated pair never exceeds 15% of the total product species. We also observe a decrease of the solventseparated species after t > 10 ps, but this might be due to the decrease in data statistics after this time point [68]. We tested the robustness of the fits by selectively removing species from the model for delays t > 50 ps. We found that, when removing each of the geminate pair distances, the goodness of the fit (χ 2 ) was notably reduced, but when the solvent separated species was excluded, only a very minor reduction in the goodness was observed (see Supplemental Material Fig. S18 [24]).
Strong dispersion forces confine the radical pairs within the same solvent shell.-The existence of geminate pairs for hundreds of picoseconds indicates that an attractive force holds the radicals together. We investigated this interaction between CH 2 I • and I • fragments with quantum chemical calculations at the complete active space selfconsistent field multireference configuration interaction (CASSCF-MRCI) level of theory (def2-SVP basis set [69]) in a three-dimensional search space (see the Supplemental Material [24] for details). The calculated potential energy surface (see Supplemental Material Figs. S11 (a)-(c) [24]) shows a Pauli repulsion at < 4 Å and an attractive interaction of −0.1 eV at longer distances. The strong interaction (∼4k B T) is caused by dispersion forces of the large iodine atoms. We found that the fragment contact lifetime increased from 34 to 204 ps when using the force field parametrized against the results of our CASSCF-MRCI calculations compared to the standard general Amber force field (Supplemental Material Fig. S12 [24]). We conclude that the dispersion force is sufficient to hold the radical pair in a mutual solvent pocket for a few hundred picoseconds. This is much longer than what was previously assumed in investigations using spectroscopy and x-ray scattering. [15,16,21,23,66,70,71].
The long contact lifetime means that the incomplete formation of the photoisomer cannot be explained by solvent escape [15,[20][21][22][23]. Instead, a chemically inactive form of the geminate pair must exist. Although our data do not conclusively reveal the reason for this, we consider two possible explanations. First, photoisomer formation may be promoted by vibrational excitation of the CH 2 I • fragment. When the vibrational excitation is dissipated, the photoisomerization reaction proceeds at a much slower rate (τ 2 ) [72]. Alternatively, a competing reaction pathway, e.g., the formation of a solvent-solute complex (I • Á Á Á C 6 H 12 [73][74][75]), hydrogen atom abstraction from the solvent, or loss of spin correlation, could generate a distribution of active and chemically inactive geminate pairs. The "active" species would form the photoisomer within the first phase (τ 1 ) and the "inhibited" species would form the photoisomer with the second phase (τ 2 ). We consider the formation of triplet radical pairs to be plausible, since the spin flip could occur in the excited state, prior to separation of the fragments.
Conclusion.-In conclusion, we have visualized the dissociation reaction of CH 2 I 2 in solution using femtosecond time-resolved wide angle x-ray scattering. The analysis yields a comprehensive movie for the first nanosecond of the reaction (Fig. 3). The iodine-carbon bond is broken directly after photoexcitation [(I) in Fig. 3  solvent molecule, and the CH 2 I • radical rotates [(II) in Fig. 3]. The translational motion of the fragments is stopped by the solvent collision, but the rotational motion is not fully inhibited. As a result, the majority of radical pairs stay within the solvent shell [(III) in Fig. 3]. We find that the radical pairs within the solvent cage are surprisingly stable, due to previously unrecognized dispersion forces between the heavy iodine atoms, but that a notable fraction of them is unreactive [(IV) in Fig. 3]. Accordingly, the photoisomer production proceeds biphasically on picoand nanosecond timescales. The sensitivity of timeresolved wide angle x-ray scattering toward relative atomic positions, without the requirement of a covalent bond, was essential in uncovering this comprehensive, microscopic reaction mechanism in solution. Use