The making and breaking of atomic bonds are essential processes in chemical reactions. Although the ultrafast dynamics of bond breaking have been studied intensively using time-resolved techniques1, 2, 3, it is very difficult to study the structural dynamics of bond making, mainly because of its bimolecular nature. It is especially difficult to initiate and follow diffusion-limited bond formation in solution with ultrahigh time resolution. Here we use femtosecond time-resolved X-ray solution scattering to visualize the formation of a gold trimer complex, [Au(CN)2–]3 in real time without the limitation imposed by slow diffusion. This photoexcited gold trimer, which has weakly bound gold atoms in the ground state4, 5, 6, undergoes a sequence of structural changes, and our experiments probe the dynamics of individual reaction steps, including covalent bond formation, the bent-to-linear transition, bond contraction and tetramer formation with a time resolution of ~500 femtoseconds. We also determined the three-dimensional structures of reaction intermediates with sub-ångström spatial resolution. This work demonstrates that it is possible to track in detail and in real time the structural changes that occur during a chemical reaction in solution using X-ray free-electron lasers7 and advanced analysis of time-resolved solution scattering data.
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Extended data figures and tables
Extended Data Figures
- Extended Data Figure 1: Comparison of the TRXSS signals at SACLA and KEK and the TRXSS data in the entire time range. (577 KB)
a, Comparison of the difference scattering curves at 100 ps time delay measured at SACLA (black) and KEK (red). The error bar at each data point indicates the standard error determined from 50 independent measurements. The two curves are nearly identical to each other within the experimental error, indicating that the difference scattering curves are highly reproducible and independent of the facility. b, Experimental difference scattering curves, qΔS(q, t), in the entire time range from –800 fs to 1 μs.
- Extended Data Figure 2: Solvent heating contribution to the TRXSS signal. (278 KB)
a, Experimental difference scattering curves, qΔS(q), of FeCl3 solution measured at several time delays (400 fs, 1.9 ps, 3.9 ps, 5.9 ps, 7.9 ps, 30 ps and 100 ps). b, SVD of the experimental difference scattering curves of FeCl3 measured from –10 ps to 100 ps. The first two right singular vectors multiplied by singular values are shown. c, The first right singular vector (black circles) fitted by an error function (red curve). This result implies that only a single difference scattering curve accounts for solvent heating in the time range up to 100 ps. d, Comparison of the difference scattering curve of the [Au(CN)2–]3 solution at 1 μs time delay (black) and the difference scattering curve for solvent heating (red). The error bar at each data point indicates the standard error determined from 50 independent measurements. At this time delay, the two curves are almost identical to each other within the experimental error, confirming that the difference scattering at late time delays are dominated by the solvent heating.
- Extended Data Figure 3: Difference RDFs in real space. (333 KB)
Difference RDFs, r2ΔS(r), obtained by Fourier sine transformation of qΔS(q).
- Extended Data Figure 4: Species-associated difference RDFs of the transient states. (239 KB)
The species-associated difference RDFs of the S0, S1, T1 and tetramer states correspond to , , and , respectively. We used a common S0 structure when fitting all four species-associated difference RDFs. By optimizing the fit between the theoretical and the experimental difference RDFs for each transient species via the structural fitting analysis, we were able to obtain the theoretical RDF of the S0 state.
- Extended Data Figure 5: Radial distribution functions, r2S(r, t). (321 KB)
The RDF of the S0 state was added to the RDFs at all time delays to emphasize only the contributions of the transient solute species associated with the bond formation.
- Extended Data Figure 6: Comparison of the scattering from Au atoms and other contributions. (239 KB)
a, Because the scattering intensities from C and N atoms are negligibly small, the total scattering pattern is almost the same as the scattering from Au atoms only. b, The contribution of the cage term is small and the total scattering pattern is therefore almost the same as the solute-only term.
- Extended Data Figure 7: Contributions of trimer and dimer to X-ray scattering signal. (463 KB)
a, Concentrations of the three species [Au], [Au2] and [Au3], calculated as a function of c, which is the initial concentration of monomers of the gold complex. We assumed that K2 is 10 M–2 in this case. b, Absorption spectra of aqueous solutions of K[Au(CN)2] at various concentrations measured with a 0.5 mm path length cell. Four points (A1, A2, A3 and A4) that are used as inputs are indicated. c, Theoretical difference scattering curves for the trimer (black) and the dimer (red). Relative intensities of the two curves were estimated realistically based on the excitation probabilities and the equilibrium of the two species.
- Extended Data Figure 8: Comparison of the TRXSS data measured with excitations at two different wavelengths, 310 and 267 nm. (326 KB)
a, Right singular vectors obtained from the SVD analysis for the 310 nm (left) and 267 nm (right) excitations. For both cases, the right singular vectors were fitted by only one kinetic component and their extracted time constants are almost identical to each other. b, Difference scattering curves at 100 ps time delay measured with excitations at 310 nm (black) and 267 nm (red). The error bar at each data point indicates the standard error determined from 50 independent measurements. The two curves are identical to each other within the experimental error. This similarity between the kinetics and the shapes of the difference scattering curves indicates negligible contribution from dimer excitation for both 310 and 267 nm excitations.
- Extended Data Figure 9: Mechanism of photoinduced bond formation in [Au(CN)2–]3. Results from our TRXSS data (red) and the previous transient absorption experiment (blue) are shown together. (221 KB)
Our findings are in good agreement with the reaction mechanism proposed in the transient absorption study, except for the structural assignments of the early kinetics. Considering that TRXSS is sensitive only to the processes accompanying structural change, the intersystem crossing processes on ~500 fs and 13 ns timescales, which were not observed in the TRXSS measurement, are likely to involve no structural change.
- Extended Data Figure 10: Species-associated RDFs of the four structures obtained from the SVD and principal-component analyses (black) and their fits (red) obtained by using the Debye–Waller factor and the constraint of the symmetric structure for the S0 state. (419 KB)
For each state, the structural parameters obtained from the fits and their standard errors determined from 50 independent measurements are shown together. It can be seen that the structural parameters of S1, T1 and the tetramer obtained from the fits using the Debye–Waller factor and the symmetric constraint for S0 are similar to the values given in Fig. 2d.
Extended Data Tables
- Supplementary Information (176 KB)
This file contains supplementary Text and Data.