Direct observation of bond formation in solution with femtosecond X-ray scattering

Journal name:
Nature
Volume:
518,
Pages:
385–389
Date published:
DOI:
doi:10.1038/nature14163
Received
Accepted
Published online

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.

At a glance

Figures

  1. Femtosecond time-resolved X-ray solution scattering at the XFEL facility and the data analysis.
    Figure 1: Femtosecond time-resolved X-ray solution scattering at the XFEL facility and the data analysis.

    a, The photochemical reaction of solutes supplied by a liquid-flowing system is triggered by a femtosecond optical laser pulse. Subsequently, a time-delayed X-ray pulse synchronized with the laser pulse probes the structural dynamics of the reaction. The scattering pattern is detected by a fast two-dimensional charge-coupled device (CCD) detector as shown at the bottom. We measure time-resolved scattering patterns while varying the time delay between the laser and X-ray pulses. b, By integrating the two-dimensional scattering pattern azimuthally, subtracting solvent contributions, performing a Fourier transform (FT) and compensating for the depletion of the initial solute contribution due to photochemical reaction, we obtain one-dimensional RDFs in real space as shown in the plot at the top left. These display the interatomic distances of transient species and products. In this way, Au–Au bond lengths of the [Au(CN)2]3 complex can be identified with sub-ångström accuracy, and the time-dependent structural changes of the metal complex can be determined in real time.

  2. Time-dependent structural changes of [lsqb]Au(CN)2-[rsqb]3.
    Figure 2: Time-dependent structural changes of [Au(CN)2]3.

    a, Experimental difference scattering curves, qΔS(q), measured at various time delays from –800 fs to 300 ns (black). For clarity, only data at selected time delays are shown. a.u., arbitrary units. b, RDFs, r2S(r), obtained by Fourier sine transformation of qΔS(q) after subtracting solvent contributions. 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 bond formation. The blue dashed arrows indicate the time-dependent changes in the locations of the p1 and p2 peaks. The red dashed line represents the position of the p3 peak, corresponding to the signature of the tetramer. c, Time-dependent concentrations of the four states and their transition kinetics. The notation for each species is indicated above each trace. The error bar at each data point indicates the standard error determined from 50 independent measurements (that is, 50 scattering images). The vertical black dotted lines indicate the temporal positions corresponding to the time constants of the three kinetic components. d, Species-associated RDFs of the four structures obtained from the singular value decomposition and principal-component analyses (black) and their fits (red) obtained by using model structures containing multiple Au–Au pairs. The blue arrows indicate the changes in R12, R23 and R13 as transitions occur between states. As fitting parameters, we considered three Au–Au pairs for the S0, S1 and T1 states and six Au–Au pairs for the tetramer. For each state, the structural parameters obtained from the fits are shown along with their standard errors determined from 50 independent measurements.

  3. Structure determination of the S1 state using the experimental scattering curve at 200 fs time delay in momentum space and real space.
    Figure 3: Structure determination of the S1 state using the experimental scattering curve at 200 fs time delay in momentum space and real space.

    a, Theoretical difference scattering curves (red) for linear (upper) and bent (lower) structures shown together with the experimental difference scattering curve at 200 fs (black). The residuals (blue) between the theoretical and the experimental curves are shown together. The linear structure gives a much better fit than the bent structure, which has the same Au–Au–Au bond angle as the S0 state, thereby indicating that the bent-to-linear transition is completed at 200 fs time delay. b, Corresponding experimental (black) and theoretical (red) RDFs, rS(r). It can be seen that in the bent structure R13 is too small to fit the experimental RDF at 200 fs.

  4. Mechanism of photoinduced bond formation in [lsqb]Au(CN)2-[rsqb]3.
    Figure 4: Mechanism of photoinduced bond formation in [Au(CN)2]3.

    a, Femtosecond TRXSS reveals the dynamics and the atomic movements associated with the Au–Au bond formation in real time with sub-ångström spatial resolution. The S0 state with weakly bound Au atoms in a bent geometry transforms to the S1 state with tightly bound Au atoms in a linear geometry. Subsequently, the S1 state transforms first to the T1 state, with further contraction of Au–Au bonds, and then to a tetramer through formation of another Au–Au bond. b, Structural parameters of each state and their standard errors determined from 50 independent measurements.

  5. Comparison of the TRXSS signals at SACLA and KEK and the TRXSS data in the entire time range.
    Extended Data Fig. 1: Comparison of the TRXSS signals at SACLA and KEK and the TRXSS data in the entire time range.

    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(qt), in the entire time range from –800 fs to 1 μs.

  6. Solvent heating contribution to the TRXSS signal.
    Extended Data Fig. 2: Solvent heating contribution to the TRXSS signal.

    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.

  7. Difference RDFs in real space.
    Extended Data Fig. 3: Difference RDFs in real space.

    Difference RDFs, r2ΔS(r), obtained by Fourier sine transformation of qΔS(q).

  8. Species-associated difference RDFs of the transient states.
    Extended Data Fig. 4: Species-associated difference RDFs of the transient states.

    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.

  9. Radial distribution functions, r2S(r, t).
    Extended Data Fig. 5: Radial distribution functions, r2S(rt).

    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.

  10. Comparison of the scattering from Au atoms and other contributions.
    Extended Data Fig. 6: Comparison of the scattering from Au atoms and other contributions.

    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.

  11. Contributions of trimer and dimer to X-ray scattering signal.
    Extended Data Fig. 7: Contributions of trimer and dimer to X-ray scattering signal.

    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.

  12. Comparison of the TRXSS data measured with excitations at two different wavelengths, 310 and 267 nm.
    Extended Data Fig. 8: Comparison of the TRXSS data measured with excitations at two different wavelengths, 310 and 267 nm.

    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.

  13. Mechanism of photoinduced bond formation in [lsqb]Au(CN)2-[rsqb]3. Results from our TRXSS data (red) and the previous transient absorption experiment (blue) are shown together.
    Extended Data Fig. 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.

    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.

  14. 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.
    Extended Data Fig. 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.

    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.

Tables

  1. Details of the data-collection parameters
    Extended Data Table 1: Details of the data-collection parameters

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Author information

  1. These authors contributed equally to this work.

    • Kyung Hwan Kim,
    • Jong Goo Kim,
    • Shunsuke Nozawa &
    • Tokushi Sato
  2. Present addresses: Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron, Notkestrasse 85, 22607 Hamburg, Germany (Tokushi Sato); Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan (Takahiro Sato); Japan Atomic Energy Agency, 8-1-7 Umemidai, Kizugawa, Kyoto 619-0215, Japan (K.O.).

    • Tokushi Sato,
    • Takahiro Sato &
    • Kanade Ogawa

Affiliations

  1. Center for Nanomaterials and Chemical Reactions, Institute for Basic Science, Daejeon 305-701, South Korea

    • Kyung Hwan Kim,
    • Jong Goo Kim,
    • Key Young Oang,
    • Tae Wu Kim,
    • Hosung Ki,
    • Junbeom Jo,
    • Sungjun Park,
    • Ryong Ryoo &
    • Hyotcherl Ihee
  2. Department of Chemistry, KAIST, Daejeon 305-701, South Korea

    • Kyung Hwan Kim,
    • Jong Goo Kim,
    • Key Young Oang,
    • Tae Wu Kim,
    • Hosung Ki,
    • Junbeom Jo,
    • Sungjun Park,
    • Ryong Ryoo &
    • Hyotcherl Ihee
  3. Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

    • Shunsuke Nozawa,
    • Tokushi Sato &
    • Shin-ichi Adachi
  4. RIKEN SPring-8 Center, Kouto 1-1-1, Sayo, Hyogo 679-5148, Japan

    • Changyong Song,
    • Takahiro Sato,
    • Kanade Ogawa,
    • Makina Yabashi &
    • Tetsuya Ishikawa
  5. Japan Synchrotron Radiation Research Institute, Kouto 1-1-1, Sayo, Hyogo 679-5198, Japan

    • Tadashi Togashi &
    • Kensuke Tono
  6. Department of Chemistry, The Catholic University of Korea, Bucheon 420-743, South Korea

    • Joonghan Kim
  7. Department of Chemistry, Inha University, Incheon 402-751, South Korea

    • Jeongho Kim
  8. Department of Materials Structure Science, School of High Energy Accelerator Science, The Graduate University for Advanced Studies, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

    • Shin-ichi Adachi

Contributions

H.I. and S.-i.A. designed the study. K.H.K., J.G.K., S.N., Tokushi Sato, K.Y.O., T.W.K., H.K., J.J., S.P., C.S., Takahiro Sato, K.O., T.T., K.T., M.Y., T.I., Jeongho Kim, H.I. and S.-i.A. did the experiment. K.H.K., J.G.K., S.N., Tokushi Sato and Joonghan Kim analysed the data. K.H.K., J.G.K., S.N., K.Y.O., R.R., Jeongho Kim, H.I. and S.-i.A. wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

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Author details

Extended data figures and tables

Extended Data Figures

  1. 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(qt), in the entire time range from –800 fs to 1 μs.

  2. 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.

  3. Extended Data Figure 3: Difference RDFs in real space. (333 KB)

    Difference RDFs, r2ΔS(r), obtained by Fourier sine transformation of qΔS(q).

  4. 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.

  5. Extended Data Figure 5: Radial distribution functions, r2S(rt). (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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  1. Extended Data Table 1: Details of the data-collection parameters (445 KB)

Supplementary information

PDF files

  1. Supplementary Information (176 KB)

    This file contains supplementary Text and Data.

Additional data