Mapping the emergence of molecular vibrations mediating bond formation


Fundamental studies of chemical reactions often consider the molecular dynamics along a reaction coordinate using a calculated or suggested potential energy surface1,2,3,4,5. But fully mapping such dynamics experimentally, by following all nuclear motions in a time-resolved manner—that is, the motions of wavepackets—is challenging and has not yet been realized even for the simple stereotypical bimolecular reaction6,7,8: A–B + C → A + B–C. Here we track the trajectories of these vibrational wavepackets during photoinduced bond formation of the gold trimer complex [Au(CN)2]3 in an aqueous monomer solution, using femtosecond X-ray liquidography9,10,11,12 with X-ray free-electron lasers13,14. In the complex, which forms when three monomers A, B and C cluster together through non-covalent interactions15,16, the distance between A and B is shorter than that between B and C. Tracking the wavepacket in three-dimensional nuclear coordinates reveals that within the first 60 femtoseconds after photoexcitation, a covalent bond forms between A and B to give A–B + C. The second covalent bond, between B and C, subsequently forms within 360 femtoseconds to give a linear and covalently bonded trimer complex A–B–C. The trimer exhibits harmonic vibrations that we map and unambiguously assign to specific normal modes using only the experimental data. In principle, more intense X-rays could visualize the motion not only of highly scattering atoms such as gold but also of lighter atoms such as carbon and nitrogen, which will open the door to the direct tracking of the atomic motions involved in many chemical reactions.

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Fig. 1: Schematics of the mechanisms for reactions involving three atoms and two bonds.
Fig. 2: Structural analysis using residual difference scattering curves.
Fig. 3: Trajectories of the excited-state and ground-state wavepackets determined from TRXL data.
Fig. 4: Harmonic oscillations of the ground-state and excited-state wavepackets at t > 360 fs.

Data availability

The datasets generated and analysed here are available from the corresponding author on reasonable request.

Code availability

The codes used for the analysis here are available from the corresponding author on reasonable request.


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This work was supported by the Institute for Basic Science (IBS-R004). This work was supported by the X-ray Free-Electron Laser Priority Strategic Program and the Photon and Quantum Basic Research Coordinated Development Program of MEXT, Japan. This work was supported by JSPS KAKENHI grant numbers JP17H06141, JP17H06372, JP17H06438 and JP19H05782. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2016R1E1A1A01941978). Experiments were performed at the XSS of PAL-XFEL (proposal numbers 2017-2nd-XSS-001 and 2018-2nd-XSS-005), and at the BL3 of SACLA with the approval of the Japan Synchrotron Radiation Research Institute (proposal numbers 2016A8035, 2016A8055, 2016B8056, 2016B8073, 2017A8043, 2017A8053, 2017B8029, 2018A8006, 2018B8015, 2019A8012 and 2019B8025).

Author information




H.I. supervised the project; S.-i.A. and H.I. designed the experiment; J.G.K. and H.I. developed the data analysis strategy; J.G.K., S.N., H. Kim, E.H.C., T.S., T.W.K., K.H.K., H. Ki, Jungmin Kim, M.C., Y.L., J.H., K.Y.O., K.I., R.F., J.H.L., J.P., I.E., S.H.C., S.K., M.K., T.K., T.T., S.O., M.Y., S.J.L., S.L., C.W.A., S.C., Jeongho Kim, S.-i.A. and H.I. performed the experiments; J.G.K., H. Kim, E.H.C., K.H.K., D.-S.A. and T.J. analysed the data; J.M. and Joonghan Kim performed quantum chemical calculations; J.G.K., S.N., Jeongho Kim, S.-i.A. and H.I. wrote the manuscript with contributions from all authors.

Corresponding author

Correspondence to Hyotcherl Ihee.

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The authors declare no competing interests.

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Peer review information Nature thanks Richard A. Mathies, Martin Meedom Nielsen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Schematic of photoinduced bond formation in [Au(CN)2]3.

Upon laser excitation (with energy represented by hv), wavepackets are created in both of the ground and excited states. The excited-state wavepacket in the \({{\rm{T}}}_{1}^{{\prime} }\) state is prepared in the FC region after the ultrafast intersystem crossing from the initially excited singlet state (S1) to a triplet excited state (\({{\rm{T}}}_{1}^{{\prime} }\)). The excited-state wavepacket created in the FC region should move towards the equilibrium structure of \({{\rm{T}}}_{1}^{{\prime} }\), which has two equivalent covalent Au–Au bonds between adjacent gold atoms (right inset, yellow spheres; blue and white spheres denote N and C atoms, respectively). The trajectory of the wavepacket from the FC region to the equilibrium structure of \({{\rm{T}}}_{1}^{{\prime} }\) eventually determines the reaction trajectories of the ultrafast bond formation and hints towards its reaction mechanism. Three candidate reaction mechanisms of bond formation (paths 1, 2 and 3), described in the text, are represented by blue arrows on the nuclear coordinates of RAB versus RBC. In short, path 2 represents a concerted bond formation mechanism and path 1 and path 3 represent asynchronous bond formation mechanism. Path 1 and path 3 are distinct, depending on which bond is formed first between the A–B pair and the B–C pair. The initial motion of the excited-state wavepacket affects the initial motion of the ground-state wavepacket in the S0 state, because impulsive Raman scattering generating the ground-state wavepacket can occur non-impulsively, owing to the finite pulse duration (~100 fs), as described in Supplementary Information. After the initial motions of the wavepackets in the ground and excited states, the wavepackets oscillate around their equilibrium structures.

Extended Data Fig. 2 TRXL data of [Au(CN)2]3 measured at PAL-XFEL and SACLA.

ab, Time-resolved difference scattering curves, qΔS(qt), of [Au(CN)2]3 measured at PAL-XFEL (a) and SACLA (b). c, The first and second RSVs (black and blue squares, respectively) obtained from the SVD analysis of qΔS(qt) measured at PAL-XFEL and their fits (red lines) using an exponential 1.1-ps time constant convoluted with an IRF with a FWHM of 170 fs. d, The first five RSVs resulting from the SVD analysis on the data measured at PAL-XFEL, multiplied by their corresponding singular values s1, s2, s3, s4 and s5.

Extended Data Fig. 3 Results of the structural analysis using residual difference scattering curves.

a, Experimental residual difference scattering curves, qΔSresidual(qt), measured from −1,040 fs to 2,235 fs. be, Theoretical fits of qΔSresidual(qt) obtained from the structural analyses considering wavepacket motions in the S0 state (b), the \({{\rm{T}}}_{1}^{{\prime} }\) state (c), the T1 state (d), or both the S0 and \({{\rm{T}}}_{1}^{{\prime} }\) states (e). Only the last analysis (using S0 and \({{\rm{T}}}_{1}^{{\prime} }\)) gives a satisfactory fit quality.

Extended Data Fig. 4 Assignment of vibrational modes using vibrational frequencies and vibrational motions.

Each vibrational normal mode has a specific structural motion with a characteristic frequency. For example, a simple nonlinear triatomic molecule has three vibrational modes named after specific structural motions: symmetric stretching, asymmetric stretching and bending. The characteristic frequency νn of a vibrational mode vibrating along a normal coordinate Qn corresponds to the energy gap between adjacent vibrational states of each mode, where n = {a, b, c} for symmetric stretching, asymmetric stretching and bending, respectively. Vibrational frequencies are routinely measured by static or time-resolved spectroscopy that can probe vibrational transitions via infrared absorption or Raman scattering. Atomic motions themselves are not directly detected by spectroscopy, and thus the assignment of the observed frequencies to specific vibrational modes requires quantum chemical calculations that provide the connection between the vibrational frequencies and their corresponding atomic motions. By comparing the vibrational frequencies determined from experiment (vexp) and quantum chemical calculation, the measured vibrational frequency can be assigned to a specific normal mode. Direct characterization of vibrational motions requires a tool with structural sensitivity, for example TRXL, as presented in this work. In a TRXL measurement, photoexcitation with a coherent optical laser pulse creates vibrational wavepackets of certain vibrational modes, and scattering of an X-ray pulse directly probes the resultant time-dependent structural changes that are characteristic of the activated vibrational modes—such as the temporal changes of the interatomic distances (RAB, RBC and RAC) in [Au(CN)2]3. On the basis of direct information of both vibrational motions and vibrational frequencies obtained with TRXL, vibrational assignments can be made more accurately, and even the locations of vibrational wavepackets and the trajectories of their motions in multidimensional nuclear coordinates can be determined.

Extended Data Fig. 5 Normal modes of the S0 state.

Normal modes of the S0 state with frequencies in a range from 20 cm−1 to 170 cm−1, obtained from DFT calculations. The frequency and atomic motions of each normal mode are shown. Displacement vectors of each normal mode are indicated by red arrows for the Au atoms (yellow) and blue arrows for the other atoms (C, grey spheres; N, blue spheres).

Extended Data Fig. 6 Normal modes of the T1 state.

Normal modes of the T1 state, as in Extended Data Fig. 5.

Extended Data Fig. 7 SVD analysis on the TRXL data of [Au(CN)2]3 measured in the previous TRXL study.

See ref. 9. Shown are the first four RSVs multiplied by their corresponding singular values.

Extended Data Fig. 8 Solvent heating contribution to the TRXL signal.

a, Experimental difference scattering curves, qΔS(q), of FeCl3 solution measured at time delays from −740 fs to 2,260 fs. b, The first four LSVs multiplied by their corresponding singular values. c, The first four RSVs multiplied by their corresponding singular values. Only the first LSV and RSV contain meaningful signals, and so a single difference scattering curve (that is, the first LSV) accounts for the contribution to solvent heating on the scattering data measured with a water solvent. In the structural analysis, the first LSV was used as a scattering intensity change upon increase in temperature of the water solvent, ΔSheat(q).

Extended Data Fig. 9 Structural analysis of the three types of vibrational motions of the T1 state.

Experimental residual difference scattering curves (black lines) at several time delays after 360 fs and their theoretical fits (red lines), obtained from the structural analysis. ac, For the structural analysis, vibrations of \({{\rm{T}}}_{1}^{{\prime} }\) at later times (>360 fs) were classified into three types of vibrational motions (symmetric stretching, asymmetric stretching and bending). We performed the structural analysis for each of the three cases considering symmetric stretching motions (a), asymmetric stretching motions (b) and bending motions (c) of \({{\rm{T}}}_{1}^{{\prime} }\). d, For comparison, all the three structural parameters of \({{\rm{T}}}_{1}^{{\prime} }\) were used for the structural analysis.

Extended Data Fig. 10 Structural analysis using asymmetric and symmetric structures of S0.

Experimental residual difference scattering curves (black lines) at selected time delays and their theoretical fits (red lines) obtained from the structural refinements considering the asymmetric bent S0 structure (left) or symmetric bent S0 structure (right). The asymmetric case gives superior fit qualities compared to the symmetric case, indicating that the equilibrium structure of S0 is asymmetric and bent.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Table 1 and Supplementary Figures 1-5.

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Kim, J.G., Nozawa, S., Kim, H. et al. Mapping the emergence of molecular vibrations mediating bond formation. Nature 582, 520–524 (2020).

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