Visualizing the non-equilibrium dynamics of photoinduced intramolecular electron transfer with femtosecond X-ray pulses

Ultrafast photoinduced electron transfer preceding energy equilibration still poses many experimental and conceptual challenges to the optimization of photoconversion since an atomic-scale description has so far been beyond reach. Here we combine femtosecond transient optical absorption spectroscopy with ultrafast X-ray emission spectroscopy and diffuse X-ray scattering at the SACLA facility to track the non-equilibrated electronic and structural dynamics within a bimetallic donor–acceptor complex that contains an optically dark centre. Exploiting the 100-fold increase in temporal resolution as compared with storage ring facilities, these measurements constitute the first X-ray-based visualization of a non-equilibrated intramolecular electron transfer process over large interatomic distances. Experimental and theoretical results establish that mediation through electronically excited molecular states is a key mechanistic feature. The present study demonstrates the extensive potential of femtosecond X-ray techniques as diagnostics of non-adiabatic electron transfer processes in synthetic and biological systems, and some directions for future studies, are outlined.


Supplementary Note 1: TOAS data analysis
The TOAS data were fitted within a standard global analysis framework. 1

Supplementary Note 2: XES data extraction and reduction
The low readout noise of the MPCCD detector allowed explicit single-photon discrimination of the XES signal. A flow-chart of the data extraction-correction process is shown in Step 1: Readout The MPCCD detector is read out as a 2D image containing the read-out value (ROV) of each pixel.
Step 2: Pedestal and common-mode detector corrections The so-called "pedestal" correction ensures that the zero-photon ROVs of all the pixels are close to 0 analogue-to-digital units (ADU). A set of 15000 dark-measurements (i.e. images with the X-rays shutter closed and no X-rays hitting the detector) was averaged, yielding the average 0-photon signal level for each pixel. This background was subtracted from all further images. Three sets of such dark-measurements were recorded in the course of the experimental run in order to confirm that this background did not change over time.
Common-mode artefacts arising from amplifier/current supply electronics were negligible.
Step 3: Calibration and scaling (pixel-based gainmap and single photon discrimination) A pixel-specific gainmap constructed from single-pixel ROVs was applied. A typical histogram of the ROVs for a pixel seeing seeing a high photon intensity is plotted in Supplementary Figure 3C (blue line), the inset shows a zoom-in.
The peaks centered at ROV= 0 ADU, at ROV= 100 ADU and the clustering of counts around 210 ADU correspond to 0-, 1-and 2-photon counting events respectively. For each X-ray illuminated pixel, Gaussian functions of RMS  were fitted to the 0-photon signal (red line), and the 1-photon signals (cyan line) individually. The single-pixel gainmap was constructed by defining the center peak positions of the two Gaussians to 0 and 1 respectively. As can be seen from the inset in Supplementary Figure 3C, many ROVs fall between the 0-and 1photon peaks. This interval is assigned to fractional photon events. The most robust approach to account for them was to define the number of detected 1-photon and 2-photon events in an exposed image as the number of pixels for which the single-pixel gain-corrected ROVs were such that 0.5<ROV<1.5 and ROV>1.5 respectively. Since the maximum count rate of any pixel was ~0.025 ph/exposure, gain-corrected ROVs corresponding to 3 or more photons were not considered. A lower threshold of 9σ of the zero-photon readout was enforced in the single-photon discrimination to remove false counting events from the readout noise.
Supplementary Figure 3B follows a detector image across the 3 stages of the data extractioncorrection procedure. Note that the high read-out noise of the third detector from the top made explicit single-photon counting in this element impossible, resulting in the absence of data in the corresponding panel of Supplementary Figure 3B. Even though this approach discards all photons hitting 1/3 of active area of the detector, it resulted in the best signal to noise ratio, with the mean standard deviation of each data point typically being within 30% of that expected from a true Poisson distribution. The final signal strength obtained in the Co Kα 1 emission peak is the sum of all the detector counts for a given pulse and was typically ~20 photons/pulse, while the background count was ~0.2 photons/pulse.

Supplementary Note 3: XES data analysis
The K  spectra originate from multiplet and spin orbit interactions. In transition metal systems, it is highly sensitive to the oxidation state and to the number of unpaired electrons. A frequent evaluation approach that is applicable to the interpretation of photoinduced transient K2p1s and K 3p1s spectra is based on constructing differences of steady-state spectra from suitable reference complexes; the integrals of the absolute values of the difference spectra are then proportional to the conversion yield. This approach is somewhat similar to the treatment of X-ray dichroism, although sum rules do not apply, and one needs to find acceptable reference compounds. 2 Still, this approach is quantitative for two-state transitions, 3  However, in the experiments reported in this work, the short effective data collection time did not permit to obtain a sufficiently large set of spectra with clear references and good statistics to fully exploit this approach. It was nevertheless indirectly applied to follow the spectral variations, since for the K  spectra, the linewidth (full-width at halfmaximum FWHM) can also be exploited to calibrate the spin momentum on the cobalt center.
Although the 2p-3d exchange interaction is rather small, its variation upon increase in spinstate appears as a clear broadening 2 . After a careful comparison with the static lineshapes obtained at the ID26 beamline of the ESRF (shown in Supplementary Figure 4), we can determine that the 0.6 eV FWHM difference observed in the current experiment for the ground and photoexcited state corresponds to a spin-state change of S=1.5 at t=20 ps. Since the initial spin momentum of the 1 Co III is S=0, this corresponds to S=3/2, a spin-state HS of 4 Co II . Given that the total integrated Kα 1 emission intensity does not depend upon the charge and spin-state 2 the relative changes in the FWHM of the emission line for the different Co species directly result in an inverse lowering of the maximum emission intensity, i.e. the peak height. This is the parameter measured and plotted in the kinetic traces presented in the main text.

Supplementary Note 4: Computational details for the DFT optimization
All the calculations were carried out with the ORCA program package. 13,14 The geometries of

S XDS (Q,t)
The 2D X-ray Diffuse Scattering (XDS) images extracted from the MPCCD detector were corrected to account for the effects of: 1) the X-ray beam polarization, 2) the X-ray absorption of 8 keV photons throughout the liquid sheet , 3) the solid angle subtended by each detector pixel, 4) the X-ray absorption probability of an 8 keV photon within a pixel.
The resulting images were then integrated azimuthally around the beam center (found by circle-fits to the liquid-peak in the 2D images) producing 1D curves of the scattering intensity is the momentum transfer, 2θ is the scattering angle, and λ is the X-ray wavelength. The first step in the analysis of S(Q) was a simple filtering procedure. Any , where S XDS (Q) Off is defined as the mean of the earliest 12 time-delays for which the X-ray pulses arrived from 12 ps to 45 ps before the laser pulse, namely 12 ) ,

Supplementary Note 6: XDS Data Analysis -SVD-based background contributions to
. Observing that this background-removal procedure reduced the subset of data for t < 0 to a negligible level validated the use of the SVD-determined descriptor vectors in an unconstrained fit of the S XDS (Q,t). The implementation of this methodology in the full global-fit analysis is described in the next section.

Supplementary Note 7: XDS Data Analysis -Sample contributions to S XDS (Q,t)
The From these considerations, the solute term was expressed as   where γ(t) is the time-dependent excitation fraction of [ 2 Ru III = 4 Co II (HS)].

The solvent term
Assuming the validity of a classical continuum description, the equilibrated state of the solvent can be expressed as a function of two independent hydrodynamical variables chosen as the temperature (T) and the density (). The S solvent that originates from the bulk-solvent response can be described in terms of their elementary variations ΔT(t) and Δρ(t). Numerous investigations at synchrotron sources have demonstrated that a first order treatment is adequate to model the response on the hundreds of picoseconds to hundreds of milliseconds time scales. Within this framework the solvent term is quantified through the following linear combination: ) ( (called the temperature solvent differential (TSD)) was acquired independently during a dedicated study at ID09b, ESRF 28 . The data were measured using multilayer optics characterized by a 2.5% bandwidth (bw). Since this is broader than the intrinsic 0.3% bw of the XFEL beam, the influence of the X-ray source spectrum had to be investigated. As a first step, a TSD that would be obtained from a monochromatic beam was constructed from the measurement in ref  Figure 8B shows the resulting curve after Gaussian deconvolution (blue trace). This "monochromatic" TSD (blue) was convoluted with the 2.5% bw of the multilayer (red) and the intrinsic 0.3% bw of an XFEL beam (green). The three curves are indistinguishable, demonstrating that the ID09b reference can be introduced in the analysis of the difference scattering signal from XFEL sources. The convolution of the simulated monochromatic TSD with the full spectrum of the U17 undulator at ID09b ('pink' beam) is included for comparison (black trace).

S XDS (Q,t) from the sample
Summarizing the previous sections, S sample could be expressed as: is the fraction of charge-separated molecules, is the difference between the signal simulated for the Ru II = 1 Co III (LS) and Ru III = 4 Co II (HS) DFT structures, is the change in temperature and is the change in scattering signal caused by an increase of MeCN temperature at constant density.

Supplementary Note 8: XDS Data Analysis -Fit-based analysis of S XDS (Q,t)
Following the methodology presented by Haldrup 29 , each individual difference scattering signal S XDS (Q,t) was expressed as a sum of a background contribution (ΔS back (Q,t) and a term ΔS sample (Q,t) from sample structural changes, both introduced above. For each time delay, the residual function: was minimized. The denominator 25 , as well as the number of data points N, and the number of free parameters p in the fit. As such, S res can be directly interpreted as a  2 estimator. This allowed extracting the absolute magnitude of every SVD scaling parameters α i (t), for each time point. While the average value for two of the α i (t) parameters changed gradually over the duration of the scan, no systematic evolution was observed around or after t = 0. Explicit inclusion of a density term S solvent returned Δρ(t) ≈ 0 for all time delays recorded. Any contribution of the solute-solvent cross-term to S XDS (Q,t) was below the detection threshold.

Supplementary Note 9: XDS Data Analysis -The heat response of the solvent on ultrashort timescales
The solvent term is derived within a classical hydrodynamic framework that assumes a homogeneous temperature distribution 24  This 'local' homogeneity of the temperature-increase ensures that its contribution to the difference scattering can be construed as arising from volume elements having undergone homogeneous temperature-increase. Thus, the contribution of the temperature-increase to the difference scattering signal: can be expressed as: With ΔT v (t) being the temperature change in a given volume element as a function of time and V being the volume of the X-ray/sample interaction volume. As the solvent temperature differential (  The observation that the variation of the simulated S XDS (Q) curves with ΔR(Co-N) is almost exclusively one of signal amplitude entails that it will be strongly correlated with the excitation fraction (γ XDS ) in the analysis of the XDS data. Due to this correlation significant differences in the excited structure of [ 2 Ru III = 4 Co II ] at early times will be manifested in the S XDS (Q,t) fits as deviations in γ XDS . Since γ XDS determined for the 3 ps time-delay (0.63 ± 0.2) is well within the uncertainty of the final γ XDS (0.67 ± 0.04), no significant deviation in the excited state structure could be detected for these measurements, even at the earliest timescales.

Supplementary Note 12: Preliminary QM/MM (solute/solvent) equilibrium MD simulations
The simulations were made using our QM/MM MD implementation in the Grid-based Projector Augmented Wave code (GPAW). 34 The system was comprised of the rutheniumcobalt dyad, modeled using PBE with a real space grid spacing of 0. 18 Figure 11B displays the corresponding thermal distributions of average Co-N.
These simulations confirm the large structural rearrangements that take place around the Co center (R ~ 0.15 Å) following photoinduced ET.