Atomic-scale observation of solvent reorganization influencing photoinduced structural dynamics in a copper complex photosensitizer

Photochemical reactions in solution are governed by a complex interplay between transient intramolecular electronic and nuclear structural changes and accompanying solvent rearrangements. State-of-the-art time-resolved X-ray solution scattering has emerged in the last decade as a powerful technique to observe solute and solvent motions in real time. However, disentangling solute and solvent dynamics and how they mutually influence each other remains challenging. Here, we simultaneously measure femtosecond X-ray emission and scattering to track both the intramolecular and solvation structural dynamics following photoexcitation of a solvated copper photosensitizer. Quantitative analysis assisted by molecular dynamics simulations reveals a two-step ligand flattening strongly coupled to the solvent reorganization, which conventional optical methods could not discern. First, a ballistic flattening triggers coherent motions of surrounding acetonitrile molecules. In turn, the approach of acetonitrile molecules to the copper atom mediates the decay of intramolecular coherent vibrations and induces a further ligand flattening. These direct structural insights reveal that photoinduced solute and solvent motions can be intimately intertwined, explaining how the key initial steps of light harvesting are affected by the solvent on the atomic time and length scale. Ultimately, this work takes a step forward in understanding the microscopic mechanisms of the bidirectional influence between transient solvent reorganization and photoinduced solute structural dynamics.


Note S0: Data collection and reduction of time-resolved XSS and XES
In the pump-probe experiment at SACLA, the data were recorded by scanning an optical delay line with a motorized stage. At each delay stage position, a shutter of the optical laser was operated with 15 Hz, which was half of the XFEL repetition rate (30 Hz), to collect alternating laser-on and laser-off shots. For laser-on shots collected at time delays ≤ 2.5 ps, the time is corrected by post-sorting into 30 fs time bins using the timing diagnostics based on the X-ray beam branching scheme 1,2 . The jitter correction is not applied for laser-on shots at time delays longer than 2.5 ps to avoid degradation of the signal-to-noise ratio (S/N) by fine time binning. Therefore, only the data at > 2.5 ps retain a jitter of ~300 fs in root-mean-square. The shot-to-shot intensity ratio between the incident and fluorescent X-rays was monitored with photodiodes, removing outlier shots due to jet instability in the following XES and XSS analyses.

XSS:
For each time delay, we collect single-shot outputs of a short-working-distance octal (SWD octal) multiport charge-coupled device (MPCCD) detector from 100 consecutive laser-on shots. After subtracting a dark background measured separately without XFEL pulses, these singleshot outputs are summed up to construct a laser-on image. A laser-off image is created in the same manner using laser-off shots adjacent to the corresponding laser-on shots. In the construction of the last laser-on and laser-off images, 100-200 shots are used depending on the number of excess shots.
This procedure produces a data set consisting of ~45 pairs of laser-on and laser-off images at each time delay. We mask shadowed pixels and dead areas of these images. The sample-detector distance and detector position are calibrated using Debye Scherrer rings of a LaB6 powder, which was loaded in a glass capillary (100 µm inner diameter) attached to an injection tip. After correcting for X-ray polarization and solid angle coverage per radial bin, the individual laser-on and laser-off images are scaled to the intensity integral of a corresponding simulated scattering curve over a range between 1.0 and 4.1 Å −1 in the length of the scattering vector , around two isosbestic points ∆ * ( , )). The anisotropic difference scattering signals are calculated with 12 azimuthal bins using the scheme described by Lorenz et al. 6 and Biasin et al. 7 . The difference scattering curves are averaged after removing outliers due to optical laser instability detected on the basis of the Chauvenet criterion [8][9][10] .

XES:
Laser-on and laser-off images are constructed from a single MPCCD detector with the same procedure employed in the XSS data collection, except that after the background subtraction, only pixel values over 70.0 analog-to-digital-units (ADU) in single-shot outputs are counted to reject the zero-photon peak, or the detector readout noise. This threshold corresponds to the detection of a single photon with an energy of 1.13 keV, well below actual photon energies detected in the experiment. From six regions of interest (ROIs) corresponding to the six crystal analyzers, a spectrum is constructed by summing up one-dimensional profiles after aligning the energy axis. The energy axis is calibrated using a static spectrum of [Cu(dmphen)2] + measured at SPring-8 BL19XU. Each spectrum is normalized to the total integrated intensity. The laser-off spectra are averaged over the entire time range and used for the subtraction from laser-on spectra to yield difference spectra. The ~45 difference spectra at each time delay are averaged and then used in the singular value decomposition (SVD) analysis.
Note S1: SVD analysis of time-resolved Cu Ka XES difference spectra Figure S1 presents the results of the SVD analysis of the time-resolved Cu Ka XES difference spectra. In Figure S1b  The 1st left singular vector (LSV) is associated with the change of Cu 3d electronic configuration (Cu 1+ : d 10 à Cu 2+ : d 9 ), due to the metal-to-ligand-charge-transfer (MLCT) transition.
The corresponding photoexcitation process promotes an electron from the ground state (S0) into the lowest singlet (S1) MLCT state and occurs within the instrumental response function (IRF). Therefore, the rise time of the 1st RSV reflects the overall time resolution of the pump-probe a c b experiment. Since the 1st RSV exhibits no clear decay within the measurement time window, we describe the temporal evolution of the 1st RSV ( +,-( )) as follows: Here is the magnitude, . is time zero, ( − . ) is the Heaviside step function, ⨂ is the convolution operator, and ( /+0 , ) is a Gaussian function with a width of /+0 . The leastsquares fit is performed by a standard * minimization and uncertainties are at the 68% confidence level. The resultant fitted curve is shown in Figure 2 of the main text and the corresponding fitting parameters are summarized in Table S1. The width /+0 obtained here is used in the kinetic fitting of the time-dependent structural parameters extracted from the analysis of the time-resolved XSS data (Note S3).  Figure S2). These Cu(I) and Cu(II) species should show Cu Ka emissions corresponding to 0% and 100% optical excitation in the pump-probe experiment at SACLA, respectively. After calibrating the energy axis, the Cu(I) and Cu(II) spectra measured at the European XFEL are interpolated and vertically offset, such that spacing between data points and the elastic scattering background underlying the emission signals are aligned to those in the pump-probe experiment at SACLA. This data correction is necessary to compare spectra measured with different instruments at the European XFEL and SACLA.
Subsequently  The excited state structures are generated according to the following procedure. First, 99 structures are generated through the image dependent pair potential (idpp) method 15 with a maximum force of 0.001 Å/fs on each atom using the S0 and T1 optimized geometries as initial and final structures.
Then, the Cartesian coordinates of the nearest idpp structures are linearly interpolated. In this way, the atomic distance between atoms i and j of an intermediate structure is approximately a linearly interpolated distance between the S0 and T1 structures: is

2-3. Structural fitting
The structural fitting is performed by minimizing for each time delay the discrepancy between ∆ 9:B6; ( , ), consisting of the sum of the three components described above (see also equation 2 in the main text), and the experimental data ∆ ( , ) using a maximum likelihood estimation with the * estimator: (∆, 9*:'+ (@,5)'∆,(@,5)) ; Here, @ is the number of data points at each time delay t, is the number of free parameters, and a b is the standard deviation of the data. Prior to performing the structural fitting at each time delay, we investigate the contribution of the three components to the scattering signal at selected time delays as described in the following steps (i) and (ii). In order to corroborate the importance of the solute-solvent contribution, we fit the difference scattering signal measured at the longest time delay (18.8 ps), when the structural evolution of the solute is completed, to two different models. One is composed of solute-solute, solute-solvent, and solvent-solvent terms (model_1), while the other excludes the solute-solvent term (model_2). Figure S6 clearly shows that the fitting quality is significantly improved when the model includes the solute-solvent term. This is further corroborated by the Akaike's Information Criterion (AIC) 20 . The AIC score is given as follows: Here, is the likelihood of the fitting with a parameter set. Using the converged parameter sets obtained by fitting the data with model_1 and model_2, we calculate the AIC difference (∆ = 9:B6;_* − 9:B6;_X ) as 2.9×10 4 . Since the model with the lower AIC score offers the better fit, the positive AIC difference indicates that model_1 is superior to model_2, demonstrating the necessity of the solute-solvent term to adequately reproduce the measured data. The data measured at several time delays are fitted using a model assuming two different solute-solvent terms (model_3), as described below:  Steps (i) and (ii) are finally followed by the structural fitting at each time delay (model_1).
The resulting fitted curves are shown in Figure 3 of the main text. Figure S8 shows     Note S3: Kinetic time constants from the XSS analysis

3-1. Summary of fitting time constants
The time evolutions of Δ ( ) , Δ ( ) , ( ) , and Δ ( ) extracted from the structural analysis are fitted with phenomenological kinetic models by the least-squares method using the standard * estimator. The uncertainties are at 68% confidence level. The applied models are described by different combinations of a step function, a damped sine function, and exponential functions, which are convoluted by the Gaussian IRF obtained in Note S1. The fitting equations are the following: The kinetic time constants obtained from the fitting are summarized in Table S3.   Figure S22 further below). This period is further close to the period of a breathing normal mode at the T1 (301 fs) and S1 (290 fs) optimized structures identified in vibrational analyses carried out using TD-DFT/CPCM calculations with PBE0 and variational excited state calculations with BLYP in vacuum, respectively (see also Figure   S21 below). For ∆ ( ), the measured period (401 fs) is significantly shorter than the period of a flattening mode (see Figure S21)

Note S5: Energetics from solvent heating
The time evolution of ∆ ( ) obtained from the fitting of the time-resolved XSS data is not discussed in the main text but is presented in Figure S16.   Note S6: SVD analysis of isotropic and anisotropic scattering data SVD provides information on how many components are required to describe the measured data, albeit the extracted singular vectors do not necessarily correspond to physically meaningful signals. Figure S19 shows the isotropic (∆ ( , )) and anisotropic (∆ * ( , )) X-ray scattering data and the results of SVD analyses. For both isotropic and anisotropic signals, there are four components exhibiting a clear temporal dependence, as deduced from the corresponding RSVs. This is evidence that the quantitative structural analysis using four time-dependent parameters does not overfit the measured data. In the anisotropic X-ray scattering, the first and second components   Isotropic scattering ∆S(q,t) Anisotropic scattering ∆S2(q,t) a b c d e f g h Figure S21. Normal modes from vibrational analysis in the S1 excited state in vacuum. Displacement vectors of the flattening and breathing modes obtained from a vibrational analysis at the S1 optimized geometry using time-independent variational density functional calculations with BLYP (DSCF approach employed in the QM/MM MD simulations 3 ). The vibrational analysis is performed in the harmonic approximation using central finite difference calculation of the Hessian matrix as implemented in the Atomic Simulation Environment with analytical atomic forces converged to 10 -4 eV/Å. The periods and frequencies of the modes are also indicated.