## 3 Chemistry Applications under Ambient Conditions
### Femtosecond Forward Scattering Capabilities  
X-ray solution scattering in WAXS configuration at FXE are performed using a LPD 1 Megapixel 4.5 MHz framerate detector [35] that has relatively high detection efficiency of up 20 keV X-ray photon energies, which represents currently the highest available photon energy at the FXE instrument. First pump-probe WAXS measurements with the LPD were performed similar to the initial femtosecond XES experiments described above. Aqueous [Fe(bpy)\({}_{3}\)]\({}^{2+}\) (concentration 15 mM) was supplied by a round jet and excited by 400 nm pulses, as in the XES measurements. The X-ray photon energy was set to 12 keV with 90 pulses per train at 564 kHz intra-train repetition rate. Again, for every second X-ray train (thus at 5 Hz) 90 synchronized laser pulses (and each pulse separated at the 564 kHz pulse delivery rate) excited the sample that was probed by 90 X-ray pulses per train. Since the X-ray trains are delivered at a 10 Hz rate, we also record the reactant (non-illuminated) sample with this scheme at a 5 Hz train repetition rate as with the pump-probe signal itself. An X-ray pulse energy of about 170 \(\upmu\)s on sample was used for the WAXS measurements to avoid saturation of the high gain stage of the LPD, where the detector approaches its non-linear detection region. The solution scattering image as detected by the LPD (Figure 5 left) and the respective azimuthally integrated difference curves (Figure 5 right) at three selected time delays show the influence of the solution excited by the laser pulse. Each delay step was collected in a 5 min scattering measurement. The difference resulting curves were fitted according to the standard methodology [12; 13; 14; 15] using a linear combination fit (LCF) of three major contributions: the solute (molecule) term, the solute-solvent cage term and the (bulk) solvent changes via  
\[\Delta S(q,t)=\Delta S_{solute}(q,t)+\Delta S_{solute}(q,t)+\Delta S_{solvent }(q,t) \tag{2}\]  
Figure 4: The kinetic traces as extracted from the difference Fe K\(\alpha\) and K\(\beta\) spectra calculated as integral of the absolute differences in the energy regions indicated by the dashed lines in Figure 3B,C respectively. The dashed black curve represents the Gaussian instrument response functions as extracted from the fit to the K\(\alpha\) data points (which is then propagated over the entire time delay in the convolution integral). The error bars on the plots correspond to one standard error directly propagated via sum of square errors of the difference traces in Figure 3B,C. where the solute and the cage terms can be calculated by the Debye formula and from the radial pair distribution functions (\(g_{nm}(r)\)) for all (n,m) pairs of different atoms in the system:  
\[\Delta S_{solute/cage}(q)=\sum_{n}\sum_{m\in n}\biggl{(}\frac{N_{n}N_{m}}{V}f_{n }(q)\cdot f_{m}(q)\int_{0}^{\infty}\Delta g_{nm}(r)\cdot\frac{sin(q\cdot r)}{q \cdot r}4\pi r^{2}dr\biggr{)}. \tag{3}\]  
The solvent response \(\Delta S_{solvent}(q,t)\) provides information on the thermodynamic parameters of the solvent bulk and contains contributions related to the solvent heating (transient temperature increase, \(\Delta T(t)\)) and thermal expansion (bulk density change, \(\Delta\rho(t)\)). \[\Delta S_{solvent}(q,t)=\left.\Delta T(t).\frac{\partial S(q)}{\partial T} \right|_{V=const}+\left.\Delta\rho(t).\frac{\partial S(q)}{\partial\rho} \right|_{T=const} \tag{4}\]  
where the derivatives \(\left.\frac{\partial S(q)}{\partial T}\right|_{V=const}\) and \(\left.\frac{\partial S(q)}{\partial\rho}\right|_{T=const}\) are determined by a separate calibration measurement [52] and the thermal expansion term is only relevant on the long nanosecond timescales [12; 13; 14; 15]. For the results presented here, the photoinduced structural changes in the solute and its solvation shell (the cage term) were taken from the AIMD simulation results [53], while the solvent (water) response to impulsive heating was extracted from literature [51].