## 3 Chemistry Applications under Ambient Conditions
### Femtosecond X-ray Emission Capabilities
The emission spectra were obtained by integrating a 4-pixel wide region-of-interest around the image maximum and then corrected for elastic scattering by the average of two background regions below and above the signal region of interest. The pixel-to-energy calibration was done by fitting the recorded spectra to calibrated reference data of the same compound. All spectra were normalized to their total area and then averaged. Differences were obtained by subtracting the spectra without laser excitation (\"unpumped\") from the spectra with laser excitation (\"pumped\"), and accumulated for each pump-probe delay, as presented in Figure 3B,C for the K\(\alpha\) and K\(\beta\) spectra, respectively. To extract the kinetic traces as a function of pump-probe time delay around time-zero (Figure 4), the absolute difference XES spectra were integrated along regions-of-interest (marked by the green horizontal bars at the top of Figure 3B,C). The error bars were calculated using the standard error propagation from the errors of the mean spectra in the data sets for the excited and non-excited solution. The resulting time traces were fitted by an exponential function convoluted with a Gaussian-shaped instrument response function (IRF) and a constraining Heaviside function around time-zero via  
\[f(A,\sigma,t_{0},\tau)=A\int_{-\infty}^{\infty}\frac{1}{\sigma\sqrt{2\pi}}e^{ -y^{2}/2\sigma^{2}}\mathrm{H}(t-t_{0}-y)(1-e^{-(t-t_{0}-y)/\tau})dy \tag{1}\]  
using the position of time-zero \(t_{0}\), the single-exponential rise-time \(\tau\), the IRF width \(\sigma\) and the signal amplitude \(A\) as fit parameters. Due to naturally much higher signal-to-noise ratio in the K\(\alpha\) measurement and because the K\(\beta\) traces were acquired truly simultaneously, the IRF width was first fitted for the K\(\alpha\) data and this value used as fixed input for the K\(\beta\) fitting routine while \(t_{0}\), \(\tau\) and remained free fit parameters in both fits. The fitted IRF FWHM yields \(113\pm 31\) fs for the K\(\alpha\) data (used as input for K\(\beta\)), and the fitted time-zero, \(t_{0}\), delivered identical values for both emission lines (within the fit uncertainty of 14 fs). The extracted value for the IRF width lies within the expected ranges for the duration of the pump and probe pulses (each 50 fs FWHM), the expected laser and the X-ray relative pulse arrival time jitter (here: about 70 fs FWHM [34]) and the thickness of the cylindrical solution jet (thus up to 100 \(\upmu\)m thickness in transmission), leading to a smearing of the temporal response due to the group velocity mismatch for laser and X-rays (here about 1.1 fs/\(\upmu\)m or 110 fs total temporal walk-off), we estimated 140 fs FWHM as an upper bound for the IRF, in agreement with the fit result of 113(31) fs. Following this basic analysis, it is evident that the rise time kinetics of the K\(\alpha\) and K\(\beta\) lines are not fully identical (Figure 4), which hints to the fact that each emission line has a different relative sensitivity with respect to the initially excited MLCT, intermediate triplet and the final high spin (quintet) states of this iron complex. This as a consequence yields different rise times for the extracted K\(\alpha\) and K\(\beta\) line traces, extending a similar observation within different regions of the K\(\beta\) emission spectrum alone [22]. It is nevertheless evident that even without a dedicated timing jitter correction the temporal resolution of pump-probe experiments at FXE is sufficient to resolve fastest intermediate states with lifetimes down to 150 fs, and e.g. the longer rise time of about 215 fs (Figure 4) most likely originates from the intrinsic dynamic processes within the molecule in agreement with previous studies [22; 24; 47].