## 2 Experimental Methods and Theory  
The time-resolved fragmentation experiments on thymine were performed at the AMO (Atomic, Molecular and Optical physics) instrument of the LCLS (Linac Coherent Light Source) free electron laser. The instrument and some of its science are described in detail in [30; 31]. Details of the setup we used for this particular experiment can be found in [17; 32]. A sketch of the most important parts is given in Figure 2a. In short, thymine powder was evaporated in an oven at 140 \({}^{\circ}\)C with an outlet to the interaction region in the form of a heated capillary, thus forming an effusive jet in the collection volume of a magnetic bottle electron spectrometer.  
Figure 2: Experimental setups. (**a**) Sketch of the setup at the free electron laser. Molecules are inserted into the interaction region by evaporation in a capillary oven. A first UV pulse ionizes and fragments the molecules. The fragments are then probed by a delayed soft X-ray pulse via core electron ionization. The Auger electrons are collected and analyzed in a magnetic bottle spectrometer. (**b**) Sketch of the setup at the synchrotron beamline. Isocyanic acid is produced close to the beamline and then transported to the spectrometer under cryogenic conditions. The sample is inserted in a differentially pumped cell. Soft X-ray radiation from the monochromator beamline core ionizes the molecules and Auger electrons of HNCO are analyzed via a hemispherical electron analyzer.  
A first UV pulse (hv = 4.65 eV, 70 fs duration) triggered the fragmentation process via resonance-enhanced three-photon ionization. A time-delayed free electron laser (FEL) soft X-ray pulse (hv = 570 eV, 70 fs duration) was used to create an oxygen core hole in the photoionized molecules. Auger electrons from O 1s core holes were detected with the magnetic bottle spectrometer as a function of time delay between UV excitation and X-ray probe pulses.  
The time resolution of the experiment is about 330 fs, which is dominated by the jitter between the optical excitation and the FEL probe pulses. This is much larger than the time resolution observed in our study of the non-adiabatic dynamics in the neutral excited states of thymine [17], since we had not implemented the single shot optical X-ray cross-correlator [33] to compensate for the jitter between optical and FEL pulses in the data analysis for the fragmentation study reported here.  
The steady state experiments on isolated HNCO were performed at the high-resolution photoelectron spectroscopy instrument of the PLEIADES beamline at the synchrotron SOLEIL [34]. A schematic overview is given in Figure 2b. Synchrotron light at a photon energy of hv = 570 eV and a bandwidth of 750 meV ionized the HNCO molecules contained in a differentially-pumped sample cell with entrance and exit windows for the synchrotron beam. The emitted O 1s Auger electrons in the direction of the light polarization were dispersed by a hemispherical analyzer. The monochromator, as well as the hemispherical analyzer were calibrated by measuring the photoabsorption and Auger spectra of CO\({}_{2}\).  
The isocyanic acid target was prepared according to the method described in [35]. After synthesis, the molecular sample was stored at liquid nitrogen temperatures to avoid polymerization. The vapor pressure at around \(-40\)\({}^{\circ}\)C was sufficient to obtain the necessary molecular density inside the gas cell attached to the hemispherical analyzer.  
The O1s core decay spectrum of HNCO has been calculated using the second-order Algebraic Diagrammatic Construction (ADC(2)), which is a well-established [PERSON]'s function-based direct method to compute double ionization and Auger spectra [36; 37] in combination with a cc-pVDZ basis [38]. The details of the simulation are described in [17].