# Photon-In/Photon-Out X-ray Free-Electron Laser Studies of Radiolysis
## 2 Methods
### Optical-Pump/X-ray Probe  
Understanding the birth and fate of an excess electron in liquid water created by ionization is a longstanding scientific problem addressed by ultrafast pump-probe techniques. Historically, all-optical techniques in liquid jets were employed using multiphoton [31; 32; 33] or two-photon ionization [34] to inject electrons and/or study the pre-equilibrated hydrated electron [35; 36]. Surprisingly the partner in the initial ionization step, the H\({}_{2}\)O\({}^{+}\) cation has remained undetected, despite a rigorous UV-pump/broadband UV-Vis probe study, due to its femtosecond lifetime and unclear spectroscopic signature in the UV/VIS region [37]. To this day, there are many unresolved questions associated with the hydrated electron in liquid water. The advent of X-ray free electron lasers with intense, tunable soft X-ray pulses in the soft X-ray water window presented a new opportunity to probe the dynamics associated with valence holes created during ionization of water, enabling our recent experiment [5]. The strategy follows our earlier studies using X-rays to probe the residual ion following following strong-field ionization [38; 39]. Our calculations demonstrate a clear signature for H\({}_{2}\)O\({}^{+}\) and other relevant radiolysis species in the water window Figure 2. The absorption resonances in the gas phase for the four species associated with elementary proton transfer: H\({}_{2}\)O\({}^{+}\) + H\({}_{2}\)O \(\rightarrow\) OH + H\({}_{3}\)O\({}^{+}\) were calculated with 6-311(2+,+)G(2 df,p) basis with uncontracted core (oxygen) using fc-cvs-EOM-CCSD [40]. We used strong-field ionization in water (800 nm, \(2\times 10^{13}\) W/cm\({}^{2}\)) [41] to impulsively eject an electron along the field polarization axis to a radius of 35 A. The ejected electron ultimately equilibrates in a spherical solvent cavity of 3 A in an s-like ground state within 1 ps. Prior to the equilibration of the hydrated electron, dynamics of the valence hole was probed with a delayed monochromatic X-ray pulse (\(\tau_{X}=20\) fs, \(\Delta E_{X}=0.20\) eV) scanned over the water window. Three detection channels were simultaneously observed: transmission, total fluorescence, and dispersed emission. The ability to vary the polarization of the optical strong-field pump relative to the linearly polarized X-ray probe between 0\({}^{\circ}\) and 90\({}^{\circ}\) allowed us to extract an isotropic transient absorption signal with milliOD sensitivity for an ionization fraction of roughly 1%. The isotropic transient absorption signal tuned directly to the OH(aq) resonance exhibited a delayed onset relative to X-ray probe energies to the red or blue, providing a signature for the ultrafast proton transfer reaction. The time resolution of these measurements was limited by the measurement of the time-delay between the optical pump and X-ray probe pulses to \(\sim\)100 fs. Importantly, our theoretical quantum mechanics/molecular mechanics (QM/MM) results showed the sensitivity of the valence hole X-ray absorption to the structural dynamics around the ionization site, particularly the O-O distance to the nearest neighbor H\({}_{2}\)O, with 0.2 eV shifts corresponding to \(\sim\)0.2 A  changes. The dispersed emission channel mapped inelastic X-ray scattering as a function of incoming photon energy [6]. When the incoming photon energy is tuned to the OH(aq) resonance, resonant inelastic X-ray scattering (RXS) of the transient radical is observed. Simultaneous detection of RIXS and transient absorption was achieved by setting the 2.0 um sheet jet at a 45\({}^{\circ}\) angle to the incoming X-ray beam. Although collection/detection efficiency was poor in this channel (\(\sim\)10\({}^{-8}\)), statistics accumulated by averaging for pump-probe delay times >200 fs allowed the extraction of an RIXS signal.